Current methods of surveying railway infrastructure and track-side assets are slow, intrusive and wholly inadequate in the present commercial climate where operational costs are very high, penalties for poor service can be Draconian, and safety is the over-riding factor. This is the context for the work presented in this thesis. A novel train-borne survey system has been developed which affords minimal disruption to service, is safe to operate and can be integrated with other asset management surveying tools. Information is naturally forthcoming about important issues such as platform gauging, landslides, limited clearances, overhead cable heights, and bridge and tunnel structure gauging.


The approach taken involves a circular scanning laser, operated along the lines of a radar system. Progression along the track generates a helical scan pattern with sufficient range to cover those environs of the track, which directly influence train operation.


A prototype system is described which demonstrates clear proof of principle, and provides the necessary supporting information for the development of a high-performance system. It is a highly complex, interacting arrangement of electrical, optical and mechanical elements. Consequently, the prototyping process raised many system integration issues. These are systematically addressed in the thesis.


To support the manipulation and analysis of the data acquired by the physical system, a suite of software tool were developed. These were based on a novel approach to large dataset management and manipulation. Using trials data from the National Railway Museum in York, three-dimensional representations of scanned infrastructure, generated using these tools are presented.


The thesis defines the limits of operability of this novel approach to railway infrastructure surveying and details the developments necessary to create a fully operational system for commercial use.


Title page. i

Abstract ii

Contents. iii

List of figures. vii

List of tables. xi

List of graphs. xii

Acknowledgements. xiii

Nomenclature. xiv

I.            Aberrations. xiv

II.          Symbols. xvi

III.        Units. xviii

1       Introduction. 1

1.1        LRS conceptual overview.. 2

1.2        Thesis overview.. 4

2       Optical subsystem.. 7

2.1        Introduction. 7

2.2        The main optical subsystem elements. 8

2.2.1         The laser pulse generator (LPG) 10

2.2.2         The delay cables. 11

2.2.3         The collecting lens. 12

2.2.4         The receiver and the optical bypass filter 13

2.2.5         The rotating diverting mirror (RDM) 14

2.2.6         The timing card. 15

2.3        System integration issues. 17

2.3.1         Raw-data into 3D model 18

2.3.2         Hardware integration. 20

2.3.3         Implicit optical processing. 22

2.3.4         The optical system resolution and accuracy. 24

2.3.5         Remote sensing and the choice of laser wavelength. 28

2.4        Optical subsystem testing. 32

2.4.1         The LIDAR range equation. 33

2.4.2         Necessary properties of the collecting lens. 34

2.4.3         Collecting lens aperture experiments. 39

2.4.4         Establishing maximum measurable distance. 43

2.4.5         Real-time data acquisition experiments. 44

2.4.6         Overall subsystem validation. 45

3       Mechanical subsystems. 48

3.1        Introduction. 48

3.2        Overall integration of the LRS subsystems. 48

3.3        Air supply subsystem.. 50

3.4        Cooling jacket subsystem.. 52

3.5        Air blower subsystem.. 53

3.6        RDM motor controller 55

3.7        LRS PC units. 56

3.8        Locomotive positioning subsystem.. 57

3.9        Vibration absorber platform (VAP) 58

3.10     Train arm support 60

3.11     Optics platform.. 60

3.12     RDM air bearings spindle. 63

3.12.1      Shaft design. 65

3.12.2      RDM mirror 68

3.12.3      Balancing. 69

3.12.4      Bearings. 70

3.12.5      Spindle heat management 76

3.12.6      Drive motor 76

3.12.7      Spindle assembly. 77

3.13     Conclusions. 78

4       Software development 80

4.1        Introduction. 80

4.2        The Real Time Acquisition Tool (RTAT) 81

4.2.1         Data structure and LRS outputs events. 81

4.2.2         The RTAT application overview.. 84

4.3        Laser Visualisation Tool (LVT) 86

4.3.1         LVT modes. 87

4.3.2         From the raw data file into the user interface. 87

4.3.3         Evaluating the distances between LRS measurements using IMU output 91

4.3.4         3D pipe design. 92

4.3.5         LVT total station application tool 94

4.4        LRS trials. 97

4.4.1         Overview.. 97

4.4.2         Measuring the infrastructure using the TS instrument 97

4.4.3         Comparing measurements from the LRS and the TS instrument 99

4.4.4         Experimental errors and assumptions. 101

4.5        Future software development 102

5       Vibration Absorber Platform.. 105

5.1        Introduction. 105

5.2        Design philosophy. 105

5.3        Real data analysis. 106

5.3.1         Data gathering. 106

5.3.2         Data analysis. 107

5.3.3         Results. 115

5.4        Modelling locomotive dynamics. 120

5.5        Proposed design. 125

6       Conclusions and further work. 130

6.1        General 130

6.2        The optical loop challenges and system integration issues. 132

6.3        The supplementary subsystems involved and their design. 137

6.4        Prototyping the LRS. 140

6.5        Future work. 141

Appendix A.       The Safety Cases. 143

A.1       Laser safety. 143

A.2       The rotary mechanical components. 144

A.3       Safety on the railway. 145

Appendix B.        Prototyping the LRS. 147

B.1       The final prototype LRS specification. 147

B.1.1   General integrated system performances. 147

B.1.2   Hardware used. 147

B.2       The prototyping stages. 148

Appendix C.       Resolutions and imaging results. 155

Appendix D.       Optics and additional information. 159

D.1       Alternative proposal for optical system.. 159

D.2       Wavelength and radar additional information. 160

Appendix E.        Experimental data and system outputs. 165

E.1        System acquisition raw data. 165

E.2        Additional experiments data. 167

E.2.1    Other values and tables. 170

Appendix F.        LRS cost and final mechanical design. 172

F.1        LRS forecast capital cost 172

F.2        Final LRS drawing. 174

Appendix G.       Data sheets. 176

G.1       The laser pulse generator (LPG) Technical data. 176

G.1.1        A Pulsed DiodeLaser Driver   (PDL 800-B PDLD) 177

G.1.2        A  Diode Laser Head (DLH) 178

G.2       The optical filter bypass. 181

G.3       The Receiver (RAPD) 183

G.4       The timing card. 185

G.5       The Total-Station. 187

7       References. 190

8       Bibliography. 193



Figure 1.1 - integration concept between the existing video train borne inspection system and the LRS  3

Figure 2.1 - drawing shows the existing optic set-up. 9

Figure 2.2 - set-up of a simple closed loop, which used in this LRS. 9

Figure 2.3 - the ratio lengths of the delay cables. 11

Figure 2.4 - two schematic views of the RDM.. 15

Figure 2.5 - timing card memory control in the FIFO mode [18] 16

Figure 2.6 – diagram showing the relationship between R,q and XYZ co-ordinates. 19

Figure 2.7 - flow chart of the inputs involved with the optical integration system. 21

Figure 2.8 - the four parameters affecting the final resolution of the 3D model 25

Figure 2.9 - three different resolutions for reconstructing the final 3D model 25

Figure 2.10 - ideal thin lens used to define and solve optical applications using ray tracing theory  36

Figure 2.11 - maximum distance to be measured, experiment implementation. 43

Figure 2.12 - experiment set up implements B&W frequency targets. 45

Figure 2.13 - 3D output scan from the LVT, shows linear object in form of XY coordinates. 46

Figure 3.1 - flow chart shows system integration between all subsystems within the LRS. 49

Figure 3.2 - air supply subsystem.. 51

Figure 3.3 - cooling jacket subsystem.. 53

Figure 3.4 - air blower subsystem.. 54

Figure 3.5 - RDM electro driven motor controller 55

Figure 3.6 - the optical platform set-up. 61

Figure 3.7 – RDM spindle including air-bearings design. 77

Figure 4.1 - the timing relationship between the timing card outputs and the IMU output 82

Figure 4.2 – file data structure. 83

Figure 4.3- RTAT low resolution 2D Image. 85

Figure 4.4 - the relationship between the 2Dbuffer and the user interface (the three images) 88

Figure 4.5 - the 2D 360 ° / longitude image (L2Dimage) 89

Figure 4.6 - the 2D profile image (P2Dimage) 90

Figure 4.7 - the 3D model constructed using IMU data. 91

Figure 4.8 - pin-hole camera concept implements 3D affine transformations. 93

Figure 4.9 - total station (TS) LVT application panel 95

Figure 4.10 - picture of the NRM scanning surrounding shows orientation of TS system coordinates  98

Figure 4.11 - L2Dimage, LVT user interface, shows allocating targets names before using the TS LVT tool 100

Figure 5.1 - cross section relationship between the wheels set and the track cross section geometry  109

Figure 5.2 – locomotive bogie suspension system.. 110

Figure 5.3 - shows one-dimensional FFT of the three accelerations and their relationship. 112

Figure 5.4 - two different set of IMU raw data, shows all three accelerations and their time events  114

Figure 5.5 - examining different time windows and filters on a single acceleration. 115

Figure 5.6 - all four stages of converting the IMU raw data into filtered displacement signal 116

Figure 5.7 – shows single set of IMU data converting into three vectors in space. 117

Figure 5.8- the worse case scenario assumed to be the maximum global value across the vectors data sets  118

Figure 5.9- three two-dimensional planes representing motions detected by the IMU. 119

Figure 5.10- the vibration transformation of the IMU detection location with relation to the LRS location (XZ) 122

Figure 5.11- the vibration transformation of the IMU detection location with relation to the LRS location (XY) 123

Figure 5.12 - the vibration transformation of the IMU detection location with relation to the LRS location (YZ) 124

Figure 5.13- the practical construction of the passive VAP system.. 127

Figure B.1 - optical set-up implementing a single lens element 148

Figure B.2- the optical set-up including the delay cables. 148

Figure B.3- the prototype solid shaft RDM.. 149

Figure B.4- the RDM hollow shaft 149

Figure B.5- the initial stage of RDM hollow shaft construction. 150

Figure B.6- the final prototype with hollow shaft arrangement, guided by the mini-rail 151

Figure B.7- implementation of the mini-rail longitudinal encoder 151

Figure B.8- back view of the fully equipped prototype at the NRM trial 152

Figure B.9- front view of the fully equipped prototype at the NRM trial 153

Figure C.1- a picture of the LRS and the customised mini-rail within the scanning surrounding  155

Figure C.2- the outcome of the scan trail (the 3d Model) 156

Figure C.3- the outcome of the scan trail which took place within a large workshop. 156

Figure C.4- shows a picture of the scanning surrounding illustrates the large size of the scanning surroundings. 157

Figure D.1 -the collecting lens. 159

Figure D.2- the option of polarised proposal 160

Figure E.1- the railway objects used in the experiment 167

Figure E.2- shows the 15 metres distance target 168

Figure E.3- shows the total station arrangement above the LRS optical enclosure. 168

Figure E.4- the targets used. 169

Figure E.5- picture of the B&W  experiment set-up. 169

Figure F.1- the mechanical drawing of the LRS. 174

Figure G.1- the LPG device. 177

Figure G.2- the LDH 780. 178

Figure G.3-LDH 780 dimensions. 179

Figure G.4- full width-half maximum (FWHM) of optical bypass filter 182

Figure G.5- the total station (TS) 188



Table 2.1 - the relationships between the collection lens diameter and maximum measurable distance  41

Table 2.2- the relationships between the railway objects surface of reflectivity. 42

Table 4.1 - example of surveying job exported by LVT Tool 96

Table 4.2 - record of measurements from the scanned environment, gathered by the TS operator 98

Table 4.3 - table shows summary of offsets measurements between both TS and LRS system   99

Table 5.1 - example of the IMU raw data file structure. 107

Table A.1- direct ocular exposure to laser radiation (redrawn from BS EN 60825-1:1994) – IR section  143

Table E.1 – three users selected the same targets an output from the LVT TS tool. 170


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Graph 2.1 - examining the necessary collecting lens aperture size. 40

Graph 3.1 - guide to selection of ball or roller bearings [22 p8-134] 64

Graph 3.2- shows the air viscosity non-linearity vs. pressure and temperature [31] 71

Graph 3.3- theoretical load-carrying parameter vs. compressibility parameter, L [22p8-129] 72

Graph 3.4- shows whirl stability threshold for infinite length 360° journal bearings’ [32] 73

Graph D.1- the relative transmission of the atmosphere [24 p352] 161

Graph D.2- blackbody radiation for different temperatures [24 p349] 161

Graph D.3- vegetation and soil spectra [38] 162

Graph D.4- one-way attenuation of electromagnetic energy propagating in the clear atmosphere [23 p565] 163

Graph E.1- shows a relationship between R, q. 165

Graph E.2- is an output of the longitudinal encoder vs. ADC.. 166

Graph F.1 – LRS cost with relations to the RDM diameter 172

I.    Aberrations  

2Dbuffer -

2D Pointer Memory Buffer

2Dbuffer -

2D Pointer Memory Buffer

2DOF -

Two Degrees Of Freedom

3D -

Three Dimensional

3Dimage -

3D image

A/D -

Analogue to Digital

A4W -

White paper sheet object

AC -

Alternating Current

ADC - 

Analogue-Digital Converters


Avalanche Photo Diode

B&W -

Black and White

BB -

Black Brick

BO -

Orange Brick

BS -

British Standards


Computer Aided Design.


Close Range Radius

CW -

Continues Wave

D/A -

Digital to Analogue

DC -

Direct Current


Differential Global Positioning System


Diode Laser Head


Fast Fourier Transform


First In First Out


Far Infrared

 FOV -

Field Of View


Far Range Radius


Full Width-Half Maximum


Global Positioning System


Graphical User Interface

HD -

Hard Drive

I/O -



Index Measurement Number


Inertial Measurement Unit

IR –



International Standards Organisation

IT -

Information Technology

KM -

Karam Mahmooda

L2Dimage -

Longitudinal Image

Laser -

Light Amplification by Stimulated Emission of  Radiation


Light Detection And Ranging


Laser Pulse Generator


Laser Radar System


Laser Visualisation Tool


Maximum Permissible Exposure

MT -

Micro Time


Near Infrared

P+D -

Proportional + Derivative controller

P2Dimage -

2D profile image

PC -

Personal Computer


Personal Computer Interface


Pulsed Diode Laser Driver


Pre-Menstrual Tension

R0-R7 -

12 bit TTL routing inputs from the RDM

Radar -

Radio detection and ranging


Redundant Array (of) Inexpensive Disc


Random Access Memory


Receiver Avalanche Photo Diode


Rotating diverting Mirror

RP -

Polished Rail


Revolution Per Minute


Real Time Acquisition Tool


Small Computer System Interface

SD -

lateral Distance

SS -

Shiny Stickers


Standard Deviation


Short Time Fast Fourier transform




Time-to-Amplitude Converters

TBA  -

To Be Advised


Time-Correlated Single Photon Counting


Time Of Flight

TS -

Total Station


Transistor-Transistor Logic


Uniform Distributed Load

UV -



Vehicle Acceptance Body


Vibration Absorber Platform







II.    Symbols


focal length / wavelength


the surface reflectivity / the target backscattering coefficient




angle in radians / angle in degrees / pitch angle




density (mass per unit volume)


angular position


stability parameter


the optical subsystem efficiency

qx, qy, qz,

the three angles within the M matrix


the collecting lens effective aperture,

ax, ay, az



observation time


length of the open shaft profile strip


Beryllium (material)


angle between the surface normal and the incident radar energy




shaft outer diameter

D2, D1


dx, dy dz



lens f-number


gyroscopic momentum vector


polar second moment of area




shaft length


bearing length


magnification / rotational matrix


clearance ratio


reversible polytrophic factor


numerical aperture on the object side of the optical system


numerical aperture on the image side of the optical system


number of signal photons




absolute pressure


the laser transmitted power


radius in metres / inner hollow shaft radius


radius or lens size


maximum LRS measurable distance


reflected laser spot radius


RAPD aperture radius


RAPD active aperture,


temperature / torque


shaft thickness/ shifting vector


maximum distance to be measure


length between the optical system and the RAPD aperture

vx, vy  vz



loading distribution (weight)

Xview,  Yview, Zview

elements representing a single point in the view coordinates


2D profile / plane / 2D coordinates 


2D planes


3D coordinates 

Ys , Xs

projection of the view coordinates


third dimension


compressibility parameter


turn rate of locomotive


bearings eccentricity ratio




Angle/ angular data / angle in radians / angle in degrees/ angle of twist


rotational speed in radians /sec




III.    Units

Units of Distance


1 nanometre


= 10-9  metre

1 micrometre


= 10-6  metre

1 millimetre


= 10-3  metre



Units of Frequency


1 Hertz

1 Hz = one oscillation per second

1 kilohertz


=103 Hz

1 Megahertz


=106 Hz

1 Gigahertz


=109 Hz



Units of Time


1 picosecond


= 10-12 second

1 nanosecond


= 10-9  second

1 microsecond


= 10-6  second

1 millisecond


= 10-3  second



Units of Temperature



Degrees Kelvin  (degrees Celsius + 273)


degrees Celsius



Other units used



Amperes/Watt (radiant sensitivity)


101325 N.m-2 (pressure)




fluid specific heat


litres per minute (flow rate)





rev/min   or RPM

rotational velocity




Watts (power)



Electromagnetic spectrum


The LRS operates with a wavelength equals to:

= 780nm

= 0.78mm





Chapter 1








1      Introduction

The transport infrastructure plays a major role in economic growth and prosperity, and forms a general foundation for trade, industry, commerce and leisure. The railway system is a well established method of transporting heavy loads across large distances, relatively quickly, at relatively low cost and with relatively low environmental impact. Railway system reliability is important and is achieved in several ways. Firstly, advance logistic systems manage traffic on the railway infrastructure, ensure safety, support and co-ordinate maintenance strategies, enable network development and encourage effective and efficient goods transport.

Secondly, through high standards set for vehicle design, mechanical reliability of the rolling stock on the railway infrastructure is imposed at a high level. Finally, only through repeated inspection, can a programme of improvement of the rail infrastructure be performed.  This last point is a strong motivation for the work of this thesis.


The necessity for highly reliable day-to-day services is ironically at odds with the requirements for infrastructure maintenance, as the latter must be carried out whilst trains are running. General inspection work leads to staff, servicing the infrastructure, risking their lives. To minimise their risk, safety procedures are in place which can cause major traffic disruption across the railway network. This in turn can damage railway network reliability [1p8].


Back in 1978, British Rail developed the first train borne inspection system which was able to perform inspection on the run. This approach was found to reduce traffic disruption and increase trackside safety [2]. However, in 1993-1994, British Rail was privatised and Railtrack became responsible for the railway infrastructure [1 p6]. Consequently, a number of spin-off companies started to specialise in surveying railway infrastructure. Most of these companies were testing infrastructure against national regulations and standards such as track gauging, clearances and track quality (National Gauging Project) [2]. They used customised train-borne inspection systems. The majority of the inspection methods implemented in these train-borne systems typically employ video capture, image processing, and laser ranging. Existing video surveying systems aim to reduce the impact of surveying patrols along the rail infrastructure. The UK rail network is surveyed repeatedly by this video system every year. It provides evidence of any infrastructure changes. The video inspection system also allows repeated analysis of infrastructure images in a safe office environment. Because these systems use passive imaging, they are not able to measure inter-object distances within the rail infrastructure with any satisfactory degree of precision or accuracy. Also they do not qualify to examine the infrastructure under the current national regulations and standards.  In this thesis, a novel, active surveying system, the Laser Radar System (LRS), is presented. It is designed to integrate with existing video-based train-borne inspection systems and overcomes their deficiencies.

Using the LRS, a three-dimensional, virtual reconstruction of railway network infrastructure can be generated and tools can then be applied to provide accurate measurement information. The LRS is a self-contained system which can be retro-fitted to current rolling stock, and can be operated in harmony with commercial traffic. Disruption is minimised and risk to operators are eliminated completely. Information is naturally forthcoming about important aspects of infrastructure such as platform gauging, landsides, limited clearances, overhead cable heights and bridge and tunnel structure gauging.

1.1      LRS conceptual overview

The LRS is a scanning system which employs laser technology. It is a highly integrated optical system comprising several interacting electro-mechanical subsystems. Attached to the front of a train, the system generates a single beam of pulsed laser light which is scanned in a lateral circular path. This creates a helical scan of the rail infrastructure through which the train passes (Figure 1.1). Using a simple RADAR principle, based upon the timing of pulses reflected back from objects in the infrastructure, a data set is built up which defines the scanned surroundings. The technique is known as LIDAR (LIght Detection And Ranging). Subsequent processing enables this to be translated into a 3D image. The LRS is able to measure railway infrastructure from a pre-defined minimal distance out to a maximum distance which, again, may be selected. Within this measurement range, railway features may be captured in detail. The integration with video data requires that the 3D reconstruction is accurately overlaid. To do this, precise location information is required, and an inertial positioning system must be used to link data sets.

Figure 1.1 - integration concept between the existing video train borne inspection system and the LRS


Therefore the LRS shares an inertial measurement unit (IMU) with the onboard video inspection system (Figure 1.1). Also, a Differential Global Positioning System (DGPS) provides global timing for the integrated LRS and video systems, in addition to latitude and longitude information. The encoder provides information about the longitudinal rolling characteristics of the train which, through the communications network, along with the other sensor systems data, is passed to a PC for logging and overall co-ordination.

In designing the LRS, two important factors were key. Firstly, railway infrastructure which is closer to the track should benefit from higher scanning resolution, since clearance between the train and the rail infrastructure is a critical issue and should reflect this in its measurement. Secondly, track with speed restrictions required better scanning resolution, since the restriction is usually caused by a problem with the infrastructure itself. Therefore, as the train carrying the LRS slows down, better longitude resolution is naturally achieved.

A major part of the overall LRS design involved software engineering. Two important issues are considered. Firstly, the data collected on a typical survey run could run to extremely high volumes. It was a necessary part of the work to consider the best way of handling data efficiently so that it did not become a slow and cumbersome operation requiring extremes of computing power.  The second important software engineering issue was the design and development of software tools to convert the LRS raw data into a 3D model and provide the user with customised measuring tool.

Because the LRS is an electro-mechanical measuring system, which must operate in a harsh railway environment, in addition to general system integration, special care and attention had to be paid to achieving accuracy, robustness and reliability.

1.2      Thesis overview

The thesis is structured as follows. 

Chapter 2 provides a complete description of the optical components of the LRS. This includes the laser source, the detector and the intervening components that make up the optical path to and from the railway infrastructure. The mechanism for range measurement is described and a novel approach to bounding the measurement envelope is presented. Integration issues are considered and finally, some results of experimentation for testing and validation given.


Chapter 3 considers the mechanical aspects of the LRS.  It begins with an overview of the functional and data-flow relationships between subsystems associated with the LRS. Details are then presented for each of the mechanical subsystems.


Chapter 4 is based upon the software utilised by the LRS directly, or indirectly for post-processing  of the raw data collected by the system during a surveying run. It begins by setting out the motivations for the final designs. It then explains the structure and features of two software applications, one of which performs the real-time data acquisition, and the other, the manipulation of the data into suitable graphical representations for post-analysis. Results of trials using the software are presented and demonstrate the power and utility of the LRS.


Chapter 5 presents a proposed solution to the problem of isolating the LRS from the natural motions of its host locomotive. A passive system is developed in conceptual form. It is based upon the analysis of data collected from actual locomotive trials. The analysis includes an interpretation of the data as actual motions in all appropriate degrees of freedom. Both spectral and temporal analyses are performed and correlated together. The analysis is only valid for the locomotive type involved in the trial. However, the methodology is valid and can be re-applied to any other vehicle.


Chapter 6 presents the conclusions from the work, drawing together the system integration aspects which are a critical part of the design process. Suggestions are then presented for future work, some of which are necessary to produce a full specification, high speed, commercial system, and others to provide enhanced functionality and therefore a stronger commercial case for the LRS.


A set of appendices are included at the end of this thesis. They contain material consigned away from the main body to preserve natural flow of material. The material is of a reference nature and comprises:

·         Appendix A - The Safety Cases

·         Appendix B - Prototyping the LRS

·         Appendix C - Resolutions and imaging results

·         Appendix D - Optics and additional information

·         Appendix E - Experimental data and system outputs

·         Appendix F - LRS cost and final mechanical design

·         Appendix G - Data sheets




Chapter 2

Optical subsystem




2      Optical subsystem

2.1      Introduction

The technique known as Light Detection And Ranging (LIDAR) is designed principally to measure distance and speed of a remote object [3]. This project implements the LIDAR technique for measuring the distance to an object within railway infrastructure based upon the time of flight (TOF) of an optical pulse [4]. LIDAR may be used to measure distances from a few millimetres up to kilometres with high resolution and accuracy, with a trade-off between resolution and maximum distance [5]. Current TOF–based ranging devices are compact and are often combined with other optical sighting devices. They are able to measure a single distance to an object in real time without requiring a special target or retro-reflecting surface, provided that sufficient light energy is available for detection at the receiver.

There are essentially two approaches used for determining distance using TOF: a short laser pulse is emitted and the delay until it returns is timed/counted, or a phase difference between emitted and reflected waves is measured [6].

This project uses the former, short laser pulse method. The delay until a reflection returns is timed very accurately using a special timing-card. Since the speed of light is known, the distance to the reflecting object can be calculated from the timing. Using a single timed pulse is not particularly effective, so a large number of pulses are used and averaged to give a more reliable distance measurement. There is a trade-off between the accuracy and speed of measurement [7].

This chapter describes how the LIDAR technique, based upon TOF, is implemented in this case. The sizing of the optics to meet the needs of a rail infrastructure surveying environment is discussed. Also, it describes all of the elements involved and other practicalities concerning construction of this type of complex system.

2.2      The main optical subsystem elements

To recap, the Laser Radar System (LRS) measures the distance to an object by calculating the two-way travelling time of light pulses. The optical process begins with the emission of a short electrical pulse from a clocking device called a Laser Pulse Generator (LPG). This device simultaneously generates two short pulses:

1.      an optical pulse emitted from a Diode Laser Head (DLH) (§2.2.1) and

2.      an electrical analogue pulse from a Pulsed Diode Laser Driver (PDLD).

The optical pulse, which passes through a laser collimator, travels along a path which is perpendicular to the final beam direction, until redirected into line by a 45° diverting-mirror (Figure 2.1).  Low power reflection of this laser radiation occurs at the object to be measured. The reflected energy is then collected and focussed by a collecting lens and passes into the aperture of a high frequency response Receiver Avalanche Photo Diode (RAPD) (Figure 2.1).  An optical bypass filter is fitted between the collecting lens and the receiver to remove backlight noise and other radiation sources from the direct view of the RAPD. It also ensures that the RAPD only observes the laser radiation wavelength. The 45° diverting mirror is fixed onto the collecting-lens at its centre. It ensures concentration and coincidence of the emitting laser beam and a direct field of view between the RAPD and the object (Figure 2.1). The function of the collecting lens is to direct as much as possible of the energy from the reflected object onto the RAPD aperture, since the reflected optical pulse will have very low power.

Figure 2.1 - drawing shows the existing optic set-up


The electrical pulse, which is simultaneously generated by the LPG, is a synchronising (SYNC) signal. This SYNC pulse travels down a delay-cable of specified length and then enters the timing-card via a SYNC input port whilst, simultaneously, the optical pulse is emitted from the laser collimator toward the object (Figure 2.2). The optical pulse passes throughout the optics set-up, as described earlier, down the atmospheric path to the object. Subsequently, a low power reflection of the same wavelength is generated at the object surface. This reflection then returns and re-enters the optics set-up and is finally directed onto the RAPD (Figure 2.2).

Figure 2.2 - set-up of a simple closed loop, which used in this LRS


The RAPD converts this optical input signal into an electrical analogue output. This signal then travels along a second, shorter delay cable of specified length, known as the short delay cable. The electrical analogue pulse then passes into the time-card via a Photo Multiplier Tube (PMT)

input port (Figure 2.2). The timing-card measures the time difference of arrival between the SYNC and PMT inputs and passes this value into its memory. This buffer memory operates in a First In First Out (FIFO) mode, allowing a stream of real time raw data from the optical system to be passed to the host PC. The raw data from the timing-card is then transferred to the PC via its PCI bus, is processed and combined with additional data, output from other subsystems, and finally saved on the hard drive (HD) (Figure 2.2).

2.2.1      The laser pulse generator (LPG)

As mentioned earlier, LPG comprises two devices, a Pulsed Diode Laser Driver (PDLD) and a Diode Laser Head (DLH) (Figure 2.3). Technical details are given in Appendix G-G.1

The PDLD (a clocking device) is designed to drive the DLH to produce laser pulses at selectable repetitions from a single shot up to a one MHz rate. In addition to an internal repetition control unit, which divides the maximum frequency by  selectable 16/8/4/2 factors, an external ±1Volt TTL input is also available. This enables the PDLD to be synchronized with other instruments over the full frequency range. The LRS is designed to operate at maximum pulse repetition rate of one MHz but occasionally this repetition is reduced because the timing card FIFO buffer may overflow. The laser power and pulse width are controlled by tuning the intensity control on the PDLD unit. A peak power of up to 0.6W can be emitted from the DLH (Figure 2.1) by setting the intensity on the PDLD to maximum. The LRS is designed to operate at this maximum intensity. The internal pulse clock of the LPG runs at a standard base frequency of 40MHz. The unit also provides interlock outputs, one of which was used as a safety feature on the laboratory entrance door. The DLH can produce light pulses as short as 70 picoseconds Full Width-Half Maximum (FWHM) at repetition rates from single shot up to 80 MHz.

2.2.2      The delay cables

Two 3mm diameter, 50W impedance coaxial delay cables are used in the LRS. To recap, they are (Figure 2.3):

1.      the SYNC cable, which is connected between the LPG and the timing-card and

2.      the PMT cable which is connected between the high speed receiver and the timing-card.

Assuming that analogue pulses travel at the speed of light through these cables, the maximum distance to be measured optically should be half of the SYNC cable length. The PMT delay cable should comprise the delay time between the PDLD and DLH part of the LPG (§2.2.1) (Figure 2.3).

Figure 2.3 - the ratio lengths of the delay cables


This arrangement operates as follows (Figure 2.3):

1.      An electrical pulses leaves the PDLD and simultaneously enters the SYNC delay cable and the signal line to the DLH. There will be a delay until the optical pulse, triggered by the PDLD electrical pulse, is emitted into the scanned environment from the DLH. Denote this delay T1 nanoseconds.

2.      The electrical pulse in the SYNC delay cable will travel a distance which is the same as the total optical path length to a physical target at the maximum detection range.

3.      Assuming that the optical pulse is reflected from a target at less than maximum range, denote the two-way time of flight of the pulse as T2. When this pulse is detected at the APD, another electrical pulse is passed down the PMT delay cable to the timing card and a clock is started. Denote the PMT delay time as T3.

4.      When the SYNC pulse arrives at the timing card, the clock is stopped. In theory, it should run for a further T1 nanoseconds. However, the clock was started T3 nanoseconds after the actual arrival of the returned optical pulse. This time, T3, would have to be subtracted from the start count time.

5.      So, on one hand T1 nanoseconds must be added to the count time, and on the other hand, T3 seconds must be subtracted. If T1 equals T3, the two operations cancel.

The two cables are kept within regulated surrounding temperatures and in a waterproof enclosure. The current prototype LRS implements lengths of 2.1m for the PMT delay cable and 30.2m for the SYNC cable.

2.2.3      The collecting lens

The collecting lens is designed to:

1.      focus the reflection from the object to be measured (i.e. the returning optical pulse) onto the RAPD aperture (Figure 2.1),

2.      transfer maximum light energy from the object to the RAPD. The lens should be designed with reference to the laser light properties and the time resolution characteristics of the high sensitivity RAPD,

3.      be able to focus the complete laser spot at all measured distances,

4.      achieve smaller overall lens diameter as a cost effectiveness issue (§2.4.2).

Most optical instruments have aberrations effects such as: vignetting and diffraction aberration, which reduce the image quality. Image quality, in the case of the collecting lens, is not an issue. However, the design concerns above are vital for the overall LRS requirements. Because the optical loop uses a single, known wavelength, the material of the collecting lens can be define and designed for up to 90° angle of incidence.

There are many ways of combining the collecting lens with the required laser path using, for example, beam splitters, reflectors lenses and bi-directional single lenses. In practice, a small 45° mirror is positioned in the front centre of the collecting-lens. This tiny diameter mirror is of negligible size when compared with the laser spot diameter at the point of entry into the collecting-lens.

The laser spot diameter is also a factor in judging the collecting-lens aperture. The optical aperture is determined by the diameter of the largest beam of light that can enter an optical system [24 p233]. Following extensive experimentation (§2.4.3), the area of the RAPD aperture and the laser spot size at maximum measured distance (§2.4.4) suggest the implementation of a collecting-lens with a focal point of 365.85mm and an aperture diameter of not less then 50mm.

However, the collecting lens/45°mirror system which was actually used in the prototype system had the following properties: focal length 28mm, Lens f number 2.8 and 45° mirror diameter 4mm.

2.2.4      The receiver and the optical bypass filter

A 780 ±2nm optical bypass filter with an FWHM 20±4nm was fitted between the collecting-lens and the RAPD to remove backlight noise and other radiation sources from the direct view of the RAPD (Figure 2.1). It also ensured that the receiver observed only the desired laser light wavelength (§2.3.5). Technical details are given in Appendix G-G.3, G.2.


The highly sensitive RAPD has a spectral response range between 400 to 1000nm. Optimal quantum efficiency occurs at 800nm with 0.5A/W radiant sensitivity. The RAPD is an integration of a silicon Avalanche Photo Diode (APD) with a bias-voltage power supply and low noise amplifier. The APD has an effective active region of 0.5mm diameter. It also provides flat frequency characteristics from 1MHz up to 1GHz and has no gain with respect to constant light (DC light/ CW laser). Its high-speed response and sensitivity suggest that the RAPD can convert the optical pulse into an electrical analogue pulse with virtually no time lag. The device is extremely sensitive to heat radiation and other environmental changing.

2.2.5      The rotating diverting mirror (RDM)

As described so far, the optics set-up can measure a single fixed point in space. The RDM is required to rotate that measurement point.

The Rotating Diverting Mirror (RDM) assembly is required to:

1.      divert the optical measuring path, which comprises the emitted laser beam and the RAPD field of view, into a 360° rotating view point,

2.      encode the position of the RDM.

To this end, a mirror is attached to a rotating shaft such that the shaft rotation axis is 45° to the mirror centre-normal (Figure 2.4). The rotation axis of the shaft is coincident with the emitted laser beam leaving the laser collimator. This ensures alignment of the RDM with the field of view of the RAPD which, in turn, views the low power reflection from the object via the RDM.


The mirror must have high reflectivity (higher than 90% at a wavelength band of 780±2ns, matched to the laser wavelength). A high resolution encoder is attached to the rotating shaft to provide instantaneous mirror position in degrees and subsequent rotation speed of the shaft. Since the collecting lens aperture (§2.2.3) diverts all of the reflection energy from the object back to the RAPD, an appropriate RDM diameter (Figure 2.4) is required with slights larger diameter than the collecting lens aperture.


However, the diameter of the RDM also determines the mechanical limitations and the overall capital cost of LRS, since the LRS performance and specification are highly dependent upon the mechanical properties of the RDM such as its maximum rotation speed (§3.1). Physical dimensions and other mechanical issues regarding to the RDM are covered in Chapter 3.

Figure 2.4 - two schematic views of the RDM


2.2.6      The timing card

The timing card is responsible for measurement of time of arrival of reflected pulse energy. It uses the principle of Time-Correlated Single Photon Counting (TCSPC) [18]. In essence, this technique is based upon the detection of single photons of light, the measurement of the detection times of the individual photons and the statistical reconstruction of the pulse waveform to enable pulse arrival time measurement [18 p13]. The SPC-600 timing card requires three input signals (Figure 2.5) (the card technical details are given in Appendix G-G.4):

1.      the analogue SYNC input from the LPG, via the long delay cable.

2.      the analogue PMT input from the RAPD, via the short delay cable,

3.      12 bit TTL routing inputs (R0-R7) from the RDM shaft encoder which define the encoder position.

The timing card can accept either positive-going or negative-going analogue signals; but they should be in the range of 10-80mV with a pulse duration greater than 1ns. The timing card provides for calibration of each individual SYNC/ PMT input and offers full control of parameters of its internal components, such as analogue-digital converters (ADC) and time-to-amplitude converters (TAC). The card also has some memory control options one of which, a First-In-First-Out (FIFO) memory mode, is used here (Figure 2.5). The output data from the timing card using this FIFO mode enables a continuous stream of information to be recorded over time. Each record contains event information for each individual photon (i.e. information about individual measurements). Interfacing between the PC and the timing card is via the PCI BUS. The transfer rate between the card and the PC is dependent upon the numbers of photons counted (and recorded) by the card.

Figure 2.5 - timing card memory control in the FIFO mode [18]



2.3      System integration issues

The LRS is a complex electro-mechanical system made up from a collection of interacting components and subsystems. Care had to be taken in the way in which these parts were integrated. The optical subsystem forms the core of the LRS, so integration issues are central to its design and implementation. This section raises some of these integration issues.


Firstly, because of high locomotive running cost and the extreme harsh railway environment, the LRS must be designed to be both physically robust and functionally reliable. The optical devices are sensitive to environmental factors such as vibration, temperature, humidity, electromagnetic fields and changing climate.

Secondly, the moving parts within the LRS, such as the RDM (§2.2.5), experience high power to size ratios, and contain fragile components, which suggest additional protection is required.

Therefore, supplementary subsystems should be introduced to the LRS as a solution to the problematic issues above in order to enable the necessary high tolerance in accuracy of measurement.

Finally, the LRS requires an additional positioning subsystem plus special software to enable recorded data to be reconstructed into a 3D model of the railway infrastructure complete with dimensional information capable of subsequent analysis.

At the start, all of the devices within the optical subsystem itself are linked and assembled according to their manufacturing specifications. Device selection was made with this in mind. The RDM unit was designed independently as a complete mechanical component (§3.12), and was matched to the optical subsystem. The positioning subsystem (§3.8), is located in close physical proximity to the LRS. It generates appropriate co-ordinate measurements for the construction of a 3D model (§2.3.1) in earth co-ordinates.


Finally, the software itself must be integrated with the electro-mechanics. On activating the LRS, the RDM spins at high speed. Simultaneously, the optical loop activates the timing card (§2.2.6). Using Real Time Acquisition Tool (RTAT) software, the raw data from the timing card is then configured for storage on the PC HD, in real time, together with output from the positioning subsystem. Later, the raw LRS data can be calibrated, viewed and manipulated by another software component: the Laser Visualisation Tool (LVT).

2.3.1      Raw-data into 3D model

Using bespoke software, a 3D model can be reconstructed from raw data from the LRS (the outputs from the optical subsystem and the positioning subsystem), replicating the railway infrastructure with accurate dimensions. Output from the optical subsystem is utilised for the construction of a 2D profile. The third dimension is assembled using the output from the locomotive positioning subsystem (§3.8).

The raw timing card output data comprises two main items:

1.      the ADC-distance, which is the delay-time between the two analogue inputs SYNC and PMT, providing a 12-bit resolution dimensional radius, R.

2.      the RDM angular position, which provides TLL 7-bit resolution angular data, q.

These parameters, in polar form (R-q ), can be converted later into 3D image form, using Cartesian co-ordinates. By assuming that the optical and analogue pulses are travelling at constant speed, the ADC-distance, in nanoseconds, is linearly-related to the true distance to be measured in metres. There are two dimensional radii used to convert the ADC-distance into true distance (Figure 2.6):

1.      The close range (minimum) radius (CRR) is set in ISO units (metres) equivalent to ADC time-resolution  bit 0.

2.      The far range (maximum) radius (FRR) is set in ISO units (metres) equivalent to ADC time-resolution bit 12.

The true range in metres between CRR and the FRR can be adjusted by changing the delay-cables lengths (§2.2.2) and by setting a specific timing card configuration feature, the time-to-amplitude converter (TAC) range (§2.2.6). The true values of the radii determine the maximum and minimum measurable distances from the RDM centre-normal by the LRS. In this way, the LRS will not detect an object nearer than the CRR nor further than the FRR (Figure 2.6).

However, the true range between the radii will always have 12-bit resolution. Consequently this gives, if the true range between the CRR and the FRR is of 4.096m and the resolution will be 1mm. Both radii are on the same vector R and share the same RDM angular position. The CRR and the FRR can be manually calibrated by the user before or after the actual scan. An alignment subsystem may be devised to automate this manual calibration task. The simple algorithm, used to convert the output raw-data from the timing card into XY co- ordinates, is given by Eq.(2.1).




At this point, the output from the timing card and the rotational position of the RDM has been used to generate a 2D (XY) profile of the scanned surrounding. From this 2D profile, a complete 3D model can be constructed by the introduction of additional information from the locomotive positioning subsystem (§3.8) in the form of the z-coordinate.

Figure 2.6 – diagram showing the relationship between R,q and XYZ co-ordinates.


The z-coordinate is a vector aligned with the longitudinal motion of the locomotive (Figure 2.6). On the LRS prototype, this longitudinal information was achieved by using a longitudinal shaft encoder. Further information about profile positioning in the longitudinal direction is given in section (§4.3.3).

2.3.2      Hardware integration

This section describes links with other surveying systems on board and explains how the LRS internal data streams are channelled. The LRS is not the only surveying system on board. Also, the LRS will require additional information from an existing locomotive positioning subsystem for 3D reconstruction.

The LRS requires a minimum of four different acquired data values for the reconstruction process. The scanning PC (§3.7) is programmed to save them in real-time (§4.2) without delay and in synchrony. These are (Figure 2.7):

1.      the ADC-distance (§2.3.1), which is output as a 12-bit data stream. It is the ratio of the distance between the normal-centre of the RDM and the object to be measured (§2.2.5). The data rate is dependent upon the laser emitting frequency and can reach up to 1MHz

2.      the RDM angular position, which comprises of the order of 4000 pulses per revolution. The system uses a shaft encoder attached to the rotating RDM shaft. Acquisition is via a timing card (§2.2.6) connected to a TTL routing port, which delivers the angular position value. The repetition rate depends upon the existence of valid ADC distances. Here, the timing card TTL routing port registers a value only when there is a match between the SYNC port and the PMT outputs

3.      the locomotive inertial position in Earth co-ordinates. This output provides the z-coordinate (§2.3.1) and has a repetition rate of up to 500Hz. The acquisition system used to obtain this value involves the integration of two IMU devices which are part of the locomotive positioning subsystem

4.      a synchronised time-base. This provides synchronisation with other non-LRS surveying systems which are also operating on the locomotive. A clocking device is used for this, operating at 50Hz. 

The Real Time Acquisition Tool (RTAT) software (§4.2) reads all inputs simultaneously from all of the four outputs itemised above. The timing card continuously and simultaneously records the ADC-distance and RDM angular position inputs using a FIFO buffer between the memory card and the PCI BUS (Figure 2.7).

Figure 2.7 - flow chart of the inputs involved with the optical integration system.


This mode can create a random shift in time between the data collected by the card memory and the rest of the interval data collected by the PC, since the FIFO buffer transfers data to the PC upon request only. Also, timing card memory fills up with valid ADC-distance. This last data set is variable in nature. The occurrence of a viable measurement depends, for example, upon the objects existence (which is not regular) in its surroundings and the reflectivity of the object.


Therefore, the timing-card memory randomly fills relative to a fixed time interval, with the FIFO buffer providing a pointer between the PC and this memory. This fact forces the necessity to flush the FIFO buffer at up to a 500Hz rate. This is the maximum sample frequency of the main IMU, which is a part of the positioning subsystem.

Using an additional acquisition instrument for reading the RDM angular position, thereby freeing the TTL routing timing card port for generating a synchronised time-base, would result in a continuously increasing data phase shift between the ADC-distance and the RDM angular position. Also, this would not provide the same level of accuracy as the current configuration and, furthermore, would be unlikely to be able to provide the required high repetition rate.

The nature of the data shift between the locomotive position and the timing card output can be defined as follows. The timing-card memory capacity is 64Kb which can contain up to 10.6 thousand measurements. Each measurement is a valid ADC-distance/RDM position pair. At the maximum 1MHz repetition rate (the maximum laser emitting rate), this memory would fill up and transfer data to the PCI BUS at a minimum fixed rate of around 100Hz. Therefore, it is a good idea to flush the FIFO buffer at a fixed rate between 500-100Hz based upon the PC transfer rate.

As an example of correctly managing failure of the FIFO buffer, a flag recognises ‘FIFO over flow’ errors [18 p71], indicating that the PC transfer rate is not fast enough i.e. the PC performance is insufficient for successful hardware integration. This error occurred often, during the experimental trials, as a result of a mismatch between the prototype PC and the maximum laser repetition rate used.


Finally, the synchronised time-base output provides a gateway link to other surveying systems and instrumentation attached to the locomotive such as any additional LRS locomotive PC (§3.7), video surveying systems, climate monitoring systems, or other user interfaces (Figure 2.7).

2.3.3      Implicit optical processing

Most conventional pulsed radar systems implement a simple procedure: they transmit pulses at a particular carrier frequency which are then reflected back from targets [24 p621]. A common problem experienced in virtually all cases is “clutter” [23 p470]. This is the reception of unwanted pulses from objects in the environment, other than the desired targets. In the case of LIDAR, an additional problem is that objects with temperatures above absolute zero naturally emit IR radiation. Therefore, the problem is compounded. The LRS uses a delay system to overcome some of these problems. It ensures that a received pulse, arriving back at the LRS, is properly associated with the matching signal sent to the timing card via the delay cable. It also ensures that a pulse received beyond a specified maximum range is not interpreted as a valid measurement at very close range (range ambiguity) [23 p53].

The system will accept signals arriving up to the occurrence of the SYNC pulse associated with that transmitted pulse. The LRS benefits from:

1.      Minimum/maximum measured distances. In the case when a SYNC registration event occurs with no prior measurement pulses arriving, the system registers no objects within that time slot. This can happen when an optical pulse sent out does not return because of either low object reflectivity or the object being beyond the maximum measurement range of the system. If the object is too close to the system, then a minimum registration period condition is invoked in a similar manner.

2.      The measurement resolution can be modified. The measurement resolution depends upon the difference between minimum and maximum range settings (as set by the two delay path lengths). Therefore, the LRS will measure, with the same resolution, objects that lie, for example, between 0m and 4 m, or objects that lie between 2m and 6 m.

3.      Time-coincident disruptions or interruptions from the surroundings are highly unlikely and consequently very infrequent. The LRS can operate with virtually no interference even from similar sources of light emitted at the same wavelength and pulse repetition frequency as itself. This enables several LRS to work in close proximity on the same train, whilst being tuned to identical pulse repetition frequencies and wavelengths.

4.      The LRS only accumulates valid measurement data. Invalid measurements are discarded in real-time.  This procedure reduces data volume for storage and prevents the need for additional offline pre-processing.

5.      The LRS output data can be use and displayed in real-time. There is no need for data reconstruction, de-noising or filtering of the received data in real-time.

2.3.4      The optical system resolution and accuracy

Many of the individual subsystem elements which go to make up the optical subsystem are, in their own right, designed to analyse such things as the reflectivity and surface texture of different materials at the molecular level. Therefore, in theory, the accuracy of the optical system is going to be extremely high when operating statically [14]. On introducing movement into the optical system, such as that resulting from the operation of the RDM, accuracy is inevitably reduced due to vibration and heat-transfer effects. Subsequent choice of sample rate and, worse still, the dynamic resolution of the positioning subsystem erode the LRS optical accuracy still further.


Because the RDM shaft is rotating on an axis parallel to the locomotive longitudinal motion, and assuming, quite reasonably, that the locomotive is travelling in a straight line at constant speed over this measurement span, there are four quantities which affect the final resolution of the 3D model (§2.3.1):

1.      Sampling frequency (Figure 2.8). This is equivalent to the laser emitting frequency in pulses per second. It can be adjusted up to a maximum value of 1MHz (§2.2.1). The 3D model increases in density (number of measurements) in all dimensions as this frequency increases.

2.      Scanning frequency (Figure 2.8). This is the rotation-speed of the RDM (§2.2.5).

3.      Longitudinal position update frequency (Figure 2.8). This is determined by the positioning subsystem output frequency (§3.8) which reports the inertial location of the locomotive. This frequency can be adjusted up to 500Hz.

4.      Longitudinal velocity of the locomotive (Figure 2.8). As the locomotive travels faster, with the above three fixed, the 3D model resolution will reduce in all dimensions.

Figure 2.8 - the four parameters affecting the final resolution of the 3D model


Figure 2.9 - three different resolutions for reconstructing the final 3D model


The quantities above can be manipulated into three different resolutions for reconstructing the final 3D model (Appendix C):

1.      Radial Resolution in metres (Figure 2.9). This is the resolution determined by the spacing on the contour projected into the XY plane. As the value of the true FRR (§2.3.1) and/ or the scanning frequency (RDM rotation speed) increases, this radial resolution will decrease. It is defined using Eq.(2.2):




2.      Longitudinal Resolution in metres (Figure 2.9). This is determined by the spacing between measurements in the longitudinal direction of locomotive motion. There is linear relationship between the longitudinal velocity of the locomotive and this resolution, if one assumes that the sampling and the scanning frequencies are both constant. It is defined using Eq.(2.3):




3.      Radius Resolution in metres (Figure 2.9). This is equivalent to the laser path sensitivity to true distance. The true distance resolution depends upon the LRS initial settings (§2.3.1) such that:




There are other restrictions on the maximum resolution (Appendix C) that can be achieved by the LRS such as laser spot size and laser wavelength.

The laser spot size increases linearly with range. The divergence angle has been determined experimentally to be 0.0305° degrees for the prototype system. Occasionally, the laser spot hits an object to be measured but does not illuminate it completely (the spot covers an edge).


As a result, the return pulse may not be powerful enough to register as a measurement. A representative example of this resolution: if the laser spot diameter is Æ20mm at maximum range, the object edge resolution will be ± 20mm and less at closer range.

Therefore, the Radial Resolution in metres should be designed with respect to the object perimeter resolution [15].


2.3.5      Remote sensing and the choice of laser wavelength

Interaction between light and matter is complex.  Some phenomena are still poorly understood [24 p109]. Light can be considered as a particle (photon) or a wave. All phenomena associated with the interaction of light and matter are usually considered in one of three contexts:

1.      absorption

2.      dispersion

3.      scattering

Other observed phenomena, such as Faraday and Kerr effects, are classified under “electro-optics and “magneto-optics” [24 p111] and do not concern LRS operation. Three types of interaction may take place between the emitted LRS optical pulse (laser beam) and the surface of an object:

1.      the emitted photon retains its original energy, as do material particles at the surface, and the photon continues on, possibly in a new direction

2.      the photon gives up part of its energy to material particles at the surface, and proceeds onward, usually in a new direction, with less energy, and hence with lower frequency and longer wavelength (Compton and /or Raman scattering) [24 p111].

3.      the photon is completely absorbed, giving up all of its energy to material particles at the surface.

Item one above is the operating regime for the LRS in which photons merely bounce off the object surface material and continue on, undisturbed but perhaps with a changed direction, back to toward the LRS.

Based on wave theory, it is necessary to assume that energy is absorbed and then re-emitted at the same frequency [24 p112] (the optical pulse returning back from an object retains its wavelength property - i.e. no ‘colour’ change). Also in this case, scattering of light occurs, if one considers light as particle.


However, firstly, because the LRS is designed to sense large particles compared with its laser wavelength. However, the scattering depends upon the nature of the particles, their size and distribution. Secondly, the theory, in general, also emphasizes that, for particles which are large with respect to the wavelength, scattering is independent of wavelength [24 p113].

Therefore, the scattering phenomenon should not be used to determine the necessary LRS wavelength, because objects in scanning surroundings are not particulate or made of a uniform material.


The scanning environment is also subject to temperature changes which, in turn, generate thermal ambient radiation. This property is expressed mathematically as the Stefan-Boltzmann law whereby the amount of energy emitted by an object is directly proportional to its temperature [24 p349]. The object ambient temperature within the LRS scanning surroundings is likely to generate thermal radiation in the FIR spectral region of 3-14mm (earth ambient temperature is about 300K° and peak at 9.67mm) (Graph D.2).

Therefore, if the LRS was to operate within this spectrum, unwanted radiation from the scanning environment would confuse the system. A simple analogy would be to shine a torch into a fire and seek a reflection.


The other side of the visible spectrum, the UV-A region (0.315-4.0mm), was also found to be unsuitable for the LRS, because:

1.      its short wavelength would be hazardous to human skin and eyes, which will violate the LRS safety case (Appendix A)

2.      UV light generates high level of scattering (Rayleigh scattering) [24 p113], as its wavelength is comparable with the size of the molecules of the atmospheric gases.

The UV band therefore experiences severe atmospheric scattering which, in turn, makes the UV band unsuitable for the LRS.


In the Near Infra Red (NIR) (0.7-1.3mm) spectrum scattering is due to particles of the same order of size as the wavelength, such as dust, water droplets and aerosol suspensions. However, for a clear atmosphere and short detection distances, this scattering phenomenon (Mie scattering) is relatively small [24 p352] and may be ignored.


Atmospheric transmission is highly selective when the entire optical spectrum is considered. This is because there is always significant quantities of water vapour, carbon dioxide and oxygen present in the atmosphere, and these gases have strong absorption bands in the infrared spectral region. It is likely that the atmosphere will transmit very little (<20%) radiation from the sun in the 0.75-0.78mm wavelength range [24 p352] (Graph D.1). Therefore, if the LRS is operated in this range, it is unlikely that LRS will mistakenly interpret direct radiation from the sun or reflection from any earth object which is illuminated by NIR sun radiation as an LRS illuminated object.  The simple analogy is extended to that of shining a torch in a darkened room.


The optical properties of air depends upon the ambient temperature of the scanning surroundings. Dispersion occurs when a beam of light travels through a transparent material: “it is observed that the velocity is a function of the wavelength, or frequency; usually the velocity is reduced for higher frequencies” [24 p113].

This means that the speed of light of the LRS optical pulse propagating thought the atmosphere can be slowed down and could affect LRS TOF measurement. However, because dispersion through air is very small, (the refractive index of air is about 1.0003 with a speed of light equal to 299 702 547 m/s) [16] and the LRS optical pulse travel forward and back within the same refractive index, air dispersion may not affect at all the LRS optical loop.

Nevertheless, variations in air temperature can cause bending of rays through inhomogeneous media (Fermat’s principle) which results in non-direct ‘optical path length’ [10]. This can happen when there are a large differences in air temperature between layers of air close to the objects and the air is at ambient atmospheric temperature. Because the LRS optical pulse has an extremely short distance to travel in view of the speed of light, and in most cases, it propagates perpendicular to the plane of incidence between the air layers, variations in the distance to travel (i.e. variations in the optical path length) are likely to be insignificant and are unlikely to affect system accuracy.


The changes in air moisture content and temperature as a result of climate changes will affect the amount of photon noise [23 p565]. Water droplets and large dust particles can cause non-selective scattering [17]. This occurs when the particles are much larger than the light wavelength and all wavelengths are therefore scattered equally. This type of scattering causes fog and clouds to appear white to a human eye because blue, green, and red light are all scattered in approximately equal quantities.

So, when operating in the NIR, in heavy fog, thick smoke, clouds and rain, light will be absorbed, preventing the LRS from gathering high quality information [23 p498, p565]. However, in mitigation,

1.      in the NIR region there is relatively low propagation attenuation in the air (~1.0dB/km) compared with visible light. This means that the NIR operation will be less noisy when compared with that in visible light [23 p562] (Graph D.4).

2.      a detector operating in the NIR band is insensitive to thermally emitted energy from materials such as rocks, water, soil, roads and pavements (Graph D.3). However, reflection from vegetation is much greater in the NIR than in the visible bands [30][29].

3.      An optical detector, such as the RAPD proposed here, has a narrow pass-band which will reduce the effects of background noise [23 p565].

Therefore, the NIR band operation of the LRS will ensure high optical signal-to-noise ratios. It also enhances the ability of the LRS to cope with the variation in temperature, ambient light intensity and air density expected in the scanned surroundings.


Because the LRS is designed to measure a variety of surfaces at different angles of incidence, it is necessary that an object with low surface reflectivity at a random angle of incidence should reflect back sufficient energy for detection. Therefore, NIR bands are chosen as the preferred wavelengths for measuring rail infrastructure. The practical considerations of integrating commercial off-the-shelf optical components and electronic devices in order to build a actual LRS, lead to a wavelength of l = 780± 2nm being chosen as the LRS desired wavelength within the NIR region.

2.4      Optical subsystem testing

Two approaches were used to investigate the performance of the complete optical subsystem:

1.      Proof of concept of the system by actual trials, comparing physical quantities with those measured by the system.

2.      Validating the results using temporal relationships. This method is essential for real-time integration issues such as:

a.    checking in real-time if the hardware elements are registering in the correct sequence.

b.    inspecting for failures within the hardware elements and the integrated sensors.

c.    Checking for poor performance due to poor integration (effects of lags and latencies) by dynamic variations in testing strategies.

Most of the elements/devices used in this LRS subsystem, and as described in this chapter, are difficult to inspect in an average laboratory using standard instrumentation (oscilloscopes, etc.).


Also, the LRS raw data output is designed for subsequent dimensional calibration through the software so actual calibration of the raw data is not implemented in hardware. Validating the LRS output under items 1 and 2 provide confidence in the performance of the system without requiring high specification laboratory facilities. Every element within the optical subsystem was examined for compliance with the requirements of each of the other elements within the optical subsystem in terms of size, weight, performance and cost. This is a good point to reflect upon the operation of a LIDAR system in terms of range performance.

2.4.1      The LIDAR range equation

The laser radar, or LIDAR, range equation relates the maximum range of the radar to the characteristics of the laser emitter, the receiver, targets and the operating environment. A simple form of the radar range [23 p3] can serve as the basis for the LRS design and can also be provide an assessment of its maximum measurable range, signal-to-noise ratio properties and the most suitable collecting lens diameter. However, in practice, a simple radar equation does not predict the range performance of the actual radar equipment to a satisfactory degree of accuracy. The predicted values of radar range are usually optimistic [23 p15] and therefore the trials described here, only gave a limited demonstration of the relationship between the LRS measurable distance and parameters within the radar equation (§2.4.3).


When the target is much larger than the laser beam, as is likely to occur in most situations, the radar equation Eq.(2.5) [23 p566] demonstrates a square-root relation between the maximum LRS measurable distance and the effective aperture of the collecting lens.




where the following constant terms are defined: the RAPD quantum efficiency,h, observation time, B, wavelength, f , the required number of signal photons (the minimum threshold of the timing card when integrated with the RAPD), np. Since they are constant, the maximum LRS measurable distance Rmax can be written as follows:




where the laser transmitted power, Pt, is in watts and the collecting lens effective aperture, Ae, is in m2 [23 p15]. The target characteristics are defined by the surface of reflectivity, r, and the angle between the surface normal and the incident radar energy is f [23 p566].


The target surface is assumed to be a diffuse (Lambertian) scatterer with an estimated cross section that depends upon the laser beam geometric properties, the target surface reflectivity and angle between the surface normal and the incident radar energy [23 p566].

Equation Eq.(2.6) shows that by increasing the emitted laser power Pt, extended measurable distance can be achieved. Laser power cannot be increased because of the LRS safety case (Appendix A). However, the effective aperture area of the collecting lens Ae, can be increased at the price of increasing the RDM diameter, the LRS overall size, running costs and system capital cost.

2.4.2      Necessary properties of the collecting lens

The main requirements of the collecting lens were itemised in Section (§2.2.3) and, as mentioned earlier in Section (§2.2.5), the diameter of the RDM determines the mechanical limitation and the overall capital cost of the LRS, since the LRS performance and specifications are highly dependent upon the mechanical properties of the RDM, such as its maximum rotation speed.

The RDM (§2.2.5) (Figure 2.4) diameter also determines the collecting lens aperture diameter because the collecting lens field of view (§2.2.4) (Figure 2.4) is sighted through the RDM aperture.


Hence, the aperture diameter of the collecting lens should be designed to a minimum and the physical dimensions of the lens front element must be slighter smaller then the RDM actual diameter (Figure 2.4). The amount of light passing thought a lens is proportion to the lens aperture area. In the case of over-reduction of the area of a lens aperture, the energy of the optical pulse collected back from the object to be measured may be reduced.

As a result, the returned optical pulse may not register above the RAPD sensitivity analogue threshold. Therefore, when planning to reduce the lens aperture diameter, considerations should be taken based upon the following.

1.      The optical set-up should be defined according to collecting lens tasks. Optical elements such as beam splitters, reflectors lenses, telephoto lenses, Fresnel lenses, etc. should be designed in advance. Selecting the proper lens within the optical set-up requires making a number of choices such as the lens shape, its conjugate ratio, f/number, transmission properties, wave-front distortion, light scattering effects, anti-reflection coating, availability and cost. These considerations are defined based upon theoretical estimations and determine the optical subsystem efficiency t0, Eq.(2.11).

2.      The aperture properties of the RAPD, such as the active area and aperture shape, should be known. The lens focal spot size and the depth of focus should be designed according to the laser wavelength and RAPD aperture properties.

3.      The maximum distance to be measured should be set in advance.

4.      The properties of the emitted laser beam (§2.2.1) such as its intensity, spot size, polarisation, wavelength, etc., and its optical pulse properties should be established and checked.

5.      The level of surface reflectivity of the objects to be measured (i.e. the railway infrastructure) should be examined in detail. This defines the target backscattering coefficient, r, Eq.(2.11).

All of the considerations listed above can be defined by the LRS requirements specification, where the collecting lens type and it arrangement have been selected carefully, according to the lens size, weight and overall cost.


A prototype lens arrangement is documented in section (§2.2.3) An alternative set-up is proposed in Appendix D-D.1. The properties of the RAPD aperture and the emitted laser beam were discussed earlier as part of the wavelength requirements (§2.3.4) and also as part of the LRS safety case (Appendix A). A selection of objects with differing surface properties, and which are representative of the targets to be encountered in commercial operation, were collected from ordinary railway infrastructure. Representative surfaces range from black sooty and irregular ones to highly-reflective, polished, metallic ones. All the objects collected were examined in the laboratory (§2.4.3) and later used for outdoor trials (4.4).


An ideal thin lens is shown in Figure 2.10. By using this and ray tracing theory, it was possible to define the actual optical implementation. An ideal thin lens has a thickness that is sufficiently small not to contribute to its focal length. In addition to this assumption, a small angle approximation was used, where angles with the substitution of θ for sin θ, are valid.

Figure 2.10 - ideal thin lens used to define and solve optical applications using ray tracing theory


In the case of collecting lens systems, the optical magnification M is a fundamental limitation placed on the geometry. M is the ratio of the image size to the object size and, in this case, is the ratio of the reflected laser spot radius RObj to the RAPD aperture radius RRA Eq.(2.7) (Figure 2.10).


Since the object, the image and the collecting lens are all circular, from the 2D case, the 3D solution also emerges. The magnification M is given by Eq.(2.7) and in based an two similar triangles having opposite angles f (Figure 2.10).




Following the initial LRS requirements, the necessary magnification is M= 0.025. Hence, there is only one lens position that will satisfy that magnification requirement if the maximum distance to be measured is U = 15m. The Gaussian Lens Equation Eq.(2.8) also uses similar triangles sharing a common vertex and angle j (Figure 2.10).




Equation Eq.(2.8) describes a fundamental relationship between the focal length f and the overall size of the optical system. This gives a focal length of, f = 365.85mm, for an object to image distance, U + V = 15.375m as the maximum length of the optical path combined with the size constraints on the system. The optical Invariant (Lagrange Invariant or the Smith-Helmholz Invariant) [24 p161] is important in designing a reducing lens system overall diameter whilst preserving high light-collection efficiency.


Ignoring wave optics theory and only considering ray optics theory, the optical invariant geometry (shown as a dotted line in Figure 2.10) uses the relationship between the distances V (Figure 2.10) and U, where U must be the larger.


An assumption can then be made that the distance V has the same length as the focal point f. Consequently, an additional approximation can be made such that q2 ~ R/f. Rearranging this approximation, using Eq.(2.8), the front aperture stop of the lens RLens can be defined where two similar triangles have opposite angles q1,2: Eq.(2.9) (Figure 2.10) [20].




The lens f-number f# = f/2R = f/D and RLens can represent the lens size or the RDM radius, being the aperture stop in front of the lens. The f# is within the range of 1<f#<22, below which the image loses the object properties (its height), and above which light transmission may be restricted by the narrow lens aperture. Decreasing RDM radius or lens size RLens will restrict the amount of light gathered by the lens and the total light focused at RRA (RAPD) would decrease Eq.(2.9) due to the restriction of the solid angle subtended by the lens.

So, the lens f# and its front stop RLens should be selected carefully according to Eq.(2.9) because RObj and U vary with the distance to be measured. The relationship between the magnification M and the numerical aperture NA in an optical system Eq.(2.10) is derived from Eq.(2.7).




NA is the lens numerical aperture on the object side of the system (i.e. the RDM shaft inner diameter or the front collecting lens numerical aperture) and NA" is the numerical aperture on the image side of the optical system (i.e. the lens exit aperture on the RAPD side of the optical system). By introducing a smaller RDM radius in front of a well-designed collecting lens, the relationship between the lens magnification M and its numerical apertures could be invalidated, as a result of creating a smaller front numerical aperture NA.

Therefore, the RDM aperture must be larger than the lens front numerical aperture NA. The overall front aperture area (collecting light area) in equal to the inner hollow shaft radial area excluding the radial area of the small 45° mirror fixed on the front-centre of the collecting lens.


As a practical consideration for increasing the system robustness to external vibration and movements along the system x-axis, it is suggested that the collecting lens exit numerical aperture NA” should be kept to minimum but must be larger than the RAPD aperture. This will reduce the both the angles q2 and f (Figure 2.10), so that movement of the RAPD along its x-axis will have less effect on changing the focussed spot size and ray properties.


Finally, system robustness can also be achieved by positioning the RAPD slightly in front of the defined actual focal length f. This can be achieved by finding, by trial and error, the actual focal point (aligning the RAPD with the collecting lens) and then shifting the RAPD slightly towards the collecting lens along the x-axis.

2.4.3      Collecting lens aperture experiments

An experiment was designed to determine the minimum necessary collecting lens aperture to ensure effective gathering of the laser reflection back from a railway environment. Eleven different objects (Figure E.1) were selected from a railway environment and positioned at fourteen different distances from the LRS.  The objects were located in front of the prototype optical subsystem within the range 0.2-4.4m. The prototype optical subsystem, in this experiment, was implemented using an ordinary camera lens (f=28mm /f#2.8) with an affixed 45° mirror of 4mm diameter (§2.2.3), the LPG (§2.2.1), the RAPD/optical filter bypass (§2.2.4) and a high sampling rate oscilloscope. The oscilloscope was connected to the RAPD analogue output port which provided measurements in the range 0-1500mV.


Each object was examined more than once and the results were subsequently plotted at Graph 2.1 as a coloured line (voltage vs. distance). An assumption was made that the voltage output for each measurement (Graph 2.1 y-axis) was a linearly related to the radiant light energy detected by the RAPD, and gathered via the collecting lens with a fixed aperture size and constant optical efficiency.

Graph 2.1 - examining the necessary collecting lens aperture size


A uniform white paper sheet named as object A4W was measured three times at all distances and plotted on Graph 2.1. These observations experimentally validate the inverse square law relationship [24 p235] over the range of observation distances, which results in Equation Eq.(2.11). Equation Eq.(2.11) is derived from the radar equation described earlier, whereas for a white paper target (A4W), the surface reflectivity, r, is assumed to have a uniform surface, high reflectivity, and is evenly diffuse.

Also, all object surfaces are examined with minimal angle between the target surface normal and the incident laser beam which results in cosf=1 in the radar equation Eq.(2.5). Equation Eq.(2.11) also shows the power distribution, S, at the RAPD active aperture (i.e. the target signal power at the LRS) [8] and is measured as the RAPD analogue output.


The transmitted pulsed power, Pt, the collecting lens effective aperture, Ae, and the optical efficiency, t0, are kept constant during the experiment. Other objects with a similar uniform surface show comparable inverse square law properties to object A4W (Graph 2.1).


Highly reflective objects such as polished rail (RP) and shiny stickers (SS) (Graph 2.1) clearly demonstrate their relatively expected properties of generally high output value, and sensitivity to angle of incidence as shown by their erratic behaviour. Low reflective objects with dark, irregular surfaces such as orange brick (BO) and black brick (BB) (Graph 2.1) show their low sensitivity to angle of incidence in the smoothness of their plots. Both objects BO and BB (Graph 2.1) appeared to hit low measurement threshold values at around 5mV at ranges close to 4.4m. The timing card (§2.2.6) has a documented minimum threshold for detection, suggested by the timing card manufacturer, at 10mV. It is deduced that, for these low reflective surfaces, it is possible to establish a relationship between the collecting lens aperture area and the maximum possible measurement distance.




By simulating equation (2.11) with the results of this experiment, Table 2.1 establishes the minimum collecting lens aperture required for detection of the worst-case surface in a railway environment.


The lens aperture diameter


The maximum measurable distance (m)





















Table 2.1 - the relationships between the collection lens diameter and maximum measurable distance


From the LRS specification, the maximum target distance is 15m. This will require a collecting lens with a minimum aperture diameter of 50mm (Table 2.1) which in turn defines an effective aperture diameter of 47.28mm. It is expected that the final LRS optical system will have a higher optical efficiency because of its larger aperture and further customised lens properties.


Table 2.1 establishes a realistic relationship between the collecting lens diameter and the LRS maximum measurable distance.


In addition to the data collected in this trial, Table 2.2 illustrates the relative reflectivity of object surfaces. Taking the uniform A4W to be the reference, Table 2.2 reveals the wide variation of reflectivity exhibited by different railway objects.


The objects are:


Factor of reflectivity

Brick (black)



Brick (orange)



Signal (metal matt black)



Rail (corroded)



Rail (polished)



Overhead cable (clean)



White A4 sheet



Table 2.2- the relationships between the railway objects surface of reflectivity


The worst-case surface is a matt black smooth surface. It is recommended that, when operating the LRS on such objects, special care should be taken.



2.4.4      Establishing maximum measurable distance

This experiment was performed to demonstrate:

1.      the delay-cables (§2.2.2) concept

2.      the ability of the LRS to detect an object at maximum distance, in accordance with the LRS specification

3.      the existence of a correlation between the actual distance to be measured and the TOF value output from the timing card.

Additionally, a total-station instrument (G.5) was used to confirm the measurement of the actual distance between the LRS and an experimental target located in front of the LRS, along the system optical path (Figure 2.11). A uniform white target was placed at several different positions along the optical path within a 15m range of the collecting lens (Figure E.2). The settings of the collecting lens (f#, f) were then adjusted to maximise the output from the RAPD. The amplitude and shape of the reflected optical pulse, as well as its TOF, were examined using the timing card. The system was implemented as described in the previous section ‘Collecting lens aperture2.4.3)’.

Figure 2.11 - maximum distance to be measured, experiment implementation


The outputs from the total-station instrument and the timing card (§2.2.6) TOF correlated well and the optical timing loop performed according to plan (Graph E.2).

However, the maximum distance was measured as 19.40m, 4.40m greater than expected through the concept of delay cables (§2.2.2).

It is concluded that the propagation velocity of analogue pulse travelling down the SYNC delay cable is less than the speed of light, which is the optical pulse velocity in space. Additionally, time lags may also occur within the RAPD (§2.2.4), the LPG (§2.2.1) and the timing card (§2.2.6) and these may also contribute to this discrepancy.

2.4.5      Real-time data acquisition experiments

This experiment validated the following:

1.      the object edge resolution, relative to the laser spot size (§2.3.4)

2.      the true acquisition abilities of the RTAT application in real time

3.      the real time integration of the optical subsystem with the locomotive position (longitudinal) measurement system.

Three different black and white (B&W) spatial-frequency targets plus specimen objects from typical railway infrastructure were positioned a short lateral distance, SD, from the LRS (Figure 2.12). Using a 4m mini-rail, the LRS was conveyed past these objects, whilst scanning was performed. The optical path of the LRS was therefore aimed to be perpendicular to the direction of motion (Figure 2.12). An encoder recorded the LRS motion and distance travelled along the mini-rail.

The output from the timing card (§2.2.6) in real time was plotted with respect to the encoder output. The timing card threshold configuration was changed to detect only optical pulses reflected from white surfaces, whilst optical pulses from black surfaces were discarded. In this way, the B&W targets should be clearly visible in the results of this experiment.

The B&W targets had different spacing of 1mm, 3mm and 30mm (Figure E.4). At all distances the 1mm B&W target produced a noisy result with indeterminate frequency characteristics. At close range, where SD was less then one metre, the output plot clearly registered the 3mm and the 30mm spacing B&W targets. At ranges greater than 1m, noise appeared on the 3mm spacing B&W target plot. This system limitation results from increased laser spot divergence with range (§2.3.4), which degrades object edge resolution. Because of the complexity of the locomotive positioning subsystem (i.e. the IMU) and its high capital cost, integration with the optical subsystem had to be simulated in the prototype LRS.

A longitude measurement system, using a shaft encoder, provided a data stream similar to that of the IMU position system. This enabled the development and testing of the RTAT software without actually using the IMU device.

Figure 2.12 - experiment set up implements B&W frequency targets


The shaft encoder system was designed to record the changes of LRS position in the longitudinal direction only, with the assumption that motions in other directions (vertical and lateral) were constant (Figure 2.12). When scanning the 30mm B&W target repeatedly, experimental data did not match the B&W target in frequency when subject to acceleration whereas, with constant forward speed, results were consistent.

The problem was found to be a time lag in attempting to record simultaneously the data from both subsystems by the RTAT software. As a result, a reordering of events within the RTAT software was made, producing correct operation.

2.4.6      Overall subsystem validation

As described earlier in the ‘Raw-data into 3D model’ section (§2.3.1), the raw data output from the timing card is presented in polar format (R,q). The RDM angular position, q, output from the RDM encoder as 8-bit data, cyclically ramps up and then resets, due to the unidirectional rotation of the RDM. In contrast, R, the optical path distance 12-bit ADC output from the timing card, measures variable distances according to surrounding object positions in the scanning path (Graph E.1). Interpretation of this raw data is impossible, unless a transformation to a Cartesian co-ordinate system is performed. It is then possible to compare relative dimensions of test objects. The RTAT software performs this task and the laser visualisation tool (LVT) then presents the results in a 3D depiction (Figure 2.13). Results show that the LRS is performing correctly as the relative sizes of objects within the scanned surroundings are, indeed, consistent.

Figure 2.13 - 3D output scan from the LVT, shows linear object in form of XY coordinates


Additionally, by measuring the actual object dimensions within the surrounding, using the total station instrument, the relative sizing of the objects (e.g. wall heights and widths) was confirmed.





Chapter 3

Mechanical subsystems




3      Mechanical subsystems

3.1      Introduction

This chapter introduces all the mechanical subsystems servicing the LRS and their integration issues. It is important to note that the LRS is one system comprised of ten individual subsystems. Most of the LRS subsystems have been designed to ensure a constant working environment for the optical subsystem and to ensure high accuracy and resolution of the LRS output. The practical considerations of developing a product such as the LRS include the following: product shelf life, robustness, rapidly changing environment, capital and running costs.

Because of the nature of this system, the subsystems utilise and share physical properties such as thermodynamics, optics, mechanics, electronics and IT. The final performance of the LRS depends upon the manner of the overall system integration.

Success can only be achieved through careful consideration of the design of each individual subsystem. This chapter therefore presents each subsystem design and additionally considers the integration issues involved.

3.2      Overall integration of the LRS subsystems

The data from the LRS is transferred to the scanning PC via three main inputs (Figure 3.1):

Input 1- Distance measurement (the ADC) (Figure 3.1-Input 1) - Using TOF technology for measuring the true dimensions of the surrounding, the optical subsystem sends an optical pulse via the RDM into the scanned surrounding and then receives a reflected optical pulse back for measurement. The output data from the optical subsystem is then transferred into the locomotive scanning PC and saved on its HD.

Input 2- Angular position measurement (Figure 3.1-Input 2) - Diverting the optical measuring path into a 360° rotating system is fulfilled by the RDM. The RDM rotates continuously at a high rotation-speed. It redirects the measurement path (laser beam) through 90° relative to the longitudinal velocity of the moving locomotive and generates profiles which construct the 3D model. Whilst, the RDM spindle is a mechanical device with ultimate physical requirements, there are numbers of subsystems servicing it. The output data generated by the RDM is transferred to the locomotive scanning PC as the angular position of the diverted measuring path.

Figure 3.1 - flow chart shows system integration between all subsystems within the LRS


Input 3 - The true location of the locomotive in Earth co-ordinates is obtained by the locomotive positioning subsystem (Figure 3.1-Input 3) - a specialist locomotive Inertial Measurement Unit (IMU) is used to generate the location of the moving locomotive in earth axes. This IMU output data is used to reposition and orientation the profile within the 3D model. Because of the complexity of the locomotive dynamics and the position shift by the vibration platform, two IMUs are needed for high accuracy and resolution measurement of the LRS. The output data from the two IMUs are then reprocessed and sent the locomotive scanning PC as a single output from the positioning subsystem.

Figure 3.1 shows the functional and data-flow relationships between subsystems associated with the LRS. In subsequent discussions of mechanical subsystems, it is assumed that a RDM spindle Æ50mm hollow shaft is used in the LRS.

3.3      Air supply subsystem

This mechanical subsystem services the air bearings of the RDM spindle (§3.12) (Figure 3.1). It is self contained, only requiring an external power supply.

The aim of this subsystem is to supply:

1.      Constant pressure and air-flow into the air-bearings of the RDM.

2.      Clean pressurised air into the air-bearings of the RDM.

3.      Dry pressurised air into the air-bearings of the RDM.

4.      Cool pressurised air into the air-bearings of the RDM.

5.      In the future this air supply may drive other subsystems such as a vibration isolation platform or additional LRS.

Air is compressed from ambient temperature and humidity into a receiver vessel (Figure 3.2). As a result of compression (assume reversible polytrophic) Eq.(3.1), the air will be heated up, but also moisture is likely to condense within the receiver (Dalton’s law and the Gibbs-Dalton law)[19 p384,145].




To ensure no condensation occurs within the RDM air-bearings, a condenser is used to remove moisture within the compressed air, prior to entering the RDM air-bearings.


The condenser also removes heat which subsequently increases RDM air-bearings efficiency. A filter is the last component. It removes any liquids or particles within the pressurised air before it enters the RDM air-bearings (Figure 3.2). An extremely fine high –performance filter is necessary due to the surface-finish and narrow space between the air-bearing casing and the rotating shaft.

Figure 3.2 - air supply subsystem


The air supply unit is built from three main devices:

1.      Air-Compressor & Receiver (Figure 3.2) – The air pressure and flow-rate produced by this unit must be stable and consistent. The air supply application (pressure& flow) should be 30% greater than the RDM air bearings requirements. As a representative example: if RDM air-bearings requirement is 6.0bar & 150l/min, then the air supply system should provide pressurised air at greater than 7.8bar & 195 l/min.

2.      Condenser (Figure 3.2) – This refrigeration unit is designed to cool and remove water from the pressurised air leaving the compressor and prior to it entering the RDM air bearings. This unit can also service the needs of the cooling jacket subsystem (§3.4).

3.      Filter (Figure 3.2) – The filter should ensure the particulate quality of the air entering the bearings. It must remove all particles with size up to 5mm and other lubricating liquids leaking from the air compressor and the condenser into the air subsystem.

The air supply unit is built from the three main components listed above. This subsystem can be built from catalogue parts but with all the appropriate devices powered by the locomotive electricity power supply.

It is not recommended to draw pressurised air from the locomotive air system, as the irregularity in pressure and flow-rate from the locomotive can affect both RDM performance and locomotive dynamic properties.

Also, the LRS may be fitted on different locomotive models in the future. This would necessitate a change in the RDM interface design with each locomotive air supply.

3.4      Cooling jacket subsystem

Again, this is a subsystem which services the RDM spindle (Figure 3.1). The aim of this subsystem is to remove heat from the RDM drive motor and the spindle bearings. This simple closed system employs a small pump which circulates cooling liquid between the RDM driving-motor and external heat exchanger (radiator).

A fan is introduced to create ‘forced convection’ over the radiator (Figure 3.3) ensuring a constant heat removal at different external conditions and increased radiator efficiency. Since the RDM spindle must be kept at a constant temperature, even though the RDM power input can vary according to the scanning requirement, this additional cooing system is vital. The cooling jacket unit is built from three main devices:

1.      Pump (Figure 3.3) – circulating the cooling-liquid and keeping the cooling liquid at constant flow-rate and pressure (assuming laminar fluid flow).

The flow-rate is calculated according to:

a.         the cooling liquid ‘specific heat’ in (kJ/kgK) the thermal conductivities of the jacket walls (Fourier’s law of conduction) [19 p562]

b.         the volume & surface area of the RDM cooling jacket (Newton’s law of cooling )

c.         and the total heat required to be removed from the RDM.

If the cooling-liquid transfers to other states such as gas or solid during the cooling process (a refrigeration system for example), an extra pressure factor is required for calculating the rate of heat removal. In most cases, pressurising the fluid increases its capacity to hold heat and therefore increases the system cooling capacity (under its enthalpy properties) [19 p501].

2.      Receiver tank (Figure 3.3) – the receiver tank capacity should have a minimum volume of 10 times the cooling-jacket volume (including pipe volume). The main reason for having this device is to allow the cooling fluid to change volume in accordance with temperature changes within this subsystem.

3.      Radiator (Figure 3.3) – this is a heat exchanger designed to dissipate 1.5 to 2 kW heat, equivalent to the maximum electrical power input of the RDM drive motor.

Figure 3.3 - cooling jacket subsystem


All the devices driving this subsystem should be powered by the locomotive electrical power supply.

3.5      Air blower subsystem

The subsystem describes in this section is designed to protect and maintain the optical subsystem (Figure 3.1). It does this by:

1.      keeping the RDM element optically clean

2.      protecting the optical devices from ambient temperature and humidity changes (Figure 3.1)

3.      maintaining constant temperature and humidity within the optical enclosure.

A high power blower is attached via a filter to the optical case (Figure 3.4). Air entering from the surroundings is pressurised by the fan and then passes through a filter attached to the optical enclosure (Figure 3.4). The air then escapes, via the viewing hole within the hollow shaft, out into the external atmosphere. As a result, positive pressure is built-up within the optical enclosure, keeping constant working conditions around the optical components. The escaping air through the viewing hole maintains the optical RDM element clean and safe from flying particles that may exist within the scanning surroundings (Figure 3.1).

The air entering from the surroundings may experience variation in temperature and humidity. To regulate constant operating conditions, heating and cooling elements can be implemented using a single device such as a Vortex Tube [9].

Figure 3.4 - air blower subsystem


The elements are attached in the inlet duct (Figure 3.4). These elements are activated by a thermostat attached to the optical enclosure.

The fan static pressure should be above atmospheric pressure and its volume flow rate should have the capacity to refresh the optical enclosure volume at the rate, which maintains laminar flow across the RDM viewing hole.


3.6      RDM motor controller

The motor controller is designed to:

1.      maintain the rotation speed of RDM drive motor to within 2% accuracy at any set speed

2.      maintain that rotation speed in the presence of gyroscopic effects and vibration 

3.      enable the rotation speed of the RDM to be set according to operating requirements.

The controller input is a ‘set-point’ value (RDM rotational speed) which is determined by the user. It is calibrated by the logger PC (§3.7) (Figure 3.5).

An encoder is used to provide feedback measurement for comparison with the set point. The encoder output is also connected to the scanning PC which reports the RDM angular position to the optical subsystem (Figure 3.1-input 2).

Figure 3.5 - RDM electro driven motor controller


A proportional plus derivative (P+D) controller is inserted before the drive unit. The drive unit provides integral action ( ), and the motor will have a dominant first order response ( ) [21]. Simulations have been performed using MATLAB/Simulink to prove this closed-loop concept (Figure 3.5). An internal interlock is required to avoid damaging the RDM spindle (§3.12) following mechanical failure. The internal interlock monitors the rotational speed (output from the encoder) and hence any variation and also the motor drive current (Figure 3.5). Under stall conditions, brought about by a system failure, the controller will cut-off the current supplied to the motor and will report a failure to the logger PC (Figure 3.5) (§3.7). Such a motor controller will reduce the running cost and increase scanning raw data quality, operating life of the RDM spindle and overall LRS robustness.

3.7      LRS PC units

Two PCs service the LRS:

1.      a scanning PC which registers the raw scanning data

2.      a logger PC which gathers information about the subsystem conditions and important information about the scanning environment.

The scanning PC integrates three main inputs (§3.2) (Figure 3.1) and it has been fitted with three cards on a single PCI Bus (Figure 2.7). The cards are:

1.      Timing card

2.      Locomotive position card

3.      Synchronized time-base card

The Real Time Acquisition Tool (RTAT) software (§4.2), implemented by the scanning PC, registers all three cards simultaneously and saves four different inputs. The three cards may require additional power consumption which suggests a PC with more than three PCI slots and additionally a more ‘powerful’ power supply than normal. The PC should be mounted on a robust rack, standing on vibration absorber pads. These pads should reduce the high frequency vibrations from the running locomotive and also isolate electrical noise and static that may build up during the scanning operation. It may also be necessary to provide environmental control of temperature and air quality. Because of the high data transfer rate and volume storage requirements, an external data storage unit may be necessary. Additionally, a logger PC with a suitable analogue I/O card and a synchronized time-base card are required for monitoring subsystem conditions such as RDM motor rotational speed, RDM power input, interlock threshold and air-bearings pressure/temperature.

The logger PC maintains a history of all subsystems states, locomotive dynamic properties and external parameters such as temperature, barometric pressure and humidity. The logger PC is also programmed to respond, in real time, to any failure event or a shortage of subsystems resources (such as coolant levels) and generate a report. The data from the logger PC may be used later for establishing accurate running costs, a suitable maintenance schedule, locomotive performance and also to correlate the scanning results with the surrounding environmental conditions. Other devices such as the LPG (§2.2.1) and external +12V for the RAPD (§2.2.4) should be placed on the same scanning PC rack and draw power from the same source.

3.8      Locomotive positioning subsystem

Two IMUs service the LRS positioning subsystem (Figure 3.1). They are used to reposition and orientate the profile within the 3D model (§2.3.1) and provide the true location of the LRS centre in an Earth co-ordinate set. The IMU set comprises:

1.      The main locomotive IMU. This is used to generate the location of the moving locomotive in earth axes.

2.      A secondary LRS IMU. This is used to generate the LRS position shift relative to the main IMU due to vibration .

Because of the complexity of the locomotive dynamics and the position shift between the locomotive body and the RDM centre, both IMUs are needed. The locomotive IMU is integrated with GPS/DGPS devices which define the ‘true’ location of the running train in inertial space in real-time. It also provides a low-level synchronised time base for a neighbouring video survey system. The main IMU records the position information alongside the synchronized time-base which simultaneously registers with the scanning PC (§3.7). Therefore, the scanning data can be integrated with the video survey system and IMU records can be used for aligning the LRS output raw data with the earth axes. The IMU should be positioned on the locomotive centre of rotation with its x-axis coincident with to the locomotive longitude direction of motion.

It should also be fastened on the same locomotive main framework as the train arm support (§3.10) upon which the LRS is mounted. The distance of the LRS from this IMU should be reduced to an absolute minimum if possible and the vector distance between the IMU centre and the RDM centre should be kept constant in the presence of locomotive bending mode deflections.

The secondary LRS IMU (Figure 5.13) registers the LRS inertial position. Hence, the true location of the LRS in space can be defined using both IMU outputs via a simple vector subtraction algorithm (Figure 3.1). The x-axis of LRS IMU should be aligned parallel with the RDM axis of rotation and the IMU centre should be located below the optical path where its z-axis is perpendicular to the optical measurement path (see final drawing in Appendix F ).

The operating frequency of the LRS IMU must be above the locomotive IMU sampling frequency and it is suggested that a calibration between the two IMU units should take place as frequently as possible to reduce gyro-drift effect, offset displacement and, finally, motions that have amplitudes below the IMU units resolutions but nevertheless integrate up and grow to become substantial.  Both IMU units should present acceleration and Angular Rate outputs in digital and analogue formats in all three orthogonal axes. For high resolution location it may be necessary to reprocess the raw IMU data offline. 

3.9      Vibration absorber platform (VAP)

A starting point for the design of a suitable vibration absorber system is the analysis of previously collected real output data from the running locomotive IMU raw data. Specification of this system is based upon vibration magnitude, phase and frequencies. It is also important to know the exact LRS second moment of area, mass, centre of gravity and the characteristics of the vibration absorber system. Three types of vibration absorber have been considered for this particular application:

a.       A low cost passive absorber system which requires accurate modelling and is only effective if used in the same vibration environment for which it was designed. This type of absorber does not require an external power supply or a control system. This makes it a physically robust option, which is also cheap to run.

b.      A high capital cost active absorber platform which requires a high level of real time control. This absorber can be fitted on different locations across the locomotive and on a variety of different locomotive models. Because the absorber is more effective than the passive system described above, there is less need for raw data reprocessing.

c.       A stabiliser system similar to those implemented widely in aerospace imaging systems. This technique ensures LRS stability in all three orthogonal axes by using a suitable arrangement of mechanical gyroscopes. The platform responds to slow directional changes only and is suitable for running train dynamics. Because the LRS is capable of generating large gyroscopic forces, integrating this type of system may require additional balancing control, modelling time and capital. However, this system may be a cost effective intermediate solution between the passive and the active systems above.

As described earlier, there is a direct relationship between the vibration absorber system and the quality of the raw scanning data. A low cost passive absorber will generate low quality raw scanning data, whereas a high cost stabiliser platform will reduce the amount of data to be post-processed. In the end, for this LRS implementation, a passive absorber system was chosen. The over-riding considerations were the time available for system development and the available capital cost.

Cables and pipes from and to the LRS unit should be fitted for minimum interference with the vibration system performance (freedom of movement) and should be designed with high flexibility to avoid transmission of vibration between the subsystems of the LRS. Hence, safety-secured cables should pass from the optical platform (§3.11) via the train arm (§3.10) to the surveying locomotive main frame. This avoids a direct vibration transmission path from the actual locomotive body.

Modelling work has been performed using MATLAB and Simulink. Using good design structural practices (§5.2) has resulted in a final design for the system (§5.5) which may be implemented on a particular locomotive model.

3.10    Train arm support

The train arm support is a passive structural element which physically attaches the LRS to the surveying locomotive. The arm should be fastened as rigidly as possible to the same structure as the main IMU (§3.8) to avoid a free displacement between them. The ideal main arm should provide infinite stiffness, light weight and a solid foundation structure for the passive absorber (§3.9). The arm must exhibit low deflection in all dimensions when carrying a self-rotating, uniform distributed load (UDL), as in the case of the LRS. Variation in load may occur due to the dynamics of the running locomotive. The arm should also be secured by a safety cable to the locomotive. Additionally, safety cables should be fastened to the passive absorber (§3.9) and to the optics platform (§3.11). This type of security is required by the Vehicle Acceptance Body (VAB) (GM-RT 2100) in cases of structural breakdown in a railway environment.

3.11    Optics platform

The optics platform, a structural subsystem, is a vital part in the overall mechanical implementation. Its mechanical functions are to:

1.      locate optical components and ensure optical alignment

2.      increase system robustness and stiffness

3.      maintain alignment between the RDM spindle, LRS IMU, vibration platform and optical components

4.      retain the air blower subsystem.

The optical platform is a combination of a structural rig unit (Figure 3.6-A1) which holds the optical components and a flat honey-comb plate with a large second moment of area (Figure 3.6-C1). The assembly is made from a stiff and light material. The platform locates on the top of the passive absorber (Figure 3.6-D1) and acts as a base-plate for the RDM spindle (Figure 3.6-E1) (§3.12). The optical platform is designed to prevent deflection of the internal LRS optical path (Figure 3.6-F1, F2) between the RDM and the RAPD aperture. The internal LRS optical path is the most sensitive path for deflection and vibration for the following reasons:

1.      It includes a dynamic structure (the RDM spindle (§3.12)) and the other parts are static.

2.      The total length of the optical path is long. It is the summation of the RDM spindle length, lens length, the lens focal length and the RAPD dimension along this path. 

3.      Elements within the path have different weights, sizes and resonant frequencies.

Therefore, the internal LRS optical path should be isolated from deflection, high frequency vibration and electrical noise. This, in turn, means that the optic platform must have a low deflection factor, low weight and should be manufactured to high tolerances in order to hold the RDM spindle (Figure 3.6-E1) unit and accommodate the optical components with precise alignment.

Figure 3.6 - the optical platform set-up


Furthermore, the physical connections between the components within the platform should have qualities of stiffness, low thermal and shock conductivity and must be locked (Figure 3.6-A2, A3 &A4) into place after optical alignment. The physical arrangement of optical components (Figure 3.6-B1, B2 &B3) within the platform is designed to assist the LRS operator in rapidly aligning the system with concern for laser safety (Appendix A). The implementation of the current optical set-up and the construction of the optical path, require the emitted laser beam to be coupled into the optical path from a perpendicular source (Figure 2.1). This optical set up, should induce additional vibration and deflection into the optical path.


However, by locating the laser emitter (Figure 3.6-B1) above the collecting lens (Figure 3.6-B2), but pointing forward and parallel to the main optical path, with an additional 45° mirror (Figure 3.6-B4) to redirect the emitted laser beam down onto the main optical path (Figure 3.6-F1), it is possible to cancel out the deflection that might otherwise occur due to vibration of the plate. It also facilitates safe and timely optical alignment. The front face of the optical assembly (Figure 3.6-E1) locates against the RDM spindle back end (Figure 3.6-E1) whilst the bottom face mounts on the honey-comb plate (Figure 3.6-C1) via an adjustment mechanism. 


The optical platform has also been designed to keep the cables, pipes servicing the RDM spindle (§3.12) and the optical components free from vibration.

The top cover of the air-blower subsystem (Figure 3.6-C2) (3.5) seals with the optical-platform (Figure 3.6-C1) to create positive air pressure around the optical components. Drainage of condensation is important, and channels are built into the bottom, honey-comb plate (Figure 3.6-C3). The optical platform should also have a safety cable securely attaching it to the train arm (§3.10).

3.12    RDM air bearings spindle

This section presents an overall mechanical proposal for a mechanical spindle designed to rotate the RDM optical element precisely at high rotational speed. The proposal also looks at the LRS specifications as part of the spindle design. The most difficult task is mechanically to divert the optical path continuously through 90° without affecting measurement accuracy.

As a result of these requirements, the thermal, electrical and mechanical properties should kept constant during scanning. The subsystems previously mentioned, such as the cooling jacket (§3.4), air supply (§3.3) and motor controller (§3.6) assist to achieve this. In general, the RDM spindle system is designed to:

1.      provide a 360° rotational view of the RDM

2.      be free of vibration

3.      rotate as fast as structurally possible

4.      be as short as possible to sustain optical robustness

5.      operate as quietly as possible and keep the optical components, optical path and the scanning surrounding  free from dirt and debris

6.      maintain a constant low operational temperature, thereby reducing variation in spindle length and RDM optical element shape (due to thermal expansion), and minimising IR noise.

Correct bearings properties are a crucial in achieving the above. In general, spindle systems are divided into two main groups:

1.      those using contact-bearings

2.      those using fluid film-bearings.

The contact-bearing type is used primarily in applications that do not require high accuracy or high- rotation speed. Those that use balls-bearings have a maximum rotation speed of up to 15,000 rev/min for systems with sizes comparable to the LRS (Graph 3.1).

Graph 3.1 - guide to selection of ball or roller bearings [22 p8-134]


However, this group of bearings produces harmonic vibration as a by-product [12 p16.16]. In contrast, fluid film-bearings, such as spindle air-bearings, allow higher rotational speed and accuracy, with lower rotating shaft vibration.


There are two main types of implementation of air-bearings:

1.      Aerostatic air-bearings using external compressed air to generate a pressurised fluid film between the bearing inner case (journal) and the rotating shaft (as part of the journal bearing). 

2.      Aerodynamic air-bearings using the kinetic and the structure properties of the bearings to create a pressurised fluid film at atmospheric pressure (self pressurised bearings).

The aerostatic air-bearings meet all of the requirements for rotating the RDM optical element. The novelty of this design, using a hollow shaft enables the LRS to scan the surrounding through 360° without the need to use a separate drive motor at the back of the RDM, as would be the case for a conventional design.

The RDM spindle system is made up of several elements (Figure 3.7):

1.      Hollow Shaft (Figure 3.7-H1).

2.      Journal bearings, both radial and axial (Figure 3.7-B1, C1).

3.      Motor (Figure 3.7-F1, F2).

4.      RDM 45° solid shaft (Figure 3.7-I1).

5.      Encoder (Figure 3.7-E1, E2).

6.      Cooling Jacket (Figure 3.7-A1, A2).

3.12.1   Shaft design

When designing a spindle, requirements such as torque, T, maximum rotation speed, w, unbalancing centre of rotation, e, and overall size present design restrictions. The low torque requirement (i.e. this spindle does not drive any external load) assists in easing the motor specification and shaft overall radius and length.

The shaft inner diameter, thickness and length are subjected to an axial torque between the RDM and the encoder (at each end of the shaft) which causes the cylinder to twist and distort about it longitudinal axis according to Eq.(3.2) [25p119].




Because of manufacturing and overall design limitations, the encoder and the RDM are fitted on opposite ends of the shaft. The angle of twist q (in radians) Eq.(3.2) between the RDM (Figure 3.7-I1) and the encoder (Figure 3.7-E2) is linear with shaft length, L, and torque, T, applied to the shaft Eq.(3.2).

Therefore the overall LRS design should aim to shorten the shaft, in order to reduce angle of twist. The angle of twist, q, may create a phase shift between the encoder output and the true measurement angle of the optical path passing though the RDM. An assumption is made that constant rotational speed results from a constant torque applied to the shaft, in turn suggesting that the angle of twist, q, is constant for a particular constant rotational speed. This sets a constant shift between the RDM and the encoder output which can be cancelled later using the RTAT software  calibration input.

Therefore, it is vital that the LRS scanning process operates at a constant rotational speed. A large number of output pulses per encoder revolution is required to minimise measurement errors due to this torsion phenomenon Eq.(3.2).

Nevertheless, a hollow shaft design is more efficient in its use of stressed material G Eq.(3.2) then a solid shaft thus the polar second moment of area J is different see Eq.(3.3) [25p107]:




Hence, the hollow shaft can carry 44% greater torque than the solid shaft for the same shaft weight (i.e. for the same shaft section of area per unit length). The hole used for the RDM lateral viewing port, which is perpendicular (Figure 3.7-H4) to the shaft axis of rotation (Figure 3.7-H6) creates smaller torsional stiffness in its vicinity, compared with the rest of the shaft profile, so the fatigue life of the shaft may be shortened as a result.

The most vulnerable part of this region is at the centre profile of the lateral hole where the shaft profile area is smallest (Figure 3.7-H4). Treating this profile as a thin rectangular strip, the polar second moment of area J is given by Eq.(3.4) [25 p118]:




where, t, is the shaft thickness and, b, is the length of the profile strip. If the diameter of hole is the same as the inner hollow shaft diameter, then b = (2pR – 2R) where R is the inner hollow shaft radius. Therefore, the stiffness (T/q) relationship between the closed hollow shaft profile and the open shaft profile can be determined using Eq.(3.2) as follows:




For example, Equation (3.5) shows that a hollow shaft, with inner radius and lateral hole radius both R=25mm and a shaft thickness t=15mm, has just 51.39% of the stiffness around the lateral hole centre (Figure 3.7-H4) compared to the rest of the shaft stiffness.

The uniform shaft profile around the longitudinal hole (Figure 3.7-H4) is also vulnerable to twisting in all dimensions and it is likely to be the source of a main spindle resonant frequency. Increasing the shaft stiffness for a preset diameter can be achieved by material treatment, particularly at the inner and outer surfaces as well applying other manufacturing methods of preloading the shaft at its radial section (for example shrink/press-fit assembly [25 p391]).

Under high rotation, radial expansion of the hollow shaft can result in non-uniform axial displacement due to the inconsistent shaft profile, whereas thermal expansion is likely to expand the shaft in all dimensions. The shaft radial expansion can result in reduction of the radial journal clearance (see later) and, as a result, the journal film fluid may lose viscosity.


Therefore, the maximum rot