U.S. Department of 

Transportation

Federal Railroad 

Administration

Research and Development of Ultrasonic 

Tomography Technology for Three-Dimensional 

Imaging of Internal Rail Flaws: Modeling and 

Simulation

Office of Research

and Development

Washington, DC 20590

DOT/FRA/ORD-13/20 Final Report

April 2013
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

April 2013

3. REPORT TYPE AND DATES COVERED

Final Report (Performance Period: 

04/04/2011–03/31/2012)

4. TITLE AND SUBTITLE

Research and Development to Demonstrate Ultrasonic Tomography Technology for ThreeDimensional Imaging of Internal Rail Flaws: Modeling and Simulation

5. FUNDING NUMBERS

DTFR53-11-C-00010

6. AUTHOR(S) and FRA COTR

Francesco Lanza di Scalea, Faye M. Reynolds, Piervincenzo Rizzo, Salvatore Salamone, and 

Ivan Bartoli

FRA COTR: Leith Al-Nazer, FRA Office of Research and Development

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Avanti Tech, LLC

5155 Seachase Street

San Diego, CA 92130

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REPORT NUMBER

0009

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation 

Federal Railroad Administration

Office of Research and Development

Washington, DC 20590

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AGENCY REPORT NUMBER

DOT/FRA/ORD-13/20

11. SUPPLEMENTARY NOTES

COTR: Leith Al-Nazer, FRA Office of Research and Development

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This document is kept temporarily confidential to the Government.

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13. ABSTRACT (Maximum 200 words)

This report covers the work performed under the FRA High-Speed BAA 2010–2011 program to demonstrate the technology of 

ultrasonic tomography for 3-D imaging of internal rail flaws. There is a need to develop new technologies that are able to 

quantify characteristics of the internal rail flaws so as to ensure increased safety of rail transportation and reduced rail 

maintenance costs. In this work, ultrasonic tomography has been applied to the detection of a 5 percent rail head area (RHA)

transverse defect in the railhead. This project has built finite element models of ultrasonic tomographic arrays on a flawed rail and 

identified an algorithm designed to perform the tomographic imaging of the internal rail flaw in 3-D and automatically. The 

results show excellent 3-D imaging performance with the proposed approach. The work therefore confirms the potential of the 

ultrasonic tomography technique for quantitative verification of internal rail flaws. 

14. SUBJECT TERMS

High-speed rail, rail flaws, tomographic imaging, ultrasonic testing, Finite Element Analysis, 

digital signal processing

15. NUMBER OF PAGES

120

16. PRICE CODE

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OF REPORT

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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. 239-18

298-102
ii

METRIC/ENGLISH CONVERSION FACTORS

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE)

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in)

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in)

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft)

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd)

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE)

1 square inch (sq in, in2) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2)

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2)

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2)

1 square mile (sq mi, mi2) = 2.6 square kilometers (km2) 10,000 square meters (m2) = 1 hectare (ha) = 2.5 acres

1 acre = 0.4 hectare (he) = 4,000 square meters (m2)

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE)

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz)

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb)

1 short ton = 2,000 pounds 

(lb)

= 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg)

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE)

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz)

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt)

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt)

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal)

1 pint (pt) = 0.47 liter (l)

1 quart (qt) = 0.96 liter (l)

1 gallon (gal) = 3.8 liters (l)

1 cubic foot (cu ft, ft3) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3)

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT)

[(x-32)(5/9)] °F = y °C [(9/5) y + 32] °C = x °F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 3 4 5

Inches

Centimeters 0 1 2 3 4 5 6 7 8 9 10 11 12 13

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSIO

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98
iii

Contents

Executive Summary........................................................................................................................ 1

1 Introduction ................................................................................................................. 2

1.1 Objectives.................................................................................................................... 2

1.2 Overall Approach ........................................................................................................ 3

1.3 Organization of the Report.......................................................................................... 4

2 Current Practice of Ultrasonic Testing Of Rails.......................................................... 5

2.1 Bulk Wave Testing...................................................................................................... 5

2.2 Ultrasonic Phased-Arrays – Basic Principles.............................................................. 7

2.3 Applications of Ultrasonic Phased-Arrays in the Rail Industry.................................. 9

2.4 Ultrasonic Tomography – Basic Concepts................................................................ 11

3 Applications of Ultrasonic Tomography to Civil Engineering ................................. 15

3.1 Plates ......................................................................................................................... 15

3.2 Pipes .......................................................................................................................... 18

3.3 Concrete Cylinders.................................................................................................... 21

3.4 Drilled Shafts............................................................................................................. 23

3.5 Wood ......................................................................................................................... 29

4 Applications of Ultrasonic Tomography to Medical Imaging .................................. 31

4.1 Ganeral Considerations ............................................................................................. 31

4.2 Fourier Diffraction Method....................................................................................... 32

4.3 Algebraic Reconstruction Method............................................................................. 38

4.4 Ultrasonic Reflection Tomography........................................................................... 41

4.4.1 B-Scan Imaging............................................................................................ 42

4.4.2 Plane-Wave and Wide-Beam Reflection Tomography................................ 43

4.5 Multiwave and Ultrafast Imaging.............................................................................. 44

5 Bi-Dimensional Finite Element Analysis.................................................................. 46

5.1 2-D Finite Element Model of Flawed Rail................................................................ 46

5.2 Results of 2-D Finite Element Model........................................................................ 51

6 Three-Dimensional Finite Element Analysis ............................................................ 57

6.1 3-D Finite Element Model of Flawed Rail................................................................ 57

6.2 Results of 3-D Finite Element Model........................................................................ 63

6.3 FEA Convergence Study........................................................................................... 70

6.3.1 Meshes for Convergence Study.................................................................... 70

7 Proposed Ultrasonic Tomographic Method for Rail Flaw Imaging.......................... 90

7.1 Difference between Phased-Array Imaging and Ultrasonic Tomographic Imaging 

with Synthetic Aperture Focus.................................................................................. 90

7.2 Synthetic Aperture Focusing..................................................................................... 91

7.3 Matched Filtering ...................................................................................................... 94

7.4 Baseline Subtraction.................................................................................................. 96

7.5 Multimode Detection................................................................................................. 97

8 2-D Rail Flaw Imaging.............................................................................................. 99

8.1 Finite Element Model for 2-D Rail Flaw Imaging .................................................... 99
iv

8.2 Imaging Results from the 2-D Model...................................................................... 102

8.3 Noise Robustness Study .......................................................................................... 102

9 3-D Rail Flaw Imaging............................................................................................ 110

9.1 Finite Element Model for 3-D Rail Flaw Imaging .................................................. 110

9.2 Imaging Results from the 3-D Model...................................................................... 116

9.2.1 Results from the Full Array (5 transmitters, 525 receivers)....................... 116

9.2.2 Results from the Reduced Array (5 transmitters, 140 receivers) ............... 123

10 3-D Rail Flaw Imaging: Case of Worn Rail........................................................... 127

10.1 Worn Rail Model..................................................................................................... 127

10.2 Imaging Results from the 3-D Model of the Worn Rail.......................................... 128

11 Conclusions............................................................................................................. 131

12 References ............................................................................................................... 134

Abbreviations and Acronyms ..................................................................................................... 141
v

Illustrations

Figure 2.1 – Common transducer arrangements for rail track inspections in the vertical plane 

(left) and in the transverse plane (right). (Lanza di Scalea 2007) ................................................. 6

Figure 2.2 – Masking of internal transverse defects under shelling in conventional ultrasonic 

testing of rails. ................................................................................................................................ 7

Figure 2.3 – Principle of multiple transducers firing at imposed delays in phased-array ultrasonic 

probes (dynamic steering and dynamic focusing). ........................................................................ 8

Figure 2.4 – Different configurations of phased-array ultrasonic probes: linear arrays and 2-D 

arrays ..................................................................................................................................... 9

Figure 2.5 – Transducer arrangements for axle inspections: (a) longitudinal transducer at axle 

free end; (b) angle-beam transducers; (c) phased-array transducers. (Lanza di Scalea 2007). .... 9

Figure 2.6 – TTCI approach of ultrasonic phased arrays for rails. (Garcia and Zhang 2006) ....11

Figure 2.7 – Basic concept of ultrasonic tomography for imaging defects in solids (S = ultrasonic 

sources, R = ultrasonic receivers). (Mekic-Stall and Grimm 2002) ........................................... 12

Figure 2.8 – Principle of synthetic aperture focusing. Left: radar. Right: ultrasonic testing. .. 13

Figure 2.9 – The MIRA tomographer that uses a 4×10 transducer array in dry-coupling for 

concrete inspection. (Bishko et al. 2008 and CTL Group 2011) ................................................ 14

Figure 3.1 – A picture of a Transverse Defect at the gage corner of the railhead ....................... 15

Figure 3.2 – The geometrical model of the rail for the 2-D FEA with the 5% RHA Transverse 

Defect in the gage corner ............................................................................................................. 16

Figure 3.3 – The total mesh for the 2-D FEA .............................................................................. 17

Figure 3.4 – A zoom of the mesh around the defect for the 2-D FEA ......................................... 18

Figure 3.5 – Shape and location of the excitation force for the 2-D FEA simulating 2.25 MHz 

ultrasonic excitation at the rail gage corner ................................................................................. 19

Figure 3.6 – Location of the excitation point and of five detection points used to sample the 

ultrasonic waves interacting with the flaw in the 2-D FEA ......................................................... 20

Figure 3.7 – Contour plots of Von Mises Equivalent Stress at t = 5 μsec after excitation from the 

2-D FEA ......................................................................................................21

Figure 3.8 – Contour plots of Von Mises Equivalent Stress at t = 10 μsec after excitation from 

the 2-D FEA ................................................................................................................................. 21

Figure 3.9 – Contour plots of Von Mises Equivalent Stress at t = 15 μsec after excitation from 

the 2-D FEA ................................................................................................................................. 22

Figure 3.10 – Contour plots of Von Mises Equivalent Stress at t = 20 μsec after excitation from 

the 2-D FEA.................................................................................................................................. 22

Figure 3.11 – Contour plots of Von Mises Equivalent Stress at t = 25 μsec after excitation from 

the 2-D FEA ................................................................................................................................. 23
vi

Figure 3.12 – Contour plots of Von Mises Equivalent Stress at t = 30 μsec after excitation from 

the 2-D FEA ................................................................................................................................. 23

Figure 3.13 – Time histories of transverse displacement ux recorded at the five detection nodes 

by the 2-D FEA ............................................................................................................................ 24

Figure 4.1 – Zone 1 geometry – coarser mesh with element size d = 3 mm for the 3-D 

FEA.......... ................................................................................................................................. 26

Figure 4.2 – Zone 1 mesh – coarser mesh with element size d = 3 mm for the 3-D FEA ........... 26

Figure 4.3 – Zone 2 geometry – intermediate mesh with element size d = 1.5 mm for the 3-D 

FEA......... .................................................................................................................................. 27

Figure 4.4 – Zone 2 mesh – intermediate mesh with element size d = 1.5 mm for the 3-D 

FEA......... .................................................................................................................................. 27

Figure 4.5 – Zone 3 geometry and mesh – fine mesh with element size d = 0.4 mm for the 3-D 

FEA......................... ............................................................................................................. 28

Figure 4.6 – Entire mesh for the 3-D FEA. The TD is in the middle of the model in the gage 

corner area with the highest mesh refinement ............................................................................. 28

Figure 4.7 – Boundary conditions for the 3-D FEA model ......................................................... 29

Figure 4.8 – Excitation used for the 3-D FEA ............................................................................. 30

Figure 4.9 – Contour plots of Von Mises Equivalent Stress at t = 1.5 μsec after excitation from 

the 3-D FEA (global view) ........................................................................................................... 31

Figure 4.10 – Contour plots of Von Mises Equivalent Stress at t = 7.5 μsec after excitation from 

the 3-D FEA (global view) .......................................................................................................... 32

Figure 4.11 – Contour plots of Von Mises Equivalent Stress at t = 15 μsec after excitation from 

the3-D FEA (global view) ........................................................................................................... 32

Figure 4.12 – Contour plots of Von Mises Equivalent Stress at t = 1.5 μsec after excitation from 

the 3-D FEA (sectional view) ...................................................................................................... 33

Figure 4.13 – Contour plots of Von Mises Equivalent Stress at t = 7.5 μsec after excitation from 

the 3-D FEA (sectional view) ...................................................................................................... 33

Figure 4.14 – Contour plots of Von Mises Equivalent Stress at t = 15 μsec after excitation from 

the 3-D FEA (sectional view) ...................................................................................................... 34

Figure 4.15 – Location of the arrays of detection nodes for the wave time-history recordings. 

Each array contains 57 nodes........................................................................................................ 35

Figure 4.16 – Numbering of nodes for the “rear” array................. ......................................... 35

Figure 4.17 – Numbering of nodes for the “front” array .............................................................. 36

Figure 4.18 – Time histories of vertical displacement recorded at sample nodes on the “rear” 

array (nodes 107 and 41) and at sample nodes on the “front” array (nodes 78 and 

204)................... ...................................................................................................................... 37

Figure 4.19 – Coarse mesh in Zone 1 (maximum element size d = 3mm)................................... 39
vii

Figure 4.20 – Transition mesh in Zone 2 (maximum element size d = 2mm).............................. 39

Figure 4.21 – Mesh 1 in Zone 3 around the defect (maximum element size d = 0.5 mm)........... 40

Figure 4.22 – Mesh 2 in Zone 3 around the defect (maximum element size d = 0.8 mm)........... 41

Figure 4.23 – Mesh 3 in Zone 3 around the defect (maximum element size d = 1.1 mm)........... 41

Figure 4.24 – Mesh 4 in Zone 3 around the defect (maximum element size d = 1.4 

mm).............................................................................................................42

Figure 4.25 – Mesh 5 in Zone 3 around the defect (maximum element size d = 1.7 mm)........... 42

Figure 4.26 – Mesh 6 in Zone 3 around the defect (maximum element size d = 2.0 mm)........... 43

Figure 4.27 – Position of the probe node for convergence study – side view .............................. 44

Figure 4.28 – Position of the probe node for convergence study – front view.......................45

Figure 4.29 – Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 1 in Zone 3 around the defect (maximum element size d = 0.5 

mm).............................................................................................................46

Figure 4.30 – Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 2 in Zone 3 around the defect (maximum element size d = 0.8 

mm)............................................................................................................47

Figure 4.31 – Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 3 in Zone 3 around the defect (maximum element size d = 1.1 

mm).......................................................................................................................................... 48

Figure 4.32 – Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 4 in Zone 3 around the defect (maximum element size d = 1.4 

mm)......................................................................................................................................... 49

Figure 4.33 – Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 5 in Zone 3 around the defect (maximum element size d = 1.7 

mm)...............................................................................................................50

Figure 4.34 – Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 6 in Zone 3 around the defect (maximum element size d = 2.0 

mm).............. ........................................................................................................................... .51

Figure 4.35 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

acceleration ax for the six different meshes considered in the convergence study..................52

Figure 4.36 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

acceleration ay for the six different meshes considered in the convergence study ...................... 52
viii

Figure 4.37 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

acceleration az for the six different meshes considered in the convergence study ...................... 53

Figure 4.38 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for velocity 

vx for the six different meshes considered in the convergence study .......................................... 53

Figure 4.39 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for velocity 

vy for the six different meshes considered in the convergence study .......................................... 54

Figure 4.40 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for velocity 

vz for the six different meshes considered in the convergence study............................................ 54

Figure 4.41 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

displacement ux for the six different meshes considered in the convergence study ..................... 55

Figure 4.42 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

displacement uy for the six different meshes considered in the convergence study ..................... 55

Figure 4.43 – Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

displacement uz for the six different meshes considered in the convergence study .................... 56

Figure 4.44 – Convergence Index for accelerations ax, ay and az (first row), velocities vx, vy and 

vz (second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for the 

six different meshes used in the convergence study ..................................................................... 57

Figure 5.1 – (a) Phased-Array Imaging. (b) Tomographic Imaging with Synthetic Aperture 

Focus...........................................................................................................59

Figure 5.2 – Principle of Synthetic Aperture Focusing (SAF) for Ultrasonic Tomography 3-D 

imaging............. ........................................................................................................................ 60

Figure 5.3 – Example of envelope detection (Hilbert Transform) of an ultrasonic waveform 

recorded from the 3-D rail imaging FEA model........................................................................... 62

Figure 5.4 – Example of Matched Filtering. Top waveform: excitation signal (two-cycle 

toneburst at 2 MHz). Middle waveform: detected signal with 10 dB white noise added (“noisy 

signal”). Bottom signal: “noisy signal” after matched filtering with excitation 

signal....................................................................................................................................... 63

Figure 5.5 – Example of baseline subtraction on the envelope signals. Notice how the defect 

reflection increases relative to the “artifact” peaks in the baseline-subtracted signal (red 

trace)........ .................................................................................................................................. 65

Figure 6.1 – The FE mesh for the 2-D rail flaw imaging study along with the linear transducer 

array for tomographic imaging with Synthetic Aperture Focus .................................................. 67

Figure 6.2 – Detail of the FE mesh around the 5% RHA Transverse Defect .............................. 68

Figure 6.3 – Von Mises stress contour plots for two different excitations showing the 

propagation of both longitudinal wave mode (travelling faster) and shear wave mode (travelling 

slower) ...................................................................................................69

Figure 6.4 – 2-D Imaging of 5% RHA Transverse Defect by Ultrasonic Tomography with 

Synthetic Aperture Focus using (a) the Longitudinal Wave mode (left-hand image) and (b) the 

Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline Subtraction 

was also implemented in these images. ........................................................................................ 70
ix

Figure 6.5 – 2-D Imaging of 5% RHA Transverse Defect with 15 dB Gaussian White Noise 

added to the signals, and using (a) the Longitudinal Wave mode (left-hand image) and (b) the 

Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline Subtraction 

was also implemented in these images ......................................................................................... 72

Figure 6.6 – 2-D Imaging of 5% RHA Transverse Defect with 25 dB Gaussian White Noise 

added to the signals, and using (a) the Longitudinal Wave mode (left-hand image) and (b) the 

Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline Subtraction 

was also implemented in these images ......................................................................................... 73

Figure 6.7 – 2-D Imaging of 5% RHA Transverse Defect with 35 dB Gaussian White Noise 

added to the signals, and using (a) the Longitudinal Wave mode (left-hand image) and (b) the 

Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline Subtraction 

was also implemented in these images ......................................................................................... 74

Figure 7.1 – Rail section model for the 3-D FEA......................................................................... 75

Figure 7.2 – Geometrical dimensions for the 3-D FEA model..................................................... 75

Figure 7.3 – Mesh for the 3-D FEA with “infinite elements” at the model boundaries to eliminate 

artificial boundary reflections of the waves.................................................................................. 76

Figure 7.4 – Mesh for the 3-D FEA: sectional view.................................................................... 77

Figure 7.5 – Full transducer array for the 3-D FEA .................................................................... 78

Figure 7.6 – Full transducer array for the 3-D FEA: sectional view. .......................................... 78

Figure 7.7 – Position of the five “sparse” transmitters in the transducer array: top view............79

Figure 7.8 – Von Mises stress contour plots for central excitation showing the propagation of 

both Longitudinal Wave mode (travelling faster) and Shear Wave mode (travelling slower), as 

well as absence of reflections at boundaries owing to “infinite” elements (longitudinal sectional 

view). ............................................................................................................................................ 80

Figure 7.9 – Von Mises stress contour plots for central excitation (transverse sectional view at 

defect position).............................................................................................................................. 81

Figure 7.10 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers)....................................................................................................................................... 82

Figure 7.11 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers)....................................................................................................................................... 82

Figure 7.12 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers)....................................................................................................................................... 83

Figure 7.13 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers)....................................................................................................................................... 83
x

Figure 7.14 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers) ...................................................................................................84

Figure 7.15 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers) ...................................................................................................84

Figure 7.16 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers)....................................................................................................................................... 85

Figure 7.17 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers) ................... 86

Figure 7.18 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 

receivers)........................................................................................................ 86

Figure 7.19 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers) ................... 87

Figure 7.20 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers). .................. 87

Figure 7.21 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Reduced Array: 5 transmitters, 

140 receivers)................................................................................................................................ 89

Figure 7.22 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Reduced Array: 5 transmitters, 

140 receivers)................................................................................................................................ 89

Figure 7.23 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

and the Shear Wave mode with Envelope Baseline Subtraction (Reduced Array: 5 transmitters, 

140 receivers)................................................................................................................................ 90

Figure 7.24 – 3-D Imaging of 5 percent RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Reduced Array: 5 transmitters, 140 receivers).. 91

Figure 7.25 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

along with Image Baseline Subtraction (Reduced Array: 5 transmitters, 140 receivers)............ 92

Figure 7.26 – 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave mode 

along with Image Baseline Subtraction (Reduced Array: 5 transmitters, 140 receivers)........... 92

Figure 8.1 – Worn BNSF rail profile (136-pound RE tangent track), and 3-D model constructed 

for the 3-D Finite Element Analysis and Tomographic Imaging ................................................. 93

Figure 8.2 – Transducer array modeled for the 3-D tomographic imaging of the worn 

rail..............................................................................................................94

Figure 8.3 – New rail versus worn rail: 3-D imaging of 5% RHA Transverse Defect using the 

Longitudinal Wave mode and the Shear Wave mode with Envelope Baseline Subtraction (Full 

Array: 5 transmitters, 525 receivers) ........................................................................................... 95
xi

Figure 8.4 – New rail versus worn rail: 3-D imaging of 5% RHA Transverse Defect using the 

Longitudinal Wave mode and the Shear Wave mode with Envelope Baseline Subtraction 

(Reduced Array: 5 transmitters, 140 receivers)........................................................................... 96
xii

Tables

Table 9.1 – Rail flaw sizing results from the 3-D tomographic imaging models........................ 98
1

Executive Summary

This work was carried out under FRA Broad Agency Announcement (BAA-2010-1) “Research 

and Demonstration Projects Supporting the Development of High Speed and Intercity Passenger 

Rail Service.” The project has provided proof-of-principle results that show the potential for 

ultrasonic tomography to offer accurate 3-D imaging of internal rail flaws. 

In the past 6 years (2006–2011), according to Federal Railroad Administration (FRA) statistics, 

rail defects accounted for 1,235 derailments and $321 million in reportable damage costs. The 

work discussed in this report is motivated by the lack of inspection techniques currently able to 

provide accurate information about the shape and size of critical internal rail flaws such as 

transverse defects (TDs) in the railhead. The current rail flaw verification system is a manual 

process through which rail flaw data is collected and subjectively interpreted by an inspector. 

This subjectivity can lead to errors in the sizing of defects, and this is a safety concern since an 

inappropriate remedial action may be taken.

Tomographic techniques are at the forefront of successful imaging systems in the medical field, 

the sonar and radar fields, and the civil engineering field. The current project has adapted 

various elements of tomographic imaging from these other fields to develop an ultrasonic 

tomographic imager specific to internal rail flaws. The numerical results presented herein show 

great potential for use of the tomographic technique in accurate 3-D rail flaw imaging. The 

advantages of this approach include the following: (1) no manual scanning of the transducers is 

required, and (2) the imaging results are provided automatically with minimal operator 

interpretation, which eliminates the potential subjectivity inherent in the manual process.
2

1. Introduction

Internal rail flaws are a cause of major concern for rail transportation safety. If left undetected, 

flaws can grow and lead to rail failure and catastrophic derailments. With the advent of highspeed rail, and the increased tonnage and frequency of freight trains, the importance of detecting 

internal rail defects before they result in a complete rail break is magnified. Because high-speed 

operations necessitate shorter rail maintenance windows, there is greater need to detect the flaws 

early and accurately. 

FRA safety statistics for the past 6 years (2006–2011) indicate that defects at rail, joint bars, and 

rail anchoring were responsible for 1,235 derailments and $321 million in reportable damage 

costs in the United States. Among the rail defects, TDs in the railhead, i.e., flaws that are 

oriented perpendicularly to the rail running direction, are consistently the most critical, causing 

the highest percentage of derailments and damage cost.

Currently, rail flaw inspection in the United States is performed from a dedicated, in-motion hirail vehicle that is outfitted with ultrasonic transducers, and a detected flaw must then be 

manually verified (“stop and confirm” mode). The hand verification is typically done using 

ultrasonic transducers operated in a pulse-echo mode. At present, the manual verification does 

not allow for precise quantification of the defect size and shape. Rather, defect sizing is 

somewhat subjective since it depends on the inspector’s judgment and level of experience. What 

is needed is a new inspection system for rails that is able to provide accurate and repeatable 

quantitative information on the shape and, more importantly, the size of an internal flaw. Hence,

the need for 3-D rail flaw imaging, which the FRA BAA-2010-1 explicitly identifies as a critical 

research need.

1.1 Objectives

The objective of this project is to demonstrate the technique of ultrasonic tomography for 3-D 

imaging of internal rail flaws. The scope of the project was limited to carrying out numerical 

analysis and simulations of the tomographic rail imaging technique. It is expected that the 

successful completion of this modeling phase will lay the foundation for the subsequent 

development of a tomographic rail imaging system for use in verification of rail flaws. The 
3

numerical work was carried out with the following requirements in mind for a possible future

field-deployable system: (1) ability to size the flaw automatically without manual scanning of 

the ultrasonic transducers, (2) ability to resolve TDs as small as 5 percent railhead area (RHA),

and (3) ability to generate a 3-D image of a defect in a reasonable timeframe, preferably less than 

10 minutes.

1.2 Overall Approach

In the first part of the project, Finite Element Analysis (FEA) models of a 136-pound RE rail 

were constructed in 2-D and, subsequently, in 3-D. Through appropriate discretization of the 

space domain (mesh refinement to represent small wavelengths) and of the time domain 

(integration time refinement to represent high wave frequencies), the models were able to 

represent ultrasonic waves (up to 2.25 MHz) propagating in the rail and interacting with internal 

rail flaws. The 3-D model also featured advanced nonreflecting boundary FEA elements (to 

eliminate artificial wave reflections at the FEA model boundaries that would not be present in an 

actual rail), as well as absorbing FEA elements to simulate wave damping. 

The FEA allowed for simulation of an array of ultrasonic transducers operated in a tomographic 

scheme. The tomographic algorithm was developed in a Matlab environment to provide 2-D and 

3-D images of an internal 5-percent RHA TD flaw simulated in the railhead. The tomographic 

algorithm used the following four key steps to generate the images: (1) Synthetic Aperture 

Focus (borrowed from ultrasonic, medical and radar imaging), (2) Matched Filtering (borrowed 

from radar imaging), (3) Baseline Subtraction (borrowed from ultrasonic testing), and (4) 

Multimode Detection (borrowed from ultrasonic testing). 

The ultrasonic tomographic array for the 3-D imaging consisted of up to 252 transducers 

arranged in a planar fashion to generate 3-D images without requiring mechanical repositioning 

of the transducers during the imaging process. Two configurations for the array were examined: 

a sparse transmitter configuration (5 transmitters) with a full receiver configuration (525

receivers), and a sparse transmitter configuration (5 transmitters) with a reduced receiver

configuration (140 receivers). In addition, different wave mode combinations were examined. It 

was found that reducing the receiver array did not have a substantial impact on the performance
4

of the 3-D imaging in a new rail profile. The tomographic algorithm produced good results; the 

estimated size of the imaged flaw was close to the 5 percent RHA actual size.

A worn rail, modeled after a tangent track profile received from Burlington Northern Santa Fe 

(BNSF) Railroad, was also examined in the final phase. It was concluded that profile wear does 

not have any effect on tomographic imaging performance when the full receiver array is used. 

For the reduced receiver array, by contrast, some degradation was seen in the worn rail case.

1.3 Organization of the Report

Section 1 of this report introduces the project and describes the overall technical approach. 

Section 2 reviews the current practice of ultrasonic testing in the railroad industry. Sections 3 

and 4 review various applications of ultrasonic tomography imaging in the civil engineering and 

medical field. Section 5 presents the 2-D FEA of ultrasonic waves propagating in the 136-pound 

RE rail. Section 6 extends the previous analysis to the 3-D case. Section 7 summarizes the steps 

of the tomographic imaging algorithm developed for 2-D and 3-D imaging of the rail flaws. 

Section 8 presents the results of 2-D tomographic imaging of a 5-percent RHA TD in the 136-

pound RE rail, along with a noise sensitivity analysis. Section 9 presents the results of 3-D 

tomographic imaging of the 5-percent RHA TD in the 136-pound RE rail. Section 10 extends 

the 3-D imaging results to the case of a worn rail. Section 11 summarizes the conclusions of this 

work. 
5

2. Current Practice of Ultrasonic Testing of Rails

This chapter reviews the current practice of ultrasonic testing in the railroad industry. 

2.1 Bulk Wave Testing

Ultrasonic Testing (UT) has been widely used by the railroad industry for rail internal defect 

detection since the 1960s. Normally, the UT inspection is targeted at detecting defects in the 

center of the rail head and web, with only limited coverage of the rail base and rail head corners. 

The frequency of rail track inspection varies from country to country. In the United States, FRA 

mandates that inspections for track defects be made at least once every 40 million gross tons 

(mgt) or once a year—whichever interval is shorter—for tracks over which passenger trains 

operate. For tracks over which passenger trains do not operate, the inspection must be carried 

out every 30 mgt or once a year, whichever interval is longer. 

UT of rail tracks is performed with longitudinal or transverse transducers operated in a pulseecho mode or in a pitch-catch mode (Figure 2.1). The transducers are located in wheels which 

roll over the surface of the of the rail head. The wheels are typically filled with water or a waterbased solution. Sleds, rather than wheels, can also be used to host several transducers in a 

smaller area. Specialized test cars typically perform the inspection. Details on common 

transducer configurations can be found in various references (Bray 1991, Anon 1990, Grewal 

1996, Lanza di Scalea 2007). The most common configuration (Figure 2.1 uses transducer 

orientations that are able to generate ultrasonic beams propagating at 0 degrees (normal 

incidence) and at 70 degrees from the normal to the rail surface. The 0-degree probe targets 

horizontal cracks while the 70-degree probe targets the transverse cracks that tend to grow in a 

20-degree direction from the transverse plane. 

A 37- or 45-degree probe is also often used in addition to the previous two orientations to target 

other defects such as bolt-hole cracks and weld defects (Figure 2.1-left). To target vertical 

defects, complete search units also host “side looking” transducers generating beams in the 

transverse plane, typically at 45-degree orientations, rather than in the vertical plane of the track

(Figure 2.1-right).

Wheels or sleds are often used in tandem to provide complete coverage. Using tandem 

configurations adds pitch-catch testing capability to the pulse-echo capability of a single wheel. 
6

The standard transducer of a rail track UT unit operates at 2.25 MHz; 3 MHz transducers can 

also be used.

Figure 2.1. Common transducer arrangements for rail track inspections in the vertical 

plane (left) and in the transverse plane (right). (Lanza di Scalea 2007)

The test car inspections of rail tracks are followed by manual scanning to confirm the presence of 

a defect and to size it. Generally, both normal-beam transducers and angle-beam transducers 

(with conventional acrylic wedges) can be used in manual scanning. As mentioned above, 

normal-beam transducers target horizontal-type defects while angle-beam transducers target 

transverse-type defects. Defect sizing is done by simply scanning the normal-beam transducer 

for horizontal defects and using the conventional 6 decibel (dB) down technique while scanning 

the angle-beam transducers. In addition to conventional normal-beam or angle-beam 

configurations, more complex transducer arrangements can be implemented during manual 

scanning. Skewed transducer orientations, for example, can be used to detect detail fractures. In 

skewed arrangements, the ultrasonic wave propagates along planes that are inclined with respect 

to both the vertical and the transverse plane so as to enhance the interaction with certain types of 

defects. 

In the United States, manual UT is required to verify any defect indication from the test car 

search units (“stop and confirm” testing mode). Europe, on the other hand, operates in a nonstop 

testing mode, whereby defect indications are verified by manual UT only days or weeks after the 

test car has passed. Modern test cars can operate, theoretically, at reasonably high testing 

vertical plane transverse plane

0 ° transducer

70° transducer 45° transducer

45° 70° 45°

side looker

45° transducer
7

speeds—up to at least 30 mph (45 km/h)—although much testing is conducted at speeds as low 

as 10 mph (15 km/h). 

One serious disadvantage to current wheel or sled transducer arrangements is that in the presence 

of shallow horizontal cracks such as head checks and shelling, internal TDs in the rail may be 

missed by inspection (Figure 2.2). Another drawback is that the high probing frequency used by 

the transducers (2.25–3 MHz) is sometimes not effective in penetrating alumino-thermic welds, 

which have a coarser grain structure compared with the surrounding steel (Clark and Singh 2003, 

Wilcox et al. 2003). Additional challenges with conventional ultrasonic inspections of rails have 

to do with detecting vertical split head defects and small TDs in the gage corner of the rail head. 

The presence of leaves, dirt, ice, and other foreign objects can affect the ultrasonic transmission 

and reception through the wheel or sled. 

Figure 2.2. Masking of internal transverse defects under shelling in conventional 

ultrasonic testing of rails.

2.2 Ultrasonic Phased-Arrays – Basic Principles

Ultrasonic phased arrays offer more flexibility than single-element ultrasonic transducers 

because they can achieve beam steering and beam focusing without physically moving the 

transducers. 

Traditional single-element ultrasonic transducers excite a beam propagating along a fixed 

direction and, if necessary, focus the beam to a fixed point via acoustic lenses. However, neither 

beam direction nor focal point can be changed in a single transducer without moving the 

transducer or replacing the acoustic lens. Phased arrays are comprised of multiple transducers

that are electronically delayed to build a constructive interference wavefront (Figure 2.3). By 

changing the time delays between the elements of the array, the resulting wavefront can be

Transverse defect Horizontal shelling

70-deg ultrasonic transducer

rail

Transverse defect Horizontal shelling

70-deg ultrasonic transducer

rail
8

pointed to different directions (beam steering) and also focused at different depths (dynamic

focusing) without mechanical motion. 

Figure 2.3. Principle of multiple transducers firing at imposed delays in phased-array 

ultrasonic probes (dynamic steering and dynamic focusing).

A minimum of three elements is required for steering and focusing capabilities. Increasing the 

number of elements increases the resolution of the beam steering and focusing. Phased arrays 

exist in different forms, including linear arrays, 2-D arrays, and circular arrays (Figure 2.4). 

Linear arrays allow steering and focusing across a plane. 2-D arrays allow complete 3-D 

steering and focusing. 
9

Figure 2.4. Different configurations of phased-array ultrasonic probes: linear arrays and 

2-D arrays.

2.3 Applications of Ultrasonic Phased-Arrays in the Rail Industry

Phased arrays in the railroad industry have been applied primarily to the inspection of axles 

(Hansen and Hintze 2002). They were used in this research effort to detect the radial cracks in 

the press fitted areas of the axle, including wheel seats, brake disk seats (for trailing axles), and 

gear seats (for driving axles). Other targets were cracks in the transition regions between two 

diameters. 

Traditional inspection systems for axles rely on either single transducers operating from the free 

end of the axle (Figure 2.5a), or angle-beam transducers requiring manual scanning (Figure 

2.5b). Ultrasonic phased arrays eliminate the manual scanning of the angle-beam transducers 

(Figure 2.5c). 

Figure 2.5. Transducer arrangements for axle inspections: (a) longitudinal transducer at 

axle free end; (b) angle-beam transducers; (c) phased-array transducers. (Lanza di Scalea 

2007).

For rail inspections, phased-arrays are not common practice, although published research has 

been performed by the authors cited herein. 

Linear array 2-D arrays

Surface crack in pressfitted region

Angle-beam Transducer

Surface crack in diameter 

transition region

Surface and internal cracks in 

press-fitted region

Transducer

Surface crack 

in diameter 

transition region

Surface crack in pressfitted region

Phased-array Transducer

Surface crack in diameter 

transition region

(a) (b) (c)
10

Utrata (2002) used a 16-element, linear phased array under dry contact to enhance the 

detectability of transverse head cracks and this was compared with the results of single-element 

inspections. Starting with the typical 70-degree angle, this phased array was used to steer the 

beam across the rail section (“lateral steering”) for a +/-20-degree angle relative to the centerline 

of the head. The lateral steering demonstrated that most transverse cracks are best detected off 

angle, specifically at a 10-degree angle from the centerline of the rail. 

Wooh and Wang (2002) proposed the use of a “hybrid array sensor” for rails consisting of a 

traditional phased array for electronic generation of beam steering and a static array for beam 

detection. Crack detection was done by elaborating the “ultrasonic shadows” detected by the 

static array. It was suggested that this concept would be capable of determining the location, 

size, and orientation of a planar transverse head defect. Although results were not shown on 

actual rails, the theory worked out in the model seems applicable to the rail case. However, the 

proposed approach assumes flat planar cracks, and therefore cannot capture the full shape of a 

curved defect. Moreover, the method uses generation and detection of ultrasound from the same 

side of the rail. This may not be the best approach, as waves must bounce from the back wall of 

the rail to be detected. A straight-path beam in a through-transmission configuration is probably 

more appropriate for capturing ultrasonic shadows. 

Tscharntke et al. (2003) developed directivity patterns for dry-coupled phased array probes. 

Their studies were mainly theoretical and showed limited laboratory results involving actual

railroad specimens.

More recently, the Transportation Technology Center, Inc. (TTCI) investigated ultrasonic phased 

arrays for rail web, base, and head inspection focusing on the defect sizing and characterization 

(Garcia and Zhang 2006). The authors used pulse-echo phased-array probes on 33.7-degree

wedges at 5 MHz positioned on the sides of the rail head (Figure 2.6). They concluded that 

phased arrays can (a) detect TDs and discriminate them from a shell, (b) determine the location 

of the TD in the rail, and (c) estimate the size of the TD in the rail. In essence, TTCI researchers

confirmed the ability of phased-arrays to dynamically steer the ultrasonic beam. 
11

Figure 2.6. TTCI approach of ultrasonic phased arrays for rails. (Garcia and Zhang 

2006).

2.4 Ultrasonic Tomography- Basic Concepts 

Ultrasonic tomography is a noninvasive and safe technique for the cross-sectional imaging of an 

object through transmission or reflection data collected by illuminating the sample from different 

directions. CT scans (Computerized Tomography) are routinely performed in the medical field 

to image tumors, organs, and other parts of the human body. Medical CT scans primarily use Xrays or Magnetic Resonance Imaging (MRI). With solids, such as rail steel, however, ultrasonic 

scans are more practical, and the corresponding technique is called ultrasonic tomography. 

Ultrasonic tomography is being applied successfully to various civil engineering fields (as the 

next chapter will discuss). 

Similarly to phased arrays, an ultrasonic tomography setup uses a series of transducers to excite 

and receive ultrasonic waves. Multiple wave paths are then recorded to cover every direction of 

the test volume (Figure 2.7). Algorithms based on wave propagation theory are then used to 

reconstruct the exact shape, position, and size of a defect from the multiple propagation paths. 

Various applications of ultrasonic tomography for imaging will be discussed in this report.
12

Figure 2.7. Basic concept of ultrasonic tomography for imaging defects in solids (S = 

ultrasonic sources, R = ultrasonic receivers). (Mekic-Stall and Grimm 2002)

2.5 Ultrasonic Tomography with Synthetic Aperture Focusing – Basic 

Concepts 

A successful method borrowed from radar technology that also uses transducer arrays for 

ultrasonic tomographic imaging of structural defects is the Synthetic Aperture Focusing 

Technique (SAFT). It is a computer enhanced imaging technique for the detection and the 

characterization of discontinuities (ASNT 2007). The technique numerically superimposes 

multiple ultrasonic pulse-echo time signals, measured at several positions, to create a high 

resolution image. The signals are assembled and integrated, or focused, with respect to the timeof-flight surface in volume and time space for each voxel (volumetric picture element) of 

material (ASNT 2007).

SAFT locates the position of the ultrasonic reflector (flaw) based on the arrival time of pitchcatch ultrasonic signals (Figure 2.8-left). In the simplest implementation, the defect position 

from a transmitter-receiver pair can be calculated using the Pythagorean Theorem for known 

transducer positions. Referring to Figure 2.8-right, this formula is:

( )

2 2 d vt X =∆ − / 2 

where v is the wave speed in the test object and ∆t the travel time of the wave between the 

transmitter and the receiver. 
13

Figure 2.8. Principle of Synthetic Aperture Focusing. Left: radar. Right: ultrasonic 

testing.

Conventional SAFT operates sequentially in two stages. First, each transducer element emits 

and receives an ultrasonic signal which is digitized and stored. Then, digital signal processing is 

applied to generate the scanning lines, which form the UT image (Martinez et al. 1999). By 

using arrays of ultrasonic transmitters and receivers in conjunction with SAFT, detailed 3-D 

imaging of internal flaws is possible. 

Since SAFT is based on the processing of stored data, multiple algorithms can be applied and 

new algorithms are being continually developed. The raw data are usually A-scans stored as the 

broadband transducer is scanned over the surface of the test object. In one implementation 

(ASNT 2007), a curve is made of the peak amplitudes caused by the reflection from the 

discontinuity for each aperture element. The size of this curve’s path is determined by the width 

of the ultrasonic beam. The curvature and apex of the curve depend on the depth of the 

discontinuity, the ultrasonic velocity in the test material, and the coupling medium. 

One of the most successful applications of SAFT for imaging internal defects is in the inspection 

of concrete slabs for civil engineering. The “MIRA Tomographer,” used by various companies,

including the CTL Group of Skokie, IL (CTL Group 2011) (Figure 2.9), uses pitch-catch 

ultrasonic tomography and SAFT to reconstruct 3-D representations of internal defects that may 

be present in concrete elements such as prestressed concrete slabs. The system uses low 

frequencies, typically 50 kHz, to penetrate the coarse concrete microstructure. A dry-coupled 

array of 4×10 transducers provides a total of 180 transit time measurements during each test. 

X

d
14

The recordings are done sequentially, with each row of transducers acting as the transmitter and 

all other rows acting as receivers. The entire scan takes approximately 3 seconds for complete 

data acquisition. SAFT is then used to reconstruct the 3-D image of the internal flaws from the 

transit times of the multiple wave paths. 

Figure 2.9. The MIRA Tomographer that uses a 4×10 transducer array in dry-coupling for 

concrete inspection. (Bishko et al. 2008 and CTL Group 2011)
15

3. Bidimensional Finite Element Analysis

This chapter discusses the 2-D FEA performed to model ultrasonic waves propagating in a 

flawed rail. 

3.1 2-D Finite Element Model of Flawed Rail

The specific case that was modeled by these initial FEA was a 2.25 MHz ultrasonic wave 

propagating in a 136-pound RE rail with a TD in the gage corner extending for 5 percent of the 

rail RHA. The TD is one of the most common flaws found in rails. 

The choice of the 2.25 MHz value reflects the most common frequency used in ultrasonic rail 

inspections (both with in-motion wheel transducers and hand-held transducers for verifications). 

Figure 3.1 shows the picture of an actual TD at the railhead gage corner taken at the Herzog, Inc. 

rail defect farm. 

Figure 3.1. A picture of a Transverse Defect at the gage corner of the railhead.
16

The corresponding geometrical model for the 2-D FEA is shown in Figure 3.2. The geometrical 

dimensions of the model were as follows:

Entire rail section:

Area = 0.0084 m2

Perimeter = 0.7087 m

Railhead alone:

Area = 0.0034 m2

Perimeter = 0.2252 m

The TD was modeled as a 5 percent RHA planar flaw. 

Figure 3.2. The geometrical model of the rail for the 2-D FEA with the 5% RHA

Transverse Defect in the gage corner. 

The material properties of the model were steel, with the following elastic constants: 

Young’s modulus E = 209 GPa

Poisson’s ratio ν = 0.28

Mass density ρ = 7800 kg/m3

.
17

Assuming a maximum wave frequency fmax = 2.25 MHz and hence a minimum wavelength λmin = 

cS / fmax = 1.33 mm (with cS the shear wave velocity in steel), the maximum dimensions of the 

finite elements were chosen as:

dmax = λmin / 10 = 0.133 mm

This level of mesh refinement ensured proper representation of the minimum ultrasonic 

wavelength (or maximum frequency). To reduce the computational burden, it was decided to 

model only the railhead—the only portion of the rail relevant for the defect considered. The 

resulting finite element mesh is shown in Figure 3.3. A close-up view of the mesh in the area 

surrounding the defect is shown in Figure 3.4.

Figure 3.3. The total mesh for the 2-D FEA.
18

Figure 3.4. A zoom of the mesh around the defect for the 2-D FEA.

The final parameters of the mesh utilized were as follows:

The total duration of the analysis, sufficient to capture the relevant wave diffractions from the 

defect, was 30 μsec. The maximum time increment was chosen according to the customary 

criterion of:

Δtmax = 1 / (20*fmax) = 0.0222 μsec 

This time increment limit ensured proper representation of the highest frequency components of 

the waves. 

In this analysis, the forcing function (simulating the ultrasonic generation) was applied to the 

gage corner of the railhead as one sinusoidal cycle at 2.25 MHz with a duration of 0.4 μsec and a 

nominal unity amplitude (Figure 3.5). The specific amplitude value of this excitation was 
19

irrelevant to the analysis, as the purpose was to capture reflections and refractions of the wave 

from the defect. 

Figure 3.5. Shape and location of the excitation force for the 2-D FEA simulating 2.25 

MHz ultrasonic excitation at the rail gage corner. 

Five detection points were considered on the field side of the railhead, as shown in Figure 3.6 

below. These points represent possible locations of the ultrasonic receivers. 

EXCITATION 

Amplitude (a.u.)

Time [sec]
20

Figure 3.6. Location of the excitation point and of five detection points used to sample the 

ultrasonic waves interacting with the flaw in the 2-D FEA.

3.2 Results of 2-D Finite Element Model

Contour plots of the Von Mises Equivalent stress are shown in the following figures (Figures 3.7 

through 3.12) at six different times during the ultrasonic wave propagation. Interesting or 

unusual behaviors are captured by these plots; for example, the strong surface (Rayleigh) wave 

travelling along the railhead top surface. 

In the region internal to the railhead, the plots also show the refraction of the wave caused by the 

5-percent RHA TD. Another interesting behavior is the smaller surface (Rayleigh) wave 

developing along the defect surface and following the defect perimeter. Strong bulk waves are 

also generated past the defect as the diffracting wavefronts interfere constructively past the 

defect. This phenomenon is analogous to the “anomalous” strong ocean waves generated at the 

downwind side of an island. As a result, a variety of wavefronts are received at the opposite side 

of the defect. These multiple wavefronts were eventually used to develop the ultrasonic 

tomographic system for defect imaging. 

INPUT

OUTPUT1

OUTPUT2

OUTPUT3

OUTPUT4

OUTPUT5
21

Figure 3.7. Contour plots of Von Mises Equivalent Stress at t = 5 μsec after excitation from 

the 2-D FEA.

Figure 3.8. Contour plots of Von Mises Equivalent Stress at t = 10 μsec after excitation 

from the 2-D FEA.

t = 5 μsec

t = 10 μsec

INPUT

SURFACE (RAYLEIGH) WAVE ALONG RAILHEAD SURFACE

BULK WAVE DIFFRACTIONS FROM 

DEFECT
22

Figure 3.9. Contour plots of Von Mises Equivalent Stress at t = 15 μsec after excitation 

from the 2-D FEA.

Figure 3.10. Contour plots of Von Mises Equivalent Stress at t = 20 μsec after excitation 

from the 2-D FEA.

t = 15 μsec

t = 20 μsec

SURFACE (RAYLEIGH) WAVE ALONG DEFECT SURFACE
23

Figure 3.11. Contour plots of Von Mises Equivalent Stress at t = 25 μsec after excitation 

from the 2-D FEA.

Figure 3.12. Contour plots of Von Mises Equivalent Stress at t = 30 μsec after excitation 

from the 2-D FEA.

t = 25 μsec

t = 30 μsec
24

Figure 3.13 shows the plots of the time histories of the transverse displacement (ux) recorded at 

the five detection nodes considered. The multitude of the wave modes detected is also apparent 

in these time histories, with the bulk waves diffracted from the flaw arriving early and the strong 

Rayleigh wave running along the railhead arriving later. For the internal defect imaging, the 

initial portion of the time histories will be of interest, as it is the section that contains information 

about the wave that has interacted with the flaw. 

Figure 3.13. Time histories of transverse displacement ux recorded at the five detection 

nodes by the 2-D FEA.

Time [sec]

Early arrivals (diffracted bulk waves) 

Late arrivals (surface 

Rayleigh wave)
25

4. Three-Dimensional Finite Element Analysis

This chapter discusses the 3-D FEA performed to model ultrasonic waves propagating in a 

flawed rail. 

4.1 3-D Finite Element Model of Flawed Rail

In order to create a more realistic model, the bidimensional analysis presented in the previous 

section was extended to the three-dimensional case. The 3-D case is more representative of an 

actual ultrasonic tomographic system as the ultrasonic transmitters and receivers will likely be 

positioned on different planes. 

A length of 10 cm for the rail was considered for the 3-D analysis. This length was adequate to 

capture the wave interaction with the defect. The geometric case considered was analogous to 

the 2-D analysis (i.e., 136-pound rail with a 5-percent RHA TD at the gage corner). 

To satisfy the mesh refinement requirements for modeling the high-frequency waves, a careful 

sectioning of the meshed region was applied. Three mesh zones were created. In Zone 1 (Figure 

4.1), the mesh was left coarser, with a maximum element size d = 3 mm. The corresponding 

mesh of this zone is shown in Figure 4.2. In Zone 2, called “transition zone,” an intermediate 

element size of d = 1.5 mm was created (Figures 4.3 and 4.4). This zone provided a smooth 

change from the coarser mesh, away from the flaw, to the highly refined mesh around the flaw. 

In Zone 3 around the flaw, a highly refined mesh with d = 0.4 mm was created to properly 

capture the complex wave diffractions at the flaw boundaries (Figure 4.5). 

The final mesh for the complete model is illustrated in Figure 4.6, showing the progression from 

the coarser mesh away from the flaw towards the more refined mesh close to the flaw. The 

parameters of the final mesh were as follows:

Total number of nodes: 2133430

Total number of elements: 1570347 Quadratic Tetrahedral of type C3D10M
26

Figure 4.1. Zone 1 geometry – coarser mesh with element size d = 3 mm for the 3-D FEA.

Figure 4.2. Zone 1 mesh – coarser mesh with element size d = 3 mm for the 3-D FEA.
27

Figure 4.3. Zone 2 geometry – intermediate mesh with element size d = 1.5 mm for the 3-D 

FEA.

Figure 4.4. Zone 2 mesh – intermediate mesh with element size d = 1.5 mm for the 3-D 

FEA.
28

Figure 4.5. Zone 3 geometry and mesh – fine mesh with element size d = 0.4 mm for the 3-

D FEA.

Figure 4.6. Entire mesh for the 3-D FEA. The TD is in the middle of the model in the gage 

corner area with the highest mesh refinement.
29

The base of the model was constrained with fixed boundaries (Figure 4.7). 

Figure 4.7. Boundary conditions for the 3-D FEA model. 

The load was applied along a 0.25-inch line at the gage corner of the railhead (Figure 4.8). The 

load time history was one sinusoidal cycle at 2.25 MHz with nominal unity amplitude. The load 

vector was inclined at 70 degrees from the vertical (y-axis) direction. This inclination was given 

to simulate the typical 70-degree ultrasonic beam used in wheel and manual ultrasonic testing of 

rails for best detection of TDs.
30

Figure 4.8. Excitation used for the 3-D FEA.

The same material properties adopted for the 2-D analysis were applied to the 3-D analysis. 

Hence:

Young’s modulus E = 209 GPa

Poisson’s ratio ν = 0.28

Mass density ρ = 7800 kg/m3

The analysis was developed in a single step using ABAQUS/Explicit code. The duration of the 

analysis was set to 30 μsec. The integration time required for the numerical stability of the 

solution was estimated based on the wave maximum frequency:

Δtmax = 1 / (20*fmax) = 0.0222 μsec 

WAVE EXCITATION (line excitation at 70 degrees from vertical)
31

4.2 Results of 3-D Finite Element Model

The following figures show the Von Mises Equivalent stress obtained at several times during the 

wave propagation. Figures 4.9 through 4.11 offer a global view, whereas Figures 4.12 through 

4.14 show a sectional view. In these contour plots, the generation of the wave at early times can 

be seen clearly, along with the complex interaction of the wave with the 5-percent RHA TD at 

later times. 

Figure 4.9. Contour plots of Von Mises Equivalent Stress at t = 1.5 μsec after excitation 

from the 3-D FEA (global view).

t = 1.5 μsec
32

Figure 4.10. Contour plots of Von Mises Equivalent Stress at t = 7.5 μsec after excitation 

from the 3-D FEA (global view).

Figure 4.11. Contour plots of Von Mises Equivalent Stress at t = 15 μsec after excitation 

from the3-D FEA (global view).

t = 7.5 μsec

t = 15 μsec
33

Figure 4.12. Contour plots of Von Mises Equivalent Stress at t = 1.5 μsec after excitation 

from the 3-D FEA (sectional view).

Figure 4.13. Contour plots of Von Mises Equivalent Stress at t = 7.5 μsec after excitation 

from the 3-D FEA (sectional view).

t = 1.5 μsec

t = 7.5 μsec
34

Figure 4.14. Contour plots of Von Mises Equivalent Stress at t = 15 μsec after excitation 

from the 3-D FEA (sectional view).

Two arrays of wave detection probes, wrapping around the railhead profile in the transverse 

direction, were chosen for this analysis. The arrays, shown in Figure 4.15, were positioned 2.6 

cm away from one another on either side of the TD. These will be herein denoted as “rear” array 

and “front” array, respectively. Each of the arrays contained 57 nodal points where all the time 

histories were recorded. The choice of this particular configuration of detection points was 

motivated by the envisaged plan to study both reflection and transmission schemes for the 

ultrasonic tomographic system to be developed in subsequent phases. The numbering of the 

probe arrays is shown in Figures 4.16 and 4.17 for the “rear” array and the “front” array, 

respectively. 

t = 15 μsec
35

Figure 4.15. Location of the arrays of detection nodes for the wave time-history 

recordings. Each array contains 57 nodes. 

Figure 4.16. Numbering of nodes for the “rear” array.

“REAR” “FRONT” 
36

Figure 4.17. Numbering of nodes for the “front” array.
37

Figure 4.18 shows a sample of these results, specifically the time histories of the vertical 

displacement (uy) for two nodes on the “rear” array prior to the defect (nodes 107 and 41), and 

two nodes on the “front” array past the defect (nodes 78 and 204). Multiple wave arrivals

consisting of first arrivals plus reflections and refractions of waves from the flaw can be seen in 

these plots. 

Figure 4.18. Time histories of vertical displacement recorded at sample nodes on the 

“rear” array (nodes 107 and 41) and at sample nodes on the “front” array (nodes 78 and 

204).
38

4.3 FEA Convergence Study

A detailed convergence study at varying degrees of mesh refinements was also carried out to 

confirm the appropriateness of the chosen mesh to represent the interaction of the ultrasonic 

wave with the defect. 

This study was carried out on the “most critical” mesh region of the 3-D model (i.e., Zone 3) or 

the area surrounding the defect. The discretization of the other two regions (Zone 1 – away from 

the defect, and Zone 2 – transition zone) were left unaltered from the 3-D model discussed in the 

previous section. 

To check the convergence, a node close to the defect was analyzed in terms of recorded 

accelerations, velocities, and displacements, as discussed later in this section. 

4.3.1 Meshes for Convergence Study

As discussed in the previous section, the entire 10 cm-long 3-D model of the rail was divided 

into three regions. The convergence study was only conducted on Zone 3 surrounding the defect 

because it provided the higher refinement requirements needed to properly model the wave 

diffraction close to the defect boundaries. Six different mesh refinements were studied in this 

region for convergence check. 

The mesh in the unaltered Zones 1 and 2 is shown again in Figures 4.19 and 4.20, respectively, 

for clarity. 
39

Figure 4.19. Coarse mesh in Zone 1 (maximum element size d = 3mm).

Figure 4.20. Transition mesh in Zone 2 (maximum element size d = 2mm).
40

The following figures (Figures 4.21 through 4.26) show the six levels of mesh refinements 

(Mesh 1 through Mesh 6) modeled for Zone 3 around the defect. The drawings are ordered from 

the most refined mesh (max. element size d = 0.5 mm) to the coarsest mesh (max element size d

= 2.0 mm). 

Figure 4.21. Mesh 1 in Zone 3 around the defect (maximum element size d = 0.5 mm).
41

Figure 4.22. Mesh 2 in Zone 3 around the defect (maximum element size d = 0.8 mm).

Figure 4.23. Mesh 3 in Zone 3 around the defect (maximum element size d = 1.1 mm).
42

Figure 4.24. Mesh 4 in Zone 3 around the defect (maximum element size d = 1.4 mm).

Figure 4.25. Mesh 5 in Zone 3 around the defect (maximum element size d = 1.7 mm).
43

Figure 4.26. Mesh 6 in Zone 3 around the defect (maximum element size d = 2.0 mm).

All six cases used explicit tetrahedral elements with linear shape functions. The details of the six 

meshes are shown in the following:

MESH 1 – d_max around the defect = 0.5 mm

Total number of nodes: 233,575

Total number of elements: 1,367,021 Linear Tetrahedral of type C3D10M

MESH 2 – d_max around the defect = 0.8 mm

Total number of nodes: 99,952

Total number of elements: 577,885 Linear Tetrahedral of type C3D10M

MESH 3 – d_max around the defect = 1.1 mm

Total number of nodes: 66,982

Total number of elements: 383,988 Linear Tetrahedral of type C3D10M

MESH 4 – d_max around the defect = 1.4 mm

Total number of nodes: 63,222

Total number of elements: 362,540 Linear Tetrahedral of type C3D10M
44

MESH 5 – d_max around the defect = 1.7 mm

Total number of nodes: 52,347

Total number of elements: 297,712 Linear Tetrahedral of type C3D10M

MESH 6 – d_max around the defect = 2.0 mm

Total number of nodes: 41,548

Total number of elements: 234,478 Linear Tetrahedral of type C3D10M

Material properties (steel), boundary conditions (fixed base), and forcing function (one 

sinusoidal cycle at 2.25 MHz, unity amplitude, at gage corner, inclined at 70 degrees from 

vertical axis y) were unchanged from the 3-D model discussed in the previous section. Also, the 

same time increment requirement was used to properly represent 2.25 MHz frequencies, hence 

Δtmax = 0.0222 μsec.

4.3.2 Results of Convergence Study

A node close to the defect was chosen as a probe to analyze the behavior of the different meshes. 

The position of the “probe node” is shown in two different views in Figures 4.27 and 4.28. 

Figure 4.27. Position of the probe node for convergence study – side view. 
45

Figure 4.28. Position of the probe node for convergence study – front view.

For each of the six meshes, the following kinematic quantities were recorded at the Probe Node: 

accelerations (x, y and z), velocities (x, y and z), and displacements (x, y and z). The time 

histories of these quantities recorded with each mesh are shown in Figures 4.29 through 4.34. In 

these plots the first row refers to the accelerations ax, ay and az; the second row to the velocities 

vx, vy and vz; and the third row to the displacements ux, uy and uz.
46

Figure 4.29. Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 1 in Zone 3 around the defect (maximum element size d = 

0.5 mm).
47

Figure 4.30. Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 2 in Zone 3 around the defect (maximum element size d = 

0.8 mm).
48

Figure 4.31. Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 3 in Zone 3 around the defect (maximum element size d = 

1.1 mm).
49

Figure 4.32. Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 4 in Zone 3 around the defect (maximum element size d = 

1.4 mm).
50

Figure 4.33. Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 5 in Zone 3 around the defect (maximum element size d = 

1.7 mm).
51

Figure 4.34. Time histories of accelerations ax, ay and az (first row), velocities vx, vy and vz

(second row), and displacements ux, uy and uz (third row) recorded at the Probe Node for 

convergence study using Mesh 6 in Zone 3 around the defect (maximum element size d = 

2.0 mm).

Following zero-padding to increase the frequency resolution, these time histories were processed 

through a Fast Fourier Transform (FFT) for frequency information. The following figures 

(Figure 4.35 through 4.43) show the FFT magnitude spectra recorded for each of the nine 

kinematic quantities (ax, ay, az, vx, vy, vz and ux, uy, uz) for the six different mesh refinements. 

What is apparent in these plots, as expected, is that the finer the mesh, the better the 

representation of the higher frequency components. The coarsest mesh, mesh 6 of d = 2.0 mm, 

for example, only properly represents frequency components up to ~ 1 MHz. In order to 

properly represent the excitation frequency of 2.25 MHz, the most refined mesh, mesh 1 with d = 

0.5 mm, is required. Use of a mesh coarser than d = 0.5 mm around the defect would not be 

adequate to represent the high frequency waves. This study therefore gives confidence in the 

results shown in the previous section (Section 3) obtained with the mesh of d = 0.4 mm in Zone 

3.
52

Figure 4.35. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

acceleration ax for the six different meshes considered in the convergence study.

Figure 4.36. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

acceleration ay for the six different meshes considered in the convergence study.
53

Figure 4.37. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

acceleration az for the six different meshes considered in the convergence study.

Figure 4.38. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

velocity vx for the six different meshes considered in the convergence study.
54

Figure 4.39. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

velocity vy for the six different meshes considered in the convergence study.

Figure 4.40. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

velocity vz for the six different meshes considered in the convergence study.
55

Figure 4.41. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

displacement ux for the six different meshes considered in the convergence study.

Figure 4.42. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

displacement uy for the six different meshes considered in the convergence study.
56

Figure 4.43. Fast Fourier Transform magnitude spectra recorded at the Probe Node for 

displacement uz for the six different meshes considered in the convergence study.

For easier reading of the convergence results, a “Convergence Index” was also calculated. This 

index was computed as the integral of the FFT magnitude spectra between 1 MHz and 2.25 MHz 

at the Probe Node. The results as a function of mesh refinement are plotted in Figure 4.44 for 

each of the nine kinematic variables discussed above. These plots clearly show that the 

Convergence Index improves with increasing mesh refinement, with the d = 0.5 mm mesh 

providing the best convergence results for the high-frequency wave content. 
57

Figure 4.44. Convergence Index for accelerations ax, ay and az (first row), velocities vx, vy

and vz (second row), and displacements ux, uy and uz (third row) recorded at the Probe 

Node for the six different meshes used in the convergence study.
58

5. Proposed Ultrasonic Tomographic Method for Rail Flaw Imaging

This chapter discusses the specific steps developed in this project for ultrasonic tomographic 

imaging of rail flaws. 

5.1 Difference between Phased-Array Imaging and Ultrasonic Tomographic 

Imaging with Synthetic Aperture Focus 

It is worth highlighting the differences between Phased Array Imaging and TomographicSynthetic Aperture Focus Imaging. A good review of this difference was given by Karaman et 

al. (1995). In conventional phased array imaging, all transducer elements transmit the ultrasonic 

waves, and focusing is achieved via wave reflections (Shoup and Hart 1988). This concept is 

shown in Figure 5.1(a). The improved contrast achieved in phased array imaging comes, 

however, at the expense of the many parallel transmit and receive circuits that are required. For 

example, medical imaging phased array 128 channel scanners require 128 independent transmit 

and receive circuits. Therefore, a phased array system with high channel count (i.e., high defect 

imaging resolution) can hardly meet the power or size requirements of a handheld system that is 

practical for field use on the rail tracks.

Alternatively, ultrasonic tomography with Synthetic Aperture Focusing (SAF) represents an 

evolution from phased array imaging, in that only a few transmitters can be used at once, as 

shown in Figure 5.1(b). The transmission beam is made as divergent as possible to span the 

inspection volume; as a result, the active channel count can be dramatically reduced. Ultrasonic 

tomography with SAF is at the forefront of recent developments in Sonar, Radar, and Medical 

Imaging. With the SAF approach, focusing is achieved with minimum complexity in both 

transmit and receive stages. Hence, a SAF-based imaging approach would be ideal for a 

handheld rail inspection system in the field. 
59

Figure 5.1. (a) Phased-Array Imaging. (b) Tomographic Imaging with Synthetic Aperture 

Focus.

The following sections describe the particular algorithms used in the SAF tomographic approach 

that has been developed for the 3-D imaging of rail flaws. The algorithms include the following:

1) Synthetic Aperture Focusing

2) Matched Filtering

3) Baseline Subtraction

4) Multimode Detection

5.2 Synthetic Aperture Focusing 

The proposed approach uses SAF implemented with envelope detection and delay-and-sum 

algorithms. The general idea of the SAF applied in 3-D is schematized in Figure 5.2. 

All elements transmit with

time delays

A few elements transmit with 

diverging beams 

Phased-Array (PA) Imaging Tomography with Synthetic 

Aperture Focus (SAF) Imaging

(a) (b)
60

Figure 5.2. Principle of Synthetic Aperture Focusing (SAF) for Ultrasonic Tomography 3-

D imaging.

The SAF method is most efficiently implemented using a delay-and-sum algorithm (Nikolov and 

Jensen 2000 and 2003, Jensen et al. 2006, Daher and Yen 2006). This is based on the time 

required for an ultrasonic wave to propagate from a transmitter i to a receiver j after reflection 

from a focus point P in the imaging volume. Referring to Figure 5.2, the delay-and-sum 

algorithm used in this study can be expressed by the following equation:

[ ]

1 1

( ) ( , ), ,

N M

P

j i

I yt i j i j

= =

rP = ∑ ∑ (5.1)

In the above equation (5.1), I( ) Pr is the imaging intensity at focal point P(x,y,z) of the volume 

(associated with 3-D position vector Pr ), N is the total number of receivers j, M is the total 

number of transmitters i, and the function yt i j i j [ P( , ), , ] is the ultrasonic waveform generated 

by the i-th transmitter and detected by the j-th receiver. The ultrasonic waveform yt i j i j [ P( , ), , ]

is calculated at the time delay value (, ) Pt ij , that is in turn calculated from the wave travel time 

from transmitter i, to the focal point P, to receiver j (Figure 5.2) as follows:

, ,

() ( ) (, ) T R

P

LS LS

i j t ij

v v

− − = + P P rr rr (5.2)
61

In the above equation (5.2), Pr is the 3-D position vector of the focus point P, ( ) T

r i is the 3-D 

position vector of the i-th transmitter, ( ) Rr j is the 3-D position vector of the j-th receiver, and 

vL S, represents the longitudinal wave velocity or the shear wave velocity in the material. The 

fact that either the longitudinal wave velocity or the shear wave velocity can be used is referred 

to as “Multimode Detection” and is further discussed below. 

In summary, Equation (5.1) and Equation (5.2) “scan” all focus points P(x,y,z) of the 3-D 

imaging volume (known as “voxels” in radar and sonar imaging) and attribute to each voxel an 

“imaging” value I(x,y,z) that corresponds to the ultrasonic intensity that is transmitted by all M

transmitters, reflected by point P, and received by all N receivers. This is what is known as 

“total focusing” (i.e., focusing in both transmit and receive). More importantly, as discussed 

above, the ultrasonic tomographic approach minimizes the number of transmitters that need to be 

excited at once, thereby greatly reducing the complexity of the electronics.

Owing to the focusing process in both transmit and receive, the Signal-to-Noise Ratio (SNR) of 

the image expected from an ultrasonic tomographic system with M transmitters and N receivers 

can be written as (Lockwood et al. 1998):

SNR N M = × (5.3) 

Therefore, as expected, the SNR of the resulting image improves with increasing numbers of 

transmitters and receivers. In practice, the hardware complexity, cost, and scan time limit the 

number of transducers that can be used—with much more restrictive limits on the number of 

transmitters. That is why, in this study, a sparse array of transmitters was used (as few as five 

transmitters for the 3-D rail imaging) in combination with a finer array of receivers (140 or 525 

receivers for the 3-D rail imaging). The same approach involving sparse transmitters and fine 

receivers has been considered in medical imaging devices based on the SAF technique

(Lockwood et al. 1998). 

The present study applies envelope detection (Frazier and O’Brien 1998) to the waveforms

yt i j i j [ P( , ), , ] before applying the delay-and-sum equations (5.1) and (5.2), as is customary in 

ultrasonic imaging. In the Matlab© program that has been written, envelope detection was 
62

achieved by taking the absolute value of the waveforms’ Hilbert Transform. For the purposes of 

analysis, the Hilbert Transform y t ˆ( ) of a signal y t( ) is expressed with the following equation: 

1 () ˆ( ) y t y t d

t

τ

π τ

+∞

−∞

= − ∫ (5.4)

Figure 5.3 shows the application of envelope detection to one of the ultrasonic signals recorded 

in the rail by the 3-D imaging system discussed later in this report. It is clear that the Hilbert 

Transform effectively captures the signal strength (amplitude) which is then summed, with the 

appropriate delays, at each point of the imaging volume.

Figure 5.3. Example of envelope detection (Hilbert Transform) of an ultrasonic waveform 

recorded from the 3-D rail imaging FEA model.

5.3 Matched Filtering

One key step that was adopted in the present study involved the implementation of matched 

filtering in the general SAF approach. The matched filtering step is used in radar imaging 

(Maitre 2008) to compress and denoise the radar pulses, thereby dramatically enhancing the SNR 

and image resolution. 

The matched filtering approach implemented for rail imaging performs a cross-correlation 

between each raw waveform detected by the ultrasonic receivers and the known excitation sent 

to the ultrasonic transmitters. For the purposes of analysis, the matched filtered signal is 

represented by the following equation:

0 5 10 15 20 25 30 35 40 45 50 -0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Time (microseconds)

Amplitude (Volts)

raw time waveform

envelope waveform - abs(Hilbert) 
63

* zt yt d () ( ) ( ) f τ ττ

+∞

−∞

= ∫ + (5.5) 

where *

f ( ) τ is the complex conjugate of the (known) excitation signal sent to the transmitters 

and y(t) is the waveform detected by the receivers. 

Figure 5.4 shows an example of the application of matched filtering. The top waveform 

represents the excitation signal, which is a two-cycle toneburst at 2 MHz (this is the same 

excitation used for the 3-D rail flaw imaging model discussed earlier). The middle waveform 

represents a simulated detection with 10 dB white noise added. The bottom signal was obtained 

by match filtering the noisy signal with the excitation signal. As shown in the figure below, the 

arrival of the waveform is clearly visible in the filtered result. This filtering was one of the keys 

to success for the 3-D rail flaw imaging results shown later.

Figure 5.4. Example of Matched Filtering. Top waveform: excitation signal (two-cycle 

toneburst at 2 MHz). Middle waveform: detected signal with 10 dB white noise added 

(“noisy signal”). Bottom signal: “noisy signal” after matched filtering with excitation 

signal.

In radar imaging, the matched filtering is more often achieved using a chirped signal, rather than 

the narrowband signal used in Figure 5.4. The chirped signal provides an added pulse 

compression performance that can further increase the resolution of the tomographic image. The 

0 5 10 15 20 25 30 35 40 45 50

-4

-3

-2

-1

0

1

2

3

4

Time (microseconds)

Voltage (a.u.)

excitation signal

detected signal with 10 dB

white noise added

detected signal after matched

filtering
64

use of chirped excitation could be considered in the future for the rail flaw imaging prototype, if 

signal noise becomes an issue. 

5.4 Baseline Subtraction

Another key feature implemented in the 3-D rail flaw imaging approach is baseline subtraction. 

This step was derived by subtracting the ultrasonic results of a defect-free rail (baseline) from the 

results of the flawed rail. This step eliminates any wave contributions that have not resulted

directly from the flaw (primarily railhead boundaries), and dramatically enhances the SNR of the 

defect image. In actual rail imaging in the field, this step simply requires taking a scan of a 

pristine region of the rail prior to scanning the flawed region. In theory, it should be sufficient to 

take only one baseline scan for each geometry of rail (136 lb, 139 lb, etc.) being inspected. 

When imaging defects in a worn rail, the baseline would be taken on the specific rail section to 

be inspected to account for the worn profile. 

In the Matlab© program developed, baseline subtraction was implemented in two different 

modalities. In the first modality (envelope subtraction), the subtraction was performed on the 

enveloped signals. In the second modality (image subtraction), the subtraction was performed on 

the resulting images. Both approaches yielded successful results. 
65

Figure 5.5. Example of baseline subtraction on the envelope signals. Notice how the defect 

reflection increases relative to the “artifact” peaks in the baseline-subtracted signal (red 

trace).

Figure 5.5 shows an example of envelope baseline subtraction on one of the signals from the 3-D 

rail flaw imaging simulation discussed in Section 4. This graph depicts an envelope signal from 

the damaged rail, the envelope signal from the pristine rail (baseline), and the baselinecompensated signal (red trace). As seen, the baseline subtraction increases the defect reflection 

(arriving at approximately 24 microseconds in this case), while decreasing the signal peaks, 

which are artifacts and not related to the flaw, on either side of the defect reflection. In 

comparison, the “artifact” peaks are larger than the defect reflection in the raw “damaged” signal 

before baseline subtraction (black continuous line).

5.5 Multimode Detection

Yet another step implemented in the imaging algorithm is the multimode detection. This unique 

possibility exists in rail flaw imaging because the rail steel allows for the two fundamental wave 

modes of propagation: longitudinal wave mode and shear wave mode. These two modes 

propagate at two different velocities (typical velocities for steel are longitudinal velocity vL = 5.3 

mm/microsec and shear velocity vS = 2.8 mm/microsec). Under longitudinal mode excitation, 

the rail flaw reflects both the same longitudinal mode (same mode reflection) and the shear mode 

(mode conversion). The existence of the two different modes allows for the use of different time 

0 5 10 15 20 25 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time (microseconds)

Amplitude (Volts)

baseline (pristine rail)

damaged (flawed rail)

abs(damaged-baseline)

defect

reflection

"artifact" peaks
66

delays in the delay-and-sum equations (5.1) and (5.2), thereby providing redundant focusing for 

enhanced SNR of the imaging result. 

The existence of both the longitudinal wave mode (travelling faster) and the shear wave mode 

(travelling slower) in a flawed rail is shown in Figure 5.6. This figure depicts the propagating 

wave fronts (Von Mises stress) from the 2-D FEA study that is discussed in detail in Section 3. 

It should be emphasized that the option to exploit both wave modes for imaging is unique to 

ultrasonic propagation in solid materials (i.e., materials with a non-negligible elastic shear 

stiffness); this option was selected for the present study of rail flaw detection because no shear 

wave mode exists in fluids or biological media (i.e., underwater sonar and medical imaging can 

only exploit the ultrasonic longitudinal mode) and no shear mode exists in electromagnetic RF 

waves (i.e., radar imaging can only exploit one RF wave mode). 

Figure 5.6. Multimode Detection: formation of both longitudinal wave mode (travelling 

faster) and shear wave mode (travelling slower) in rail flaw imaging (from the 2-D FEA 

model discussed in the next section).
67

6. 2-D Rail Flaw Imaging 

This chapter presents the results of the ultrasonic tomographic imaging of the 5-percent RHA TD 

in the 136-pound RE rail from the 2-D simulations.

6.1 Finite Element Model for 2-D Rail Flaw Imaging

The FEA model for 2-D rail flaw imaging consisted of a 136-pound rail with a TD in the railhead 

extending for 5 percent of the rail RHA, as shown in Figure 6.1. ABAQUS Explicit was used for 

the model. The FE mesh was generated for a maximum ultrasonic frequency of 2.25 MHz and 

10 elements per wavelength as required to properly represent the ultrasonic waves. The resulting 

FE parameters were as follows:

• Total number of nodes: 188,256

• Total number of elements: 187,112

• Element type: linear quadrilateral elements of type CPS4R

Figure 6.1. The FE mesh for the 2-D rail flaw imaging study along with the linear 

transducer array for tomographic imaging with Synthetic Aperture Focus.

For 2-D imaging (plane strain), a linear transducer array with N = 23 elements and 1.5 mm 

spacing was simulated in the model. The array was used for SAF in a reflection mode where 

each of the transducers acted as a transmitter of a 2.25 MHz wave and all the remaining 

33 mm

Transducer 1 Transducer N

5% Head Area TD
68

transducers acted as the receivers of the wave. The total number of transmitter-receiver 

combinations was therefore N^2 = 529 combinations. In addition to the flawed rail model, a 

pristine rail model was analyzed for baseline subtraction.

The transducer signals were analyzed in Matlab© to perform the tomographic imaging steps that 

were described in the previous section. Specifically, the following steps were conducted for the 

2-D imaging:

• Synthetic Aperture Focus (see Section 5.2)

• Baseline Subtraction (see Section 5.4)

• Multimode Detection (see Section 5.5)

The matched filtering step was not implemented in the 2-D imaging, only in the 3-D imaging. In 

addition, noise robustness studies were performed in 2-D by adding artificial noise.

Figure 6.2 shows a detail of the mesh around the 5-percent RHA TD to demonstrate the high 

level of refinement used. 

Figure 6.2. Detail of the FE mesh around the 5% RHA Transverse Defect.

Figure 6.3 shows an example of wave propagation generated in this model. The cases shown are 

those of wave generation with the leftmost transducer in the array (transducer 1) and wave 

generation with the central transducer in the array (transducer 12). The excitation signal in all 

cases was a one-cycle sine wave at 2.25 MHz frequency directed vertically. The figure shows, in 
69

terms of Von Mises stress, that both longitudinal wave modes (travelling faster) and shear wave 

modes (travelling slower) are generated by the excitations, and both modes are generated at the 

reflections from the defect, which confirms the “same-mode reflection” and “mode-converted 

reflection” expected for this kind of wave-defect interaction. 

The existence of both longitudinal mode and shear mode allowed us to exploit multimode 

detection for enhanced imaging performance. The following values of longitudinal wave 

velocity and shear wave velocity were used in the time delays used for the delay-and-sum 

algorithm (Equations 5.1 and 5.2):

Longitudinal Wave speed: vL = 5.3 mm/microsec

Shear Wave speed: vS = 2.8 mm/microsec

These velocity values were measured from the FEA animations.

Figure 6.3. Von Mises stress contour plots for two different excitations showing the 

propagation of both longitudinal wave mode (travelling faster) and shear wave mode 

(travelling slower).
70

6.2 Imaging Results from the 2-D Model

Representative results of the 2-D defect imaging with the Matlab©

ultrasonic tomographic 

algorithm are presented in this section. Figure 6.3 shows the result for two cases. The left-hand

plot is the imaging result obtained using the longitudinal modes and the envelope baseline 

subtraction. The right-hand plot is the imaging result obtained using the longitudinal mode and 

the shear mode (Multimode Detection), as well as image baseline subtraction. In both images, 

the top of the 5 percent RHA defect is clearly visible in the correct position. A small “shadow” 

artifact is present in the longitudinal-shear image. The fact that only a portion of the defect 

contour was successfully imaged has to do with the limited width of the array considered. These 

results therefore serve as a successful proof-of-principle 2-D imaging. 

Figure 6.4. 2-D Imaging of 5% RHA Transverse Defect by Ultrasonic Tomography with 

Synthetic Aperture Focus using (a) the Longitudinal Wave mode (left-hand image) and (b) 

the Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline 

Subtraction was also implemented in these images.

6.3 Noise Robustness Study

In an effort to test the robustness of the ultrasonic tomographic imaging method, noise was 

artificially added to the FEA waveforms prior to use of the SAF algorithm. Specifically, 

Gaussian white noise was added using the Matlab© function “awgn” at increasing power levels 

(relative to the original signals) from 10 dB to 35 dB in 5 dB increments. 
71

Figures 6.5 through 6.7 show the imaging results corresponding to the same two cases shown 

earlier in Figure 6.4, but with the signals corrupted by the increasing levels of Gaussian noise. 

These figures show representative signals (after envelope detection) without noise (red traces) 

and with noise added (blue traces). The results shown in Figures 6.5 through 6.7 lead to the 

following conclusions:

• Noise levels up to 35 dB in power over the original signals do not degrade substantially 

the images created by the longitudinal and shear wave combination.

• Noise levels up to 25 dB in power over the original signals do not degrade substantially 

the images created by the longitudinal and shear wave combination. However, above the 

25 dB noise level, longitudinal and shear wave combination images are substantially 

degraded. 

Overall, the results suggest a strong robustness against noise, and particularly so when 

multimode detection is implemented in the tomographic imaging algorithm, in addition to 

baseline subtraction. Clearly, these results are also limited by the ultrasonic frequency used in 

excitation (2.25 MHz). The use of a higher frequency (which is challenging to model in FEA, 

but easy to implement experimentally in a prototype) would enhance the resolution of the defect 

images shown here. 
72

Figure 6.5. 2-D Imaging of 5% RHA Transverse Defect with 15 dB Gaussian White Noise 

added to the signals, and using (a) the Longitudinal Wave mode (left-hand image) and (b) 

the Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline 

Subtraction was also implemented in these images.
73

Figure 6.6. 2-D Imaging of 5% RHA Transverse Defect with 25 dB Gaussian White Noise 

added to the signals, and using (a) the Longitudinal Wave mode (left-hand image) and (b) 

the Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline 

Subtraction was also implemented in these images.
74

Figure 6.7. 2-D Imaging of 5% RHA Transverse Defect with 35 dB Gaussian White Noise 

added to the signals, and using (a) the Longitudinal Wave mode (left-hand image) and (b) 

the Longitudinal Wave mode and the Shear Wave mode (right-hand image). Baseline 

Subtraction was also implemented in these images.
75

7. 3-D Rail Flaw Imaging 

This chapter presents the results of the ultrasonic tomographic imaging of the 5-percent RHA TD 

in the 136-pound RE rail from the 3-D simulations.

7.1 Finite Element Model for 3-D Rail Flaw Imaging

The 3-D FEA ABAQUS model consisted of a 175.2-milimeter long section of a 136-pound RE

rail sectioned at the web height as shown in Figure 7.1. The flaw modeled was a circular TD

extending for 5 percent of the rail RHA as shown in the sectional view of Figure 7.2. 

Figure 7.1. Rail section model for the 3-D FEA.

Figure 7.2. Geometrical dimensions for the 3-D FEA model.

175.2 mm

Dimensions in meters (m)
76

The FE mesh used 8-node linear hexahedral elements with “reduced integration” (ABAQUS 

element HEXA C3D8R) and a characteristic size of 0.5 mm. Another important feature was the 

use of 8-node “infinite elements” (ABAQUS element HEXA CIN3D8) at the boundaries of the 

model to avoid spurious reflections of the ultrasonic waves that would not be existent in an 

actual inspection in the field. The resulting mesh is shown in Figures 7.3 and 7.4. 

The resulting FE parameters were as follows:

• Total number of nodes: 3,948,855

• Total number of elements: 4,023,918

• Element type on model: linear hexahedral elements of type HEXA C3D8R 

• Element type on boundaries: “infinite” elements of type HEXA CIN3D8

Figure 7.3. Mesh for the 3-D FEA with “infinite elements” at the model boundaries to 

eliminate artificial boundary reflections of the waves.

“INFINITE ELEMENTS” to 

eliminate artificial 

boundary reflections of 

waves
77

Figure 7.4. Mesh for the 3-D FEA: sectional view.

For 3-D imaging, a planar transducer array with a total of 525 elements and 2 mm spacing was 

simulated in the model. The array was used for SAF in a reflection mode. Different views of the 

transducer array simulated in the FEA model are provided in Figures 7.5 and 7.6.

To simplify the procedure, and also with a future prototype design in mind, it was decided that a 

scheme with sparse transmitters, i.e. only five transmitters (M = 5), would be used (Figure 7.7). 

As discussed earlier in the report, minimizing the number of transmitters is an effective way to 

decrease the complexity, cost, and scan time of an imaging system. For the reception, the 

following two cases were considered: all elements receiving (Full Array: N = 525), and only 

140 elements receiving (Reduced Array: N = 140). The total transducer combinations used in 

the 3-D SAF algorithm was therefore: 

- Full Array: N×M = 525×5 = 2,625

- Reduced Array: N×M = 140×5 = 700. 

The excitation signal to the five transmitters was a force inclined at 70 degrees from the vertical 

and following a one-cycle toneburst at 2 MHz. The 70-degree orientation is consistent with the 

70-degree wedge angle used in conventional ultrasonic hand verification of Transverse Head 

defects in the rail head.

5% H.A. Transverse Defect
78

Figure 7.5. Full transducer array for the 3-D FEA.

Figure 7.6. Full transducer array for the 3-D FEA: sectional view.
79

Figure 7.7. Position of the five “sparse” transmitters in the transducer array: top view.

For the 3-D imaging case, a pristine rail model was analyzed along with the flawed rail model for 

baseline subtraction. In addition, the matched filtering step was adopted by cross-correlating the 

received signals with the known excitation signal. In summary, the tomographic imaging 

Matlab© program for the 3-D case included all of the necessary imaging steps discussed earlier:

• Synthetic Aperture Focus (see Section 7.2)

• Matched Filtering (see Section 7.3)

• Baseline Subtraction (see Section 7.4)

• Multimode Detection (see Section 7.5)

As was the case with the 2-D FEA results, the existence of both longitudinal mode and shear 

mode in the 3-D case allowed multimode detection to be used for enhanced imaging 

performance. The following values of longitudinal wave velocity and shear wave velocity were 

used in the delay-and-sum algorithm of the 3-D analysis:
80

Longitudinal Wave speed: vL = 5.9 mm/microsec

Shear Wave speed: vS = 3.1 mm/microsec

These velocity values were measured from the 3-D FEA animations. 

Screenshots of the wave propagation in the 3-D model, under excitation by the central 

transmitter, are shown in Figures 7.8 and 7.9 in terms of Von Mises stress. 

Figure 7.8. Von Mises stress contour plots for central excitation showing the propagation 

of both Longitudinal Wave mode (travelling faster) and Shear Wave mode (travelling 

slower), as well as absence of reflections at boundaries owing to “infinite” elements 

(longitudinal sectional view).
81

Figure 7.9. Von Mises stress contour plots for central excitation (transverse sectional view 

at defect position).

7.2 Imaging Results from the 3-D Model

7.2.1 Results from the Full Array (5 transmitters, 525 receivers)

Representative 3-D imaging results from the ultrasonic tomographic algorithm with the full 

receiver array are shown in this section. 

Figures 7.10 through 7.16 show different views of the imaging result obtained using the 

longitudinal mode and the shear mode (multimode detection: L-wave velocity for transmitter-todefect path and S-wave velocity for defect-to-receiver path) using matched filtering and envelope 

baseline subtraction. The defect indication is clearly shown with excellent contrast, with no 

extraneous artifacts, image noise, or uncorrelated speckle noise. The defect imaged with this Lmode and S-mode combination (L-mode/S-mode) appears in a position that is slightly 

underestimated horizontally (direction z in the figures), and slightly overestimated vertically 

(direction y in the figures). A more precise location will likely require a change in the value of 

the shear wave velocity adopted for the SAF algorithm. The overall shape of the defect and, 
82

more importantly, the size of the defect (which is the most important parameter for 

decisionmaking for an in-service rail inspection) are estimated very accurately. In fact, with an 

actual defect size of 141 mm2 (or 5 percent rail RHA), the L-wave and S-wave tomographic 

imaging yields a defect size of 150 mm

2 (or 5.3 percent rail RHA). In summary:

Full array (5 transmitters, 525 receivers)

• Actual defect size: 5 percent rail RHA

• Defect size calculated from L-wave/S-wave Tomographic Imaging: 5.3 percent rail RHA

Figure 7.10. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers).

Figure 7.11. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers). 
83

Figure 7.12. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers). 

Figure 7.13. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers). 
84

Figure 7.14. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers). 

Figure 7.15. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers). 
85

Figure 7.16. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Full Array: 5 

transmitters, 525 receivers). 

Figures 7.17 through 7.20 show the imaging result obtained using the longitudinal mode only (Lwave velocity for transmitter-to-defect path and for defect-to-receiver path) using matched 

filtering and image baseline subtraction. Again, the defect indication is clearly shown with 

excellent contrast, with no extraneous artifacts, image noise, or uncorrelated speckle noise. The 

defect imaged with the L-mode alone appears in a position that is very accurate in both 

horizontal direction (direction z in the figures) and vertical direction (direction y in the figures). 

The circular contour of the defect image in this mode is more irregular, with contour lobes that 

are not present in the L-wave/S-wave imaging mode discussed previously. The origin of these 

contour lobes will be investigated in the following phase. More importantly, the size of the 

defect (to reemphasize the most important parameter for decisionmaking from an in-service rail 

inspection perspective) is imaged, again, very accurately. With an actual defect size of 141 mm2

(or 5 percent rail RHA), the L-wave tomographic imaging yields a defect size of 154 mm

2 (or 5.4

percent rail RHA). In summary:
86

Full array (5 transmitters, 525 receivers)

• Actual defect size: 5 percent rail RHA

• Defect size calculated from L-wave tomographic imaging: 5.4% rail RHA

Figure 7.17. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers). 

Figure 7.18. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers). 
87

Figure 7.19. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers). 

Figure 7.20. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Full Array: 5 transmitters, 525 receivers). 
88

7.2.2 Results from the Reduced Array (5 transmitters, 140 receivers)

Representative results obtained by the reduced receiver array are shown in this section. Figures 

7.21 through 7.23 show different views of the 3-D imaging by the longitudinal mode and the 

shear mode (Multimode Detection: L-wave velocity for transmitter-to-defect path and S-wave 

velocity for defect-to-receiver path) using matched filtering and envelope baseline subtraction. 

The results are very similar to those obtained with the full array. This finding is encouraging 

because it means that it is possible to substantially reduce the number of receivers (from 525 to 

140), thereby reducing the electronic complexity and scan time of a future field prototype 

without substantially degrading the quality of the imaging results. 

With an actual defect size of 141 mm

2 (or 5 percent rail RHA), the L-wave/S-wave tomographic 

imaging with reduced array yields a defect size of 148 mm

2 (or 5.25 percent rail RHA). 

In summary:

Reduced array (5 transmitters, 140 receivers)

• Actual defect size: 5 percent rail RHA

• Defect size calculated from L-wave/S-wave tomographic imaging: 5.25 percent rail 

RHA
89

Figure 7.21. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Reduced Array: 5 

transmitters, 140 receivers). 

Figure 7.22. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Reduced Array: 5 

transmitters, 140 receivers). 
90

Figure 7.23. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode and the Shear Wave mode with Envelope Baseline Subtraction (Reduced Array: 5 

transmitters, 140 receivers). 

Figures 7.24 through 7.26 show the imaging result obtained by the reduced array using the 

longitudinal mode only (L-wave velocity for transmitter-to-defect path and for defect-to-receiver 

path), along with matched filtering and image baseline subtraction. Again, the results are very 

similar to those obtained with the full array, confirming the possibility of greatly reducing the 

computational complexity and scan time of a future field prototype. 

With an actual defect size of 141 mm2 (or 5 percent rail RHA), the L-wave tomographic imaging 

with the reduced array yields essentially the same defect size of 154 mm

2 (or 5.4 percent rail 

RHA) as the full array. 

In summary:

Reduced array (5 transmitters, 140 receivers)

• Actual defect size: 5 percent rail RHA

• Defect size calculated from L-wave tomographic imaging: 5.4 percent rail RHA
91

Figure 7.24. 3-D Imaging of 5 percent RHA Transverse Defect using the Longitudinal 

Wave mode along with Image Baseline Subtraction (Reduced Array: 5 transmitters, 140

receivers).
92

Figure 7.25. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Reduced Array: 5 transmitters, 140

receivers).

Figure 7.26. 3-D Imaging of 5% RHA Transverse Defect using the Longitudinal Wave 

mode along with Image Baseline Subtraction (Reduced Array: 5 transmitters, 140

receivers).
93

8. 3-D Rail Flaw Imaging: Case of Worn Rail

This chapter presents 3-D flaw imaging results from the proposed tomographic analysis applied 

to a worn rail profile (BNSF – worn rail geometry, tangent track). 

8.1 Worn Rail Model

The effect of rail head wear on the performance of the tomographic imaging technique was 

examined. A profile of a worn tangent track was obtained from the BNSF Railway. The 3-D FE 

model was then constructed on the worn profile. Figure 8.1 shows the worn profile, along with 

the 3-D geometrical model developed for the FE analysis.

Figure 8.1. Worn BNSF rail profile (136-pound RE tangent track), and 3-D model 

constructed for the 3-D Finite Element Analysis and Tomographic Imaging.

The same 5-percent RHA TD considered for the new rail in the previous section was modeled for 

the worn rail case (Figure 8.2). Also, the same planar transducer array (up to 525 transducers) 

modeled for the new rail in section 7 was considered for the worn rail case (Figure 8.2). The 

array was considered “flat,” hence the positions of each transducer considered in the SAF

algorithm were on an ideal plane. As for the new rail study, “sparse” transmitters (5) were 

considered for the excitation. 
94

Figure 8.2. Transducer array modeled for the 3-D tomographic imaging of the worn rail.

8.2 Imaging Results from the 3-D Model of the Worn Rail

The imaging procedure followed the same steps taken for the imaging of the new rail discussed 

in section 7. Only the longitudinal shear mode combination was considered for the worn rail 

because it was proven more robust against noise by the 2-D imaging results (see section 8). In 

terms of transducer configurations, the following two configurations were modeled:

• “Sparse” transmitter array (5) with “full” receiver array (525), and

• “Sparse” transmitter array (5) with “reduced” receiver array (140).

The 3-D imaging results for the “full” receiver array on the worn rail are shown in Figure 8.3

(right) and compared with the equivalent results previously obtained for the new rail (left). It 

can be seen in the illustration that the degree of wear does not degrade the performance of the 

flaw images in any appreciable way. 
95

Figure 8.3. New rail versus worn rail: 3-D imaging of 5% RHA Transverse Defect using 

the Longitudinal Wave mode and the Shear Wave mode with Envelope Baseline 

Subtraction (Full Array: 5 transmitters, 525 receivers).

The 3-D imaging results for the “reduced” receiver array on the worn rail are shown in Figure 

8.4 (right) and compared with the equivalent results obtained for the new rail (left). It can be 

seen in the illustration that the reduced number of receivers does affect the performance of the 

imaging method on the worn rail; however, the image degradation is not too severe. More 

importantly, the positions of the 140 reduced receivers were chosen quite randomly, and 

different positions would likely yield different results. Finally, in the case of severe rail wear, it 

is always possible to correct for any changes in the railhead profile by inputting the exact 

positions of the transducers in the SAF algorithm. Using the exact transducer positions will 

theoretically eliminate any effect of rail wear on the performance of the imaging technique. 
96

Figure 8.4. New rail versus worn rail: 3-D imaging of 5% RHA Transverse Defect using 

the Longitudinal Wave mode and the Shear Wave mode with Envelope Baseline 

Subtraction (Reduced Array: 5 transmitters, 140 receivers).
97

9. Conclusions

This report has shown the successful 3-D imaging using ultrasonic tomography of a 5-percent

RHA TD in the rail head. The work has been purely numerical, involving FEA to simulate the 

behavior of the tomographic ultrasonic array on a flawed rail, followed by a tomographic 

algorithm for the 3-D imaging of the rail’s interior. 

The report begins with a review of ultrasonic testing in the railroad industry, followed by a 

review of tomographic imaging in several fields, including the medical field and the civil 

engineering field. The report then describes the FEA model developed to simulate the 

tomographic imaging procedure using transducer arrays. 

Imaging of the 5-percent RHA TD in the railhead was conducted first in 2-D and then in 3-D. 

The 3-D FEA used the rather sophisticated features of “infinite elements” (to eliminate the 

artificial wave reflections at the model boundaries—which would be nonexistent in an actual 

experimental testing), as well as “numerical damping” to introduce a realistic level of wave 

damping as applicable to the imperfect surface of a rail.

The ultrasonic tomographic method developed in this project combines several algorithmic steps 

that are at the forefront of medical, sonar, and radar imaging, and adapts these steps to rail flaw 

imaging. In particular, the following steps were implemented: (1) SAF with Sparse 

Transmitters, (2) Matched Filtering, (3) Baseline Subtraction, and (4) Multimode Detection. A 

Matlab© program was written and tested to combine all of these steps so that the imaging result 

in 3-D is obtained in one single analysis. The Matlab© interface also allows the researchers to 

rotate the view of the inspected volume at will, a feature that would likely be useful in a possible

future field-deployable system.

The imaging process envisages a planar array of ultrasonic transducers located at the top of the 

railhead and operating in a reflection scheme. Since the array is stationary, no transducer 

movement is required for full 3-D visualization of the railhead. The full array considered in this 

report uses 525 elements (overall size of 28 mm×68 mm) with only 5 elements acting as 

transmitters. For the reception, two cases were considered: a full array (all 525 elements receive) 

and a reduced array (only 140 elements receive). 
98

The best tomographic 3-D imaging results of the 5-percent RHA TD were obtained using either a 

combination of the L-wave mode and the S-wave mode, or the L-wave mode alone. In both 

modalities, the defect size was estimated very accurately. Table 1 summarizes the flaw sizing 

results extracted from Figures 9.10 through 9.26. Another encouraging conclusion was that the 

full array (all 525 receivers) and the reduced array (only 140 receivers) yielded very similar 

images and flaw sizing estimates. This indicates the possibility of greatly reducing the electronic 

complexity and the scan time required by a future field-deployable prototype. 

Table 9.1. Rail flaw sizing results from the 3-D Tomographic Imaging models.

Full Array

(5 transmitters, 525 receivers)

Reduced Array

(5 transmitters, 140 receivers)

L-wave mode + 

S-wave mode

L-wave mode 

alone

L-wave mode + 

S-wave mode

L-wave mode 

alone

Imaged Transverse 

Flaw Size

5.3% Head 

Area

5.4% Head 

Area

5.25% Head 

Area

5.4% Head

Area

Actual Transverse 

Flaw Size

5% Head Area

Although defect sizing was very accurate, in some cases errors were found in the estimation of 

the precise defect location and defect contour shape. Specifically, the L-wave/S-wave modality 

presented slight inaccuracies in defect location while retaining excellent defect contour shape 

representation. The L-wave alone modality, on the other hand, presented artificial contour 

“lobes” while retaining excellent defect location. 

The final analyses of this project were conducted on a model of a worn rail whose geometry was 

provided by BNSF (136-pound RE tangent track). The tomographic array was considered to be

in the ideal “flat” position to test the effect of the worn profile on the image reconstruction. The 

results showed that when using the full array (5 transmitters, 525 receivers), rail wear had 

virtually no effect on the performance of tomographic imaging of the 5-percent RHA TD. When 
99

the array was reduced to 140 receivers, some degradation of the flaw image was noted, although 

the degradation was not too severe. Clearly, the results depend on the exact level of wear 

considered. In addition, it is worth noting that for severely worn profiles it is always possible to 

input the actual positions of the array transducers in the tomographic imaging algorithm. 

Accounting for the actual transducer positions will theoretically eliminate the effect of any worn 

profile on the resulting SAF image. 

It is also important to emphasize that the ultrasonic frequency of 2 MHz used in the 3-D imaging 

was limited by the FEA computational requirements. With any ultrasonic testing, higher 

frequencies generally yield increased defect resolution. Therefore, an actual tomographic 

imaging system for the field would likely use frequencies higher than what was simulated in 

these models.

The models developed within this project have shown excellent potential for using ultrasonic 

tomographic techniques to produce 3-D images of internal rail flaws. Based on these results, it 

seems possible to develop an ultrasonic tomographic system for rail flaw characterization in the 

field. 
100

10. References

Anderson, A. and Kak, A. (1982). “Digital ray tracing in two-dimensional refractive index field,” 

Journal of Acoustical Society of America, 72, pp. 1593–1606. 

Anon, F. (1990). “Rail-flaw detection. A science that works,” Railway Track and Structures, 86, 

pp. 30–32.

ASNT. (2007). Nondestructive Testing Handbook, Volume 7 Ultrasonic Testing, 3rd edition. 

American Society for Nondestructive Testing.

Berndt H., Schniewind, A.P. and Johnson, G.C. (1999). “High resolution ultrasonic imaging of 

wood,” Wood Science and Technology, 33, pp. 185–98.

Bian, H. and Rose, J.L. (2005). “Sparse array ultrasonic guided wave tomography,” Materials 

Evaluation, 10, pp. 1035–1038.

Bishko, A., Samokrutov, A. and Shevaldykin, V. (2008). “Ultrasonic echo-pulse tomography of 

concrete using shear waves low-frequency phased antenna arrays,” Proceedings 17th World 

Conference on Nondestructive Testing, October 25–28, 2008, Shanghai, China.

Bray, D.E. (1991). “Ultrasonic testing applications in the transportation industries-part 1.” ASNT 

Nondestructive Testing Handbook-Ultrasonic Testing, 2nd Ed. Vol. 7. Columbus, OH: The 

American Society for Nondestructive Testing, pp. 609–634.

Bucur, V. (2003). “Techniques for high resolution imaging of wood structure: a review,” 

Measurement Science and Technology, pp. R91–R98.

Chan, F.W. and Tsang, F.W. (2006). “Quality assurance of concrete foundation elements using 

an ultrasonic evaluation technique,” Insight - NDT and Condition Monitoring, Journal of the 

British Institute of NDT, 48, pp. 360–367.

Chernauskas, L.R. and Paikowsky, S.G. (2000). “Defect detection and examination of large 

drilled shafts using a new cross-hole sonic logging system,” Performance Verification of 

Constructed Geotechnical Facilities, Amherst: GeoInstitute/ASCE Specialty Conference, April 

9–12, 2000.

Clark, R. and S. Singh. (2003). “The inspection of thermite welds in railroad rail – a perennial 

problem,” Insight - NDT and Condition Monitoring, Journal of the British Institute of NDT, 45, 

pp. 387–393.

CTL Group. (2011). Ultrasonic Shear Wave Tomography or “MIRA,” 

http://www.ctlgroup.com/OurExpertise/ConsultingServices/Detail/43
101

Daher, N.M. and Yen, J.T. (2006). “2-D Array for 3-D ultrasound imaging using synthetic 

aperture techniques,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 

53, pp. 912–924.

Daigle, M., Fratta, D. and Wang, L.B. (2005). “Ultrasonic and X-ray tomographic imaging of 

highly contrasting inclusions in concrete specimens,” Proceedings of GeoFrontier Conference, 

Austin, TX.

Denis, F., Basset, O. and Gimenez, G. (1995). “Ultrasonic transmission tomography in refracting 

media: reduction of refraction artifacts by curved-ray techniques,” IEEE Transactions on 

Medical Imaging, 14, pp. 173–188.

Devaney, A. (1982). “A filtered back-propagation algorithm for diffraction tomography,” 

Ultrasonic Imaging, 4, pp. 336–350.

Devaney, A. (1984). “Geophysical diffraction tomography,” IEEE Transactions on Geological 

Science, Special Issue on Remote Sensing, GE-22, pp. 3–13.

Duric, N., Littrup, L., Poulo, P, Babkin, A., Pevzner, R., Holsapple, E., Rama, O. and Glide, C. 

(2007). “Detection of breast cancer with ultrasound tomography: first results with the Computed 

Ultrasound Risk Evaluation (CURE) prototype,” Medical Physics, 34, pp. 773–785.

Federal Railroad Administration. (2011). Safety Statistics Data. Washington, DC: Federal 

Railroad Administration, Office of Safety Analysis (http://safetydata.fra.dot.gov/officeofsafety).

Fink, M., Montaldo, G. and Tanter, M. (2003). “Time-reversal acoustics in biomedical 

engineering,” Annual Review of Biomedical Engineering, 5, pp. 465–497.

Fink, M. and Tanter, M. (2010). “Multiwave imaging and super resolution,” Physics Today, pp. 

28–33, February 2010. 

Frazier, C. and O’Brian, W.D. (1998). “Synthetic aperture techniques with a virtual source 

element,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 45, pp. 

196–207.

Garcia, G. and Zhang, J. (2006). “Application of ultrasonic phased arrays for rail flaw 

inspection,” Report DOT/FRA/ORD-06, July 2006.

Grady, M., Spera, Z. and Truong, L. (2009). “Case study of cross-hole sonic logging: a nondestructive testing method for determining the integrity of drilled shafts,” Technical Report, 

http://tyu.eng.uml.edu/14.511_2012/doc/Final_T3_GradySperaTruong.pdf

Grewal, D.S. (1996). “Improved ultrasonic testing of railroad rail for transverse discontinuities in 

the rail head using higher order Rayleigh (M21) waves,” Materials Evaluation, 54, pp. 983–986.
102

Hansen, W. and Hintze, H. (2002). “Ultrasonic testing of railway axles with phased array 

technique,” Proceedings of 8th European Conference on Nondestructive Testing, Barcelona, June 

2002.

Haramy, K. and Mekic-Stall, N. (2000a). “Cross-hole sonic logging and tomographic imaging 

surveys to evaluate the integrity of deep foundations - case studies.” Federal Highway 

Administration (FHWA).

Haramy, K. and Mekic-Stall, N. (2000b). “Evaluation of drilled shafts at Piney Creek Bridge 

using Crosshole Sonic Logging data and 3-D tomographic imaging method,” Proceedings of 

Highway Geopgysics – NDE Conference, St. Louis, MO, December 4–7, 2006.

Ho, K.S., Billson, D.R. and Hutchins, D.A. (2007). “Ultrasonic Lamb wave tomography using 

scanned EMATs and wavelet processing,” Nondestructive Testing and Evaluation, 22, pp.19–34.

Jensen, J.A., Ivanov, S.N., Gammelmark, K.L., and Pedersen, M.H. (2006). “Synthetic aperture 

ultrasound imaging,” Ultrasonics, 44, pp. e5–e15.

Johnson, S., Greenlaf, J., Tanaka, M., Rajagopalan, B. and Bahn, R. (1978). “Quantitative 

synthetic aperture reflection imaging with correction for refraction and attenuation. Application 

of seismic techniques in medicine,” Proceedings of San Diego Biomedical Symposium, San 

Diego, CA, 1978.

Kak, A, and Slaney, M. (2001). Principles of Computerized Tomographic Imaging. Society for 

Industrial and Applied Mathematics (SIAM).

Karaman, M., Li, P-C., and O’Donnell, M. (1995). “Synthetic aperture imaging for small scale 

systems,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 42, pp. 

429–442.

Lanza di Scalea, F. (2007). “Ultrasonic testing applications in the railroad industry,” Chapter 15: 

Special Applications of Ultrasonic Testing, in Non-destructive Testing Handbook, 3rd edition, 

P.O. Moore, ed., American Society for Nondestructive Testing.

Leonard, K.R., Malyarenko, E.V. and Hinders, M.K. (2002). “Ultrasonic Lamb wave 

tomography,’’ Inverse Problems, 18, pp. 1795–1808.

Leonard, K.R. and Hinders, M.K. (2003). “Guided wave helical ultrasonic tomography of pipes,”

Journal of the Acoustical Society of America, 114, pp. 767–774.

Leonard, K.R. and Hinders, M.K. (2005). “Multi-mode Lamb wave tomography with arrival 

time sorting,” Journal of the Acoustical Society of America, 117, pp. 2028–2038. 

Lewitt, R.M. (1983). “Reconstruction algorithms: transform methods,” Proceedings IEEE, 71, 

pp. 390–408.
103

Likins, G., Piscsalko, G., Rausche, F. and Hussein, M. (2004a). “Monitoring quality assurance 

for deep foundations,” Proceedings of Conference on Current Practices and Future Trends in 

Deep Foundations (GSP 125), pp. 222–238.

Likins, G., Webster, S. and Saavedra, M. (2004b). “Evaluation of defects and tomography for 

CSL,” http://www.pile.com/reference/stresswave2004/SW2004-046-

Eval_of_Defects_and_Tomography_for_CSL.pdf

Lockwood, G.R., Talman, J.R., and Brunke, S.S. (1998). “Real-time 3-D ultrasound imaging 

using sparse synthetic aperture beamforming,” IEEE Transactions on Ultrasonics, Ferroelectrics 

and Frequency Control, 45, pp. 980–988.

Maitre, H. (2008). Processing of Synthetic Aperture Radar Images. Wiley and Sons, United 

Kingdom.

Malyarenko, E.V. and Hinders, M. K. (2000). ‘‘Fan beam and double crosshole Lamb wave 

tomography for mapping flaws in aging aircraft structures,’’ Journal of the Acoustical Society of 

America, 108, pp. 1631–1639.

Malyarenko, E.V. and Hinders, M. K. (2001). ‘‘Ultrasonic Lamb wave diffraction tomography,’’ 

Ultrasonics, 39, pp. 269–281.

Martinez, O., Parrilla, M., Izquierdo, M.A.G. and Ullate, L.G. (1999). “Application of digital 

signal processing techniques to synthetic aperture focusing technique images,” Sensors and 

Actuators, 76, pp. 448–156.

Martinis, R. (2002). “Nondestructive techniques for decay diagnosis on standing trees (Analisi di 

tecniche non destruttive per la diagnosi di carie su alberi in piedi),” M.S. Thesis, University of 

Florence, Italy.

McKeon, J.C.P. and Hinders, M.K. (1999a). ‘‘Lamb wave contact scanning tomography,’’

Review of Progress in QNDE, D.O. Thompson and D.E. Chimenti, eds., Plenum Press, New 

York, 18, p. 951–960.

McKeon, J.C.P. and Hinders, M.K. (1999b). ‘‘Parallel projection and crosshole Lamb wave 

contact scanning tomography,’’ Journal of the Acoustical Society of America, 106, pp. 2568–

2577.

Mekic-Stall, S. and Grimm, P. (2002). “2D & 3D crosshole sonic logging tomography (CSLT) 

versus crosshole sonic logging (CSL) for drilled shafts,” Proceedings of 2nd Annual Conference 

on Applied Geophysics and NDT Technologies and Methods to Transport Facilities and 

Infrastructure, FHWA-02-001(CD-ROM), Paper #32.

Nahamoo, D., Pan, S. and Kak, A. (1984). “Synthetic aperture diffraction tomography and its 

interpolation-free computer implementation,” IEEE Transactions Sonics and Ultrasonics, SU31, pp. 218–229.
104

Neuenschwander, J., Niemz, P. and Kucera, L.J. (1997). “Studies for visualizing wood defects 

using ultrasonic in reflection and transmission mode,” Holz Roh-Werkst, 55, pp. 339–340.

Nikolov, S. and Jensen, J.A. (2000). “3-D Synthetic aperture imaging using a virtual source 

element in the elevation plane,” Proceedings 2000 IEEE Ultrasonics Symposium, 1743–1747.

Nikolov, S. and Jensen, J.A. (2003). “Investigation of the feasibility of 3-D synthetic aperture 

imaging,” IEEE Ultrasonics Symposium, 1903–1906.

Oralkan, O., Ergun, A., Johnson, J., Karaman, M. and Khuri-Yakub, B. (2002). “Capacitive 

micromachined ultrasonic transducers: next-generation arrays for acoustic imaging?” IEEE 

Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 49, pp. 1596–1610.

Paikowsky, S.G., Chernauskas, L.R., Hart, L.J., Ealy, C.D. and DiMillio, A.F. (2000). 

“Evaluation of a new Cross-hole Sonic Logging system for integrity examination of drilled 

shafts,” Proceedings 6th International Conference Application of Stress-Wave Theory to Piles, 

Niyama & Beim, eds., Rotterdam, pp.223–230.

Pan, S. and Kak, A. (1983). “A computational study of reconstruction algorithms for diffraction 

tomography: interpolation vs. filtered-backpropagation,” IEEE Transactions on Acoustical 

Speech Signal Processing, ASSP-31, pp. 1261–1275.

Prada, J., Fratta, D. and Santamarina, J. C. (2000). “Tomographic detection of low-velocity 

anomalies with limited data sets,” ASTM Geotechnical Testing Journal, 23, pp. 472–486.

Rathore, S., Kishore, N., Munshi, P. and Singhal, S. (2000). “Ultrasonic tomography of closely 

spaced defects,” Proceedings of the 15th World Congress in Nondestructive Testing, Rome. 

Rizzo, P. (2010). “Water and wastewater pipe health monitoring: a review,” Advances in Civil 

Engineering, Article ID 818597, doi:10.1155/2010/818597.

Sandrin, L., Tanter, M., Catheline, S. and Fink, M. (2002). “Shear modulus imaging with 2-D 

transient elastography,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency 

Control, 49, pp. 426–435.

Shoup, T.A. and Hart, J. (1988), “Ultrasonic imaging systems,” Proceedings 1988 IEEE 

Ultrasonics Symposium, 863–871.

Simonetti, F. and Huang, L. (2008). “From beamforming to diffraction tomography,” Journal of 

Applied Physics, 103, pp. 1101–1107. 

Sperry Rail Service. (1989). Rail Defect Manual. Danbury, Connecticut.
105

Tscharntke, D., Heckel, T., Boehm, R., Erhard, A., Krull, R., Lutzner, J. and Hintze, H. (2003).

“Development of ultrasonic railway inspection systems using phased array methods,” Railway 

Engineering International Conference, London, April 30–May 1, 2003.

Utrata, D. (2002), “Exploring enhanced rail flaw detection using ultrasonic phased arrays 

inspection,” Review of Progress in Quantitative Nondestructive Evaluation, Vol. 21, Thompson 

and Chimenti, eds.

Wells, P. (1977). Biomedical Ultrasonics. London, Academic Press.

Wilcox, P., Evans, M., Pavlakovic, B., Alleyne, D., Vine, K., Cawley, P. and Lowe, M. (2003). 

“Guided wave testing of rail,” Insight - NDT and Condition Monitoring, Journal of the British 

Institute of NDT, 45, pp. 413–420. 

Wooh, S-C. and Wang, J. (2002). “Nondestructive characterization of defect using a novel 

hybrid ultrasonic array sensor,” NDT&E International, 35, pp. 155–163. 
106

Abbreviations and Acronyms

BNSF Burlington Northern Santa Fe Railway

FE Finite Element

FEA Finite Element Analysis

RHA Rail Head Area

TD Transverse Defect

L-wave Longitudinal Wave

RCF Rolling Contact Fatigue

RHA Rail Head Area

SAF Synthetic Aperture Focus

SAFT Synthetic Aperture Focus Technique

S-wave Shear Wave