NDT.net • May 2006 • Vol. 11 No.5

Quantification of Ultrasonic Beams Using Photoelastic Visualisation

Edward Ginzel
Materials Research Institute, Waterloo, Ontario, Canada
Zheng Zhenshun
Lee Pipe and Tubing Inc., Beijing, PR China


This paper describes methods used to quantify aspects of ultrasonic beams using photoelastic images of pulses in transparent media. Position and intensity of light pulse images are used to provide an alternative to the pulse-echo and through transmission signal analysis typically used with A-scan displays for industrial ultrasonics.


In the early 1970s the photoelastic technique for viewing ultrasonic pulses was made popular in published papers by Hanstead, Wyatt, Hall and Sachse. [1, 2, 3, 4, 5]. According to Sachse, earliest examples of the technique date back to the 1930s [6]. All images appearing in these early publications were black and white photos. Some utilised long time-exposures to improve detection of the faint aspects of weaker intensities and others took advantage of multiple exposures on the same frame to illustrate the evolution of the wave field progressing through the medium of transmission.

Sadly, by the end of the 1970s not much work was being done using the photoelastic technique. Hall made a few other investigations on his specific applications in railways [7] but little else followed for nearly 2 decades. Parallel visualisation development using acousto-optic methods was examined in the 1990s [9]. In 2003 a video was published in an on-line paper [8]. This provided a colour moving image. In addition to the fact that the 2003 publication was a video, a significant difference between the colour video and the previous published images was the fact that the 2003 images were digital. In his 1973 presentation, Wyatt [3] indicated that quantification of relative stresses could be accomplished using the Senarmont method which uses rotation of the analyser to produce extinction at the point of interest. This was carried out in the 1980s [11, 12] and provides an assessment of local stress levels in glass. Zhang's paper noted a linear relationship between stress and applied voltage to the piezo element when plotted but it is a relatively cumbersome process when assessing an entire wavefront. Sachse [5] also suggested quantification could be accomplished but suggested digitisation of the photo images. There seemed to be no follow-up on proposed digitisation of the photoelastic images in the 1970s. This paper examines some of the methods that are now possible using the features of digital processing of photoelastic images.


The spark-gap system used for this project is designed after Wyatt [10] and image capture effected by a Panasonic AG-DVC30P 3CCD camera. An IEEE 1394 "firewire" allowed for direct image capture to a video card in bmp format. The setup is shown in Figure 1.

Fig 1: System Setup (with camera to computer)
1. Delay circuit, 2. Sweep generator (timing clock), 3. Spark-gap light source, 4. Polariser, 5. Collimating lens, 6. Glass sample, 7. quarter-wave plate, 8. Analyser, 9. Camera, 10. Probe, 11, Computer, 12. Computer monitor (Ascan and image capture), 13. Television monitor

The pulser used was an Adaptronics PR100. This allowed maximising performance by means of a tuneable square-wave that could be used in uni-polar or bi-polar mode. It was selectable for voltage (up to 375 Volts) and duration (generally tuned to the natural frequency of the probe). Up to 7 cycles of the square wave could be selected; however, only 1 or 2 cycles were used to avoid interfering ringing-on of the signals in the images.

In order to allow a fine adjustment of delay difference between firing the pulser and the time at which the illumination spark was fired, a delay circuit was designed. The delay time was monitored using a Tektronix 100MHz oscilloscope. This could also be used as a means of delta-delay for velocity determinations.

A selection of probes of different dimensions and frequencies was selected that would allow the imaging of the pulses to about two or three near zone distances in the imaging medium, clear fused-silica glass. These are tabulated in Table 1. Imaging pulses in water would require long soundpaths, e.g. for a 12.5mm diameter 5MHz probe the near zone point for the beam would be about 132mm but the same probe would only require 54mm and 33mm for the transverse and compression modes respectively. Silica glass is the preferred imaging medium. It has acoustic velocities similar to that of steel. For the silica glass samples used, VL = 5970m/s and the VS=3770m/s as determined by pulse-echo analyses. The glass samples were annealed and most imaging was done on samples with sufficient size to avoid edge effects. All samples were 25mm thick.

Table 1 Probes analysed
Size Frequency Near Zone Distance*
6mm diameter 5MHz 7.3mm
9mm diameter 5MHz 16.7mm
10mm diameter 5MHz 21.6mm
12.5mm diameter 5MHz 32.4mm
20mm diameter 2.5MHz 41.3mm
*Near zone determined for compression mode in silica glass

Custom software was provided by Eclipse Scientific Products that allowed the images to be imported for intensity assessment using cursors scaled to allow measurement of distance and angles directly off the images.

Ultrasonic Image Quantification

Images were collected at a variety of locations along their soundpaths. The following parameters were assessed for quantitative measure:
  • Velocities for compression, SV shear and Rayleigh modes
  • Wavelengths compared to nominal at maximum natural frequency determined by tuning
  • -6dB spot size
  • Refracted angles for angled beams
  • Divergence angles

    Images and Quantification Techniques

    Image intensity assessment measures the relative brightness of the pulses as detected by the CCD camera. Zhang's work [12] verified that the degree of rotation of the linearly polarized light from the extinction position is proportional to the local pressure. Therefore, more local sound pressure results in increased light passing through the analyzer to the CCD camera when the polariser and analyser are cross-polarised. Uniformity of the surrounding background from one exposure to the next is generally similar but small variations exist due to spark jitter and the exposure averaging parameters used in the camera.

    For quantitative measurements the Image Intensity Analysis software requires some input in order that the angles and distances of pixels be related to real units. Figure 2 illustrates a multiple exposure image of a 10mm diameter 5MHz probe with exposures at 10mm, 20mm, 30mm and 40mm from the entry surface. The reference cursors are placed on a known dimension and orientation. This allows the measurement cursors to be scaled to indicate actual distance and angle on the image. On the image to the left in Figure 2, the reference cursor is placed horizontal with the tips at the edges of the probe and the measurement cursor is vertical and passes through the peak amplitudes of the pulses.

    Fig 2: 4 exposure image, 10mm diameter 5MHz 0° probe

    Processing as a rendered spectral image (Figure 1 right) provides a qualitative perspective on the relative amplitudes using both colour and extrusion to represent amplitude.
    The measurement portion of the software plots the relative image intensity at each point along the measurement cursor and provides a co-ordinate system that presents the scaled distance as the abscissa and the intensity as the ordinate. The intensity plot for the series of pulses in Figure 2 is shown in Figure 3.

    Fig 3: Intensity plot of image in Figure 2

    Vertical cursors on the intensity plot allow distance determination and the horizontal cursors are used for relative intensity measurements. The lower horizontal cursor is placed at the base level. This is somewhat empirical as there is a slight variation to the background. In this image the background level is very low (dark) but in some imaging it is possible achieve a higher background and identify the positive and negative phase components of the pulses. The upper cursor is placed at the peak amplitude point and the middle horizontal cursor is then used to assess the dB equivalent difference between any point on the plot relative to the peak value. The dB assessment cursor in the image is placed at a point 3dB down from the peak amplitude which, in the through transmission mode we are effectively examining, is equivalent to the 6dB drop in the pulse-echo mode.

    The calculated near zone distance for a 10mm diameter 5MHz probe transmitting a compression mode into a solid with velocity of 5970m/s is 20.6mm. The intensity plot can be seen to indicate a peak essentially at the calculated near zone. Similarly, beam width dimensions are made placing the measurement in the image parallel to the beam as illustrated in Figure 4.

    Fig 4: Assessment of beam width

    Except for velocity, all assessments used the intensity plots to determine the quantitative values for the beams analysed in this paper.

    Velocity Assessments

    Velocity is easily assessed by measuring the time delay required to move a specific point on the wavefront a measured distance. Figure 5 shows a compression wave and a steel rule. Time delay observed to move a specific point on the wavefront over a known distance provides velocity by dividing the distance moved by the delay time.

    V= d/t

    Fig 5: Displacement of pulse-position for velocity determination

    Results of the visually observed velocities compare well with the electronic version whereby the pulse-echo signals are observed on an A-scan presentation and the time interval between echoes is used. Typically the two methods are within 30m/s of each other.

    Velocities for the silica glass used in these experiments are tabulated in Table 2.

    Table 2 Acoustic Velocities for Silica Glass
    Mode Compression SV shear Rayleigh
    Photoelastic 6000m/s 3780m/s 3330m/s
    Electronic (pulse-echo) 5970m/s 3770m/s 3360m/s

    Wavelength Assessments

    Wavelength was assessed using the reflected shear and mode converted compression mode echoes that result when the plane wave reflects off the cylindrical hole as seen in Figure 6. Results for two of the probes used are tabulated in Table 3.

    Fig 6: Two modes after reflecting a 5MHz pulse

    Table 3 Wavelengths determined from intensity plots
    Frequency (MHz) Compression Shear
    Calculated Measured Calculated Measured
    2.25 2.65mm 2.5mm 1.68mm 1.6mm
    5.0 1.19mm 1.0mm 0.75mm 0.7mm

    Figure 7 is a collage of 5 images. The 5MHz 6mm diameter probe was mounted on a 60° refracting wedge and the pulse amplitude optimised by tuning the pulser to a bi-polar pulse with a frequency of 4.88MHz. The pulser was then tuned off the optimum frequency to 3.88MHz and 2.88MHz, then 5.88MHz and 6.88MHz with images captured at the same point in the glass for each image. The amplitude can be seen to drop off by the image intensity reducing and the wavelength increases and decreases as the tuning is adjusted.

    Fig 7: Effect of tuned frequency pulsing (2.88MHz to 6.88MHz in 1MHz increments from top to bottom).

    Wavelength changes with changing pulse width are as follows in Table 4:

    Table 4 Wavelengths varied with tuning of the pulse
    Pulse Tuning Frequency
    Wavelength (Shear)
    2.88 1.27
    3.88 0.96
    4.88 0.79
    5.88 0.71
    6.88 0.68

    Note that the probe used for this test was not the same as that used to demonstrate wavelength measurements in Figure 6 so the 0.7mm wavelength in Table 3 is not exactly the same as the 0.79mm indicated at peak response in Table 4.

    Spot Size Assessments

    Spot size is a term used to indicate the dimension of the isobar of a pulse measured perpendicular to the axis of travel. For an unfocused probe the point of usual interest is the near zone. At this point the pressure on axis is a maximum and the dimensions are calculated based solely by the element size. For a circular element the formula given to approximate the 6dB isobar diameter is S=0.26D. Here "D" is the element diameter. Other solutions exist for the spot size of a focused probe and these too are mostly concerned with the dimension of the isobar at the focal spot (i.e. the point along the beam axis where the maximum pressure exists).

    For this portion of the assessments, only zero degree (compression mode) was used. Spot sizes were determined using traditional pulse-echo techniques with an A-scan response from a 1.5mm diameter side drilled hole being peaked and then measuring the total probe displacement to drop the echo to half amplitude. These were recorded as Mechanical Measured in Table 5. Photoelastic assessment was made by positioning the pulse image at the calculated near field distance.

    Table 5 Spot sizes of zero degree compression beams
    Probe Diameter Spot Size
    Calculated Mechanical
    6mm 1.6mm 3.5mm 3.1mm
    9mm 2.4mm 6.5mm 7.3mm
    10mm 2.7mm 5.5mm 5.9mm
    12.5mm 3.4mm 8.5mm 8.3mm
    20mm 5.4mm 14mm 11.2mm

    Note in all cases, the mechanical and photoelastic assessments are
    similar and these are both on the order of twice the theoretical value.

    Divergence Angle Assessments

    For the zero degree compression mode, assessment of the divergence angle was a relatively simple measurement. Using the software, one end of the measurement cursor was positioned at the midpoint of the probe at the contact point to the glass and the other end of the cursor swung from the peak amplitude to the 3dB drop points either side. Ideally the angle of divergence applies to all points along the beam having the same amplitude drop once the Far Zone is reached. But this assumption only applies for the theoretical circular piston generator having a single frequency. Table 6 illustrates that for real probes the ideal condition is reached only after some distance greater than the Near Zone.

    Table 6 Divergence angles of zero degree compression beams
    10mm Dia. 5MHz
    Calculated Half Angle of Divergence
    Soundpath Left Displacement Right Displacement Theory
    30mm 5.5° 6.7° 4.7°
    40mm 5.1° 5.0° 4.7°
    50mm 5.2° 4.7°
    9mm Dia. 5MHz
    Calculated Half Angle of Divergence
    Soundpath Left Displacement Right Displacement Theory
    16mm 9.3 10 5.3°
    32mm 4.6° 4.5° 5.3°
    43mm 4.2° 3.8° 5.3°
    6mm Dia. 5MHz
    Calculated Half Angle of Divergence
    Soundpath Left Displacement Right Displacement Theory
    7mm 16° 18°
    14mm 8.6° 7.5°
    21mm 7.2° 7.7°
    20mm Dia. 2.3MHz
    Calculated Half Angle of Divergence
    Soundpath Left Displacement Right Displacement Theory
    37mm 12.6° 12° 5.3°
    50mm 9.0° 8.0° 5.3°
    60mm 5.7° 5.4° 5.3°

    As with mechanical assessments, photoelastic assessment of divergence indicates that there is a slight asymmetry to response. Deviation of assessed half angle of divergence from the ideal is typically 0.5° to about 1°.

    Refracted Angle Assessments

    Traditionally all main assessments of beam characteristics for angled beams using manual techniques rely on indirect or extrapolated methods. The refracted angle itself is determined by first obtaining a nominal exist point of the beam from the refracting wedge. This is done by obtaining a peaked signal from a radius (as on the IIW block). This point is aligned with an angle scribed on the side of a block with the beam directed at a side drilled hole.

    Manual determination of beam profile is even more indirect. A series of side drilled holes is used and the maximised response from these holes is then made to drop to a predefined level (e.g. 6dB down from the peak). But in order for this to be effective a distance amplitude correction for the centre of beam need be made prior to the assessment. This is required since the hole is at a single depth. Moving the probe backwards to assess the front edge of the beam moves the hole to a greater sound path than the centre of beam and conversely moving probe forward moves the beam to a shorter sound path to the same side drilled hole.

    A typical plotting of hole positions using the IOW (Institute of Welding) block results in a series of points at specific depths with front of beam and back of beam displacements. This might appear as plotted in Figure 8. Beam spread is approximated by a trendline through the front and back of beam positions. Beam dimension at any specific sound path must be estimated using the distance measured perpendicular to the beam axis.

    Fig 8: Typical side drilled hole plot for beam profile using IOW block.

    Multiple exposures of a 5MHz 6mm diameter probe were made using a refracting wedge intended to produce 60° in steel. When used on the fused silica glass the calculated refracted angle would be about 81°. The measured angle using several of the peak intensities is 80°. This is illustrated in Figure 9.

    Fig 9: Beam divergence of angle beam shear mode

    Summary Comments and Conclusions

    Use of photoelastic visualisation to make basic quantitative assessments of beam characteristics has been demonstrated. Common parameters such as velocity, beam dimension and refracted angles have been demonstrated. Wavelength of the bulk wave has been determined and the effect on wavelength by tuning off the natural frequency has been demonstrated. These values are typically evaluated using other methods in NDT. For some, such as the dominant frequency, acoustic velocity and refracted angle the "traditional methods" may be more convenient. However, beam profiling and determining the spot size is highly dependent on the target used. This becomes more empirical for angled beams where the beam size perpendicular to the centre axis is an indirect assessment made by geometric calculations. Here visualisation techniques provide a more reliable method of assessment.

    Assessments were made using fused silica glass. When comparing results to what might be occurring in steel this is a suitable approximation for compression mode. However, the shear mode velocity is substantially higher in fused silica than in steel. Instead of developing conversion methods, future work will look at using a glass that has a shear mode velocity closer to that in average steels.


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