NDTnet - October 1997, Vol.2 No.10
THICKNESS-INDEPENDENT ULTRASONIC IMAGING APPLIED TO CERAMIC
Don J. Roth
Dorothy V. Carney
A single transducer ultrasonic imaging method that eliminates the effect of thickness variation
in the image, and its application to plate and hollow tubular ceramic materials, are described. The
method thus isolates ultrasonic variations due to material microstructure. Its use can result in
significant cost savings, because the ultrasonic image, and consequently assessment of material
and manufacturing quality, can be interpreted correctly without the need for precision thickness
machining during nondestructive evaluation stages of material development. The thickness-independent
ultrasonic imaging method is shown to provide more accurate and quantitative
materials characterization as compared to that for conventional ultrasonic c-scan and apparent
velocity images. The method has been commercialized via a cooperative agreement between
NASA Lewis Research Center and Sonix, Inc.
- RELATED WORK
- SCOPE OF INVESTIGATION
Ultrasonic c-scan imaging is an effective nondestructive evaluation (NDE) technique used for
materials analysis and quality control in the aerospace, electronics, and other industries .
C-scan imaging in its most conventional implementation is used to map variations in ultrasonic
echo peak amplitude that occur when scanning across a material part . In the pulse-echo
c-scan configuration, echoes that are sometimes monitored or "gated" include those reflecting off
the sample front and back surfaces . For currently available commercial scan systems, the
amplitude variations are generally scaled to values between zero and 255 [8-bit dynamic range]
and displayed on video in terms of gray or color scale. In this manner, gray scale variations in the
image are associated with amplitude, or attenuation, variations. An additional implementation of
c-scan imaging involves mapping variations in the time of occurrence of an ultrasonic echo peak
with respect to a reference time. These "time-of-flight" variations are scaled and displayed in a
similar fashion to echo peak amplitude. Both amplitude and time-of-flight variations of a back
surface echo can many times be related to variations in a volumetric microstructural property such
as density which can affect physical material properties such as stiffness and thermal conductivity.
However, a weakness of conventional ultrasonic c-scan imaging regarding both peak amplitude
and time-of-flight modes is that gray scale variations in images for back surface reflections
indicate part thickness variations as well as microstructural variations unless the part is uniformly
By their very nature, both peak amplitude and time-of-flight measurements of back wall
echoes are directly dependent on thickness. Back wall peak amplitude (A) is affected by thickness
(d) according to the expression for pulse-echo attenuation where 
A = A0 exp( -[2d])) (1)
|Figure 1. Effect of thickness on ultrasonic echo peak amplitude for PMR-15 polymide sample.
d = thickness.|
(a) Rectified back wall echo for two thicknesses using 5 MHz broadband trans-
(b) Percent increase in back wall echo peak amplitude versus decrease in thickness.
where A0 is an initial reference amplitude, ais the material attenuation coefficient, and d is the
thickness of the part. In practical application, the severity of the effect of thickness variation on
peak amplitude depends on the frequency of ultrasound used, because the ultrasonic attenuation
coefficient normally increases with increasing frequency. Generally it is desirable to use the
highest frequency of ultrasound possible to maximize resolution of nonuniformity. As an example
of the effect of thickness variations on peak amplitude, fig. 1 shows the effect of thickness on back
wall ultrasonic signal amplitude obtained from PMR-15 polyimide samples for pulse-echo
experiments conducted at NASA Lewis Research Center. Thickness of the samples ranged from
approximately 2.3 to 5 mm. The experiments were conducted using both 5 and 20 MHz broadband
transducers. Results are shown for the time-domain broadband back wall pulse. Figure 1 illustrates
that the back wall echo amplitude increases with decreasing thickness at both frequencies, but
much more significantly so at 20 MHz than at 5 MHz due to the considerably higher attenuation
coefficient () at 20 MHz for PMR-15 material (
PMR-15 at 20 MHz = 2.761 ± 0.2 Neper/cm and
PMR-15 at 5 MHz = 1.184 ± 0.1 Neper/cm as obtained from experiments at NASA Lewis). Thus,
peak amplitude c-scan images, including the effect of thickness variations on them, will be highly
The situation is more straightforward for interpreting the effect of thickness variations on
time-of-flight of ultrasonic pulses off the sample back wall. Back wall pulse-echo time-of-flight
(2t) is affected by thickness variation according to
where V is the velocity of ultrasound in the material. No frequency dependence exists as it does
for attenuation (disregarding dispersion effects of frequency on material velocity (V)). Thickness
effects on time-of-flight can also be interpreted by rearranging eq. (2) to calculate velocity
such that velocity is inversely proportional to time-of-flight. For velocity mapping from scan
results, only one thickness value can be used practically in the velocity map calculation (eq. (3)).
This thickness value is usually an average value obtained from several measurements at different
sample locations. For scan locations where actual thickness is less than the value chosen for the
calculation, time-of-flight will be less, and apparent velocity will be greater, than that if the scan
location had the chosen value of thickness. The situation is opposite for scan locations where
actual thickness is greater than the value chosen for the calculation. Hence, velocity and time-of-flight
maps will be affected similarly (although inversely in terms of magnitude) by thickness
variations, and velocity maps are used in this investigation to indicate time-of-flight variations.
Since the attenuation coefficient () and velocity (V) in a material will not be constant if
microstructural variations are present, eqs. (1) to (3) indicate that maps of peak amplitude, time-of-
flight, and velocity will show a combination of microstructural and thickness variations.
Several attempts to account for thickness variation effects in ultrasonic measurements were
noted in the literature. Reference  used a two-transducer method whereby the transducers,
located on opposite sides of the sample, were used in both pulse-echo and through-transmission
mode to produce thickness-independent peak amplitude c-scans. Accurate thickness at each scan
location was obtained via both transducers using the time-of-flights acquired from pulse-echo
front-surface reflections off both surfaces of the sample, and using the known constant velocity in
water and the known distance between the two transducers. Peak amplitude information was
obtained in through-transmission mode. A peak amplitude c-scan free of thickness effects was then
computed using eq. (1) where A, A0 , d, anda were the thickness-corrected peak amplitude,
measured peak amplitude, measured thickness, and assumed constant material attenuation
coefficient, respectively, at each scan location. Reference  also used a two-transducer method,
but the transducers were employed solely in pulse-echo mode to produce thickness-independent
ultrasonic velocity images. Thickness information was obtained in a similar manner to that
described for ref. . Additionally, time-of-flight from the first reflected pulse off the sample back
surface was obtained by one of the transducers at each scan location. Knowing thickness (d) and
time-of-flight (2t) at each scan location, thickness-independent velocity (V) images were
calculated according to eq. (3).
Figure 2.-Ultrasonic pulse-echo immersion testing. (a) Schematic of ultrasonic pulse-echo
immersion testing. (b) Resulting waveforms.
References [4 to 7] described a single-point ultrasonic velocity measurement method using a
reflector plate located behind and separated from the sample, that does not require prior
knowledge of sample thickness. The latter method, chosen for study in this investigation, was
studied with success in prototypical scanning configurations in refs. [8 to 10], and incorporated
into a commercial scan system in refs.  and . Figure 2 shows a schematic of the immS¡"ion
pulse-echo testing set-up required to use this method and the resulting ultrasonic waveforms. The
mathematical basis for the method is derived in ref.  and results in ultrasonic velocity being
calculated according to
V=c[(dt)/(2t) +1] (4)
where c is water velocity, 2t is the pulse-echo time delay between between a front and back
surface echo or between two successive back surface echoes, and dt is the pulse-echo time
difference between the first echo off the reflector plate front surface with and without the sample
present, respectively. Water velocity (c) is determined from:
c (mm/µsec) = (1410 + 4.21T - 0,037T2)x10-3 (5)
where T is temperature in °C. Water velocity can also be determined by direct measurement using
the time difference of ultrasonic wave travel in water between two transducer heights.
This thickness-independent ultrasonic imaging method does not require prior knowledge of
sample thickness as shown in eq. (4), and, if engineered for scanning, the effect of thickness
variation is eliminated in the resulting image. Precision and accuracy associated with this method
are estimated at nearly 1% as described in ref. . The methods of refs. [2 to 10] all require
access to both sides of the sample, i.e. there is not a single-sided technique available for scanning
that will result in thickness-independence.
SCOPE OF INVESTIGATION
In this investigation, the single-transducer-reflector plate method of refs. [4 to 10] and
fig. 2 is applied to obtain thickness-independent ultrasonic images of monolithic silicon nitride
ceramic plate and hollow tubular materials. Thickness-independent ultrasonic images for these
materials are compared to c-scan peak amplitude images and apparent velocity images (the latter
being obtained using eq. (3)). The single-transducer-reflector plate method was chosen over the
two-transducer methods because of its simplicity and potential applicability to inspection of
hollow tubular samples currently being fabricated for high-temperature structural duty. Some of
these tubes recently inspected at NASA by ultrasonic methods have inner regions too small to
contain a perpendicularly-positioned second transducer but large enough to contain a reflector
The silicon nitride plate material was in the form of a wedge of nominal thickness
3.3 mm and 36 mm length, and it had a 0.3 mm edge-to-edge thickness gradient (lengthwise)
(approximately 10% of total thickness), 3 areas of higher-than-average (HTA) pore fraction
(approximately 3 to 5% HTA as determined from optical analysis) and an edge-to-center pore
fraction gradient of 2 to 3%. The thickness gradient was machined into the wedge. The silicon
nitride tubular material was of nominal wall thickness 7.5 mm, 48 mm outside diameter, and
150 mm height. It was manufactured unintentionally with a 0.8 mm thickness variation
(approximately 10% of total thickness) and currently unknown microstructural variation.
The thickness-independent ultrasonic imaging method requires at least two scans to collect
the necessary echoes required for calculation of time delays (fig. 2). The first of two scans is run
with the sample in place, and echoes B1 (first back surface echo), B2 (second back surface echo),
and M' (first echo off reflector plate front surface with sample present) are collected. Following
this, the sample is removed and a second scan is run to collect M" (first echo off reflector plate
front surface with sample removed). In this investigation, three scans were used to obtain all
echoes as required using the version of this method that is commercially-available . B1and B2
are obtained in scan 1, M' is obtained in scan 2, and M" is obtained in scan 3. A computerized
cross-correlation method was used to calculate precise time delays .
The silicon nitride wedge was ultrasonically scanned with a 20 MHz (nominal center
frequency) broadband unfocused transducer to obtain apparent velocity and thickness-independent
velocity images, and additionally scanned with a 50 MHz broadband spherically-focused
transducer to obtain conventional peak amplitude c-scan images. A machined tungsten reflector
plate was positioned approximately 1 cm beneath the wedge. An 800 MHz analog-to-digital
sampling rate was used during data acquisition. The scan grid was 45 by 90 points with a 0.5 mm
scan increment for the apparent velocity and thickness-independent velocity scans, and 90 by 180
points with a 0.25 mm scan increment for the peak amplitude c-scan images. The scan set-up for
the wedge is approximated by the schematic of fig. 2.
Images were contrast-expanded to better
reveal global material variation by filtering relatively high and/or low data values that occurred in
very low numbers (stray data values). Further experimental details are given in ref. .
The silicon nitride tube was ultrasonically scanned with a 10 Mhz broadband spherically-focused
transducer to obtain preliminary apparent velocity and thickness-independent image
| Figure 3.-Ultrasonic set-up using turntable scan for application to tubes.|
Scan 1: sample
present, collect B1, B2, M'.
(b) Scan 2: sample removed, collect M".
Photographs of the set-up for the tube scan are shown in fig. 3.
A 250 MHz analog-to-digital
sampling rate was used during data acquisition. The tube was scanned using a turntable
assembly upon which the tube was placed. The transducer was positioned perpendicularly to the
tube. The turntable was spun so that one scan line corresponded to a full rotation (360°) of the
tube. Ultrasonic echoes were acquired at 1° increments. After the turntable completed a full
rotation and thus returned to the scan starting position, the transducer was raised in height by
1 mm so that a new 360° line of data could be obtained. The scan proceeded in this manner such
that 105 lines of data encompassing most of the tube height were obtained. The resulting scan grid
was 360 by 105 points. A machined stainless steel reflector plate was suspended from the scanner
bridge and positioned internal to the tube approximately 1 cm from the inside wall. In this manner,
the reflector plate remained stationary throughout the scan. Data filtering for contrast expansion of
tube ultrasonic images was used as before.
Figure 4. Ultrasonic images of silicon nitride wedge having pore fraction variations and
a 300 µm thickness gradient edge-to-edge (lengthwise).|
(a) C-scan peak amplitude
image where back wall echo was gated, 50 MHz.
(b) Apparent velocity image, 20 MHz.
(c) Thickness-independent velocity image, 20 MHz.
| Figure 5. Ultrasonic images of silicon nitride wedge, shown as 3-D renderings. |
(b) Thickness-independent velocity.
Figures 4 and 5 show imaging results for the silicon nitride ceramic wedge with the
0.300 mm (10%) edge-to-edge thickness gradient (lengthwise), 3 areas of higher-than-average
(HTA) pore fraction and an edge-to-center pore fraction gradient. Consider fig. 4. The peak
amplitude c-scan image does not reveal the thickness or microstructural variations. This is likely
due to the fact that the attenuation coefficient at ~50 MHz in silicon nitride (even with some
porosity) is extremely low, such that a system with 8-bit digital dynamic range cannot resolve
them. The apparent velocity image shows an ~10% velocity variation from top-to-bottom edge;
some microstructural variation is evident but is mostly masked by the thickness variation. In this
image, the HTA pore fraction area at the top of the disk is accentuated while the lower HTA pore
fraction area is masked totally by the thickness gradient. In the thickness-independent image, the
lower HTA pore fraction area is revealed, the top HTA area is de-emphasized, and an ~ 4% total
velocity variation is seen. Additionally, the edge-to-center pore fraction gradient is disclosed. The
latter image correctly portrays the microstructural condition in this material. Figure 5 shows
three-dimensional renderings of the apparent velocity and thickness-independent velocity images
which further highlight the differences between the results.
Figure 6. |
"Unwrapped" ultrasonic Images of silicon
(a) Apparent velocity
Figures 6 and 7 show preliminary imaging results for the silicon nitride tube of nominal wall
thickness 7.5 mm and 150 mm height having a 0.8 mm (10%) thickness variation and currently
unknown microstructural variation. Apparent velocity and thickness-independent velocity results
are shown in flat, unwrapped form (fig. 6) and decaled onto a cylindrical / tubular model (fig. 7).
Both views can be useful depending on the scan results. For these results, the tubular views (fig. 7)
prove more useful since major image indications appear 180° apart (rotationally about the vertical
axis) from each other, and one of the features is interrupted by the image end in the unwrapped
view of the apparent velocity image of fig. 6(a). A funnel-like feature containing concentric open
contours showing decreasing velocity from tube bottom-to-top is indicated in the apparent velocity
image decal of fig. 7(a). This feature disappears for the most part in the thickness-independent
image of fig. 7(b), indicating it was primarily due to thickness variation. Consider an orientation
for the tube rotated 180° (about the vertical axis) from the views shown in figs. 7(a) and (b). For
this orientation, the images of which are shown in figs. 7(c) and (d), an oval-like feature is
indicated in the apparent velocity image decal image of fig. 7(c).
The oval-like feature contains
concentric contours indicating different apparent velocity regions, but overall the feature shows
higher-than-average apparent velocity as compared to the surrounding region. In the thickness-independent
image of fig. 7(d), the overall oval-like feature remains, although the internal details
have changed as compared to its portrayal in the apparent velocity image. The results of figs. 7(c)
and (d) indicate that the features associated with the oval-like area may be the result of a com-bination
of microstructural (possibly density/pore fraction) and thickness variation. Destructive
testing with optical analysis is required to confirm these results. These preliminary results for the
silicon nitride tube indicate the increased degree of inspection accuracy that the thickness-independent
ultrasonic imaging method can provide for tube-type structures.
Figure 7. Ultrasonic images of silicon nitride tube with ultrasonic info "decaled" onto
| (a) Apparent velocity, initial orientation. ||(c) Apparent velocity, rotated 180° with respect to
| (b) Thickness-independent
velocity image, initial orientation.|| (d) Thickness-independent velocity image, rotated 180° with respect
to initial orientation.
This article described a single-transducer ultrasonic imaging method based on measurement
of ultrasonic velocity that eliminates the effect of thickness variation in the image. The method
thus isolates ultrasonic variations due to material microstructure. Results were shown for silicon
nitride ceramic plate and tubular materials. It was found that the peak amplitude c-scan image
(gating the back wall echo) for the silicon nitride wedge was not visibly affected by the 300 µm
(10%) thickness variation. Additionally, however, the peak amplitude c-scan did not reveal the
microstructural variation in the wedge either. Apparent velocity images indicating time-of-flight
variations showed significant superposition of thickness effects which masked the true picture of
material microstructure for the silicon nitride wedge. For the wedge, the thickness-independent
ultrasonic imaging method accurately quantified (in terms of velocity variation) the pore-fraction
variations. For the tube, two major indications were revealed in the apparent velocity image
results. Preliminary thickness-independent ultrasonic image results showed that one of these
indications was due to thickness variation and that the other was likely a combination of micro-structural
and thickness variation. Further characterization needs to be performed on the tube
sample to confirm these results. The use of the thickness-independent ultrasonic imaging method
can result in significant cost savings, because the ultrasonic image, and consequently assessment
of material and manufacturing quality, can be interpreted correctly without the need for machining
to achieve precise thickness uniformity during nondestructive evaluation stages of material
Nondestructive Testing Handbook, second edition, Volume 7 Ultrasonic Testing, eds.
A.S. Birks, R.E. Green, and P. McIntire, American Society For Nondestructive Testing, 227-230,
387-390, 405, 225, (1991).
- M. Bashyam, Thickness Compensation and Dynamic Range Improvement For
Ultrasonic Imaging of Composite Materials. Proc. Of the 17th Annual Review of Progress in
Quantitative Nondestructive Evaluation, La Jolla, CA, 10A. Plenum Press, 1991,1035-1042,
July 15-20, 1990.
- J.J. Gruber, J.M. Smith, and R.H. Brockelman, Ultrasonic Velocity C-scans for Ceramic
and Composite Material Characterization. Mater. Eval., 46, , 90-96 (1988).
- B.D. Sollish, Ultrasonic Velocity and Thickness Gage, United States Pat. No. 4,056,970,
Nov. 8, 1977.
- L. Pichè, Ultrasonic Velocity Measurement for the Determination of Density in
Polyethylene. Polymer Engineering and Science, 24, , 1354-1358, Mid-Dec. 1984.
- I.Y. Kuo, B. Hete, and K.K. Shung, A novel method for the measurement of acoustic
speed. J. Acoust. Soc. Am. 88, , 1679-1682, Oct. 1992.
- D.K. Hsu and M.S. Hughes, Simultaneous Ultrasonic Velocity and Sample Thickness
Measurement and Application in Composites. J. Acoust. Soc. Am. 92, , Pt. 1, 669-675, Aug.
- V. Dayal, An Automated Simultaneous Measurement of Thickness and Wave Velocity
by Ultrasound, Experimental Mechanics, 32, , 197-202, Sept. 1992.
- M.S. Hughes and D.K. Hsu, An Automated Algorithm for Simultaneously Producing
Velocity and Thickness Images, Ultrasonics, 32 , 31-37, 1994.
- D.J. Roth, Single Transducer Ultrasonic Imaging Method That Eliminates the Effect of
Plate Thickness Variation in the Image. NASA TM-107184, 1996.
- D.J. Roth, et. al., Commercial Implementation of Ultrasonic Velocity Imaging Methods
via Cooperative Agreement Between NASA Lewis Research Center and Sonix, Inc. NASA
- D.R. Hull, H.E. Kautz, and A. Vary, Measurement of Ultrasonic Velocity Using Phase-Slope
and Cross-Correlation Methods. Mater. Eval., 43, , 1455-1460, 1985.
Don J. Roth
|Top to this page|
Dorothy V. Carney
NASA Lewis Research Center
21000 Brookpark Rd.
Cleveland, Ohio 44135
For more information see: Focus on Thickness Measurement in UTonline 10/97
© Copyright 1. Oct 1997 Rolf Diederichs,
/DB:Article /AU:Roth_J_D /AU:Carney_D_V /IN:NASA /CN:US /CT:UT /CT:thickness /CT:ceramic /ED:1997-10