S

NASA Technical Memorandum 107184

Single Transducer Ultrasonic Imaging Method

That Eliminates the Effect of Plate

Thickness Variation in the Image

Don J. Roth

Lewis Research Center

Cleveland, Ohio

July 1996

National Aeronautics and

Space Administration
Trade names or manufaconers' names are used in this report for identification

only. This usage does not ccmlitute an official endozsement, eilher expressed

or implied, by the National Aeronautics and Space Administration.
SINGLE TRANSDUCER ULTRASONIC IMAGING METHOD THAT ELIMINATES THE EFFECT OF PLATE

THICKNESS VARIATION IN THE IMAGE

Don J. Roth

National Aeronautics and Space Adminstration

Lewis Research Center

Cleveland, Ohio 44135

ABSTRACT

This article describes a single transducer ultrasonic imaging method based on ultrasonic velocity

measurement that eliminates the effect of plate thickness variation in the image, i.e. the method is thicknessindependent. The method, currently being commercialized under a cooperative agreement between NASA Lewis

Research Center and Sonix, Inc., thus isolates ultrasonic variations due to material microstructure. Its use can result

in significant cost savings because the ultrasonic image can be interpreted correctly without the need for precision

thickness machining during nondestructive evaluation stages of material development. Images obtained using the

thickness-independent methodology are compared with apparent velocity maps and c-scan echo peak amplitude

images for monolithic ceramic (silicon nitride), metal matrix composite and polymer matrix composite materials

having thickness and microstructural variations. It was found that the thickness-independent ultrasonic images reveal

and quantify correctly areas of global microstructural (pore and fiber volume fraction) variation due to the

elimination of thickness effects.

ACKNOWLEDGMENTS

The author wishes to thank Dr. James K. Sutter from NASA Lewis Research Center, Dr. Kamal Amin of

3M Co., and Mr. James R. Bodis of Cleveland State University for their help in providing samples and general

assistance during this investigation.
INTRODUCTION

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 (Ref. l ). 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 (Ref. 1). In the pulse-echo c-scan configuration, echoes that are sometimes monitored or

"gated" include those reflecting off the sample front and back surfaces (Ref. 1). 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 are many times 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 thick.

BACKGROUND

By their very nature, both peak amplitude and time-of-flight measurements are directly dependent on

thickness. Peak amplitude (A) is affected by thickness according to the expression for pulse-echo attenuation where

(Ref. 1):

A = Ao exp(-ot[2dl) (1)

where A o is an initial reference amplitude, o_is 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 signals obtained from PMR-15 polyimide samples for pulse-echo experiments
0.50 --

(a)

0.40

O

> 0.30 --

6

"O

0.20 --

0.10 --

0.0

0.0

• d=2.382mm

d = 3.510 mm

=o m

0.2 0.4 0.6 0.8 1.0

Relative time position, Imec

60

50

O4

O

¢¢ 40

O

> 30

L.

o 20

o.

(d)

0

8.14

' d = 2.382 mm

d = 3.510 mm

= 5.004 mm

I .!

8.24 8.34 8.44 8.54 8.64

Frequency, MHz

600

500

,0o

300

200

O

100

-- d = 2.382 mm

(b)

- /['_, d = 3.510 mm

l,"'t

_/_ d = 5.004 mm

0 5 10 15 20 25

Frequency, MHz

O

-_ 300

-_ 200

e,J.--

e- 10o

o

O

c-

_ 0

(e) 20 MHz []

s"

Broadband,.-"

e S

s S

e S

s

r-f

rn.... 43 ..... _

," 5 MHz

s'

,' Broadband

0 500 1000 1500 2000 2500 3000

Decrease in thickness, gm

0.20 _c) ,lOO = 015 • d--2.382mm _ 1600t_

-_ ," _ 1400 l-- 20 MHz ,'"'"

_ 12oot- ."

0.10 I,/lld = 3.510 mm _ ._ 1000 _-- ,"

•_, _ 800_- .O"

_0.05 d = 5.004 mm _ E 600 _-- ...o'""

400 _ ,D-"

•_ 2ooI-"'" 5_.z

o.oo (c) " '_V-. ="=" o _,_4_ [ --'t° I

0.0 0.1 0.2 0.3 0.4 0.5 0 500 1000 1500 2000 2500 3000

Relative time position, imec Decrease in thickness, lim

Figure 1 .--Effect of thickness on ultrasonic echo peak amplitude for PMR-15 polymide sample, d = thickness.

(a) Rectified back wall echo for three thicknesses using 5 MHz broadband transducer. (b) Fourier power spectra of back wall echo for three thicknesses using 5 MHz broadband transducer. (c) Rectified back wall echo

for three thicknesses using 20 MHz broadband transducer. (d) Fourier power spectra of back wall echo for

three thicknesses using 20 MHz broadband transducer. (e) Percent increase in back wall echo peak amplitude

versus decrease in thickness. (f) Percent increase in power spectra magnitude versus decrease in thickness.
conducted at NASA Lewis Research Center. Thickness of the samples ranged from -2.3 to 5 mm. The experiments

were conducted using both 5 and 20 MHz broadband transducers. Results are shown for both the time-domain

broadband back wall pulse (Figs. l(a), (c) and (e)) and the frequency-domain power spectra of the pulse (Figs. l(b),

(d) and (f)). 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 (O_PMR_15 at 20 MHz = 2.761 __0.2 Neper/cm and _PMR-15 at 5 MHz =

1.184 __0.1 Nepeffcm as obtained from experiments at Lewis). These results indicate that results of peak amplitude

c-scans including the effect of thickness variations will be highly frequency-dependent.

The situation is more straight forward 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 (2x) is affected by thickness variation

according to:

2x- (2d) (2)

V

where V is the velocity of ultrasound in the material. No frequency dependence exists as 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 according to:

(3)

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 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 by thickness

variations, and velocity maps are used in this investigation to indicate time-of-flight variations.

Since the attenuation coefficient (ct) 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.
PRIOR ART

Several attempts to account for thickness variation effects in ultrasonic images were noted in the literature

(Refs. 2 and 3). Reference 2 used a two-transducer method whereby the transducers were used in both pulse-echo

and through-transmission mode to monitor thickness via time-of-flight information and track echo peak amplitude.

Knowing the thickness at each scan location, the material attenuation coefficient, and the assumption that the

attenuation coefficient is constant throughout the part, a c-scan image can be produced free of thickness effects.

Ref. 3 used an ultrasonic velocity imaging method combined with error analysis methodology to define the percent

velocity variation due to each of thickness and microstructural variation in a velocity image. This allowed one to

conclude whether the percent variation seen in the velocity image was due to thickness variation, microstructural

variation, or a combination of the two. However, this methodology allowed only a global generalization and the

image itself could not be changed to eliminate thickness effects. Several references showed single point (nonimaging) ultrasonic measurement methodology that accounted for thickness variation effects (Refs. 4 and 6). The

method of Ref. 4 simultaneously determined ultrasonic velocity, plate thickness and wedge angle and conceivably

could be extended to imaging. However, it is most applicable to samples having "regular" thickness variation such as

for a wedge shape. References 5 and 6 described a single point ultrasonic velocity measurement method using a

reflector plate located behind the sample that does not require prior knowledge of sample thickness and lends itself

to multiple measurements within a sample of nonuniform thickness.

SCOPE OF INVESTIGATION

In this investigation, the methods of Refs. 5 and 6 are engineered to perform automated imaging so that the

resultant velocity image is free of thickness variation effects, i.e. is thickness-independent. Results are shown as

obtained from a lab-based prototype system and a commercial c-scan system in which the method of this article was

implemented under a NASA - industry (Sonix, Inc., 8700 Morrissette Drive, Springfield, VA 22152) cooperative

agreement (Ref. 7). Scans are performed on silicon nitride ceramic, metal matrix composite, and polymer matrix

composite materials containing microstructural and thickness variations. Thickness-independent ultrasonic images

for these materials are compared to c-scan peak amplitude images and conventional (apparent) velocity images

obtained using Eq. (3).
THICKNESS-INDEPENDENT VELOCITYIMAGINGMETHODOLOGY

A pulse-echo ultrasonic velocity measurement is generally made with a transducer either contacting the

sample (contact mode) or separated by a liquid coupling path (immersion mode). Figure 2 shows a schematic of

immersion pulse-echo testing and resulting waveforms with a reflector plate positioned underneath, and separated

from, the sample. Conventional velocity (V) values as obtained from Eq. (3) are calculated using the time delay (2x)

between the first front surface and first back surface echo, or between 2 successive back surface echoes, according to

Eq. (3).

The pulse-echo immersion method described by Refs. 5 and 6 for measuring velocity in a material sample

uses echoes off of the reflector plate as well as front and/or back surface echoes. The following steps show how

velocity (V) in a sample of thickness (d) is determined without needing prior knowledge of thickness. Notation

consistent with that of Ref. 6 is used. With the sample present between the transducer and the reflector plate (Fig. 2),

the pulse that travels from the transducer through the sample to the reflector plate and back to the transducer is

labeled Ill and will be observed at time t' where:

t' = (2t I + 2_ + 2t 2) (4)

where 2t 1, 2x, and 2t2 are the pulse-echo time delays of the ultrasonic pulse from the transducer face to the sample

front surface, from the sample front surface to the sample back surface, and from the sample back surface to the

reflector plate front surface, respectively (Fig. 2(b)). With the sample removed, the pulse that travels from the

transducer to the reflector plate and back to the transducer is labeled M" and will be observed at time t" where:

t"=(2tl + 2 d+ 2t2] (5)

where c is the temperature-dependent velocity of sound in water. (In this case with the sample removed, 2t 2 is the

pulse-echo time delay of the ultrasonic pulse from a point equivalent to the sample back surface to the reflector plate

front surface and is equal to 2t 2 noted originally.) Subtracting Eq. (4) from Eq. (5) gives:

t" - t' = At = 2 d _ 2_ (6)

C
Ultrasonic transducer

Water

L Ultrasonic

beam

(a)

(9

d

L'

v

Sample

Lucite

support

Reflector plate

(b)

Initial transducer pulse M"

FS B B2 ,,

! I

M' i I

I

i

, ',, ,,,

I ! ! i / L_

w y i! _

0

Time delay: I_ 2tl

Time

, _ 27 _ I _.. 2t2 _ i_l_l_lAt

'! i/

I

i

i'

I i

corresponding _

i

i

i '1

to echo y y

traveling

distance: 2L 2d 2L'

Figure 2.--Ultrasonic pulse-echo immersion testing. (a) Schematic of ultrasonic pulse-echo immersion

testing. (b) Resulting waveforms.

u 1.488

::L

"_ 1.484

E

-_ 1.480

0

> 1.476

19

I I I I

20 21 22 23

Temperature, °C

I [ I [ I I I I

67 68 69 70 71 72 73

Temperature, °F

Figure 3.mVelocity of water versus temperature from ref. 1. C = (1410 + 4.21T - 0.037T 2) xlO-3 where C = water

velocity (mm/l_sec) and T= water temperature (°C).
The thickness (d) of the sample can be determined from:

d = "cV (7)

Substituting Eq. (7) into Eq. (6) gives:

Rearranging Eq. (8) gives:

(8)

V =c( At 2x + l)\ (9)

As for conventional velocity measurements, 2z is experimentally obtained from the pulse-echo time delay

between the first front surface (FS) and first back surface (B 1) echoes, or between 2 successive back surface echoes

(such as B 1 and B2 [Fig. 2]). At 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) can be determined in the pulse-echo

configuration by recording the times (twi) where ultrasonic echo peaks occur for 2 height (Zi) positions of the

transducer and calculating:

c- 2(Z1 - z2) - 2(z_,) (10)

twl - tw2 At w

Alternately, water velocity (c) can be calculated from (Ref. 1):

c(mm#t sec) = (1410 + 4.21T - 0.037T 2) x 10-3 (1 l)

where T is temperature in °C. Figure 3 shows a plot of water velocity (c) versus temperature.

As seen from Eq. (9), sample thickness (d) is not a variable in the equation. Thus, this method does not

require prior knowledge of sample thickness and if extended to multiple measurements across the sample (imaging),

sample thickness variation effects are eliminated in the image.
ERRORINTHICKNESS-INDEPENDENT VELOCITYMEASURE

The precision (uncertainty) in the thickness-independent velocity (c_v) due to the random errors in the

measurements of the variables At, 2x, Atwi, and AZ was obtained by use of Eqs. (9) and (10) and the variance relation

(Ref. 8) to give:

(12)

where o_, O2_, (_Atwi and o_z are the uncertainties in measuring: the time difference between the first echo off the

reflector plate front surface with and without the sample present, the time delay between the first front surface (FS)

and first back surface (B 1) echoes (or between 2 successive back surface echoes), the time difference between the

two ultrasonic echo peaks that occur at two height positions of the transducer, and the positional difference between

two height positions of the transducer, respectively. Percent uncertainty in the thickness-independent velocity is

given by

Using typical values of At = 3 _tsec, 2"_= 0.5 I,tsec, Atwi = 6.8 lasec and AZ = 0.25 cm, Fig. 4(a) shows percent

uncertainty in the thickness-independent velocity (U v) as a function of uncertainties in measuring echo time

difference (oAt = o2x = oatwi) and transducer positional difference (oaz). Noting that the uncertainty in measuring

echo time difference can be expressed in terms of the experimental analog-to-digital sampling rate (SR) according to:

(_AI ----t_A2"c = (_Atwi =

(14)

Fig. 4(b) shows percent uncertainty in the thickness-independent velocity (U v) as a function of sampling rate (SR)

and uncertainty in measuring transducer positional difference (t_Az). It can be seen from Fig. 4 that the U v is less

than 1 percent for reasonable sampling rates (>100 MHz) and reasonable uncertainty in measuring echo time

(<0.005 _tsec) and transducer positional differences (< 10 I,tm).
0.9

0.8

_°g0.7-

_0.5

_ 0.4

=-8 o.3

_ 0.1 -_ _

(a)

1

c

o o.

c a)

P

Q.

oo _ _ _ _,'_

_4t'Uncertainty in 0 _ DOO 0.1

OX_,,_-, •

f,

J

_1"1 _"_ ._'_ - 0.9

_t_1" ,../ " ,-

_, o.9 _ _'_'-'-- 0.8 ._

._ >,0.8 _ _ 0.7 _

,-- "_ / 0.6 c

00.7

.e _ 0.6 o.4 = _

"E c 0.5 / _

_e _0.3 c e

:3- 0

_,_0.4 o.,_._=

c ._ 0.3 / ®

_ 0.1

_- o.o_

_ _'_ _._ '_0_"

(b) O_'_

Figure 4.--Percent uncertainty in thickness-independent velocity. (a) Percent uncertainty

in thicknsss-independent velocity as a function of uncertainties in measuring changes

in time and transducer positional difference. (b) Percent uncertainty in thicknessindependent velocity as a function of analog-to-digital sampling rate and uncertainty

in measuring change in transducer positional difference.

10
The accuracy (vicinity to true value) in the thickness-independent velocity is the result of both random error

identified above plus the systematic error caused by diffraction effects. The latter is estimated to be -0.5 percent for

the experimental setup of this investigation where unfocused transducers were utilized (see Appendix).

EXPERIMENTAL

Materials.--The specimens ultrasonically imaged were several monolithic silicon nitride ceramic disks, a

silicon nitride wedge, a metal matrix composite (MMC) sample, and a polymer matrix composite (PMC) panel. The

ceramic disks were 2 to 4+0.005 mm thick and 40 mm in diameter and contained 6 distinct areas of higher-thanaverage (HTA) pore fraction located 60 ° apart (Fig. 5). They also contained a pore fraction gradient from edge to

center. The ceramic wedge was machined to provide a 0.300 mm edge-to-edge thickness gradient (lengthwise). The

ceramic wedge contained 3 areas of HTA pore fraction and a pore fraction gradient from edge-to-center. The MMC

panel was several plies thick with continuous alumina fibers in an aluminum matrix. It contained unspecified major

fiber volume fraction variations and varied in thickness from ~2.4 to 2.7 mm (-0.300 mm thickness variation)

lengthwise over the entire sample. The panel was -4 by 15 cm in lateral dimensions. The PMC panel was 12-ply

unidirectional with continuous graphite fibers in a polyimide matrix. It contained a 10 percent fiber volume fraction

variation and an -60 _tm thickness variation in a 5 by 5 cm central region.

General Set-up For The Thickness-independent Reflector Plate (TIRP) Velocity Imagin_.--For the

ceramic materials, 20 MHz unfocused and 50 MHz focused transducers with 3 mm element diameter and 12.5 mm

focal length were used for scanning. For the MMC panel, focused 10 MHz transducer with 9.5 mm element

diameter and 76 mm focal length, and focused 30 MHz transducer with 6 mm element diameter and 19 mm focal

length, were used for scanning. For the PMC sample, a focused 3.5 MHz wave transducer with 12.5 mm element

diameter and 50 mm focal length was used for scanning. All transducers were of the longitudinal wave type. The

time difference between 2 successive back surface echoes B 1 and B2, and between the reflector echoes M' and M",

were used for 2x and At, respectively (Fig. 2). A cross-correlation computer algorithm (Ref. 9) was used to

calculate 2"_and At, and velocity was subsequently calculated using Eq. (9). Phase relationships were examined for

1) B1 compared to B2 and 2) M' compared to M". If echoes were in-phase with respect to each other, the time

occurrence of the maximum in the correlation function was used to calculate time delay. If the echoes were phaseinverted, the time occurrence of the minimum in the correlation function was used to calculate time delay.

Tungsten sheet of thickness equal to 0.159 cm (1/16 in.) was used as the reflector plate because tungsten

has an acoustic impedance -70 times higher than water, resulting in the highest possible reflection echo amplitude

11
L J

1 cm

_i,_ _i _I-__• ,%!_ ._;._:_,_

_i_,_i_,.; :. _/

m

Iml

100 _m

o.

to

o

2

2 Left

edge

Lighter

region

Center

I I

Lighter

region

Right

ridge

I I

Figure 5.--Silicon nitride ceramic disk containing higher-than-average pore fraction areas and

edge-to-center density gradient.

]2
of any reflector plate material. The sample to be scanned was placed on plastic supports of thickness equal to

1.27 cm (0.5 in.) sitting on the reflector plate. The supports were placed so they were as unobtrusive as possible

with regards to sample contact since ultrasonic waves needed to pass through the sample to the reflector plate for

an entire sample to be scanned.

After the sample was placed on the supports, pulser-receiver gain and/or attenuation settings and voltage

amplifier settings were adjusted so that echoes off the sample surfaces and the reflector plate were visible.

Transducers were positioned (defocused off sample front surface) above the sample at distances where highest back

surface echo B 1 amplitude was present. As an example, for the 20 MHz unfocused transducer interrogating the

ceramic materials, the transducer-to-sample distance was ~4 cm. (It is critical not to confuse the echoes off the

reflector plate with the second set of echoes originating from the front surface and back surface of the sample when

executing the TIRP velocity imaging method. The methodology for avoiding confusion is to raise and lower the

sample off the supports while noting the time position of the stationary echo train associated with the stationary

reflector plate. Additionally, the second set of echoes originating from the front and back surface of the sample will

always occur at twice the delay time where the first set of those echoes occurs. As an example, if the first set of

sample echoes begins at 50 _tsec time position, the second set will begin at 100 lasec. It has been found that if the

water path between the reflector plate and an -3 mm thick sample is -1.27 cm (0.5 in.), the first echo off the

reflector plate front surface will occur at -20 lasec after the time where the first set of sample echoes originates.)

Prototype System Configuration for TIRP Imaging.--The prototype was a VAX/IEEE-GPIB-controlIed

scan system originally built for contact scans but modified for immersion mode for this investigation. The reader is

referred to Ref. 10 for more detail on the instrumentation used in this system. Two scans were required to execute

the TIRP velocity imaging method. In the first scan, echoes B1, B2 and M' were acquired by time windowing and

digitizing individual echoes. A programmable time synthesizer allowed sequential windowing at the correct time

location of each echo. In the second scan, the sample was removed and M" was acquired. The prototype analog-todigital (A/D) converter had bandwidth capability greater than 1 GHz (200 to 500 MHz sampling rates were used)

and 9-bit digital dynamic range. A recirculating constant temperature bath was employed to keep the temperature

of a small water bath (0.003785 m 3 [1 gallon]) constant within +0.3 °C. A 1 mm-scan increment was used in the

scans obtained with the prototype TIRP system. Images are shown with 255 discrete levels of gray scale that

appear continuous to the eye.

(A "slant correction" procedure was required before the scan to account for nonleveiness in the set-up

[which outweighed thickness variations in the samples tested] so that echoes would remain - centered in time

windows throughout the scan. The slant correction procedure (1) allowed the maximum time resolution of

13
individualechoeswithoutlosinganypartof the time domain waveform and (2) negated the need for specialized

leveling equipment. This procedure was started by placing the transducer at the proper height above the sample and

positioning it at the left-most portion of the scan. The transducer was then moved over the extent of the sample four

separate times in the left-to-right (x-) direction. Each movement corresponded to one of echoes B1, B2, M', and M"

being kept centered in the time window via time synthesizer manual adjustment (Ref. 10). Then, the transducer was

positioned at the bottom-most portion of the scan and the procedure repeated for the four echoes with the

transducer moved in the bottom-to-top (y-) direction. In each case, the total time adjustment required to keep the

echo centered was noted which allowed the calculation of eight "slant correction factors" [nsec/Ftm ] total in the xand y- directions. The slant correction factors were placed into scanner control software so that during the

windowing of the echo during the scan, the echo was automatically repositioned to stay ~ centered within the

oscilloscope time window throughout the whole scan.)

Sonix System Configuration For TIRP Imaging._The Sonix, Inc. system used was a 486/33 MHz PC-ATcontrolled scan system. A large water bath (>0.3785 m3 [100 gallons]) was present not requiring temperature regulation.

An A/D converter having 100 MHz bandwidth and 8-bit digital dynamic range was employed. 800 MHz effective

sampling rate obtained using the Sonix Equivalent Time Sampling (ETS) algorithm (Ref. 1l) was required to obtain

accurate TIRP images on the Sonix system. (It is recommended to use an A/D converter with true l GHz sampling rate

so that the ETS algorithm is not needed. Such a converter is commercially available from Sonix.) The Sonix

implementation of TIRP velocity imaging required 3 scans to acquire the waveform data (Ref. 7). (The Sonix c-scan

system is 100x faster than the prototype system so the extra scan required as compared to the prototype method was not a

significant issue.) B 1 and B2 were acquired in the first scan. M' was acquired in the second scan. M" was acquired in

the third scan after removing the sample. To account for sample nonlevelness, the front surface follower gate feature

(Ref. 11 ) was applied in the scan where B l and B2 were acquired and the data gates (Ref. I l) were made as long as

required during the scans where the reflector echoes M' and M" were acquired. 0.5 and 1 mm scan increments were

used in the scans. Images are shown with 248 discrete levels of gray scale that appear continuous to the eye.

Additional Imaging.--Additional images were obtained using the Sonix system for comparison with TIRP

velocity images. Peak amplitude c-scan images where the echo off the specimen back wall was gated were obtained

using 0.25 scan increment. Apparent velocity images were obtained as calculated using Eq. (3) with a single value

for thickness (d). The thickness value was an average value obtained from several measurements at different sample

locations. Scan increments of 0.5 and l mm were used for scans where apparent velocity images were obtained.

Please note that that apparent velocity and c-scan time-of-flight maps will be affected similarly by thickness

variations, so only the apparent velocity images are shown.

14
RESULTS

Prototype versus Sonix System Configuration TIRP Images. Figures 6(a) and (b) show TIRP images of

one of the uniformly-thick silicon nitride disks obtained with the prototype and Sonix systems, respectively. The

disk was scanned with the same 20 MHz unfocused transducer in both cases. The prototype image was smoothed

while the Sonix system image was low-pass filtered and then smoothed. Note that the images are nearly identical

qualitatively (in revealing the 6 higher-than-average [HTA] pore fraction areas) and quantitatively (the range of

velocity values is nearly identical [maximum - minimum value -2 to 3 percent]). The imaging method was thus

validated on two ultrasonic systems having different instrumentation and control/data acquisition methods.

Peak Amplitude C-scan and Apparent Velocity Images versus TIRP Velocity Image.--Figure 7 shows

imaging results for the silicon nitride ceramic wedge with the 0.300 mm edge-to-edge thickness gradient

(lengthwise), 3 areas of HTA pore fraction and an edge-to-center pore fraction gradient. Figure 7(a) shows for the

wedge a 50 MHz focused peak amplitude c-scan image where the back wall was gated (0.25 mm scan increment).

Figure 7(b) shows a 20 MHz unfocused apparent velocity image (0.5 mm scan increment). Figure 7(c) shows a

20 MHz unfocused TIRP velocity image (0.5 mm scan increment). The peak amplitude c-scan image (Fig. 7(a))

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 it. The apparent velocity image (Fig. 7(b)) shows an -10 percent 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 TIRP velocity image (Fig. 7(c)), the lower HTA pore

fraction area is revealed, the top HTA area is de-emphasized, and an -4 percent total velocity variation is seen. By

eliminating the effects of thickness from the ultrasonic image, the TIRP method accurately quantified (in terms of

velocity variation) the pore fraction variations that were not revealed in the peak amplitude c-scan image and

incorrectly represented in the conventional velocity image for this ceramic material.

Figure 8 shows imaging results for the MMC panel containing fiber volume fraction variations and a

0.300 mm edge-to-edge thickness gradient (lengthwise). Figures 8(a) and (b) show for the panel 10 and 30 MHz

peak amplitude c-scan images where the back wall was gated (0.25 mm scan increment). Figure 8(c) shows an

apparent velocity image (1 mm scan increment) obtained at 10 MHz. Figure 8(d) shows a TIRP velocity image

(1 mm scan increment) obtained at 10 MHz. The l0 MHz peak amplitude c-scan image (Fig. 8(a)) reveals alternate

light and dark bands that may indicate continuous fibers and also indicates the discrete steps of the varying fiber

15
Velocity,

Velocity, mm/psec

-11.10

Figure 6.nThickness-independent velocity images of

silion nitride disk obtained from lab-based prototype system and Sonix, Inc. C-scan system implementation. (a) Image obtained from prototype

system. (b) Image obtained from Sonix system.

20 MHz unfocused transducer was used for scans.

16
% full scale height

f_lq

Velocity, mm/_sec

1.6

.4

(b) e 28

iqnm

Velocity, mm/l_sec

•OB

2e0 28 t,_

(c)

Figure 7.---Ultrasonic images of silicon nitride wedge

having pore fraction variations and a 300 pm 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.

17
m

Region 1

Region

so,

Region 3

El.

(a) _SO

% full scale height

O SO nm

m

9.

(b) -SO SO

% full scale height

mot

100 -

(c)

Velocity, mm/.psec

°0

.s

Velocity, mm/l_sec

m

tOOc:0 .

Oe se _ (d) e se m

Figure 8.EUItrasonic images of MMC panel having fiber volume fraction variations and a 300 _m thickness

gradient edge-to-edge (lengthwise). (a) C-scan peak amplitude image where back wall echo was gated,

10 MHz. (b) C-scan peak amplitude image where back wall echo was gated, 30 MHz. (c) Apparent velocity

image, 10MHz. (d) Thickness-independent velocity image, 10MHz.

]8
volume fraction regions resulting from manufacture. However, no discernible gray variations are indicated between

the three regions that would indicate significantly different microstructure between the steps. In contrast, the

30 MHz peak amplitude c-scan image (Fig. 8b) shows a major gray difference indicating fiber volume fraction

differences between region 3 and the other two regions. A gray difference between regions 1 and 2 is still not

resolvable. The 30 MHz peak amplitude c-scan being more revealing than the 10 MHz c-scan is consistent with the

fact that a greater amount of scattering and/or absorption occurs as frequency is increased. Thickness variation was

not revealed in these peak amplitude c-scan images. Most likely this was because it was not large enough to cause

significant attenuation at 10 to 30 MHz to be resolved with 8-bit digital dynamic range. The apparent velocity image

(Fig. 8(c)) very clearly reveals the three regions' microstructural differences but also incorrectly indicates due to

thickness variation that the bottom of the panel is - the same velocity as region 1. The TIRP velocity image

(Fig. 8(d)) most clearly reveals the regions' microstructural differences and also shows that the bottom of the panel

is 10% lower in velocity than region 1. By eliminating the effects of thickness from the ultrasonic image, the TIRP

method accurately quantified (in terms of velocity variation) the fiber volume fraction variations that were not

revealed in the 10 MHz peak amplitude c-scan image, only partially revealed in the 30 MHz peak amplitude c-scan

image, and incorrectly quantified in the conventional velocity image for this MMC material. It is important to note

that the peak amplitude c-scan images appear to resolve individual fibers while the TIRP and conventional velocity

images do not. Thus the TIRP method is most applicable to accurate global microstructural variation as opposed to

discrete feature/defect characterization.

Figure 9 shows imaging results for the PMC sample containing 10 percent fiber volume fraction variations

and a 60 _tm thickness variation over a 5 by 5 cm area. Figure 9(a) shows for the 5 by 5 cm area a peak amplitude

c-scan image where the back wall was gated (0.25 mm scan increment). Figure 9(b) shows an apparent velocity

image (1 mm scan increment). Figure 9(c) shows a TIRP velocity image (1 mm scan increment). All scans were

performed using a 3.5 MHz focused transducer. The peak amplitude c-scan image (Fig. 9(a)) shows gray scale

variation including 2 darker-than-average (low amplitude) indications near the center. These darker regions were

found to have on average 10 percent lower fiber volume fraction than that of surrounding regions after

metallographic preparation followed by optical image analysis. The apparent velocity image (Fig. 9(b)) shows

approximately the same gray scale variation as the c-scan image. The TIRP velocity image (Fig. 9(c)) shows

increased contrast between light and dark areas as compared to the apparent velocity image due to the elimination of

thickness effects. Approximately 10 percent velocity variation is indicated in this region. The redistribution of

velocity values after elimination of thickness variation effects is shown in the histograms of Figs. 9(d) and (e). For

this PMC material, the TIRP method confirmed and accurately quantified (in terms of velocity variation) the fiber

volume fraction variations seen in the peak amplitude c-scan image.

19
o_

>E

drt

t_ m

N

:,m

.....i

i_'

f

al

-_|.__

0

,o

|

¢,)

e" .-- 0

_E

_,___

_o7_

,, ,_ _,.-

._.-, _

e5_ g

.___ "_

U.

2O
DISCUSSION: EFFECT OF FLUID TEMPERATURE

Viewing Eqs. (9) and (11), it would appear that even minor variations in fluid temperature would have a

major effect on the velocity obtained for a material. To investigate the effect of fluid temperature on velocity in

silicon nitride, an experiment was performed several times in which 2"c (the pulse-echo time delay between B 1 and

B2) and At (the pulse-echo time difference between the first echo off the reflector plate front surface with and

without the sample present, respectively) from Eq. (9) were obtained at 15.6 to 32.2 °C (60 to 90 °F) in increments

of 2.77 °C (5 °F) at a point on the silicon nitride disk. Water velocity (c) was calculated according to Eq. (11 ).

Velocity in silicon nitride was then calculated as a function of temperature according to Eq. (9). Table I and Fig. 10

show a typical result from the experiments. The following results were seen with respect to increasing the

temperature from 15.6 to 32.2 °C according to the precision available: water velocity increased -2.7 percent, At

decreased -2.8 percent, 2x remained constant (0.482 _tsec), and velocity in silicon nitride remained nearly constant

(varied in an unpredictable fashion by only 0.74 percent, at least a portion of which was likely due to the random

error in the measurement of the variables in Eq. (9) as discussed earlier). To understand the almost exact offsetting

changes between At and water velocity, note that Eq. (6) when rearranged can be used to predict water velocity (c) as

function of At:

2d

c = (15)

(At+2"0

Using Eq. (15), Substituting the values of silicon nitride disk thickness (d) equal to 0.2619 cm and 2"_equal to

0.482 I.tsec, and plotting predicted water velocity (c) versus At for the range of At values seen experimentally, the

result is shown in Fig. 11. It can be seen that over the temperature range (15.6 to 32.2 °C [60 to 90 °F])

corresponding to this range of At values, predicted water velocity (c) is inversely proportional to At in a highly linear

manner and the ratio of the predicted percentage change in water velocity over the percentage change in At is ~-1.

This result helps explain the offsetting changes between At and water velocity seen experimentally. The overall

result of this experiment indicates very little temperature-dependence of velocity in silicon nitride between 15.6 to

32.2 °C (60 to 90 °F).

From a practical standpoint, it is still important to keep temperature nearly constant during the scan

procedure. First, other materials may exhibit more significant change in velocity with temperature than does silicon

nitride leading to masking (or accentuation) of microstructural variation if fluid temperature varies. Secondly, most

ultrasonic imaging systems including the two used in this investigation implement a windowing or gating procedure

to isolate and digitize individual ultrasonic echoes. The windows or gates are usually a time extent just large enough

to envelope the echo for maximum digital resolution or to reduce calculation time. If temperature varies during the

21
TABLEI.--RESULTSOFINVESTIGATIONOFEFFECTOFWATERTEMPERATUREON

VARIABLESINE(

Temperature,

oF

(__0.1°F)

Temperature,

oC

(_0.1°C)

Watervelocity,

mm/_sec

(+0.005mm/I.tsec)

60 15.5 1.466

65 18.3 1.474

70 21.1 1.482

75 23.8 1.489

80 26.6 1.495

85 29.4 1.501

90 32.2 1.507

,UATION(9)

2%Bsec

('1-0.001psec)

0.482

At, Bsec

(+0.001 lasec)

3.066

Silicon nitride

velocity, mm/ptsec

4_+0.01 mm/_tsec)

10.79

0.482 3.057 10.82

0.482 3.050 10.86

0.482 3.028 10.84

0.482 3.014 10.85

0.482 3.005 10.86

0.482 2.98 10.82

22
10.87

10.86

10.85 --

O

(D

10.84 --

E

E 10.83 --

o 10.82 --

10.81 _

10.80

10.79

14

I I I t I I I I I

16 18 20 22 24 26 28 30 32

Temperature, °F

I I I I

60 70 80 90

Temperature,°F

I

34

Figure lO.--Velocity versus temperature for silicon nitride sample. Error in

velocity measurement -0.01 mm/t_sec.

1.52

2-(2.619 mm)

1.51 = ----

1.50

1.49

1.48

I [ I I I I t I t I

1"472.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07

At, t_sec

Figure 11 .--Water velocity (c) versus At as predicted from Eq. (15). Disk thickness (d) = 2.619 mm and 2_r = 0.482 I_sec.

23
scan procedure, the echoes off the reflector plate front surface with and without the sample present will move out of

the gate extent (i.e., t' and t" will vary [see Eqs. (4) and (5)]) (Fig. 12), and digitizations containing incomplete

echoes will result leading to invalid velocity values. For temperature control, it is suggested to use a large water tank

(_>0.3785 m 3 [100 gal]) that due to its capacity is slow to respond to ambient temperature changes. A recirculating

constant temperature bath is recommended for use with smaller tanks such as those used in tabletop or lab-based

scan systems.

SUMMARY AND SIGNIFICANCE

This article described a single transducer ultrasonic imaging method that eliminates the effect of plate

thickness variation in the image, i.e., is thickness-independent. The method thus isolates ultrasonic variations due to

material microstructure. Its use can result in significant cost savings because the ultrasonic image can be interpreted

correctly without the need for machining to achieve precise thickness uniformity during nondestructive evaluations

of material development. The method is based on measurement of ultrasonic velocity and is precise to less than

1 percent using conditions of this investigation.

The thickness-independent imaging method was validated on two ultrasonic systems having different

instrumentation and control/data acquisition methods. Images obtained using the thickness-independent

methodology were compared with apparent velocity maps and c-scan echo peak amplitude images for monolithic

ceramic (silicon nitride), metal matrix composite (MMC), and polymer matrix composite (PMC) materials having

thickness and microstructural variations. It was found that peak amplitude c-scans were not visibly affected by the

up to 300 mm thickness variation in these materials. Additionally, the peak amplitude c-scans did not clearly reveal

the microstructural variations in these materials. However, apparent velocity images indicating time-of-flight

variations showed significant superposition of thickness effects which skewed the true picture of material

microstructure. By eliminating the effects of thickness from the ultrasonic image, the method (l) accurately

quantified (in terms of velocity variation) the pore fraction variations that were not revealed in the peak amplitude

c-scan image and incorrectly represented in the conventional velocity image for a ceramic material, (2) accurately

quantified the fiber volume fraction variations that were only partially revealed in a peak amplitude c-scan image

and incorrectly quantified in the conventional velocity image for an MMC material and (3) highlighted and

accurately quantified the fiber volume fraction variations originally detected in the peak amplitude c-scan image for

a PMC material. The thickness-independent method, currently being commercialized under a cooperative agreement

between NASA Lewis Research Center and Sonix, Inc, has applicability to inspection of some complex shapes such

as hollow tubes as indicated in Ref. 5.

24
10 (_

+'_ u)

Q.--

E_ =

100 --

50--

0

-50--

(a)

-1 O0

68.8 69.0

I v I ' I

69.2 69.4 69.6

Time, I_sec

10 ¢0

<c

100 --

50--

0

-50 -

(b)

-1 O0

68.8 69.0 69.2 69.4

Time, i_sec

o=z=

•-I 0

_.=

E_

<c

100 -

5O

0

-50

-1 O0 I I I

68.8 69.0 69.2 69.4 69.6

Time, I_sec

Figure 12.mUItrasonic echo position as a function of

temperature for M", the first echo off the reflector plate

front surface with the sample removed. (a) Echo

position at 22.2 °C (72 °F). (b) Echo position at 23.3 °C

(74 °F). (c) Echo position at 24.4 °C (76 °F).

25
REFERENCES

1. Nondestructive Testing Handbook, second edition, Volume 7 Ultrasonic Testing, eds. Birks, A.S., Green, R.E.,

and McIntire, E American Society For Nondestructive Testing, 1991, pp. 227-230, 387-390, 405,225.

2. Bashyam, M.: 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, July 15-20, 1990. Vol. 10A. Plenum Press, 1991, pp. 1035-1042.

3. Roth, D.J., et. al.: An NDE Approach For Characterizing Quality Problems in Polymer Matrix Composites.

Proc. 40th International SAMPE Symposium, Anaheim, CA, May 8-1 l, 1995, pp. 288-299.

4. Hsu, D.K., et. al.: Simultaneous determination of ultrasonic velocity, plate thickness and wedge angle using

one-sided contact measurements. NDT&E International 1994 Volume 27, Number 2, pp. 75-82.

5. Sollish, B. D.: Ultrasonic Velocity and thickness gage, United States Patent No. 4,056,970, Nov. 8, 1977.

6. Pich_, L.: Ultrasonic velocity measurement for the determination of density in polyethylene. Polymer

Engineering and Science, Vol. 24, No. 17, Mid-December 1984, pp. 1354-1358.

7. Roth, D. J., et. al.: Commercial Implementation of Ultrasonic Velocity Imaging Methods via Cooperative

Agreement Between NASA - Lewis Research Center and Sonix, Inc. NASA TM-107138, 1996.

8. Bevington, R. E, Data Reduction and Uncertainty Analysis for the Physical Sciences, Chapter 4, 1969.

McGraw-Hill, New York, NY.

9. Hull, D.R.; Kautz, H.E.; and Vary, A.: Measurement of Ultrasonic Velocity Using Phase-Slope and CrossCorrelation Methods. Mater. Eval., vol. 43, no. 11, 1985, pp. 1455-1460.

10. Roth, D.J., et. al.: Quantitative Mapping of Pore Fraction Variations in Silicon Nitride Using an Ultrasonic

Contact Scan Technique. Res. Nondestr. Eval., vol. 6, 1995, pp. 125-168.

11. Ultrasonic C-scan Users Guide, V3.10d, January, 1995. Sonix, Inc. 8700 Morrissette Drive, Springfield, VA

22152.

26
APPENDIX--EFFECTS OFDIFFRACTION(BEAMSPREAD)

Inthereflectorplatemethodologyofthisexperiment, thetransducer isseparatedfromthesamplebya

waterpath,andthesampleisfurtherseparatedfromthereflectorplatebyanotherwaterpath.Thepulse-echo

distances(twicethedistancetraveledbytheultrasonicbeamtothereflectorplate)forvariouset-upscanbecome

significant atimes.Becauseofthis,it maybeimportanttoconsidertheeffectsofdiffraction(beamspread)on

absolutevelocityvaluesif usingunfocusedtransducers suchaswasdoneinthesiliconnitridescans. Beam

spreadingbecomesanissueatdistancesfromthetransducer greaterthanthatdefinedbythenearfieldorFresnel

length(Z')(Ref.A1).Theneteffectofbeamspreadingistomakeanechosmallerandshiftedintime,withtheeffect

becomingmoresignificant asdistancefromtransducer isincreased. Nearfieldlength(Z')isdefinedby:

Z ' =-_-=a2 a2(f / (A1)

where a is transducer element radius, _. is the ultrasonic wavelength, V is the velocity of ultrasound in the medium,

andfis the frequency. A normalized distance (S) can be defined (Ref. AI ):

(A2)

where Z is the path length the ultrasonic beam travels in the pulse-echo configuration. Normalized distance denotes

the ratio of actual ultrasonic path length to near field length. Beam spreading becomes significant at normalized

distances from the transducer greater than 1. Based on Eq. (A2), Fig. AI shows the effect of path length, frequency,

and transducer radii on normalized distance (S) for a path composed solely of water with V = 1.48 mm/ktsec.

For our simulation, the experimental set-up utilized to obtain the TIRP image of the ceramic disk of

Fig. 6(a) in the body of the article was modeled. Curves of diffraction loss and phase shift as a function of

normalized distance were obtained from Ref. A1 and used to correct for diffraction effects the ultrasonic echoes

obtained for the ceramic disk. The TIRP velocity image was subsequently recalculated by cross-correlating the

corrected echoes. Diffraction effects are dependent on ultrasonic bandwidth and a choice of curves from Ref. AI are

available based on transducer bandwidth. Since a broadband transducer of 20 MHz nominal center frequency was

employed in the silicon nitride scans, curves for 120 percent (widest) bandwidth were used (Ref. A1) These curves

are shown in Fig. A2 with Fig. A2(a) showing loss in nepers (having been converted from dB given in Ref. A1 ).

27
12 -- Frequency, Transducer radius,

11 -- MHz c_

== 9 0.159

8

7 / 0.159 or

,,, / 0.318, respectively

6 uuf o., °

_5 _20 or .e_we, y... o o o O:15: _

5 o.... °

/ 5,,e' :7o°-

roll I== I o 3 .. o " .....-.

0 ° "T" I I I ] I 1 [ t

0 2 4 6 8 10 12 14 16 18 20

Z (composed solely of water), cm

A1 .--Normalized distance versus water path length for various transducer

frequencies and radii, z = path length of ultrasonic beam, X = ultrasonic

wavelength, a = transducer radius.

Since each echo at each scan point was diffraction-corrected, normalized distance (S) was calculated for

echoes B 1 (first echo off sample back surface), B2 (second echo off sample back surface), M' (first echo off reflector

plate with the sample present) and M" (first echo off the reflector plate with the sample removed), respectively

(Fig.2 in the body of the article). For the sample echoes,

Sol =2a--_+ a f

(A3a)

where SB1 is the normalized distance for echo B1, L and d are the length of the water path and thickness of the

sample, respectively, and c and VSN are the velocity in water and silicon nitride sample, respectively. Similarly:

2 Lc dVsN

SB2 = a2 f + 4 a2 f

(A3b)

where SB2 is the normalized distance for echo B2. For the reflector plate echoes:

28
0.7 m

0.6

0.5

Q.

0.4

_o

'10

0.3

r-.

0.2

0.1

0.0

0

m

1 2 3

z-,_

Normalized distance, s = a---_--

1.0 --

0.9

0.8

0.7

0.6

-_ 0.5

¢1

.c 0.4

O.

0.3

0.2

0.1

0.0

m

I I I I

J

4

0 1 2 3 4

z',_

Normalized distance, s = a---_-

A2.--Magnitude loss and phase shift versus normalized distance (120% bandwidth)

resulting from beam spreading (diffraction) from ref. AI. (a) Magnitude loss versus

normalized distance. (b) Phase shift versus normalized distance, z =path length of

ultrasonic beam _ = ultrasonic wavelength, a = transducer radius.

29
Lc dVsN L' c

SM, = 2a--_+ 2 a---_- + 2--a2f (A3c)

where SM, is the normalized distance for echo tl4' and L' is the water path length from the sample back surface to the

reflector plate front surface. Similarly:

SM.=2 Lc + 2 dc +2-- L'c

a2f a2f a2f

_A3d_

where SM, is the normalized distance for echo M". In the silicon nitride scans of this study, c = 1.48 mrn/_tsec,

VSN = the velocity obtained at that particular scan point, L = 4 cm, L' = 1.3 cm, a = 0.159 cm and f= a frequency

contained within each broadband echo.

To apply diffraction corrections and then recalculate the velocity image, a fortran program was written inwhich:

(1) the curves of Fig. A2(a) and (b) were divided into discrete values allowing the computerized

application of diffraction corrections as a function of normalized distance (S) for each echo.

(2) For each of time-domain echoes B1, B2, M', and M" at each scan point:

(a) the echo was fast-fourier-transformed into the frequency domain to obtain real and imaginary

coefficients which were subsequently used to obtain magnitude and phase spectra. 2n radians were

subtracted from phase spectra at discrete frequencies where needed to make phase spectra continuous

(phase unwrapping procedure) as a function of frequency (Ref. A2).

(b) Normalized distance (S) was determined at each frequency of the spectra of the fourier-transformed

echoes according to Eqs. A3(a) to (d).

(c) the magnitude at each frequency within the spectra was corrected for loss according to:

CMAG(f) = MA G(f)xl 0(l°ss/20) (A4)

where CMAG(f) and MAGOO are the diffraction-corrected and original magnitudes at a particular

frequency, respectively, and loss is in nepers. The value of loss was determined as a function of

normalized distance from Fig. A2(a) according to step 1.

30
(d)thephaseateachfrequencywithinthespectrawascorrectedforphaseshiftaccordingto:

CPHA(f) = PHA(f) + shift (A5)

where CPHA(]) and PHA(D are the diffraction-corrected and original phase at a particular frequency,

respectively, and shift is the phase shift in radians. The value of phase shift was determined as a function

of normalized distance from Fig. A2(b) according to step 1.

(e) Two reconstructions were performed for each fourier-transformed echo. Fourier-transformed echoes

having corrected magnitude only, and corrected magnitude and phase were reconstructed in the time domain

by performing inverse-fast-fourier-transformation. The former was performed to test for consistent echo

polarity. It was found that in some cases, magnitude-only corrected echoes were -n radians out-of-phase

(or inverted) compared to original time-domain echoes. This is an incorrect result since no phase

corrections were applied and is thought to be due to a signal processing anomaly. Phase inversion such as

this results in improper cross-correlations and thus improper velocities. For such cases, the same echoes

having been corrected for both magnitude and phase were inverted so that correct polarity was restored.

(f) A cross-correlation algorithm (Ref. A3) was performed to obtain time delays between reconstructed

B1 and B2 echoes, and between reconstructed/14' and M" echoes. Phase relationships were examined for

B1 compared to B2 and M' compared to M" before implementing the algorithm. If the echoes were not

phase-inverted with respect to each other, the time occurrence of the maximum in the correlation

function was used to calculate time delay. If the echoes were phase-inverted, the time occurrence of the

minimum in the correlation function was used to calculate time delay.

(g) velocity was recalculated according to Eq. (9) in the body of the article.

Figure A3 shows a set of original and diffraction-corrected magnitude and phase spectra, and time-domain

waveforms, for a scan point in the center of the silicon nitride disk. Figure A4 shows the TIRP velocity images of the

disk before and after diffraction corrections. It can be seen that for the experimental set-up of this investigation,

diffraction effects were negligible. Diffraction-corrected velocity values were on the order of 0.5 percent greater than

original velocity values.

31
,=

O

>

nD

¢-

O_

=1

nD

6

n

11.4

00.0

0

-10

-20

-30

-40

-50

-6O

-70

f_

(a) ; ', I Without

//_, I diffraction

/J _, I corrections '/ I- Diffraction-

_ _ corrected

0 10 20 30 40 50

Frequency, MHz

--\

%%%

(d) ,'_

I |

I I

I I

/ \

0 10 20 30 40 50

Frequency, MHz

O

>

6

"O

-1

C

"O

d

in

8.5

0.0

0

-10

-20

-30

-40

-50

-60

__ %

10 20 30 40 50 0 10 20 30 40 50

Frequency, MHz Frequency, MHz

O

>

"O

-1

E

<_

1.0 --

0.8--

0.6--

0.4--

0.2--

0.0

-0.2--

-0.4--

-0.6--

-0.8 _)

-1.0

57.0

1.0 --

0.8--

0.6--

0.4--

0.2--

0.0

-0.2--

-0.4--

-0.6--

¢0

O

>

"O

-I

O.

E

<_

-0.8 --

1 I t I I -1.0 (f) I I I I I

57.1 57.2 57.3 57.4 57.5 57.5 57.6 57.7 57.8 57.9 58.0

Time position, i_sec Time position, l_sec

A3._et of non-diffraction-corrected and diffraction-corrected magnitude, phase spectra, and time-domain

waveforms for scan point at canter of silicon nitride disk. (a) B1 Magnitude spectra. (b) B1 Phase spectra.

(c) B1 Time domain wave. (d) B2 Magnitude spectra. (e) B2 Phase spectra. (f) B2 Time domain wave. (g) M °

Magnitude spectra. (h) M ° Phase spectra. (i) M' Time domain wave. (j) M"magnitude spectra. (k) M" Phase

spectra. (I) M" Time domain wave.

32
(9

,=

._,

0

>

'0

C

2.8

0.0

(g) //_-_

//\ °

?

// \ -d

"0

O)

!_. ,Y \

0 10 20 30 40 50

Frequency, MHz

8.5

0.0

0 10 20 30 40 50

Frequency, MHz

"O

ca.

0

-10

-20

-30

-40

-50

-60

-70 I

0 10 20 30 40 50

Frequency, MHz

¢-

J_

a.

0

-20

-40

-60

-80

-100 --(k) I I

0 10 20 30 40

Frequency, MHz

50

O

>

"O

(3.

E

0.1

0.0

V

ii / o

! I

"O

O. tJ <

0.3 B

0.0

(i) I I I I t -0.3 (I) -0.1

76.3 76.4 76.5 76.6 76.7 76.8 76.3

Time position, psec

L L L L L

76.4 76.5 76.6 76.7 76.8

Time position, p.sec

A3._oncluded. (g) M' Magnitude spectra. (h) M' Phase spectra. (i) M' Time domain wave. (j) M" magnitude

spectra. (k) M" Phase spectra. (I) M" Time domain wave.

33
Velocity, mmll_c

A4.mThickness-independent velocity images of silicon nitride

disk before and after diffraction corrections. (a) Before

diffraction corrections. (b) After diffraction corrections.

APPENDIX REFERENCES

AI. Papadakis, E.E: Ultrasonic Diffraction from Single Apertures with Application to Pulse Measurements and

Crystal Physics, Physical Acoustics, Vol. XI, 1975. edited by W.E Mason and R.N. Thurston, Academic Press.

pp. 173-178.

A2. Sachse, W. and Pao, Y.H." On the Determination of Phase and Group Velocities of Dispersive Waves in Solids.

J. Appl. Phys., Vol. 39, 1978, p. 4320.

A3. Hull, D.R.; Kautz, H.E.; and Vary, A.: Measurement of Ultrasonic Velocity Using Phase-Slope and CrossCorrelation Methods. Mater. Eval., vol. 43, no. 11, 1985, pp. 1455-1460.

A4. Nondestructive Testing Handbook, second edition, Volume 7 Ultrasonic Testing, eds. Birks, A.S., Green, R.E.,

and McIntire, E American Society For Nondestructive Testing, 1991, pp. 225.

34

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REPORT DOCUMENTATION PAGE OMB NO.0704-0188

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

July 1996 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Single Transducer Ultrasonic Imaging Method that Eliminates the Effect of Plate

Thickness Variation in the Image

6. AUTHOR(S)

Don J. Roth

7. PERFORMINGORGANIZATIONNAME(S)AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

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

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

WU-505-63-12

8. PERFORMING ORGANIZATION

REPORT NUMBER

E-10151

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-107184

11. SUPPLEMENTARY NOTES

Responsible person, Don J. Roth, organization code 5250, (216) 433--6017.

1211. DISTRIBUTION/AVAILABlUTY STATEMENT

Unclassified - Unlimited

Subject Category 38

This publication is available from the NASA Center for AeroSpace Information, (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

This article describes a single transducer ultrasonic imaging method that eliminates the effect of plate thickness variation

in the image. The method thus isolates ultrasonic variations due to material microstructure. The use of this method can

result in significant cost savings because the ultrasonic image can be interpreted correctly without the need for machining

to achieve precise thickness uniformity during nondestructive evaluations of material development. The method is based

on measurement of ultrasonic velocity. Images obtained using the thickness-independent methodology are compared

with conventional velocity and c-scan echo peak amplitude images for monolithic ceramic (silicon nitride), metal matrix

composite and polymer matrix composite materials. It was found that the thickness-independent ultrasonic images reveal

and quantify correctly areas of global microstructural (pore and fiber volume fraction) variation due to the elimination of

thickness effects. The thickness-independent ultrasonic imaging method described in this article is currently being

commercialized under a cooperative agreement between NASA Lewis Research Center and Sonix, Inc.

14. SUBJECTTERMS

Ultrasonics; Thickness; Velocity; Technology transfer

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSlRCATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

36

16. PRICE CODE

A03

20. LIMITATION OF ABSTRACT

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

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