digitized frequency modulated thermal wave imaging for ndt

ABSTRACTThis paper proposes novel techniques for thermal nondestructive test-

ing based on frequency modulated thermal waves. A mild steel sample hav-ing discontinuities at different depths is taken as a test sample. The limiteddepth resolution of the lock in thermography due to the fixed driving fre-quency of the excited heat sources is overcome by the proposed new tech-nique. A pulse compression approach is used to detect subsurface disconti-nuities using linear frequency modulated thermal wave imaging anddigitized linear frequency modulated thermal wave imaging. In this way,the peak power for probing the specimen can be decreased markedly by in-creasing the average transmitted energy, which is proportional to thelength of the modulated excitation signal. Comparison between the tech-niques based on the analog frequency modulated signal and its digital formare presented. Keywords: nondestructive testing, thermal wave, nonstationary sig-nals, frequency modulation, time bandwidth product, correlation, pulsecompression.

INTRODUCTIONInfrared thermography is a noncontact and whole field tech-

nique that can be usefully employed in nondestructive testing(NDT) of materials. Presently, three different types of active thermalnondestructive techniques are predominantly in use: pulse, lock inand pulse phase thermography (Maldague, 2001; Maldague et al.,2002; Lhota et al., 2000; Wu and Busse, 1998). In pulse thermogra-phy, the tested material is warmed or cooled with a short durationenergy pulse and a measurement of the temporal evolution of thesurface temperature is performed with an infrared camera throughrecording the infrared image sequence, indicating subsurface dis-continuities at different depths (Maldague, 2001; Lhota et al., 2000).The surface temperature gradients are affected because of presentsubsurface discontinuities by local inhomogeneities of the materialsurface as well as nonuniform heating. Lock in thermography usesperiodic sinusoidal thermal excitation in order to derive informa-tion of reflected thermal wave phase and magnitude (Wu andBusse, 1998). The phase angle has the advantage of being less sensi-tive to local variations of illumination or of surface emissivity. Be-cause of its monofrequency excitation, the depth resolution of thetest is fixed (fixed thermal wavelength). The experimental arrange-ment of pulse phase thermography (Maldague, 2001; Maldague etal., 2002) is similar to that of pulse thermography, but the funda-mental idea of processing the captured image sequence is different.In pulse phase thermography, the extraction of various frequencycomponents in the captured sequence is performed by Fouriertransform on each pixel of the thermogram sequence. The phase

images thus obtained show all the merits of the phase images ob-tained with lock in thermography (that is, they are less sensitive tosurface inhomogeneities and illumination variations). Theoretically,the short duration excitation pulse in pulse phase thermographydoes launch a large number of frequency components into the testsamples, but the higher order components may not have sufficientenergy to propagate deep into the sample. Further compared withpulse phase thermography, the proposed technique controls thebandwidth of the thermal waves being launched into the samplethickness of interest, leading to higher sensitivity (Maldague et al.,2002). To overcome some of the traditional limitations of conven-tional thermal wave imaging techniques (resolution, peak power,depth of penetration), the present work focuses on two related,nonstationary forms of thermal excitation techniques: frequencymodulated thermal wave imaging (Mulaveesala and Tuli, 2005; Tuliand Mulaveesala, 2004; Tuli and Mulaveesala, 2005) and digitizedfrequency modulated thermal wave imaging.

The basic concept of lock in thermography is the periodic heat-ing of the sample surface by a sinusoidal intensity modulated heatsource. The absorbed heat generates thermal waves at the surface ofthe object, which then propagate into the material under test. Thethermal waves will be reflected back onto the surface from wherev-er the physical heat propagation parameters are different (for exam-ple, voids and delaminations). For the purpose of analysis, the sam-ple is considered as semiinfinite, onto which a uniform heat sourceperiodically deposits heat at a modulating angular frequency ω.Then, neglecting convection losses, the temperature T, as a functionof depth z and time t is given by (Maldague et al., 2002; Wu andBusse, 1998)

(1)

whereT0 = amplitude of the oscillating temperature on the surfacez = the depth below the surfaceλ = the wavelength of the thermal waveµ = the thermal diffusion length (Wu and Busse, 1998), defined

as

(2)where

α = thermal diffusivity of the material.

The depth of penetration µ of thermal waves in a given material(thermal depth range) is therefore dependent not only on the mate-rial properties but also on the modulating frequency of the heatsource — the smaller the modulation frequency, the deeper the pen-etration of the thermal wave. Beyond this thermal diffusion length,the heat wave amplitude will drop to 1/e of its surface value.

µ λπ

αω

= =2

2

T z t T ez

tz

, cos ( ) = −

−

0 2µ πλ

ω

1046 Materials Evaluation/October 2005

Digitized Frequency Modulated Thermal WaveImaging for Nondestructive Testing

by Ravibabu Mulaveesala* and Suneet Tuli†

Submitted June 2005

* Centre for Applied Research in Electronics, Indian Institute ofTechnology Delhi, New Delhi 110016, India; e-mail <[email protected]>.

† Centre for Applied Research in Electronics, Indian Institute ofTechnology Delhi, New Delhi 110016, India; e-mail <[email protected]>.

08_1035_1050_TPs_16pgs 9/15/05 11:31 AM 046

NONSTATIONARY SIGNAL EXCITATIONSMost signals encountered in engineering applications are inher-

ently nonstationary: that is, they have time varying frequencies oramplitudes. Such signals are widely used in seismic, sonar andradar applications and lead to solutions for combined range resolu-tion problems (Wehner, 1994). The present work focuses on usingfrequency modulated thermal excitation of the sample surface toovercome the problems associated with long measurement timeand high peak powers. The advantage of using a frequency modu-lated (chirp) heating (Mulaveesala and Tuli, 2005; Tuli andMulaveesala, 2004; Tuli and Mulaveesala, 2005) on the sample sur-face is that it provides good accuracy for time of flight measure-ments, as it only correlates well at a single well defined instant oftime of arrival. Additionally, the received chirp signal can be detect-ed even when its level is well below the noise floor.

A frequency modulated signal xcs(t) can be represented in timeas follows (Mulaveesala and Tuli, 2005; Tuli and Mulaveesala, 2005)

(3)

wherea(t) = the envelope of the chirp signal, which is zero outside the

time interval tDθ(t) = the phase of the chirp signal (Figure 1a).

The instantaneous frequency fm(t), of the chirp signal can be ob-tained as follows

(4)

The chirp rate represents the rate of change of instantaneous fre-quency and is defined by

(5)

The waveform is said to be an up chirp if µ(t) > 0 and a downchirp if µ(t) < 0. For a linear chirp, µ(t) is constant and, hence, fm(t) isa linear function of time.

Conventional pulse thermography demands that the excitationpulse should have a high peak power in order for the energy topenetrate deep into the test sample. This becomes a limitation forthe high peak powers, but it can be overcome by coded excitation,in which instead of increasing the peak power of the excitation sig-nal, the average power is increased (O’Donnell, 1992). The funda-mental concept of the digitally coded excitation system is shown inFigure 1.

In digitized frequency modulated thermal wave imaging, theinput signal is clipped and converted into a binary (digital) form(Figure 1b). The digitized signal xcd(t) can be derived from its ana-log counterpart signal xca(t), by the nonlinear signum operation asfollows

(6)

wheresgn(xca) = 1 when xca > 0sgn(xca) = 0 when xca = 0sgn(xca) = –1 when xca < 0.

The advantages of digitization of the analog chirp signal overthe conventional analog form can be explained by considering theirspectra. The difference between the spectrum of a sine wave chirp(analog chirp) and the digital chirp can be estimated, if we comparethe spectrum of a single frequency sine wave and a square wave ofthe same basic frequency. A sine wave has one spectral componentat a frequency f, whereas a square wave can be represented by itsFourier series as below

(7)

where

By computing root mean square values of sine and square, it’sclear that the energy of a square wave is two times higher than theenergy of a sine wave of the same amplitude. However, in thesquare wave, the larger amount of additional energy is due to high-er harmonics, which do cause a thermal wave inside the materialbut of very small amplitude levels that can be neglected. The fun-damental frequency has an amplitude (= 4/π) 1.273 times higherthan the sine signal, causing a greater depth of penetration andleading to an increase in the reflected signal amplitude.

PRINCIPLE OF PULSE COMPRESSIONThe pulse compression technique (Tuli and Mulaveesala, 2005;

Wehner, 1994) prevalent in radar allows for the transmission of alow peak power, long duration modulated wave. This providesdetection range and resolution comparable to or better than thatachieved by short duration, high peak power pulse techniques.

The most widely used technique for pulse compression is thecorrelation technique. Let s(t) be the thermal response on the sam-ple surface over a designated reference region. Let h(t) be the ther-mal response on the sample surface over the defective region. Boths(t) and h(t) can be considered to be the same as the incident heat

an

nn = ( )4π

is odd

x t a t a t a n tnsquare sin sin 3 sin( ) = ( ) + ( ) + + ( )1 3ω ω ωK

x t x tcd ca( ) = ( ) sgn

µπ

θt

dfdt

d

dtm( ) = =

12

2

2

f tddtm ( ) =

12π

θ

x t a t t t tcs D( ) = ( ) ( ) < <sin ,θ 0

Materials Evaluation/October 2005 1047

Figure 1 — Intensity profile of heat source over time: (a) linearfrequency modulated signal (b) digitized linear frequency modulatedsignal.

(a)

(b)

08_1035_1050_TPs_16pgs 9/20/05 3:08 PM Page 1047

flux except for a delay and a change in amplitude (Tuli andMulaveesala, 2004; Tuli and Mulaveesala, 2005; Wehner, 1994). Thecross correlation of the two sequences of the thermal responses onthe sample surface at problematic and unproblematic regions, h(t)and s(t), is a narrow correlation peak g(t) called a compressed pulse(Figure 2), which can be represented as

(8)

Widening the bandwidth of the transmitted pulse by modulat-ing it in either frequency or phase yields a finer range resolutionthan can be achieved with conventional thermographic techniques.Increasing the bandwidth of the excitation signal not only helpsto get fine range (depth) resolution but also improves the signalto noise ratio (Tuli and Mulaveesala, 2004) as follows

(9)

whereτ = the durationB = the bandwidth of the excitation signal.

It is possible to get a high signal to noise ratio by either increasingthe bandwidth or duration of the excited signal. Here, the pulsecompression technique has been applied to thermal nondestructivetesting for discontinuity detection by choosing the reference anddiscontinuity thermal responses as the inputs to the cross correlator.Increasing the bandwidth leads to an improvement in depth res-olution for the detection of discontinuities at various depths be-cause it induces more probing frequencies into the samples.However, further increase in the bandwidth beyond a certainlimit for a given sample (depending on thermal properties andthickness) will not help in extracting discontinuity information.

EXPERIMENTAL PROCEDURE

Linear and Digitized Linear Frequency Modulated ThermalWave Imaging

Experiments to validate the proposed linear frequency modulat-ed thermal wave imaging technique and the digitized techniquewere carried out on a mild steel sample (Figure 3) using an infrared(3 to 5 µm [1.2 × 10-4 to 2 × 10-4 in.]) system. The sample contains 10circular flat bottom holes, each 20 mm (0.8 in.) in diameter, at differ-ent depths from the sample top surface. A frequency modulatedthermal wave imaging signal (sine chirp) of 169 s duration, with itsfrequency linearly varying from 0.01 to 0.5 Hz, is generated from asignal generator and used to drive the heat sources via a sourcecontrol unit as shown in Figure 4. For the digitized (digitizedchirp) technique, the experimental setup was the same exceptthat the excitation is through a digitized signal with frequency

SN

Bdb

= ( )10 10log τ

g t s t h t( ) = ( )∗ ( )


Figure 2 — Pulse compression principle: (a) s(t) is the temperature profile at the reference region over the surface; (b) h(t) is the temperature profileon the sample surface over the discontinuity region; (c) g(t) is the compressed pulse after correlation of s(t) and g(t).

(a) (b) (c)

Figure 3 — Schematic description of the mild steel sample with flatbottom holes. Sample measures X = 210 mm (8.3 in.), Y = 112 mm(4.4 in.) and Z = 11.2 mm (0.4 in.). Holes are 20 mm (0.8 in.) indiameter, with the following depths: a = 9.1, b = 11.1, c = 10.2,d = 10.1, e = 7.0, f = 5.4, g = 8.3, h = 7.1, i = 6.3 and j = 5.4 mm(a = 0.36, b = 0.44, c = 0.40, d = 0.39, e = 0.275, f = 0.21, g = 0.33,h = 0.28, i = 0.25 and j = 0.21 in.).

Figure 4 — Schematic of the experimental setup for linear frequencymodulated thermal wave imaging and digitized linear frequencymodulated thermal wave imaging.

08_1035_1050_TPs_16pgs 9/15/05 11:31 AM Page 1048

varying similarly from 0.01 to 0.5 Hz. The infrared camera observesthe sample surface and records the temporal response of the sampleby capturing a sequence of images during the chirp heating. Vari-ous frequency components in the captured image sequence are ex-tracted using a Fourier transform on each pixel of the thermograph-ic image sequence. The amplitude and phase images are formed byrepeating this process for all pixels in the frame. The phase andmagnitude images are generated using software.

Figure 5 shows the generated phase images using linear fre-quency modulated thermal wave imaging and its digitized coun-terpart at a modulation frequency of 0.05 Hz. The digitized image(Figure 5b) clearly illustrates the capability to detect the deep dis-continuities shown in Figure 3 (those labeled h, i and j) with betterresolution than through conventional linear frequency modulatedthermal wave imaging. It is clear that digitized imaging has the ca-pability to preserve the shape of the discontinuity like the existingpulse phase thermography. It may be noted that measurementswere made over only one frequency modulated cycle for both thechirp excitations (0.01 to 0.5 Hz in 169 s) and the image sequencewas captured at a frame rate of 20 Hz. It can be seen that chirp heat-ing can scan the entire sample thickness by utilizing thermal waveswhose diffusion length changes with time (Equation 2), dependingon the appropriate frequency modulated surface heating. The fre-quency dependent thermal diffusion length determines the spatialresolution of lock in thermography. In comparison, for a fixed testfrequency, the thermal diffusion length (Equation 2) gets fixed andlimits the depth resolution of the test. However, in chirp heating thevariable frequencies cause variable depth probing. Compared topulse thermography, considerably less peak power is required from

the heat sources. Further, as compared to pulse phase thermogra-phy (Lhota et al., 2000; Maldague et al., 2002), even though a muchwider range of frequencies are probed simultaneously, higher orderharmonics may not have sufficient energy to scan the test sample.

Discontinuity Detection by Pulse CompressionDiscontinuity depth can be conceptually estimated in two ways:

from the magnitude of the resultant thermal response at the discon-tinuity location and by measuring the time delay of the thermal re-sponse at the problematic region with respect to a reference region.Estimation from the former can be misleading because of the pres-ence of surface inhomogeneities and nonuniform heating of thesample surface. Therefore, a correlation approach (based on timedelay) has been considered.

In this study, for both thermal wave imaging techniques, thethermal response on the sample surface over a 0.1 mm(3.9 × 10-3 in.) deep discontinuity from the sample surface has beenconsidered as the reference. The image sequence was captured for aduration of 169 s at a frame rate of 20 Hz. Taking the sequence ofpixel intensity values at a discontinuity location throughout the se-quence provides a temporal thermal profile. Before doing correla-tion between the reference thermal profile and the thermal profile atthe discontinuity regions, the mean increase in temperature hasbeen removed by linear curve fitting. Correlations of the thermalresponse of the sample from various depths, with respect to thechosen reference (signal from 0.1 mm [3.9 × 10-3 in.] discontinu-ity), were obtained. Figure 6 shows the correlation peaks ob-tained for 1.1, 2.9, 4.2 and 4.9 mm (0.04, 0.11, 0.17 and 0.19 in.)discontinuities with respect to the reference for both thermal

Materials Evaluation/October 2005 1049

Figure 5 — Phase images at 0.05 Hz of the mild steel sample with blindholes, experimentally obtained using: (a) linear frequency modulatedthermal wave imaging; (b) digitized linear frequency modulatedthermal wave imaging. Measurements are made over only onefrequency modulated cycle.

(a)

(b)

Figure 6 — Correlation peaks obtained from experimental results fromvarious discontinuity depths with: (a) linear frequency modulatedthermal wave imaging; (b) digitized linear frequency modulatedthermal wave imaging.

(a)

(b)

08_1035_1050_TPs_16pgs 9/15/05 11:31 AM Page 1049

wave imaging techniques. However, the discontinuities locatedat 1.1, 2.9, 4.2 and 4.9 mm (0.04, 0.11, 0.17 and 0.19 in.) from thefront surface are considered as 1.0, 2.8, 4.1 and 4.8 mm (0.04, 0.11,0.16 and 0.19 in.) because two signals (thermal response of prob-lematic and unproblematic or reference regions) are requiredwhile doing cross correlation. In the present case, the referencethermal signal has been chosen as the one corresponding to a0.1 mm (3.9 × 10-3 in.) deep discontinuity very close to the sur-face. The concept of discontinuity detection by shifts in correla-tion peaks for thermal wave imaging techniques is thus intro-duced and illustrated.

CONCLUSIONIn this paper a novel approach (digitized linear frequency mod-

ulated thermal wave imaging) is proposed which circumventssome of the limitations of conventional infrared thermographictechniques. This novel approach simultaneously combines advan-tages of modulated and pulse phase theromographic techniques byprobing with thermal waves into the test specimen in a desiredrange of frequencies and extracting the phase information from theobserved thermal response. Pulse compression has been carriedout for discontinuity detection in a mild steel sample. The advan-tages of the proposed new method over pulse, lock in, pulsephase and linear frequency modulated thermal wave imaginghave been described.

REFERENCESLhota, J.R., S.M. Shepard, B.A. Rubadeux and T. Ahmed, “Enhanced Spa-

tial and Depth Resolution of Pulsed Thermographic Images,” Review ofProgress in Quantitative Nondestructive Evaluation, Vol. 20A, D.O.Thompson and D.E. Chimenti, eds., New York Plenum Press, 2000, pp.492-498.

Maldague, X.P.V., Theory and Practice of Infrared Thermography for Non-destruc-tive Testing, Hoboken, New Jersey, Wiley-Interscience, 2001.

Maldague, X.P.V., F. Galmiche and A. Ziadi, “Advances in Pulsed PhaseThermography,” Infrared Physics & Technology, Vol. 43, 2002, pp. 175-181.

Mulaveesala, R. and S. Tuli, “Implementation of Frequency ModulatedThermal Wave Imaging for Non-destructive Subsurface Defect Detec-tion,” Insight, Vol. 47, No. 4, 2005, pp. 206-208.

O’Donnell, Matthew, “Coded Excitation System for Improving the Penetra-tion of Real-time Phased-array Imaging System,” IEEE Transactions on Ul-trasonics, Ferroelectrics, and Frequency Control, Vol. 39, No. 3, 1992, pp. 341-351.

Tuli, S. and R. Mulaveesala, “Frequency-modulated Wave Thermogra-phy for Non-destructive Testing, Quantitative Infrared ThermographyProceedings, Rhode-Saint-Genese, Belgium, von Karman Institute forFluid Dynamics, 2004, pp. H.6.1-6.6.

Tuli, S. and R. Mulaveesala, “Defect Detection by Pulse Compression in Fre-quency Modulated Thermal Wave Imaging,” Quantitative Infrared Ther-mography, Vol. 2, No. 1, 2005, pp. 41-54.

Wehner, D.R., High Resolution Radar, Norwood, Massachusetts, ArtechHouse, 1994.

Wu, D. and G. Busse, “Lock-in Thermography for Nondestructive Evalua-tion of Materials,” Revue Générale de Thermique, Vol. 37, 1998, pp. 693-703.


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digitized frequency modulated thermal wave imaging for ndt

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