Depth Resolved Thermal Wave Imaging Approach for Non-Destructive Testing and Evaluation of Steel Sample

Reliability of sub-surface defects is imperative for safer functionality of critical materials/components/structures used in a wide variety of applications in various industries. The need for reliable, fast, remote, safe inspection and evaluation methods for detecting hidden defects increases in parallel with the demand for more sustainable solutions, which helps in inherent design and manufacturing specifications modifications. During in-service operations, the hidden defects typically originated from various loading conditions leading to catastrophic failure. This work explores the best possible reliable, fast, remote, and safe inspection and evaluation experimental method and the associated post-processing approach using InfraRed Imaging (IRI) for Thermal Non-Destructive Testing and Evaluation of mild steel materials. This proposed work provides an insight into the state-of-the-art research in the field of thermal/infrared non-destructive testing and evaluation methods and associated post processing approach to visualize the hidden subsurface defects not only resolved by spatial thermal gradients but also simultaneously provide temporal thermal gradients at the defective regions.

Therefore, the presence of defects may yield critically negative consequences like the loss of products, reduction of a component's service life, environmental damage, repair costs, and overall downtime costs.The detection of these defects not only avoids fails in service of critical components but in concept, will also enable the healing of those components by repairment of the defects.
The most common Non-destructive Testing and Evaluation (NDT&E) techniques are Visual Inspection Testing (VT), Dye Penetrant Testing (PT), Magnetic Particle Testing (MPT), Electromagnetic Testing (ET), Thermal/InfraRed Imaging (IRI), Radiographic Testing (RT), Acoustic emission Testing (AET), and Ultrasonic Testing (UT).Depending on the level of sophistication involved, the variants of these techniques are frequently classified and commercialized as conventional or advanced solutions.NDT&E is commonly an essential requirement to qualify the raw materials before being processed, to inspect sub-components and final products during and after their manufacture, and to inspect structural systems and equipment during operation and maintenance periods.
In recent times, IRI for Thermal Non-destructive Testing & Evaluation (TNDT&E) has confronted widespread

Introduction
Defects presented during the design or manufacturing stage due to imperfections in the processor introduced during the in-service stage may jeopardize the component's integrity and functionality, making it not suitable for its intended requirement, which may consequently lead to failure.demands for the inspection and characterization of various industrial and biomedical materials [1][2][3][4][5][6].The principle involved contingent on the mapping of thermal distribution over the test object to find its surface and sub-surface defects, their thermo-physical properties, and stress mapping [6][7][8][9][10].Due to the potential likelihood of IRI, it finds numerous applications in various fields, such as aeronautical, automotive, civil, electrical, mechanical, and bio-medicine industries [11][12][13][14][15].
Among various NDT&E techniques, IRI has emerged as a reliable inspection method due to its non-contact, wholefield, quick, safe and non-invasive inspection capabilities.
In passive infrared imaging, a natural thermal profile over the test object is procured to detect its surface and subsurface abnormalities (without any external stimulus).It is useful for applications in which the object exhibits enough thermal gradients over it.Some of its applications are to test the thermal energy leakage in buildings, losses in power transmission lines, corrosion monitoring of pipe walls in thermal power plants, power dissipation in electronic chips, condition monitoring of bridge decks, building seepage inspection applications, etc. Insufficient thermal contrast from the excessive deep subsurface features and the ineffectiveness of providing quantitative analysis limit the applicability of the passive approach.
Active thermography [20][21][22][23][24][25][26] uses a predetermined guided heat stimulus to launch similar thermal waves into the test object with known bandwidth, amplitude, and phase.Extracting deeper subsurface anomalies of relatively smaller lateral dimensions demands appropriate signal, image, and video processing schemes onto the recorded temporal thermal response captured over the test object.This technique is preferred over the passive approach due to the significant  improvement of the thermal contrast provided by subsurface anomalies in addition to its added quantification capabilities and enhanced deep penetration, which promotes deeper depth analysis for the object under inspection.
PT is the fastest and simplest among the other thermal NDT & E methods [1,3,5].In PT, a short run of high peak power heat stimulus is deposited over the test object, and its temporal thermal distribution is generally recorded in the test sample's cooling cycle.The difference in thermal properties at defective and non-defective regions contributes to thermal contrast over the test object.Hot or cold spots at defective locations and their time of appearance etc. can be used for analysis in PT to get the thermophysical properties of hidden anomalies.Applicability of PT is restricted due to the demand for significant power heat sources to probe the high-frequency thermal waves into the test sample to detect the sub-surface defects with enough resolution along with the problems related to non-uniform emissivity and uneven heating over the object, which highly influences the thermal distribution over the test object.
LT utilizes a continuous mono-frequency incident heat flux onto the test object with relatively low or moderate peak power heat sources [2].It leads to the generation and propagation of thermal waves into the test object.Phase analysis is carried out on the obtained thermal response to reveal subsurface details of the test object either by using the Fourier transform (FT) approach or the phase shifting approach.This post-processed phase information minimizes the impact of emissivity variations and non-uniform heating [14][15][16][17][18][19][20] effects on the obtained results.To provide continuous depth scanning and to resolve the defects located at various depths with different spatial dimensions, repetitive experimentation is to be performed at different excitation frequencies [26][27][28][29][30][31][32][33].This makes LT a tedious approach to resolve the defects located at various depths of different lateral dimensions due to its mono-frequency sinusoidal thermal distribution.
PPT is like PT as far as the experimentation is concerned, but analysis is carried out by the application of FT over the temporal temperature history of each pixel during its cooling period [4,5].It grabs the advantages of wide bandwidth of PT and the merits of phase-based analysis of LT.However, Frequency Modulated Thermal Wave Imaging (FMTWI) [16][17][18][19][20][21][22] probes the thermal waves into the test object within a suitable band of frequencies in a limited time span decided by the thermal properties of the sample and its physical dimensions as shown in Fig. 1(a).
The frequency response and its auto-correlation function are as shown in Fig. 1(b) and Fig. 1(c) respectively.This makes FMTWI as economical and reliable inspection technique which overcome the limitations of the demand of high peak power thermal sources of pulse-based techniques (PT and PPT) and requirement of tedious experimentation of LT to detect the defects located at different depths of various spatial dimensions with enough resolution.The feasibility of sweeping the desired band assures a continuous depth scanning of the object in a single experimentation cycle even with the usage of low peak power heat sources.
Further, as far as the post-processing approaches are concerned, the most widely used conventional FT phase-based analysis redistributes the entire imposed thermal energy over the sample under examination into the discrete frequency components [23,24] leading to a restricted processing resolution and sensitivity for detecting the subsurface duration is compressed to a localized narrow time duration rather than redistribution of the imposed energy in to the associated frequency components as in the case of FT analysis.This time-domain based matched-filter approach's capability has been compared with the widely used conventional frequency domain phase approach not only for the defect detectability by the spatial thermal gradients but also the depth (temporal) resolvability.The potentiality of the defects with a chosen frequency component phase information as shown in Fig. 2.This conventional approach is outperformed by the matched-filter based time domain (correlation coefficient and phase) analysis [24,25] as shown in Fig. 3.
In the matched filter-based time-domain data processing approaches, the supplied energy with the required band of frequencies swept in the relatively limited span of predefined

Results and Discussions
To investigate the detection capabilities of widely used active infrared imaging techniques and the associated postprocessing approaches, experiments have been carried out using FMTWI on a mild steel test object having blind holes as defects as shown in Fig. 4.
Further, the FT and time domain (correlation coefficient and phase) based post-processing schemes have been adopted.FMTWI has been carried out for 100s duration with a sweep frequency of 0.01 Hz to 0.1 Hz by keeping the capturing frequency 20 Hz by using two halogen lamps of 1 KW peak power.Further the frequency domain (stack of phase image sequence) and time-domain based data processing (stack of pulse compressed and phase image pulse-compression based correlation coefficient and time domain phase approaches for defect detection has been investigated. The matched filter based pulse-compression post-processing data analysis method has its merits over the conventional approaches, such as immune to multiplicative noises produced during the experimentation from the test sample (non-uniform illumination, emissivity variations over the sample surface) as well as the additive noise generated in the detection process (thermal noise).exhibits superior sub-surface defect detection capabilities than that of frequency-domain and time-domain phase based post-processing schemes by not only providing the enough spatial contrast over the defective regions but also exhibits enhanced depth resolvability.sequence) approaches have been adopted on the obtained mean zero experimental thermal response.The pulse compression is achieved by correlating the mean zero thermal response over the test sample at a chosen location as a reference thermal response and it is correlated with the temporal thermal profiles obtained over the pixels in the field of view.Figure 5 to Fig. 7 shows reconstructed stack of thermograms of the proposed frequency and time domain data processing approaches on the data obtained from the FMTWI experiments.
It is clear from the thermal stacks reconstructed with different cross-sectional views from the obtained results that the time domain phase images (Fig. 6) show the superior spatial thermal contrast than that of the widely used frequency domain phase approach (Fig. 5).
Further it is clear from the thermal stacks reconstructed from the pulse-compressed approach exhibits superior depth as well as spatial resolvability (Fig. 7) than that of the conventional frequency domain phase approach.

Conclusions
Widely used post processing modalities for thermal nondestructive testing and evaluation (frequency-domain and time-domain based analysis) are discussed for inspection of sub-surface blind hole defects in the mild steel specimen.Further, defect detection capabilities of the time-domain phase analysis obtained from matched-filter based scheme have been highlighted over the conventional frequencydomain based analysis in providing the superior spatial contrast over the defective locations.It is further emphasized that correlation coefficient based post-processing approach for pulse compression favorable excitation scheme (frequency modulated incident heat flux over the sample)

Fig. 2
Fig. 2 Data processing to obtain frequency domain based phasegrams

Fig. 1
Fig. 1 Aperiodic thermal excitation (a).Linear frequency modulated thermal response for an incident frequency modulated heat flux over the mild steel test specimen with frequencies varying from 0.01-0.1 Hz

Fig. 3
Fig. 3 Data processing to obtain time-domain based correlation coefficient images and phasegrams

Fig. 4
Fig. 4 (a) (Left to right) Schematic of the experimental steel sample, cross-sectional view at the beginning of the defect, cross-sectional view at the middle of the defective region (b) The schematic of the experimental set up

Fig. 6 Fig. 5 (
Fig. 6 (a)-(c) illustrate the constructed stack of time-domain phasegrams for three different cross-sectional slices from the recorded thermal data from FMTWI

Fig. 7
Fig. 7 (a)-(c) show the reconstructed stack of correlation coefficient images for three different cross-sectional slices from the recorded thermal data from FMTWI