Scanning Acoustic Microscopy Images Research Articles

The respective and dependent effects of scattering and bone matrix absorption on ultrasound attenuation in cortical bone

Cortical bone is characterized by a dense solid matrix permeated by fluid-filled pores. Ultrasound scattering has potential for the non-invasive evaluation of changes in bone porosity. However, there is an incomplete understanding of the impact of ultrasonic absorption in the solid matrix on ultrasound scattering. In this study, maps were derived from scanning acoustic microscopy images of human femur cross-sections. Finite-difference time domain ultrasound scatter simulations were conducted on these maps. Pore density, diameter distribution of the pores, and nominal absorption values in the solid and fluid matrices were controlled. Ultrasound pulses with a central frequency of 8.2 MHz were propagated, both in through-transmission and backscattering configurations. From these data, the scattering, bone matrix absorption, and attenuation extinction lengths were calculated. The results demonstrated that as absorption in the solid matrix was varied, the scattering, absorption, and attenuation extinction lengths were significantly impacted. It was shown that for lower values of absorption in the solid matrix (less than 2 dB mm−1), attenuation due to scattering dominates, whereas at higher values of absorption (more than 2 dB mm−1), attenuation due to absorption dominates. This will impact how ultrasound attenuation and scattering parameters can be used to extract quantitative information on bone microstructure.

Intelligent diagnosis of flip chip solder joints with resolution enhanced SAM image

Scanning acoustic microscopy (SAM) technique has been applied to defect inspection in electronic devices. With the increase of packaging density, detection of the micro-defects in high density devices becomes more and more challenging. The SAM test is suffering from sacrificing the spatial resolution to reach a certain penetration depth of the ultrasonic waves. So it is necessary to enhance the resolution level of the SAM image. In this paper, a wavelet based resolution enhancement technique was investigated to reconstruct a high quality image for SAM test of the flip chip packages. The stationary wavelet transform was adopted to decompose the captured SAM image into four frequency subbands, and the high frequency subbands were enhanced by adding the difference matrix in the intermediate stage, and a super resolution SAM image was derived from combining all the subbands by using the Inverse Discrete Wavelet Transform. Then the solder joints segmented from the SR-SAM image were classified by using the SVM algorithm. The results validated that the proposed technique is effective to improve the detection accuracy of SAM test.

Small sample classification based on data enhancement and its application in flip chip defection

With the development of chip integration, scanning acoustic microscopy (SAM) technology is widely used in the intelligent inspection of chips. However, only a few SAM images of the chip are acquired for the SAM test, which will lead to a lack of sufficient data for intelligent recognition of the chip defects. To solve this problem, a generative adversarial network with the addition of a residual attention module, RA-GAN, was proposed and applied to a small sample. Firstly, the original generative adversarial network (GAN) was constructed and the residual attention module was added to GAN. Secondly, the part of the generator network was improved for the SAM images of flip chip, which increases the perceptual field and enriches the details of the generated images. Then, the appropriate learning rate was adjusted during the network training phase, which can prevent the overfitting of the model. Finally, an enhanced dataset with improved image quality and quantity was obtained. To evaluate the effectiveness of the reconstructed dataset, deep learning algorithms were used for SAM image classification. The results validate the effectiveness and advancement of combining RA-GAN with traditional image data enhancement, which can be applied for small sample classification in engineering applications.

Micro solder bump detection of flip chip using improved decision tree model based on SAM image

The increasing packaging density of flip chips brings great challenges for micro defect detection. It is necessary to develop an efficient and automatic inspection system for electronic industrial application. In this paper, the scanning acoustic microscopy (SAM) technology and the optimized classifier were investigated for the automatic detection of solder joint defects of flip chips. Ultrasonic images of 1902 solder bumps from 6 chip samples were obtained using a SAM equipment. The decision tree model was improved by introducing the granularity decision entropy. The feature vectors were extracted from the images of solder bumps, and then used for classification. The results show that the decision tree model correctly detected 1812 solder bumps with the accuracy of 95.3%. It is verified that the ultrasonic defect detection system based on the improve decision tree model has high accuracy for micro defect inspection, which has potential and promising application in the electronic packaging industry.

The intelligent detection method for flip chips using CBN-S-Net algorithm with SAM images

Flip chip has become one of the mainstream technologies in microelectronic packaging. Solder bumps play an important role in the interconnection of flip chips packages. The scanning acoustic microscopy (SAM) technology and a new network model were investigated for intelligent detection of flip chips. A new network model called CBN-S-Net was proposed based on a deep convolution network CBN and an optimized Siamese network. The CBN convolution network was used to extract the deep fusion features of solder bumps, and new triplet sample pairs were designed to measure the similarity between solder bumps. With the strategy of triplet sample pairs, the SAM images of the flip chip were used to verify the effectiveness of the designed network model. The results showed that the improved network has a high detection accuracy of 98.73%, and the proposed method is effective for the intelligent detection of solder bumps in high-density electronic packages.

Biomechanical changes in myopic sclera correlate with underlying changes in microstructure

Myopia alters the microstructural and biomechanical properties of the posterior sclera, which is characterized as a layered structure with potentially different inter-layer collagen fibril characteristics. Scanning acoustic microscopy (SAM) has been used to investigate how the micron-scale bulk mechanical properties of the posterior sclera are affected by myopia. Other investigators have employed second harmonic generation (SHG) imaging to characterize the collagen microstructure of tissues. In the present study, SAM and SHG imaging were used to investigate the existence of biomechanically-distinct scleral layers and identify relationships between mechanical properties and tissue microstructure in myopic guinea pig (GP) eyes. Diffusers were worn over the right eyes of six, 1-week-old GPs for one week to induce unilateral form-deprivation myopia. GPs were euthanized, enucleated, and eyes were cryosectioned. Twelve-micron-thick adjacent vertical cryosections were scanned with SAM or SHG. SAM maps of bulk modulus, mass density, and acoustic attenuation were estimated. A fiber-extraction algorithm applied to SHG images estimated collagen fiber length, width, straightness, alignment, and number density. Results revealed that the posterior sclera may exhibit biomechanically distinct layers that are affected differently in myopia. Specifically, a layered structure was observed in the mechanical-parameter maps of control eyes that was less apparent in myopic eyes. Collagen fibers in myopic eyes had smaller diameters and were more aligned. Myopia-associated biomechanical changes were most significant in the outermost and innermost scleral layers. SAM-measured mechanical parameters were correlated with collagen fiber microstructure, particularly fiber length, alignment, and number density, which may imply the biomechanical parameters estimated from SAM measurements are related to tissue microstructure. Interestingly, some changes were greatest in more-peripheral regions, suggesting interventions to strengthen the sclera may be effective away from the optic nerve and efficacy may be achieved best when intervention is applied to the outermost layer.

The effects of nominal absorption in bone on the extinction lengths for scattering, absorption, and overall attenuation

In cortical bone, the effect of absorption in the solid matrix on ultrasound scattering and propagation is not well understood, and for absorption, it is not easily incorporated into simulations and is difficult to measure independently from scattering attenuation. In this study, finite-difference time-domain simulations were conducted in maps derived from scanning acoustic microscopy images of human femur cross-sections. These maps were modified by controlling pore density (fixed at 10 pores/mm2) and diameter distribution (ranging between 30 and 100 μm). Eight nominal absorption values, ranging from 0 to 100 dB/cm, were attributed to the solid matrix. Absorption in the pores was set to 0.01 dB/cm. Propagation of ultrasound pulses centered at 8 MHz was simulated in both backscattering and through-transmission configurations. The scattering, absorption, and overall attenuation extinction lengths were obtained. T-tests demonstrated that varying the absorption significantly impacts the extinction lengths for scattering, overall attenuation, and absorption. The differences in values for the scattering, attenuation, and absorption extinction lengths when absorption varied from 20 to 40 dB/cm are statistically significant (respective p-values: 9.1 × 10−14, 3.3 × 10−5, and 8.8 × 10−5). It was also demonstrated that attenuation due to scattering dominates overall attenuation at low-nominal absorption values, whereas the converse is true at higher absorption values.

A novel practical approach for monitoring the crosslink density of an ethylene propylene diene monomer compound: Complementary scanning acoustic microscopy and FIB-SEM-EDS analyses

Tuning of the crosslink density (CLD) in the rubber compounds is very crucial for optimizing the physical and mechanical properties of the ultimate rubber products. Conventionally, CLD can be measured via rheological methods such as moving die rheometer (MDR), via mechanical tests such as temperature scanning stress relaxation analysis (TSSR), or via direct swelling experiments using Flory–Rehner approach. In the current study, two novel techniques, focused ion beam - scanning electron microscopy (FIB-SEM) processing, with simultaneous energy dispersive X-ray spectrometry (EDS) mapping analysis and scanning acoustic microscopy (SAM) were combined and correlated to conventional methods on a model recipe of ethylene propylene diene monomer (EPDM) compound having different sulphur contents. Depending on the applied technique, the increase in the crosslink density with sulphur content was found to be 1.7 fold for the Flory–Rehner approach and 1.2 fold for both TSSR and MDR. It is directly monitored from the FIB-SEM-EDS analysis that the sulphur distribution and agglomeration behavior increased in line with ZnO content, which is an indirect indication of the rise in crosslink density. The impedance maps of the crosslinked samples obtained through SAM analysis revealed that the impedance of the samples increased with the increasing sulphur content, which can be attributed to higher level of crosslink density. A quantified correlation was obtained between SAM images and the crosslink density of the samples. It was shown that SAM is a promising tool for practical and non-destructive analysis for determining the formation of crosslink density of the rubbers.

Using convolutional neural network for intelligent SAM inspection of flip chips

The flip-chip (FC) technology is widely used in microelectronic packaging. As the dimensions and pitch of the chip solder bumps are getting smaller, defect inspection becomes increasingly challenging. In this paper, scanning acoustic microscopy (SAM) was used for the non-destructive inspection of FC packages. However, the detection accuracy may be limited by a low resolution of the SAM image. Therefore, the image super-resolution (SR) method was employed to enhance the SAM image quality. The modified very-deep SR (VDSR) algorithm, based on a convolutional neural network (CNN), was investigated to reconstruct high resolution acoustic micrographs. In addition, a CNN-based classification model was designed for the classification of the solder joints. The results obtained in the present study demonstrate that the improved VDSR combined with the CNN classification model provides excellent performance for improving the SAM detection accuracy of the inspection of flip chip packages.

Scanning acoustic microscopy imaging of cellular structural and mechanical alterations from external stimuli

Cells incur structural and functional damage from external stimuli. Under scanning acoustic microscopy (SAM), speed of sound (SOS), attenuation, and thickness values are plotted to visualize cellular stiffness, viscosity, and size. The obtained digital data are then compared using statistical analysis. In the present study, we aimed to investigate the alterations in the mechanical and structural characteristics of cancer cells in response to anticancer drugs, acidic fluids, and microwave burdens using SAM. We found that active untreated cells showed increased thickness and reduced SOS and attenuation, whereas dying treated cells displayed reduced thickness and increased SOS. Tannic and acetic acid treatments and microwave irradiation all increased SOS and attenuation and reduced thickness, which meant that these treatments made cells thinner, stiffer, and more viscous. Furthermore, the different anticancer drugs interacted with cancer cells to induce characteristic changes in SAM values. These structural and mechanical alterations induced in cells were difficult to observe under light microscopy. However, under SAM, cancer cell activity and function corresponded consistently with changes in SAM values. Cellular damage parameters were statistically compared between the different treatments, and time-dependent cellular changes were established. SAM observation can therefore reliably evaluate cancer cell damage and recovery after chemotherapy and physical therapy. These results may help evaluate the therapeutic efficacy of various treatments.

Layer Configurations for Al-Ge Eutectic Wafer Bonding

Introduction Heterogeneous integration between CMOS and MEMS devices can be realized by using Al-Ge which are compatible materials in both fabrication environments. Al is widely used in the CMOS-industry and does not involve any contamination risk in contrast to other eutectic systems like Au-Si[1]. Si-Ge is also widely used to augment transistor switching speed [2]. The eutectic reaction for Al-Ge takes place around 420oC, which is CMOS-compatible[3], [4].The limitation of the Al-Ge system is the need for removal of the surface oxides. It was previously reported that Ge can be deposited on top of Al using evaporation or sputtering without vacuum-break [4]. This prevents oxide formation on the Al layer. By contrast, GeO2 is easy to remove with a dilute-HF dip [5]. The current work investigates using a single layer or dual layers of Al and Ge for bonding. Depositing single layers is advantageous since it enables patterning by dry etch and avoids the need for a lift-off process. The layers are deposited in separate tools, so oxide formation is expected. The effect of the presence of the oxide layers will be investigated. Method Al and Ge layers are deposited on 200 mm wafers with 500 nm thermal oxide. Thicknesses are matched to eutectic composition. (300 nm Ge and 500 nm Al) The wafers are bonded and then analyzed using scanning acoustic microscopy (SAM) and cross-sectional scanning electron microscopy (X-SEM). Results and discussion The first group of wafers are prepared with a single layer of Al and Ge on either substrate while the second group has a double layer of either Al on top of Ge or Ge on top of Al. All wafers are joined by using forming gas pre-treatment at 390oC, 15 min of solid state inter-diffusion at 410oC followed by bonding for 30 min at 450oC with 25 kN of force. The bonding recipe is illustrated in figure 1. The wafers are analyzed using SAM and X-SEM. The SAM results are shown in figure 2.In figure 2.a the result of the single layer configuration bond is visible. Micro-voids are visible in the center. The outer region has larger voids. The X-SEM image of the bonding interface confirms the presence of small voids, as shown in figure 3. The formation of the eutectic in the single layer configuration is only possible where the two wafers are in contact. Non-uniformity and roughness could be preventing full contact and result in voids.The SAM result of the Al on top of Ge double layer configuration bond is shown in Figure 2.b, the outer region is mostly unbonded. The bonding interface is clearly visible on the X-SEM image, as shown in figure 4. There is no interface between the Al and the Ge layer visible. The native oxide on top of the Al layer could be preventing the two sides from mixing but the Ge oxide layer does not seem to hinder the eutectic formation.The SAM image of the Ge on top of Al configuration bond is shown in figure 2.c. The wafer looks well bonded. X-SEM reveals a triple layer structure. (see figure 5) The bond interface is clearly visible and additionally two thinner interfaces are visible. These could be the remainder of the native Al-oxide. Conclusion Three configurations of Al-Ge eutectic bonds were investigated using SAM and X-SEM. The highest bond uniformity is obtained with Ge being the top layer prior to bonding. The presence of the oxide layers could be preventing the mixing of the eutectic across the bonding interface. In this regard especially the Al-oxide seems problematic.[1] B. Pathangey, L. D. McCarthy, and D. C. Skilbred, “Effect of metal contaminants in pre-gate oxide cleans for sub-100-nm devices,” IEEE Trans. Device Mater. Reliab., vol. 5, no. 4, pp. 631–638, Dec. 2005, doi: 10.1109/TDMR.2005.861161.[2] M. L. Lee, E. A. Fitzgerald, M. T. Bulsara, M. T. Currie, and A. Lochtefeld, “Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors,” J. Appl. Phys., vol. 97, no. 1, p. 011101, Jan. 2005, doi: 10.1063/1.1819976.[3] H. Takeuchi, A. Wung, X. Sun, R. T. Howe, and T.-J. King, “Thermal Budget Limits of Quarter-Micrometer Foundry” IEEE Trans. Electron Devices, vol. 52, no. 9, pp. 2081–2086, Sep. 2005, doi: 10.1109/TED.2005.854287.[4] A. Hilton and D. Temple, “Wafer-Level Vacuum Packaging of Smart Sensors,” Sensors, vol. 16, no. 11, p. 1819, Oct. 2016, doi: 10.3390/s16111819.[5] B. Onsia et al., “The Influence of Wet Treatments on the Germanium Wafer Surface,” Solid State Phenom., vol. 103–104, pp. 27–30, Apr. 2005, doi: 10.4028/www.scientific.net/SSP.103-104.27. Figure 1

Enhancement of Acoustic Microscopy Lateral Resolution: A Comparison Between Deep Learning and Two Deconvolution Methods.

Scanning acoustic microscopy (SAM) provides high-resolution images of biological tissues. Since higher transducer frequencies limit penetration depth, image resolution enhancement techniques could help in maintaining sufficient lateral resolution without sacrificing penetration depth. Compared with existing SAM research, this work introduces two novelties. First, deep learning (DL) is used to improve lateral resolution of 180-MHz SAM images, comparing it with two deconvolution-based approaches. Second, 316-MHz images are used as ground truth in order to quantitatively evaluate image resolution enhancement. The samples used were mouse and rat brain sections. The results demonstrate that DL can closely approximate ground truth (NRMSE = 0.056 and PSNR = 28.4 dB) even with a relatively limited training set (four images, each smaller than 1 mm ×1 mm). This study suggests the high potential of using DL as a single image superresolution method in SAM.

Power Module Interconnection Reliability in BTS Applications

In this paper, the reliability of RF power transistors’ solder attachments is characterized through experiments and simulations. Test cases consisted of power amplifier (PA) modules on AlSi10Mg substrates with either a low or high mutual thermal mismatch. The module’s flange interconnections were stressed by means of thermal cycling testing (TCT) in the 15 °C–95 °C range. Scanning acoustic microscopy (SAM) was used intermittently to inspect the interconnections of selected structures during cycling breaks. Optical cross-polarization microscopy and scanning electron microscopy were used in the failure analysis of the solder joints. Different materials and dimensional variations were tested in simulations to observe differences in thermal stress. The viscoplastic behavior of lead-free solder in the interconnection was modeled using Anand’s constitutive equations. The first cracks could be observed with SAM after 100 cycles. SAM imaging showed that in the worst case, 72% of the interconnection area had cracked at the end of the 1100-cycle TCT. Only a marginal amount of cracks could be observed in PA modules with a better coefficients of thermal expansion match to the substrate. Simulations indicated that it is possible to decrease creep energies significantly and thereby increase the lifetime expectancy of interconnections by selecting the correct materials and structures.

The Auto-focus Method for Scanning Acoustic Microscopy by Sparse Representation

As an efficient non-destructive checking technique, scanning acoustic microscopy has been rapidly developed and widely used in nondestructive detection for composites, chip manufacturing, bio-pharmaceuticals and so on. Scanning acoustic microscopy can obtain the two-dimensional image and reconstruct three-dimensional model of the internal structure inside the sample, compared with the optical microscope. Due to the geometrical features of high frequency transducer, the precision of focus has already become the key factor for the digital imaging and defect detecting. Especially for the current 3D packaging chips and multi-layer composite materials, thickness of layer has reached the level of nm. Different focus plane will provide a completely different digital image. However, the process of focusing has been relying on manual operation without great development until now. To improve the speed and accuracy of the focusing, we proposed a quick auto-focus method on scanning acoustic microscopy. This method can be divided into three steps. The first one is fast auto-focusing on upper surface, the second other one is auto-focusing on the interlayer base on V(z) curve, and the last one is to improve the A-Scan signal of points in the V(z) curve with spars signal representation. This method is integrated into Scanning Acoustic Microscopy imaging software and has been validated in the experiment with Olympus transducers at 30\\50 MHz. It can be seen that this method can effectively improve the accuracy of focus and shorten the focus time of Scanning Acoustic Microscopy through experiments.

Electrical Performance and Reliability Characterization of a SiC MOSFET Power Module With Embedded Decoupling Capacitors

Integration of decoupling capacitors into silicon carbide (SiC) metal oxide semiconductor field effect transistor ( mosfet ) modules is an advanced solution to mitigate the effect of parasitic inductance induced by module assembly interconnects. In this paper, the switching transient behavior is reported for a 1.2-kV SiC mosfet module with embedded dc-link capacitors. It shows faster switching transition and less overshoot voltage compared to a module using an identical package but without capacitors. Active power cycling and passive temperature cycling are carried out for package reliability characterization and comparisons are made with commercial Si and SiC power modules. Scanning acoustic microscopy images and thermal structure functions are presented to quantify the effects of package degradation. The results demonstrate that the SiC modules with embedded capacitors have similar reliability performance to commercial modules and that the reliability is not adversely affected by the presence of the decoupling capacitors.

Use of golden samples for the assessment of the quality and reproducibility of scanning acoustic microscopy images of electronics samples

Scanning Acoustic Microscopy (SAM) is a widely used technology for non-destructive failure analysis in electronics samples. The primary information generated by SAM is a grey scale image, which is the basis for the interpretation by the failure analysis engineer. The quality of this primary image depends, amongst others, on the system setup by the operator and on the selected transducer. Therefore, if SAM analyses of a given sample are performed by several engineers using different types of SAM systems, then in general the obtained images differ.In the present study we introduce specifically manufactured golden samples with single or stacked dice including known defects for assessing the image quality and reproducibility of SAM images. These golden samples represent a robust measurement standard. They are particularly suited for studying and then minimizing differences in SAM image quality obtained by different operators and/or different types of SAM measurement equipment. Ultimately, they will allow to homogenize the SAM image quality on different kinds of typical standard samples on a high level, and thus contribute to reliable failure identification independently of the specific operator or measurement system.

Scanning Acoustic Microscopy Image Super-Resolution using Bilateral Weighted Total Variation Regularization.

Scanning acoustic microscopy (SAM) is an imaging modality used to obtain 2D maps of acoustical and mechanical properties of soft tissues and uses ultrasound transducers operating at very high-frequencies. Such transducers are challenging and costly to manufacture, and SAM systems at higher frequencies become more sensitive to experimental issues. Nevertheless, biomedical applications of SAM often require spatial resolutions nearly as good as light microscopy. In addition, stained histology photomicrographs of thin sections of tissues are easily obtained with the necessary resolution and accuracy. Consequently, the aim of this study is to introduce a bilateral approach that enhances the resolution of SAM images by leveraging the co-registered high-resolution histology image. We propose to use bilateral weighted total variation regularization to solve the super-resolution problem. A fast matrix-less solver is developed by utilizing the Alternating Direction Method of Multipliers (ADMM) and solving the least squares problem in one ADMM step in the Fourier domain. Reconstruction results on experimentally recorded SAM and histology data show promising improvement over the classical techniques.

Defect inspection of flip chip package using SAM technology and fuzzy C-means algorithm

Solder bumps are widely used in surface mount components, which provide electrical and mechanical connection between the chip/package and the substrate. As the solder bump getting smaller in dimension and pitch, it becomes more difficult to inspect the solder defects hidden in the IC package. In this paper, an intelligent inspection method using the scanning acoustic microscopy (SAM) and the fuzzy C-means (FCM) algorithm was investigated. A flip chip package of FA10 was chosen as the test sample. The SAM tests of FA10 were carried out in C-scan mode. The sub-image of every solder bump was segmented from the SAM image. The statistical features were then calculated and adopted for clustering of solder bumps using the FCM algorithm. The recognition results of FCM reached a high accuracy of 94.3%. The intelligent system is effective for defect inspection in high density packages.

Impulse excitation scanning acoustic microscopy for local quantification of Rayleigh surface wave velocity using B-scan analysis.

A new technique for performing quantitative scanning acoustic microscopy imaging of Rayleigh surface wave (RSW) velocity was developed based on b-scan processing. In this technique, the focused acoustic beam is moved through many defocus distances over the sample and excited with an impulse excitation, and advanced algorithms based on frequency filtering and the Hilbert transform are used to post-process the b-scans to estimate the Rayleigh surface wave velocity. The new method was used to estimate the RSW velocity on an optically flat E6 glass sample, and the velocity was measured at ±2 m/s and the scanning time per point was on the order of 1.0 s, which are both improvement from the previous two-point defocus method. The new method was also applied to the analysis of two titanium samples, and the velocity was estimated with very low standard deviation in certain large grains on the sample. A new behavior was observed with the b-scan analysis technique where the amplitude of the surface wave decayed dramatically on certain crystallographic orientations. The new technique was also compared with previous results, and the new technique has been found to be much more reliable and to have higher contrast than previously possible with impulse excitation.

Diffusion constant and frequency dependent attenuation for the assessment of cortical bone porosity

The objective of this study is to assess cortical bone porosity through measurements of the diffusion constant and attenuation as a function of frequency. Using FDTD simulations, the diffusion constant was calculated for 45 modified human femur shaft bone geometries obtained from a reference binarized 100-MHz Scanning Acoustic Microscopy image. The diffusion constant was sensitive to cortical porosity and demonstrated around 85% decrease for 10% increase in porosity. This suggests that lower diffusion constant values could be associated with more severe cases of osteoporosis. Using a spectroscopy approach in the 1–8 MHz range, we demonstrate that the attenuation coefficient as a function of frequency can be approximated as:α(f) = AfB + C, where “A”, “B” and “C” are related to pore diameter and pore concentration. For a constant pore density (10 mm2), “A” increased from 0.03 to 19.79 when pore diameter increased (Po.Dm ∈40–130μm), while “B” and “C” were found to decrease from 2.654 to 0.5741 and from −0.061 to −21.43, respectively. A similar trend was observed when pore diameter was kept constant. A model was derived to quantify pore size and concentration through constrained nonlinear optimization method. This parametric model combined with estimation of the diffusion constant has the potential to enable the quantification of pore size and concentration.