By combining dynamic mechanical testing with spectral-domain polarization-sensitive optical coherence tomography (SD-PS-OCT) performed at 1550 nm we are able to directly investigate for the first time changes within scattering technical materials during tensile and fracture tests. Spatially and temporally varying polarization patterns, due to defects and material inhomogeneities, were observed within bulk polymer samples and used to finally obtain – with the help of advanced image processing algorithms – quantitative maps of the evolving internal stress distribution. Furthermore, locally increased stress within fiber-reinforced composite materials was identified in situ with SD-PS-OCT to cause depolarizing sites of fiber-matrix debonding prior the onset of complete structural failure.
©2010 Optical Society of America
1. Introduction and motivation
Since the first presentation of optical coherence tomography (OCT) as a novel imaging method for the interior of scattering media , it has become a well established diagnostics technique for biomedicine and advanced life science applications. Meanwhile, a broad spectrum of extensions for conventional OCT including novel contrast mechanisms have been developed, with polarization-sensitive OCT being one prominent example [2,3]. Common to all these developments - including PS-OCT - is that they are nearly exclusively driven by the before mentioned field of biomedical diagnostics, although OCT provides the potential to significantly contribute to research in alternative disciplines .
In the case of PS-OCT, the main applications can be found to date in dentistry and dental research , ophthalmology , dermatology  and in the investigation of cartilage structures . Novel applications of PS-OCT reported outside the biomedical field are scarce and nearly exclusively dedicated to the investigation of the internal strain/stress state of technical materials [9–15]. PS-OCT acts in this case as a depth-resolved equivalent to standard photoelasticity, which is a well established method in experimental mechanics . In contrast to PS-OCT, for photoelasticity the sample is generally measured in transmission in order to obtain a lateral distribution of the strain-induced birefringence. Therefore, the sample has to be either transparent (or at least very thin ) or its surface is measured in reflection with a transparent coating on top, which provides the - to be detected - change of polarization of the probing light. Besides classical photoelasticity, other established optical methods like digital image correlation (DIC)  or speckle interferometry (SI)  are used to measure the displacement/deformation field in response to applied stress. However, these techniques give also no depth information and are in general constrained to the observation of the sample surface. Only recently, measurements of displacement fields within scattering media could be demonstrated in a depth-resolved way with low-coherence modifications of these techniques [20–23].
In this view, methods which can provide spatially resolved information also from the inside of materials, will be of increasing importance for understanding the performance of materials, with PS-OCT being a most promising candidate, since it simultaneously gives access to the internal microstructure and the resulting strain/deformation. However, all to date reported investigations with PS-OCT were carried out only in the time-domain (TD) on samples under quasi-static loading conditions [9–15]. In that way important aspects are omitted, since mechanical tests - like tensile loading, bending, impact experiments,… - are routinely performed in a dynamic way. Fourier-domain (FD)-OCT now provides – in contrast to TD-OCT – higher system sensitivities at increased scan rates [24,25], promoting e.g. spectral-domain PS-OCT (SD-PS-OCT)  for time-resolved studies. Interestingly, these advantages of SD-PS-OCT have to date and to the best of our knowledge not been exploited for the above introduced applications in experimental mechanics. Consequently, in this paper the - what we believe - first dynamic investigations performed in situ with SD-PS-OCT are presented to provide new insight in optical properties of technical materials and their relation to the corresponding mechanical properties: changes of sample birefringence and depolarization as well as of the observed internal microstructure are successfully put in relation to the global materials performance, as exemplified on bulk polymer and fiber composite samples subjected to mechanical testing.
2. Experimental setup
The majority of FD-PS-OCT systems - since developed for biomedical applications - were realized in SD-OCT or swept-source (SS-OCT) configuration in the 800 nm  and to a smaller extent in the 1300 nm wavelength region , but not for imaging at 1550 nm. Since absorption due to water is not an issue for most technical materials, imaging at longer wavelengths seems favorable due to increased penetration depth, as shown by a comparative TD-OCT study : the accessible depth for a variety of polymers was proven to be more than twice for imaging at 1550 nm than for 800 nm. Consequently, we realized a custom-built SD-PS-OCT system, as schematically depicted in Fig. 1 , dedicated to the imaging of technical materials. It is based in general on the free-space interferometer concept of an 800 nm biomedical SD-PS-OCT for retinal imaging , but exhibits an interferometer head which is built in a compact and robust way in order to be easily integrated into and being compatible with state-of-the-art mechanical testing equipment. Furthermore, a 1550 nm superluminescence diode with a spectral width of 55 nm (Exalos, Switzerland) is used, providing a depth resolution of 19 µm in air, which corresponds to roughly 13 µm in typical polymer materials with refractive index n ~1.45.
For PS-imaging, a polarizer and quarter wave plate ensure that the sample is irradiated with circular polarized light. In case of birefringent samples, elliptical polarized light is in general reflected back towards the polarizing beamsplitter (PBS). The quarter wave plate in the reference arm provides linear polarized light oriented at 45° with respect to axes of the PBS. The PBS then guides the two orthogonal polarization channels to two separate spectrometer units with pigtailed collimators (OZ-Optics), transmission gratings (600 l/mm, Wasatch Photonics, USA) and digital InGaAs CCD line cameras (1024 pixels, 25 µm pitch, 4 kHz; Sensors Unlimited, USA). A galvano scanner mirror (size 5 mm, GSI, Germany) in front of the objective lens (f = 50 mm) scans the measurement spot, providing a lateral resolution of ~14 µm (FWHM) in the focal plane - as verified on a resolution target - over the sample. The power on the sample was measured to reach 2.5 mW, resulting in a total system sensitivity of 95 dB. The sensitivity decay over three quarters of the total axial range (~2.5 mm) was determined to be 9.8 dB. B-scans with 1000 x 512 pixels (500 x 512 pixels) are acquired with a frame rate of 4 Hz (8 Hz): in accordance with , reflectivity images, optical retardation and axis orientation images can be simultaneously obtained with our setup. The data processing procedure is as follows: reference spectra, periodically acquired - e.g. every 10 seconds by automatically deflecting the measurement beam with the galvano mirror from the sample - are subtracted for both cameras from the raw interference spectra. The usual approach used in biomedical imaging, i.e. taking a moving average of acquired interference spectra for obtaining reference spectra, is not followed due to potential artifacts as sometimes observed for very regular structures of some technical specimens. Subsequently, the data is mapped to k-space, additionally corrected according the effective dispersion of the grating, and Fourier transformed. Reflectivity profiles are obtained by taking the squared sum of both polarization channels. The retardation is computed by taking the inverse tangent of their ratio, and the orientation of the optical axis is encoded in the phase difference between the two Fourier transformed profiles . Careful alignment of both spectrometers finally resulted in a minimal residual drift of the optical retardation and of the optical axis, measured over three quarters of the whole axial range, being as small as ~6° and ~9°, respectively.
For tensile testing the setup is combined with an electrodynamic testing machine (Bose Electroforce 3200, USA) operating at constant strain rates with velocities between 0.1 – 10 mm/s. Force and strain values are simultaneously acquired with the registered PS-OCT frames on the same computer system with a custom made software to ensure correct correlation between observed internal changes and the global strain/stress response of the materials.
As samples for the tensile tests, 1 mm thick shouldered test bars from elastomer particle filled polyamide (PA) and polypropylene (PP) polymeric materials were prepared (cross-section in middle area: 4 mm2). In addition, fracture tests were performed on glass fiber-reinforced epoxy sheets (pre-impregnated fiber composite materials), as used for the fabrication of helicopter rotor blades .
3. Results and discussion
3.1 SD-OCT for tensile testing of polymer materials
Routinely, materials under development are mechanically tested to obtain parameters like elastic modulus, yield stress or flow stress. In the case of polymer materials, the introduction of rubber particles into a rigid homopolymer matrix, like PP, is currently an issue of high interest for obtaining components with improved performance, e.g. for the automotive industry: the finely dispersed particles ensure increased toughness and impact strength of the polymer parts when compared to the pure, particle free matrix (however at the cost of decreased modulus and yield stress) [29,30]. Samples from such PP materials with dispersed rubber particles (average particle diameter ~1 µm) were investigated in a first set of experiments, as shown in Fig. 2 , with recorded SD-OCT reflectivity images taken during a typical tensile test.
For the experiment, the sample was scanned along the loading direction (y-direction) and distinct stages can easily be identified which correspond well to the simultaneously measured strain/stress response of the sample: at first the sample is of only slightly scattering nature with brighter spots visible in the bulk, as seen in Fig. 2(a), attributed to cavitations (i.e. air inclusions) around agglomerated rubber particles and as verified with conventional microscopy on (destructive) micrograph sections. From the simultaneously acquired strain-stress curve (Fig. 2(e)) it is evident that the sample is in the linear viscoelastic regime. As the strain increases, the slope of the curve decreases until the curve reaches a maximum, usually known as yield point (also called yield stress and yield strain). It should correspond to the point at which permanent irreversible plastic deformation takes place, but already a permanent deformation is in general observed for polymers when loaded to stress values below the maximum where the curve becomes non-linear . This behavior can now be directly observed for the first time by the depth-resolved imaging capabilities of SD-OCT: in the non-linear region of the strain-stress curve (Fig. 2(b)) more and more scattering sites are appearing within the sample. As the sample approaches the yield point (Fig. 2(c)), the degree of scattering dramatically increases, leading to the full suppression of an artifact (bright horizontal line at the bottom of Fig. 2(b)) caused by the strong reflection of the sample backside, which moved out of the imaging range during loading. The nature of the increased scattering characteristics is attributed at first to the formation of additional, small-scale cavitations between the rubber particles and the host matrix, leading finally to matrix crazing and stress whitening. At the yield point the opacity of the sample stabilizes and the region of flow stress is entered (Fig. 2(c)): necking occurs, with the transition between flowing and static material visible as a growing kink in the surface (Fig. 2(d)), until the sample fractures. It is well visible in the movie that within the static part of the sample (right side with respect to the arrow of Fig. 2(d)) the speckle pattern is stable, whereas flowing of the material causes fluctuations in the pattern. By taking the standard deviation of the individual image pixels over several consecutive frames the bowed flow front, indicated by dotted line in Fig. 2(f), can now clearly be discerned due to the different statistical behavior of the speckles, leading to – in average – higher values in the left (flowing) sample region. This is also an indication that with correlation analysis of successive reflectivity B-scans information on the local strain distribution can be derived, similar as performed e.g. in OCT elastography . From these results it is obvious, that SD-OCT already provides deeper insight by highlighting the temporal changes in the microstructure within the materials and by the capability to correlate these changes with the global performance (i.e. characteristics of the strain/stress curve) of the samples in the dynamic tests. In a complementary way to these presented results, our interest is focused for this particular work on the change of the polarization properties of the test samples, as detailed in the following sections for combined SD-PS-OCT imaging and testing.
3.2 SD-PS-OCT for tensile testing of polymer materials
Instead of using only OCT reflectivity data, the corresponding retardation images provided by SD-PS-OCT give additional contrast and information, as depicted in Fig. 3 , where recordings taken during tensile tests performed on rubber particle filled PA samples are presented.
The sample in Fig. 3(a) exhibits a defect on the surface, giving rise to necking in a confined region. The necking causes increased true stress, due to a decrease of the sample cross-section, immediately detectable in the retardation pattern (bottom images of Fig. 3). The retardation images are gray-scale encoded and have to be read in the following way: the light is impinging from the top onto the sample and a change from black to white corresponds to an increase of the retardation between the two orthogonal polarization directions by an amount of π/2 (single pass). Another phase lag of π/2 is reached by going from the white region to the next black region underneath, and so on. A high spatial frequency of stripes is therefore a sign of increased values of birefringence.
Such surface defects – especially in their initial stages – are easily detected by the above introduced DIC and SI methods. In contrast, in Fig. 3(b), also presenting an experiment performed on rubber filled PA material, for the first time to the best of our knowledge, the influence of inhomogeneities within scattering materials is directly observed in a spatially resolved way, which would go otherwise totally undetected in conventional material testing (or can only be observed in a very indirect way by SI or DIC via the sample surface): solely by OCT performed in a dynamic way the interior of such thick and scattering samples is successfully and directly accessed during the testing run. In detail, even in the reflectivity images only a slightly darker shadow (bow-shaped) can be distinguished from the brighter surrounding signal of the bulk material, indicating that in this restricted area the density of scattering particles (rubber particles and PA crystallites) is lower. However, the inhomogeneity itself gives rise to higher retardation values, which is immediately picked up by the polarization channels of the SD-PS-OCT system. Since the retardation pattern varies also strongly in the adjacent areas, the effect is most probably not caused by a different stress-birefringence response of the inhomogeneous material (i.e. by a different stress-optical coefficient) but by increased stress in these surrounding regions due to the presence of the material inhomogeneity.
The qualitative findings of the above testing runs are put to a quantifiable direction by analyzing and demodulating the fringe pattern of the retardation images, as detailed in the following. Although simple stripe patterns observed in typical tensile testing can be in principle efficiently processed by one-dimensional (1D) demodulation methods of the individual A-scans, a two-dimensional (2D) analysis offers the advantage of exploiting the full 2D spatial frequency information encoded in the fringe pattern, as demonstrated in the following on a simulated retardation image, which is depicted in Fig. 4(b) . In this context, we also want to underline, that such a 2D approach – in contrast to 1D ones – will also work on partly and fully closed fringes, as observed for sample geometries with adjacent compressive and tensile strained regions . The simulated pattern of Fig. 4(b) is deduced from an assumed strain/birefringence distribution (normalized), as depicted in Fig. 4(a), and degraded by speckle noise showing increasing variance over depth.
For modeling of the speckle noise a random phasor sum approach, as described in , is used. In addition, we modified this complex-valued speckle noise model in such a way that the SNR is decreasing over depth. In general, for a retardation fringe pattern φR(x,z) degraded by severe speckle noise, direct demodulation of the un-preprocessed retardation images is not feasible. Therefore, adequate denoising steps have to be applied before, with an anisotropic diffusion method - in particular coherence enhancing diffusion (CED)  – chosen by us, due to the fact that this method takes the local coherence of the 2D fringes structures in an adaptive way into account. Additionally, we include weighting with the variance map of the image for setting the initial condition of the CED method. Furthermore, we would like to note, that for retardation images exhibiting a slowly varying background, superimposed on the fringe pattern, we recommend to additionally apply a 2D Empirical Mode Decomposition (EMD) method  for a locally non-zero mean background correction to obtain more robust results in case of low fringe visibility. After these preprocessing steps the smoothed fringe pattern, as depicted in Fig. 4(c), can approximately be expressed as an amplitude- and frequency modulated 2D signal IP(x,z):
The next step in our analysis leads to the computation of the quadrature component IQ(x,z) to the in-phase fringe pattern image IP(x,z), expressed as:Fig. 4(d). With both components IP and IQ available, the amplitude modulation A(x,z) and the wrapped phase φW(x,z), as depicted in Fig. 4(e), is determined as magnitude and argument of the complex-valued image IM(x,z) by:
It is worth noting, that according to  the required quadrature component can be approximated via the Fourier transformℑby following relationship:36] as defined in monogenic signal theory . In addition, the variable β(x,z) represents the direction of the fringes. Therefore, in order to obtain the quadrature component IQ, an additional orientation/direction estimation step is required to remove the exponential term on the right hand side of Eq. (4).
Such an estimation of the orientation can be performed in a two-fold way, first – within the spiral filtering approach – by taking the argument of the complex-valued energy operator EΘ , with:Fig. 4(f)) can be estimated as:39]. J is already inherently computed in the CED-denoising step  and given as the outer product (∘) of the image gradient weighted over a local region of scale size ρ:Eq. (3), to the wrapped phase φW(x,z). 2D unwrapping of φW(x,z) is finally performed to extract the continuous phase φC(x,z) [41,42], resulting in Fig. 4(g). Finally, the local birefringence image nB(x,z) is obtained by numerical differentiation of the continuous phase image in depth direction z. In order to suppress spurious imaging artifacts, numerical differentiation is realized by including an additional spline interpolation and a Tikhonov-regularization term , with parameters balancing the trade-off with respect to the loss of spatial resolution in the direction of differentiation (z). As can be seen, the finally reconstructed birefringence map, as depicted in Fig. 4(h) and as given in the comparative plot of Fig. 5 with profiles along the z-direction running through the maximum, reflects well the initially assumed birefringence map of Fig. 4(a), with an average deviation of less than 1.4% from the original values. By scaling the image of Fig. 4(h) with a stress-optical coefficient we then obtain the corresponding local stress values within the material .
The above presented image processing method is applied in the following on real measurement data, obtained from a material with known stress-optical coefficient Copt (polyurethane elastomer with Copt = 1.9 x 10−9 Pa−1 @ 1550 nm ). For demonstration and in order to enhance the effect caused by spatially varying strain, the cross-section of the tested sample is of irregular shape (average cross-section ~4 mm2). Corresponding OCT reflectivity and retardation images were taken for this experiment perpendicular to the loading direction (x-direction). Cyclic loading and unloading is performed, with the results as depicted in Fig. 6 . From the globally measured strain-stress curve it is at first evident, that a mechanical hysteresis loop is formed, as mostly prevalent in strain-crystallizing and filled elastomers . Beside the reflectivity images, showing the full cross-section of the scattering material, the retardation images exhibit a higher spatial frequency in the stripe pattern for regions with decreased sample thickness. Quantification of the internal in-plane stress state is then obtained from these retardation images: the retardation patterns - exhibiting strong speckle noise - are smoothed by CED and the above introduced 2D demodulation algorithm is performed to obtain the quadrature images, needed for the calculation of the wrapped phase retardation images as depicted in Fig. 6. Unwrapping, regularized differentiation in axial direction and multiplication with the known stress-optical coefficient finally give the spatially resolved in-plane stress maps. In this context one should also note, that due to the uni-axial direction of the present tensile testing experiment a rather uniform orientation of the optical axis over depth is expected , as also verified on the simultaneously acquired images of the orientation of the optical axis. For other cases, the differential change of axis orientation and local birefringence has to be taken into account [44–46]. However, straight-forward application of our above introduced algorithm on acquired retardation images with slowly varying optical axis over depth will then give a lower limit for the local stress values. For our experiment, the averaged optical stress values taken from the obtained stress images closely match the global stress measured by the testing machine, reaching values of ~2.5 MPa for nearly 150% strain. Interestingly, at the same time locally constrained regions with highest stress values up to 6-8 MPa can be observed in the spatially and temporally resolved stress maps, proving the promising potential of SD-PS-OCT for obtaining complementary and detailed information when in future routinely used in combination with tensile testing equipment.
3.3 Fracture testing of fiber composite materials investigated with SD-PS-OCT
The investigation of structural integrity as well as obtaining knowledge on the formation of defects, like the identification of preferential sites for appearance of cracks and their propagation, finally leading to fracture, are topics of continuous high interest in the research for advanced materials and composite structures . In order to show the potential of SD-PS-OCT in these fields we study for the first time the evolution of such defects in scattering media in a spatially-resolved and dynamic way. For this purpose, fracture tests are performed by bending glass-fiber reinforced epoxy sheets, as used by the helicopter industry for the fabrication of rotor blades. In Fig. 7 , single frame excerpts from a SD-PS-OCT recording taken during such a fracture test are shown.
The probing light is impinging from the left side onto the composite sheet (thickness ~0.35 mm) with its distinctive fiber bundles appearing in the reflectivity images as brighter and roundly shaped areas inside the composite structure. Individual fibers, exhibiting mean diameters of only a few microns, however, cannot be resolved with the currently used light source. The corresponding topmost retardation image (color encoded) of the unbent structure shows no sign of birefringence. In addition, the orientation of the optical axis is given, as well as the degree of polarization uniformity (DOPU), which was recently introduced for the segmentation of retinal structures by evaluating the depolarizing characteristics of the retinal pigment epithelium . By clamping one end of the fiber to the testing device and by bending the structure over a rigid edge, locally confined stress is introduced, which is detected via SD-PS-OCT in the retardation images (e.g. color change from blue to yellow and red in the retardation image of the third row of Fig. 7). In addition, the formation of large-scale fiber-matrix delaminations in the vicinity of locally increased birefringence is directly observed, as marked by arrows in the reflectivity images of Fig. 7 (e.g. brighter curved line in the magnified view of the third reflectivity image, located on the interface between matrix and the outermost fiber bundle). Further bending finally results in the complete fracture of the structure (bottom images), with debris from the epoxy matrix flying off the sample and with additional pronounced cracks between supporting fiber structure and matrix.
Knowing that it was up to now not possible to observe in situ the formation of such large-scale defects and cracks within scattering materials on such short time-scales, we take the analysis even further by calculating DOPU images from the dynamically acquired polarization data. The analysis of the final stages of fracture in the DOPU images suggests that the bending procedure creates a fragmentation of the brittle epoxy matrix, resulting in multiple depolarizing scattering sites. This observation is confirmed by the appearance of a diffuse background in the reflectivity images, which is extending towards the right side over the physical dimensions of the sheet (e.g. final frames in the movie of Fig. 7, when the fractured sample is released). Averaged DOPU values taken from regions exhibiting such a highly micro-fractured matrix reach down to a value of ~0.25 in comparison to DOPU values of ~0.9 taken from unaffected regions. Most interestingly, depolarization due to small scale fragmentations seems already to take place long before distinctive, large-scale delaminations and defects become visible in the reflectivity images and also before increased stress-induced birefringence shows up in the retardation images: as demonstrated in the second row of Fig. 7, a slight bending of the fiber structure leads to no detectable structural changes within the reflectivity image. At the same time, there is also no remarkable increase in the sample retardation, whereas noticeable changes are already showing up in the corresponding DOPU image. Averaged DOPU values taken from the marked regions (black-dotted squares) underline this observation: a DOPU value of 0.73 is obtained from the region most affected by the bending (region 1), whereas a less affected region situated below (region marked with 2) exhibits an averaged DOPU value of 0.89. This fact, namely that the initial formation of defects can be pinpointed by carefully evaluating complementary optical sample properties, instructively illustrates the added high value that SD-PS-OCT provides with respect to conventional optical methods or even with respect to standard OCT, and forms the basis for a novel methodology of optically detecting small-scale defects within scattering materials.
Summarizing - on a general scale - we have shown how research in OCT for biomedical diagnostics successfully triggers new developments for the optical characterization of technical samples in materials science. Vice versa, developments made for optical material characterization have the potential to find their application also in their biomedical counterparts, like the application of advanced mathematical image analysis methods for the 2D analysis of complex optical fringe structures.
In detail, we have shown that SD-PS-OCT combined with mechanical testing provides essential novel aspects for experimental mechanics by delivering complementary information in a time and spatially resolved way, derived from the observed optical properties of the dynamically changing samples. The fact that structural details as well as information on the internal stress distribution obtained via strain-induced birefringence can simultaneously be obtained from the inside of scattering materials – even in a quantitative way by means of advanced image processing – demonstrates the superior characteristics of SD-PS-OCT over conventional techniques, like e.g. standard photoelasticity methods. These results and additional novel findings, like the successful detection of areas affected by micro-defects via DOPU analysis, are paving the way for SD-PS-OCT to be established in the future as promising high-resolution and high-speed optical characterization technique for applications in materials science.
The financial support by the Austrian Science Fund (project P19751-N20), the European Regional Development Fund in the framework of the EU-programme Regio 13, the Federal state Upper Austria, the Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged.
References and links
1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
2. R. Hee, D. Huang, and E. A. Swanson, “J. G. and Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992). [CrossRef]
3. J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997). [CrossRef] [PubMed]
4. D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007). [CrossRef]
5. A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000). [CrossRef]
6. M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999). [CrossRef]
7. J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998). [CrossRef] [PubMed]
8. S. J. Matcher, “A review of some recent developments in polarization-sensitive optical coherence tomography imaging techniques for the study of articular cartilage,” J. Appl. Phys . 105, 102041–1 - 102041–11 (2009). [CrossRef]
9. D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003). [CrossRef]
11. K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005). [CrossRef]
12. K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006). [CrossRef] [PubMed]
13. K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007). [CrossRef]
14. J. S. Chen and Y. K. Huang, “Full-field mapping of stress-induced birefringence using a polarized low coherence interference microscope,” Proc. SPIE 7133, 7133I–1 (2009).
15. B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010). [CrossRef]
16. K. Ramesh, Digital Photoelasticity: Advanced Techniques and Applications. (Springer, 2000).
17. Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009). [CrossRef]
18. M. A. Sutton, J. J. Orteu, and H. Schreie, Image Correlation for Shape, Motion and Deformation Measurements Basic Concepts, Theory and Applications (Springer, 2009).
19. P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–59 (2008). [CrossRef]
20. G. Gülker, K. D. Hinsch, and A. Kraft, “Deformation monitoring on ancient terracotta warriors by microscopic TV-holography,” Opt. Lasers Eng. 36, 501–512 (2001). [CrossRef]
22. M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography,” Opt. Express 14(21), 9643–9656 (2006). [CrossRef] [PubMed]
23. M. H. De la Torre Ibarra, P. D. Ruiz, and J. M. Huntley, “Simultaneous measurement of in-plane and out-of-plane displacement fields in scattering media using phase-contrast spectral optical coherence tomography,” Opt. Lett. 34(6), 806–808 (2009). [CrossRef] [PubMed]
25. J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003). [CrossRef] [PubMed]
26. E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005). [CrossRef] [PubMed]
27. B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005). [CrossRef] [PubMed]
28. C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001). [CrossRef] [PubMed]
29. S. Wu, “Phase structure and adhesion in polymer blends: A criterion for rubber toughening,” Polymer (Guildf.) 26, 1855–1863 (1985). [CrossRef]
30. P. A. Tzaika, M. C. Boyce, and D. M. Parks, “Micromechanics of deformation in particle toughened Polyamides,” J. Mech. Phys. Solids 48, 1893–1929 (2000). [CrossRef]
31. e.g.: R. J. Young, and P. A. Lovell, Introduction to Polymers (Chapman & Hall, 1991).
32. J. W. Goodman, “Random phasor sums,” in Speckle phenomena in optics (Roberts and Comp., Englewood, 2007), 7–25.
33. J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999). [CrossRef]
34. C. Damerval, S. Mignen, and V. Perrier, “A Fast Algorithm for Bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704 (2005). [CrossRef]
35. K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001). [CrossRef]
36. T. Bülow, D. Pallek, and G. Sommer, “Riesz Transforms for the Isotropic Estimation of the Local Phase of Moiré Interferograms”, Mustererkennung2000, ed., G. Sommer et al. (Springer Verlag, Berlin, DAGM 2000), 333–340.
37. M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001). [CrossRef]
39. B. Jähne, Digital Image Processing, (Springer, Heidelberg-Berlin, 2002).
40. J. Weickert, Anisotropic Diffusion in Image Processing, ECMI Series, (Teubner, Stuttgart, 1998)
41. D. C. Ghiglia, and M. D. Pritt, Two-dimensional Phase Unwrapping, (Wiley, New York, 1998).
42. B. G. Zagar, B. Arminger, and B. Heise, “Comparison of Various Algorithms for Phase Unwrapping in Optical Phase Microscopy,” IEEE Proc. IMTC Warsaw, Poland (2007).
43. B. Hofmann, Mathematik inverser Probleme (Teubner, Stuttgart-Leipzig, 1999).
44. M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004). [CrossRef] [PubMed]
45. S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004). [CrossRef] [PubMed]
46. N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005). [CrossRef] [PubMed]
47. K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, R. Oster, and D. Stifter, “Ultrahigh-resolution transversal polarization-sensitive optical coherence tomography: structural analysis and strain-mapping,” in: Fracture of Nano and Engineering Materials and Structures, E.E. Gdoutos, ed., (Springer, 2006).
48. E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008). [CrossRef] [PubMed]