Optical coherence tomography (OCT) and its extension, polarization-sensitive (PS-)OCT, are techniques for contactless and non-destructive imaging of internal structures. In this work, we apply PS-OCT for material characterization. We use a transversal scanning, ultra-high resolution (UHR-)PS-OCT setup providing cross-sectional as well as in-plane information about the internal microstructure, the birefringence and the orientation of the optical axis within the material. We perform structural analysis and strain-mapping for different samples: we show the necessity of UHR imaging for a highly strained elastomer sample, and we discuss the effect of large birefringence on the PS-OCT images. Furthermore, we investigate high-aspect ratio photoresist moulds for the production of micro-electromechanical parts (MEMS), demonstrating that transversal UHR-PS-OCT is a promising tool for non-destructive strain-mapping.
©2006 Optical Society of America
1. Introduction and motivation
Optical coherence tomography (OCT) is a contactless and non-destructive technique for high-resolution imaging of internal structures. Originally developed for ophthalmologic investigations of the human retina [1,2], it has been established as versatile method widely used in the biomedical sector. Over the last decade, new OCT methods have been developed, providing enhanced sensitivity and acquisition speed (e.g. Fourier-domain OCT [3–5]), improved image quality (e.g. ultra-high resolution UHR-OCT ), and exploiting different contrast mechanisms (e.g. Doppler OCT , polarization-sensitive PS-OCT [8,9]) or using different scanning and imaging concepts (transversal OCT [10,11], full-field OCT , optical coherence microscopy [13,14]). Regarding PS-OCT, this technique is sensitive to birefringence present due to anisotropies or strain within the tissue and has been used, for example, to obtain enhanced contrast in multi-layered anisotropic fibrous tissue , for the quantification of collagen denaturation in burnt human skin , or to study the polarization and birefringence properties of the different retinal layers [17,18], providing a better understanding of the properties and functionalities of the single layers.
The benefits of OCT for the characterization of biological tissue are well known, and it increasingly attracts attention as a tool for non-destructive testing of materials. A number of examples can be found where OCT has been applied for the characterization of materials: OCT has been used to detect subsurface cracks in ceramics, Teflon or SiC [19,20], to image polymer matrix or glass-fibre composites [21–23], injection moulded plastic parts , thin multi-layer foils and coatings , but also to investigate the properties of paper  or the subsurface morphology of archaic jades . Beside structural analysis, the investigation of internal anisotropies or strains adds valuable information for material characterization. So far, the number of applications of PS-OCT for material investigations is rather small, although the examples such as presented e.g. in refs. ,  and  clearly demonstrate the high potential of PS-OCT for strain-mapping and for an even quantitative stress analysis in plastic parts.
In this work, we apply PS-OCT for the investigation of different materials samples. We have extended the OCT technique beyond the state-of-the-art, combining the concepts of transversal scanning OCT developed by Hitzenberger et al.  and refined by Pircher et al. for PS-OCT [29,30] with ultra-high resolution imaging (transversal UHR-PS-OCT) using a femtosecond (fs-)laser as light source. This setup provides, to the best of our knowledge, transversal UHR-PS-OCT with the highest axial resolution obtained so far. As demonstrated recently in our previous work , UHR-OCT imaging is essential for material investigations because often features with sizes of only a few microns are of interest, and we have also shown the advantages of transversal scanning for different types of samples. In combination with PS-OCT imaging, this configuration is capable of imaging micro-size structures and internal strains simultaneously and is therefore a promising tool for material investigations and strain-mapping down to the micrometer scale.
In a set of experiments we show the necessity of UHR-imaging for highly strained samples, where we discuss the effect of large birefringence on the PS-OCT images. Additionally, we investigate the correlation between the orientation of the optical axis and the direction of the internal strain fields. We also apply transversal UHR-PS-OCT for the investigation of high-aspect ratio photoresist moulds for the production of micro-electromechanical parts (MEMS), where we perform transversal PS-OCT measurements for in-plane strain mapping within the moulds.
2. Experimental setup
Our transversal UHR-PS-OCT system shown in Fig. 1 is based on the setup described in detail in ref. . It follows the principles of time-domain OCT and uses a Mach-Zehnder interferometer geometry. Specific characteristics of the setup are the acousto-optic modulators (AOMs) in the reference arm, introducing a carrier frequency of 2 MHz for heterodyne signal detection, and the xy-galvano scanner unit, which scans the laser beam over the sample with a frequency up to 500 Hz. Cross-sectional imaging (i.e. a B-scan) is obtained by one depth scan of the reference mirror while scanning the laser beam repeatedly along the x direction. For transversal (en-face) imaging the reference mirror is kept at a fixed position, while the laser beam raster-scans over the sample in x and y directions. Transversal scan areas as large 3×3 mm2 can be measured with a pixel rate of 500 kHz. Dynamic focusing where the focal position matches the coherence gate can be realized easily within this setup by automatically shifting the sample accordingly along the z direction during a depth scan, and has been implemented for our OCT measurements (using a refractive index of 1.4–1.6 common for most polymers).
For ultra-high resolution imaging, we use a femtosecond (fs-)Ti:sapphire mode-locked laser (Integral OCT from Femtolasers) with attached single mode fibre and an averaged output power of 50 mW ex-fibre at a pulse rate of 85 MHz, resulting in a power of 4 mW at the sample position. The fs-laser provides a nominal spectral full-width-at-half-maximum (FWHM) of 150 nm at a centre wavelength of 800 nm.
For polarization sensitive measurements, a polarizer and two quarter-wave plates (QWPs) are added. After the polarizer, the laser beam is horizontally polarized and becomes polarized by 45° with respect to the horizontal after double-passing the QWP (oriented by 22.5° with respect to the horizontal) in the reference arm. The sample is illuminated by circularly polarized light (QWP oriented by 45°). Any birefringence within the sample changes the polarization into a generally elliptical one. Polarization sensitive detection of the two orthogonal polarization components is performed by adding polarization sensitive beamsplitters (PBS in Fig. 1) and a second set of balanced photoreceiver and lock-in amplifier. From the signals of the two detection channels, three types of images can be obtained simultaneously: in addition to the conventional reflectivity image, the retardation between the signals and the orientation of the optical axis can be calculated . The retardation provides depth resolved information about the birefringence within the material .
Experimentally, we have determined a depth resolution for the PS-OCT setup, i.e. a FWHM of the coherence peak of 2.45 µm in air, corresponding to a depth resolution of 1.63 µm in material (assuming a refractive index of 1.5 which is a typical value for plastics and polymers). This slightly larger value compared to the theoretical coherence length  of 1.9 µm in air is due to not fully compensated differences in higher order dispersion of the two interferometer arms. In combination with a lateral resolution of 4 µm measured experimentally, our setup is capable of ultra-high resolution PS-OCT measurements. A sensitivity of 97 dB of the UHR-PS-OCT system has been determined for the pixel rate given above.
3. UHR-PS-OCT imaging of highly birefringent samples
In a first set of experiments, we have studied the influence of high strain and birefringent values on UHR-PS-OCT imaging by stretching a thermoplastic polyurethane (PU-) elastomer sample (refractive index n=1.56 at 800 nm) up to 600%. As can be seen in Fig. 2(a), the cross-sectional reflectivity image of the unstrained sample shows no noticeable internal structures and a corrugated rear surface. The retardation image (Fig. 2(b)) indicates that no internal strain is present. With increasing strain, a growing number of equidistant birefringence fringes is observed (Fig. 2(c)–(f)). The retardation is colour-coded, where every transition from blue to red or red to blue, respectively, represents an additional retardation of 90° between the fast and the slow optical axis within the sample. It should be noted that in Fig. 2 the scale of the vertical axis is not the same for all images. They have been vertically stretched with increasing strain in order to enhance the visibility of the fringes.
We have shown in ref.  that the birefringence Δn is given by
where λ is the central wavelength and ret is the derivative of the retardation in degrees. When evaluating the fringes for the images in figs. 2(c)–(f), we obtain birefringence values of 0.2*10-2 (c), 0.9*10-2 (d), 1.8*10-2 (e), and 4.3*10-2 (f). For the highest birefringence, the optical distance for 90° retardation (transition from blue to red or vice versa) is only around 6.5 µm. This value is close to or beyond the depth resolution of conventional PS-OCT systems with standard light sources, such as, e.g. single superluminescence diodes. Therefore, focusing on PS-OCT as method for the investigation of highly strained samples, ultra-high resolution provided by high-broadband light sources is required for appropriate strain-mapping.
The chosen material system is especially suitable for demonstrating measurement artefacts which have to be taken into consideration when dealing with UHR-PS-OCT and highly anisotropic materials, a situation normally not encountered for biological samples. In a material with a given birefringence Δn, the ordinary and the extraordinary rays travel with different velocities. In the following, we assume that the orientation of the birefringence is constant, as it is the case for the sample shown in Fig. 2. At a certain depth z l within the sample, a lag of the ray parallel to the slow direction equal to the coherence length l c is present with respect to the fast ray. This will happen when
At depths larger than z l, every feature within the sample appears twice in the images since the amount of vertical separation Δn * z f (z f…depth of feature within sample) exceeds the depth resolution of the system. In Fig. 2(d)–(f), this effect can be clearly seen on the rear surface of the sample. The measured virtual “splitting” of the back surface is 8.3, 11.2 and 17.0 µm for images 2(d)–(f), respectively. We observe that Δn increases faster with increasing strain than the sample thickness decreases, so the net splitting increases.
When the lag between fast and slow axis exceeds l c, another effect occurs: for depths larger than z l, the retardation information (i.e. the visibility of the fringes) gets gradually lost. This can be observed in figs. 2(d)–(f) where the blue and red fringes vanish at certain depths below the surface. Assuming a constant birefringence over depth and substituting Δn from equ.(1) in equ.(2), one obtains a limit for the maximum clearly observable retardation ret max:
This value is constant for a given PS-OCT system, regardless of the birefringence of the sample and equals 1100° for our setup, which corresponds to roughly 6 transitions from blue to blue in the birefringent images (arrows in Fig. 2(d)–(f)). For comparison, in case of the standard PS-OCT setup in ref.  (l c=19 µm, λ=1.55 µm) a value of 4410° is obtained, corresponding to 24 transitions that are at least observable. Consequently, a trade-off between resolution and birefringence information has to be made for UHR-PS-OCT imaging.
It has to be stressed that the above described doubling effect of features is present in both orthogonal detection channels and cannot be avoided by suitably orienting the azimuth of the sample, e.g. to obtain an undistorted reflectivity image by taking the data from only one channel. Since the oscillations of the electric field vectors of the two orthogonal components are not correlated anymore after a certain depth in the sample, they now can be considered as independently linearly polarized. These two rays pass the QWP oriented at 45° to the direction of the detector channels, and therefore both channels always measure a signal from the slow as well as from the fast axis. In the case of the rear surface of the sample, its total reflected intensity is equally divided into four signals (fast image and slow image for each of the two detector channels).
Finally, an additional effect should be discussed: it is very improbable, especially for UHR-PS-OCT setups, that a sample acts as a broadband retarder, i.e. that the introduced retardation is constant for all wavelengths of the used light source (700–900 nm in our case), which can cause an additional fading of the observable retardation fringes.
4. Orientation of the optical axis in presence of strain
The orientation of the optical axis (OA) is a measure of the direction of anisotropy and, for strained samples, of the strain fields within a material. This has been demonstrated by stretching another thermoplastic PU-elastomer sample perpendicular to the direction of its slow OA which the sample showed in unstrained state.
For the externally unstrained sample, only low birefringence is present (Fig. 3(a)), and the slow OA is oriented perpendicularly to the image plane of the B-scan, as indicated in Fig. 3(c), where the orientation of the slow OA is colour-coded from 0° to 180°. For the unstrained sample, the orientation of the OA is presumably resulting from intrinsic anisotropies due to the production process. Thereafter, we have externally strained the elastomer sample to about 10%, with the strain direction perpendicular to the orientation of the slow OA in the unstrained state (The direction of the strain is indicated by the arrows in Fig. 3(b)). As a result, the orientation of the slow OA changes and is aligned along the strain direction (Fig. 3(d)). The squares in Fig. 3 mark areas with similar retardation values, where the change of the orientation of the OA is visible. These experiments clearly demonstrate that the orientation of the OA is indicative of the directions of strain fields when strains are present within a sample.
5. Strain-mapping of photoresist moulds for MEMS production
The above considerations about the orientation of the OA in presence of strain are useful for the investigation of high aspect-ratio moulds in thick photoresist layers, a current field of research for the production of micro electromechanical parts (MEMS). These moulds are obtained by X-ray lithography using Nano™SU-8 resists (MicroChemCorp) as photo-sensitive films on silicon wafers, with layer thicknesses of the resist exceeding 1 mm for some applications. For a high reproducibility of the MEMS devices, a fast and non-invasive quality control of the resist moulds is required. Of interest is e.g., the resist layer thickness which can be obtained directly from cross-sectional OCT measurements . Measure of the quality of the resist moulds are in particular the in-plane geometry of the MEMS mould structures, possible defects or contaminations within the resist layer or at the bare wafer regions, and the properties of the resist-wafer interface. As demonstrated in our previous work, these parameters can be accessed directly by transversal OCT . Additionally, the investigation of internal strains of the resist structures is of great interest. During the lithographic production process, drying, thermal treatment and relaxation processes due to resist removal by etching induce strains within the resist structures. Highly strained areas are potential sources of defects such as e.g., cracks or delaminations of the resist layer. If the strain distribution is known, highly strained areas can be avoided by a proper design of the moulds. As will be demonstrated in the following, our transversal UHR-PS-OCT setup provides information about the in-plane strain-distribution and is therefore valuable tool for strain-mapping of the resist moulds.
We have investigated moulds for the fabrication of micromechanical gear wheels etched in a 1.3 mm thick photoresist layer on a gold coated wafer (Fig. 4(a)). Conventional cross-sectional UHR-OCT across a wheel structure (Fig. 4(b)) reveals the layer thickness, and from the different optical depths of the bare wafer surface and the resist-wafer interface, the refractive index of the resist can be determined. When we record transversal images at different optical depths, the shape of the structure itself and possible defects at the surface, the bare wafer and the resist-wafer interface are revealed immediately . As an example, Fig. 5(a) shows an en-face image recorded at the optical depth of the resist-wafer interface where no particular defects are visible.
Information about the in-plane strain distribution within the moulds is obtained when polarization-sensitive transversal OCT is performed. Figures 5(b) and (c) show en-face images of the retardation and the orientation of the slow OA, respectively, recorded at the optical level of the resist-wafer interface. In the circular centre of the wheels shown in (b), no birefringence is present, corresponding to a retardation value of 0°. The orange areas between adjacent wheels indicate an increased birefringence due to in-plane strain when etched trenches are close to each other. Especially at the teeth of the wheels, a high density of birefringence fringes is observable (marked by the arrows), indicating large strains in these regions. The orientation of the slow OA shown in Fig. 5(c) is displayed colour-coded from 0° to 180°, and as vector-field. Because the orientation of the OA is only defined for birefringent regions, the vectors are scaled by the magnitude of the retardation. The orientation of the slow OA, corresponding to the direction of the strain fields in the birefringent regions, indicates radial strains around the wheel.
6. Conclusions and outlook
In this work, we have extended transversal ultra-high resolution OCT for polarization sensitive measurements with, to the best of our knowledge, highest axial resolution obtained so far. We have applied the UHR-PS-OCT setup for investigation of the influence of large strains on PS-OCT imaging: The necessity of UHR-imaging for highly strained samples has been shown, and we have observed a splitting of the rear surface and a loss of birefringence information at large strain values. In addition, it has been experimentally shown that the orientation of the optical axis is indicative for the orientation of the strain fields within a material. The potential of transversal UHR-PS-OCT for non-destructive and contactless material characterization has been demonstrated by performing strain-mapping of photoresist moulds for the production of MEMS. We have selectively investigated the structures at the optical level of the resist-wafer interface, and highly strained areas and the direction of the strain fields have been identified, adding valuable information for quality control of the moulds.
This work has been supported by the Austrian Science Fund FWF (Projects: P16585-N08 and L126-N08) and the European Commission (FP6 CRAFT Project: COOP-CT-2003-507825).
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