## 2 Materials and Methods
### Image Post Processing  
The interference patterns are recorded in dependence of the respective wavelength and need to be mapped into k (= 2\(\pi\)/wavelength) -space before performing Fourier transformation for retrieving a depth profile (A-scan). However, the exact mapping depends on the alignment of the spectrometer and any differences between the spectrometers influence the polarization sensitive measurements. This can be overcome by either an identical alignment of the spectrometers [18] (which in our case was not possible as we are using commercially available off the shelf spectrometers) or by individual mapping of the interference pattern recorded by each spectrometer into k-space [19]. Although the spectrometers were delivered with calibration factors to associate each spectrometer pixel with the corresponding wavelength, it was found that this conversion was not accurate enough for reliable polarization sensitive imaging. Thus, an auxiliary bulk-optics Michelson interferometer was constructed that was placed into the reference arm of the system while the sample arm was blocked. Both arms of the auxiliary interferometer were terminated by mirrors and the resulting interference fringes were recorded in the two orthogonal polarization channels with both spectrometers. From these fringes, rescaling functions for each channel were derived that allowed the transformation of the spectral data from both spectrometers into the same range in k-space. The resulting calibration functions differed significantly between the channels. This transformation was applied to all spectral data before further post processing and corrected for any mismatch in the alignment of the two spectrometers. In order to remove the DC term and fixed pattern noise, the averaged (mean) spectrum of all A-scans within a B-scan was subtracted from each spectrum. The dispersion mismatch between the interferometer arms introduces a wavelength dependent phase shift on the spectral data. This can be compensated for in a post processing step introduced by [PERSON] et al. [20]. The first step was the generation of a complex valued spectrum for each A-scan by applying the Hilbert transformation. Then, we added a quadratic (in wavenumber, for second order (group velocity) dispersion compensation) phase term weighted by a dispersion compensation parameter to the spectrum and performed a Fast Fourier transformation on the real part of the phase corrected data that resulted in an A-scan. In order to find the optimum value for the dispersion compensation parameter, this parameter (200 different values) was varied within a pre-defined and empirically found range (similar to [20]) and calculated the corresponding A-scan. However, instead of a sharpness metric over the entire image as used in [20], the parameter that resulted in the highest peak intensity of each A-scan was used. The value was stored and the procedure was repeated for all A-scans within a B-scan. Thus, the varying dispersion parameters along the B-scan were found. As these resulting parameters fluctuate around the optimum value because of noise issues, the function (dispersion parameter in dependence on A-scan number) was fitted with a polynomial of the 5 th order to eliminate this fluctuation. The parameters for each A-scan corresponding to the fit were then used to produce the final image. This procedure was performed independently for all recorded B-scans of the co-polarized channel in order to account for varying dispersion introduced by y-scanning. The same dispersion compensation parameter was then applied to generate the images of the cross-polarized channel. In principle, a third order dispersion parameter can be found in a similar way. However, in our data set, an improvement was not noticed when varying the third order dispersion parameter as the optimum value for this parameter was approximately 0. Thus, the search for this parameter was omitted in our final evaluation procedure.