Three-dimensional complete polarization sensitive imaging using a confocal Mueller matrix imaging polarimeter David Lara and Chris Dainty Applied Optics Group, Department of Experimental Physics, National University of Ireland, Galway.
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Abstract: We present experimental three-dimensional complete polarization sensitive scans using the combination of a confocal microscope with a complete Mueller matrix polarimeter [1]. Axial scans are also included, and how they compare to the forward simulation. ©2005 Optical Society of America OCIS codes: 110.6880, 180.1790, 120.5410, 120.2130
1. Introduction Polarization sensitive imaging is a form of optical inspection that can reveal features in a sample that appear invisible to intensity and/or phase detection systems. The complete effect of any optical element that modifies the state of polarization can be represented as a 4 by 4 matrix (a Mueller matrix) that acts as a linear operator on a Stokes vector. Prior to our work, these 16 Mueller coefficients, which are in general linearly independent, have only been measured using two-dimensional imaging techniques. All other 3-D polarization sensitive imaging devices reported in the literature have only been able to obtain subsets of these 16 coefficients, leading sometimes to incomplete interpretations of polarization dependent features [2]. 2. Methods We built a confocal microscope within a Mueller matrix polarimeter to measure the complete polarization signatures of different samples at different depths within the specimen. The Mueller matrix polarimeter was similar to the one implemented by Delplancke [3]. We used two Pockels cells as linear variable retarders in the polarisation state generator, and a division of amplitude polarimeter [4] with non-polarizing beamsplitters for the polarisation state analyzer. There are no moving parts in this type of instrument, which simplifies its assembly and helps to make the calibration robust. The possibility of obtaining Mueller matrices at high acquisition rates, made this type of polarimeter our choice of design because one of our ultimate motivations is to inspect biological samples in-vivo. The confocal microscope used in this work was constructed in the reflection configuration, which is a requirement to obtain Mueller matrix depth-resolved measurements in the paraxial approximation regime. This imposed a new requirement for the calibration that had not been addressed before. For the calibration of the doublepass polarimeter, we implemented a modified version of the eigenvalue calibration method developed by Compain et al [5]. The method is very robust and applicable to any polarimeter configuration. 3. Results A stack of three linear 560 nm quarter wave-plates, made of cellulose acetate butyrate, was placed between two microscope glass slides and it was measured with the confocal Mueller matrix polarimeter. The stack of retarders was scanned along the optical axis, using a manual micrometer screw. The results were compared to a forward simulation of the stack, and the agreement was always better than 11.6%. The first three-dimensional complete polarization sensitive scans of a sample will also be shown, and some features of the inverse problem concerning the disentanglement of the measured complete Mueller matrices of contiguous axial positions will be described. This research was funded by CONACYT Mexico, scholarship 150238, and by Science Foundation Ireland, grant SFI/01/PI.2/B039C.
References [1] D. Lara and C. Dainty, “Axially-resolved complete polarization sensitive imaging with a confocal Mueller matrix imaging polarimeter,” submitted to Applied Optics, (2005). [2] J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Journal of Biomedical optics 7, (3) 359-371, (2002). [3] F. Delplancke, “Automated high-speed Mueller matrix scatterometer,” Applied Optics 36, (22) 5388-5395 (1997). [4] R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all Stokes parameters of light, Optica Acta 29, (5) 685-689 (1982). [5] E. Compain, S. Poirier and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters and Mueller-matrix ellipsometers” Applied Optics 38, (16) 3490-3502, (1999).
