THREE LINEAR PROBE POLARIZATION METHOD IN MUELLER POLARIMETRY WITH A SOURCE OF ARBITRARY ELLIPTICITY S. N. Savenkov, * V. I. Grygoruk, A. S. Klimov, Ye. A. Oberemok, and Yu. A. Skoblya UDC 535.51 This is a study of the effect of the ellipticity of the polarization of radiation at the inlet of the shaping polar- izer in the probe channel of a Mueller polarimeter operating with three linear probe polarizations on the ac- curacy with which the incomplete Mueller matrix is determined (without a fourth beam). It is shown that the appearance of and variations in the ellipticity cause a change in the conditions for optimization of the set of polarizations of the probe radiation from the standpoint of minimizing the measurement error. In the case of linear polarization (zero ellipticity), the measurement error is the same as the error when four probe polari- zations are used. This allows measurement of the complete Mueller matrix and makes this version of the po- larimeter especially promising, because in the input channel of the polarimeter, a single polarizing element, i.e., a linear polarizer with a controllable azimuthal orientation, can be used as the polarization transducer. Keywords: Mueller matrix, Mueller polarimeter, condition number, optimization Introduction. Mueller polarimetry is a high information-content method for studying the anisotropic properties of objects [1–3]. The advantages of polarimetric techniques include, in particular, their high sensitivity and nonpertur- bative character, which is especially important in work with biomedical objects [4]. The change in the polarization of electromagnetic radiation when it interacts with the test object can be described completely using a 4 × 4 matrix with real elements, the Mueller matrix [1]. Recently, improvements in techniques for measuring the Mueller matrices of test objects have come to be of pressing interest in the context of constructing so-called image-forming or scanning polarimeters [5]. Here, approaches to organizing the polarimetric measurements that involve only a necessary minimum of measurements play a special role [5–8]. This minimum is determined by the number of independent parameters for describing the test object and which, thereby, determine the structure of its Mueller matrix. In fact, the class of uniform, anisotropic (determined) ob- jects is described in the general case by no more than seven parameters [1, 9], so that measurement of all 16 elements of their Mueller matrix is excessive. In practice, however, the number of independent parameters for completely de- scribing the polarimetric characteristics of a given class of objects may be even fewer [1–3]. One such technique is the three probe polarization method [9–11]. It has been shown that the measured in- complete Mueller matrix completely describe the class of uniform anisotropic objects. The group of elements which form these incomplete matrixes are measured as a whole with greater accuracy than the elements of the corresponding complete matrix in a single measurement cycle. In particular, this method makes it possible to reduce the time and lower the absolute magnitudes of the limits of relative error (referred to below as the error) of the measurement by 25 and 30%, respectively. From the standpoint of practical realization (both in point and in scanning polarimetry), the most promising variant of this method is to use three linear polarizations for the probe radiation. In this variant, in the input probe channel of the polarimeter the polarization transducer is designed as follows: a quarter wave plate, re- quired to obtain circular polarization of the radiation, plus a linear polarizer with a controllable azimuth orientation for shaping. In practice, however, shaping the polarization of the radiation to an ellipticity angle ε = ±45 o is difficult [12]. Taras Shevchenko Kiev National University, 64 Volodymyrska Str., Kiev 01033, Ukraine; e-mail: sns@ mail.univ.kiev.ua. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 875–880, November–Decem- ber, 2008. Original article submitted March 25, 2008. Journal of Applied Spectroscopy, Vol. 75, No. 6, 2008 0021-9037/08/7506-0872 ©2008 Springer Science+Business Media, Inc. 872 ∗ To whom correspondence should be addressed.