Optimal Mueller matrix estimation in the presence of Poisson shot noise

Anna, Guillaume; Goudail, François

doi:10.1364/oe.20.021331

Cited by 36 publications

(18 citation statements)

References 15 publications

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“…While in the case that the dominant noise is Poisson shot noise, the variance of intensity vector V 8 I is equal to its true value [13], [15], [21], and thus the variance onV 8 M depends on the true value of V 8 M as:…”

Section: Polarimeter/ellipsometermentioning

confidence: 99%

“…, we can see that the variances σ 2 i do not only depend on the measurement matrices (A, W ), but also on the Mueller matrix under the Poisson shot noise, which is different from the case of Gaussian additive noise. Therefore, an optimal set of measurement matrices being independent of the Mueller matrix should satisfy f [15].…”

Section: Polarimeter/ellipsometermentioning

confidence: 99%

“…As an important application of the polarimeter, the characterization of films and surfaces mostly focuses on the measurement of smooth and isotropic samples, whose Mueller matrix is block diagonal, and two ellipsometric parameters are determined by the eight nonzero elements in this diagonal block of Mueller matrix [2], [13], [14]. In these cases, the complete Mueller polarimeter, which requires 16 intensity measurements, could no longer be the best choice for measuring ellipsometric parameters [15], [16]. Moreover, it seems that eight intensity measurements are enough for measuring these eight nonzero Mueller elements.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, considering the measurement for ellipsometric parameters of isotropic samples in the presence of two common types of noise (Gaussian additive noise and Poisson shot noise) [13], [15], [19], we optimize the measurement matrices of partial polarimeter based on only eight intensity measurements. The proposed optimal measurement matrices minimize the total variance of the elements related to the ellipsometric measurements.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters With Eight Intensity Measurements

Wang

et al. 2019

IEEE Access

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We demonstrate that the ellipsometric parameters of the isotropic samples can be measured by a partial polarimeter with only eight intensity measurements. Under the Gaussian and Poisson noises, we propose the optimal measurement matrices for the polarization state generator and the polarization state analyzer that minimize the total estimation variance of eight nonzero Mueller elements related to the ellipsometric parameters. In addition, since considering only four of the eight elements, the estimation variance can be further reduced, and we also introduce two proper criteria to find the optimal measurement matrices that robustly minimize the total estimation variance for these four Mueller elements. Compared with the existing measurement matrices based on 16 intensity measurements, our proposed matrices can effectively decrease the total estimation variance and, thus, improve the measurement precision of the Mueller matrix and ellipsometric parameters with only eight measurements. Furthermore, the proposed optimal measurement matrices do not depend on the Mueller elements of samples and thus not on the ellipsometric measurements.

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Section: Polarimeter/ellipsometermentioning

confidence: 99%

Section: Polarimeter/ellipsometermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters With Eight Intensity Measurements

Wang

et al. 2019

IEEE Access

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“…The condition number formalism gives an overall estimation of noise propagation from the intensity matrix, B, to the Mueller matrix, M. It fails, however, to provide a particular estimation of noise propagation for each Mueller matrix element. This drawback can be solved using an alternative approach based on the variance-covariance matrix shown in [26]. In the following, it will be assumed that the data of each matrix element in B, is characterized by a Gaussian noise with null mean and constant standard deviation σ0.…”

Section: B Experimental Validation Of the Optimized Optical Configurmentioning

confidence: 99%

Mid-infrared Mueller ellipsometer with pseudo-achromatic optical elements

et al. 2015

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The purpose of this article is to present a new broadband Mueller ellipsometer designed to work in the midinfrared range, from 3 to 14 microns. The Mueller ellipsometer, which can be mounted in reflection or in transmission configuration, consists of a polarization state generator (PSG), a sample holder, and a polarization state analyzer (PSA). The PSG consists in one linear polarizer and a retarder sequentially rotated to generate a set of four optimal polarization states. The retarder consists in a bi-prism made of two identical Fresnel rhombs disposed symmetrically and joined by optical contact, giving the ensemble a "V" shape. Retardation is induced by the four total internal reflections that the beam undergoes when it propagates through the bi-prism. Total internal reflection allows to generate a quasi-achromatic retardation. The PSA is identical to the PSG, but with its optical elements mounted in reverse order. After a measurement run, the instrument yields a set of sixteen independent values, which is the minimum amount of data required to calculate the Mueller matrix of the sample. The design of the Mueller ellipsometer is based on the optimization of an objective criterion that allows minimizing the propagation of errors from raw data to the Mueller matrix of the sample. The pseudo-achromatic optical elements ensure a homogeneous quality of the measurements for all wavelengths. The performance of the Mueller ellipsometer in terms of precision, and accuracy, is discussed and illustrated with a few examples.

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Impact of intensity integration time distribution on the measurement precision of Mueller polarimetry

et al. 2019

Journal of Quantitative Spectroscopy and Radiative Transfer

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Optimal Mueller matrix estimation in the presence of Poisson shot noise

Cited by 36 publications

References 15 publications

Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters With Eight Intensity Measurements

Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters With Eight Intensity Measurements

Mid-infrared Mueller ellipsometer with pseudo-achromatic optical elements

Impact of intensity integration time distribution on the measurement precision of Mueller polarimetry

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