Mueller matrix ellipsometry with imperfect compensators

Hauge, P.S.

doi:10.1364/josa.68.001519

Cited by 171 publications

(79 citation statements)

References 19 publications

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“…(2) is consistent with the assumption that the last detector is nonreflecting or totally absorptive. Equations (12) can be cast in matrix form as I = KDL, (13) where K is the diagonal responsivity matrix,…”

Section: The Explicit Instrument Matrix Amentioning

confidence: 99%

General analysis and optimization of the four-detector photopolarimeter

1988

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The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (ri, /i, Ai) of the first three detectors. The instrument matrix A, which relates the output signal vector I to the input Stokes vector S by I = AS, and its determinant are derived explicitly. The essential condition that A be nonsingular (det A $ 0) is satisfied in general with uncoated absorbing detector surfaces, assuming that the plane of incidence (POI) is rotated between successive reflections by other than 90°. Therefore no special coatings on the detectors are required, and a thin dielectric (e.g., thermal oxide) layer would suffice. The differential reflection phase shift A is unrestricted for the first and third detectors and has optimum values of ±90' for the second. The optimum rotation angles of the POI are +45 0 and +135'. The optimum values of the surface parameter ip are 27.37°, 22.50 or 67.50, and 0 or 90° for the first, second, and third reflections, respectively. The following topics are also considered: (1) the partition of energy among detectors, (2) the effect of tilting the last detector, (3) operation of the FDP over a broadband spectral range, (4) choice of the light-beam path, and (5) calibration.

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Section: The Explicit Instrument Matrix Amentioning

confidence: 99%

General analysis and optimization of the four-detector photopolarimeter

1988

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“…These approaches are often accompanied by the Fourier transform technique for the analysis of modulated intensity signals, which requires at least ten-odd image frames. Fast ellipsometry measurement techniques like the polarization modulation method using phase modulators [15][16][17] have also been reported. Fast ellipsometry requires four image frames and measures two ellipsometric quantities S (=sin 2ψ sin ∆) and C (= sin 2ψ cos ∆).…”

Section: Ellipsometric Measurement Principle and Measurement Resmentioning

confidence: 99%

Rotatable Offner imaging system for ellipsometric measurement

Jin

Tanaka

Kondoh

et al. 2017

Review of Scientific Instruments

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To realize high spatial resolution imaging ellipsometric measurement with large field of view, we developed a rotatable Offner system with unit magnification. When the conventional Offner imaging system is tilted relative to the sample plane for the ellipsometric measurement, only a small region of plane is in focus. The rotatable Offner system developed here renders the entire object in focus through all rotations. The performance of the prototype of the Offner system and imaging ellipsometer is tested by generating maps of the ellipsometric parameters Δ and Ψ for samples such as a silicon wafer and a resolution target made of chromium film evaporated on a glass substrate.

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“…두 개의 회전하는 사분파장판(quarter-wave plate)으로 구성된 타원편광분석기 역시 투과 혹은 반사하는 광학계의 광학적 특징을 알아내기 위하여 많이 사용되고 있는 방식이다. 이러한 투과 혹은 반 사 광학계의 광학적 특징은 4×4 Mueller 매트릭스를 구하면 완벽하게 광학적 매질의 물리적 특성을 알 수 있다는 것이다 [4] . 그러므로 뮬러 매트릭스 타원편광분석기의 주요 목적은 뮬 러 매트릭스의 16개 요소를 알아내는데 있다고 할 수도 있다.…”

Section: Figunclassified

Systematic Error Correction in Dual-Rotating Quarter-Wave Plate Ellipsometry using Overestimated Optimization Method

Kim¹,

Cheong²,

Kim³

2014

Korean Journal of Optics and Photonics

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We have studied and demonstrated general, systematic error-correction methods for a dual rotating quarter-wave plate ellipsometer. To estimate and correct 5 systematic error sources (three offset angles and two unexpected retarder phase delays), we used 11 of the 25 Fourier components of the ellipsometry signal obtained in the absence of an optical sample. Using these 11 Fourier components, we can determine the errors from the 5 sources with nonlinear optimization methods. We found systematic errors          are more sensitive to the inverted Mueller matrix than retarder phase delay errors       because of their small condition numbers. To correct these systematic errors we have found that error of any variety must be less than 0.05 rad. Finally, we can use the magnitudes of these errors to correct the Mueller matrix of optical components. From our experimental ellipsometry signals, we can measure phase delay and the rotational angular position of its fast axis for a half-wave plate.

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Mueller matrix ellipsometry with imperfect compensators

Cited by 171 publications

References 19 publications

General analysis and optimization of the four-detector photopolarimeter

General analysis and optimization of the four-detector photopolarimeter

Rotatable Offner imaging system for ellipsometric measurement

Systematic Error Correction in Dual-Rotating Quarter-Wave Plate Ellipsometry using Overestimated Optimization Method

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