Abstract

We study the optimum operating conditions for a rotating retarder fixed polarizer (RRFP) when the measurements are not quasi-instantaneous but time-averaged. We obtain the optimum retardance and retarder orientations as a function of the integrated angle interval. We also study how the increase in the number of time-averaged measurements leads to a better equally weighted variance (EWV) value, and thus, to a better performance of the polarimeter in terms of noise amplification for the case of additive noise. Two different analyzers configurations are studied in this work: uniformly spaced retarder angles and when measurements are taken at optimum angles (non-uniformly spaced angles). We also consider the case of polychromatic illumination. We discuss the best measurement conditions in terms of the signal-to-noise ratio depending on whether there is a fixed or a limited amount of photons per measurement.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

M. R. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
[Crossref]

A. Lizana, J. Campos, A. Van Eeckhout, and A. Marquez, “Misalignment error analysis in polychromatic division of focal plane Stokes polarimeters,” OSA Continuum 2(5), 1565–1575 (2019).
[Crossref]

2018 (2)

J. Dai, F. Goudail, M. Boffety, and J. Gao, “Estimation precision of full polarimetric parameters in the presence of additive and Poisson noise,” Opt. Express 26(26), 34081–34093 (2018).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

2016 (2)

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

F. Goudail, “Equalized estimation of Stokes parameters in the presence of Poisson noise for any number of polarization analysis states,” Opt. Lett. 41(24), 5772–5775 (2016).
[Crossref]

2015 (1)

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal Frames for Polarization State Reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

2014 (1)

2013 (1)

2010 (2)

2008 (3)

2006 (2)

2000 (1)

1997 (1)

1987 (1)

Aiello, A.

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal Frames for Polarization State Reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Anastasiadou, M.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Banerjee, C.

Bénière, A.

Boffety, M.

Campos, J.

A. Lizana, J. Campos, A. Van Eeckhout, and A. Marquez, “Misalignment error analysis in polychromatic division of focal plane Stokes polarimeters,” OSA Continuum 2(5), 1565–1575 (2019).
[Crossref]

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, “Optimization and performance criteria of a Stokes polarimeter based on two variable retarders,” Opt. Express 18(10), 9815–9830 (2010).
[Crossref]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[Crossref]

Carvalho, S.

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

Chandel, S.

Chenault, D. B.

Chipman, R. A.

Chironi, E.

Clement, D.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Cohen, H.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Cope, M.

Dai, J.

De Martino, A.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

Delpy, D. T.

Dereniak, E. L.

Descour, M. R.

Drévillon, B.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

Dreyfuss, J.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Durfort, M.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

Elsner, A. E.

Escalera, J. C.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

Estévez, I.

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

Favaro, A.

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal Frames for Polarization State Reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Firdous, S.

S. Firdous and M. Ikram, “Stokes Polarimetry for the Characterization of Bio-Materials using Liquid Crystal Variable Retarders,” in Therapeutic Laser Applications and Laser-Tissue Interactions III, A. Vogel, ed., Vol. 6632 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6632_14.

Foldyna, M.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

Foreman, M. R.

M. R. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
[Crossref]

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal Frames for Polarization State Reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Gao, J.

Garcia-Caurel, E.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

Garnatje, T.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

Ghosh, N.

Gil, J. J.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

J. J. Gil and R. Ossikovski, “Polarized Light and the Mueller Matrix Approach,” in Series in Optics and Optoelectronics, (CRC, Taylor&Francis Group, 2016).

Goldstein, D. L.

González, E.

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

Goudail, F.

Gueiral, N.

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

Henrique, R.

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

Hough, J.

J. Hough, “Polarimetry: a powerful diagnostic tool in astronomy,” Astron. Geophys. 47(3), 3.31–3.35 (2006).
[Crossref]

Huynh, B.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Iemmi, C.

Ikram, M.

S. Firdous and M. Ikram, “Stokes Polarimetry for the Characterization of Bio-Materials using Liquid Crystal Variable Retarders,” in Therapeutic Laser Applications and Laser-Tissue Interactions III, A. Vogel, ed., Vol. 6632 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6632_14.

Jellison, G. E.

Kemme, S. A.

Kumar, U.

Lakhotia, H.

Laude-Boulesteix, B.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Liège, F.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Lizana, A.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

A. Lizana, J. Campos, A. Van Eeckhout, and A. Marquez, “Misalignment error analysis in polychromatic division of focal plane Stokes polarimeters,” OSA Continuum 2(5), 1565–1575 (2019).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, “Optimization and performance criteria of a Stokes polarimeter based on two variable retarders,” Opt. Express 18(10), 9815–9830 (2010).
[Crossref]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[Crossref]

Marquez, A.

Márquez, A.

Matcher, S. J.

Moreno, I.

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[Crossref]

Nazac, A.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Nogueira, E.

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

November, L. J.

L. J. November and L. M. Wilkins, “Liquid Crystal Polarimeter for solid state imaging of solar vector magnetic fields,” in D. H. Goldstein and D. B. Chenault, eds. (International Society for Optics and Photonics, 1994), Vol. 2265, p. 210.

Oliveira, L.

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

Ossikovski, R.

J. J. Gil and R. Ossikovski, “Polarized Light and the Mueller Matrix Approach,” in Series in Optics and Optoelectronics, (CRC, Taylor&Francis Group, 2016).

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

Peinado, A.

Phipps, G. S.

Pierangelo, A.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

Purwar, H.

Quang, N.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Rodríguez, C.

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

Sabatke, D. S.

Sansa, A.

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

Schwartz, L.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

Shaw, J. A.

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P. Taylor, “Theory and Applications of Numerical Analysis,” (Academic, 1974).

Tuchin, V. V.

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

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Van Eeckhout, A.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

A. Lizana, J. Campos, A. Van Eeckhout, and A. Marquez, “Misalignment error analysis in polychromatic division of focal plane Stokes polarimeters,” OSA Continuum 2(5), 1565–1575 (2019).
[Crossref]

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

VanNasdale, D.

Vidal, J.

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

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[Crossref]

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Zhao, Y.

Appl. Opt. (3)

Astron. Geophys. (1)

J. Hough, “Polarimetry: a powerful diagnostic tool in astronomy,” Astron. Geophys. 47(3), 3.31–3.35 (2006).
[Crossref]

J. Biomed. Photonics Eng. (1)

S. Carvalho, N. Gueiral, E. Nogueira, R. Henrique, L. Oliveira, and V. V. Tuchin, “Wavelength dependence of the refractive index of human colorectal tissues: comparison between healthy mucosa and cancer,” J. Biomed. Photonics Eng. 2(4), 040307 (2016).
[Crossref]

J. Biophotonics (1)

A. Van Eeckhout, A. Lizana, E. Garcia-Caurel, J. J. Gil, A. Sansa, C. Rodríguez, I. Estévez, E. González, J. C. Escalera, I. Moreno, and J. Campos, “Polarimetric imaging of biological tissues based on the indices of polarimetric purity,” J. Biophotonics 11(4), e201700189 (2018).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

M. R. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

OSA Continuum (1)

Phys. Rev. Lett. (1)

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal Frames for Polarization State Reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Phys. Status Solidi (1)

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008).
[Crossref]

PLoS One (1)

A. Van Eeckhout, E. Garcia-Caurel, T. Garnatje, M. Durfort, J. C. Escalera, J. Vidal, J. J. Gil, J. Campos, and A. Lizana, “Depolarizing metrics for plant samples imaging,” PLoS One 14(3), e0213909 (2019).
[Crossref]

Other (8)

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L. J. November and L. M. Wilkins, “Liquid Crystal Polarimeter for solid state imaging of solar vector magnetic fields,” in D. H. Goldstein and D. B. Chenault, eds. (International Society for Optics and Photonics, 1994), Vol. 2265, p. 210.

S. Firdous and M. Ikram, “Stokes Polarimetry for the Characterization of Bio-Materials using Liquid Crystal Variable Retarders,” in Therapeutic Laser Applications and Laser-Tissue Interactions III, A. Vogel, ed., Vol. 6632 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6632_14.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. De Martino, “Advanced Mueller Ellipsometry Instrumentation and Data Analysis,” in M. Losurdo and K. Hingerls, eds., (Springer-Varlag, 2013).

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https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=1564 (visited 30th October 2019)

J. J. Gil and R. Ossikovski, “Polarized Light and the Mueller Matrix Approach,” in Series in Optics and Optoelectronics, (CRC, Taylor&Francis Group, 2016).

P. Taylor, “Theory and Applications of Numerical Analysis,” (Academic, 1974).

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Figures (16)

Fig. 1.
Fig. 1. Diagram for the rotating retarder fixed polarizer (RRFP) Stokes polarimeter.
Fig. 2.
Fig. 2. Dependence of the DOP with $\Delta \theta$ for the angle averaged analyzers in the RRFP.
Fig. 3.
Fig. 3. Optimization results for the RRFP with uniformly spaced angles. (a) CN map, and (b) EWV map, obtained as a function of the number of analyzers N and the integrated angle interval $\Delta \theta$ .
Fig. 4.
Fig. 4. Optimization results for the RRFP with uniformly spaced angles. (a) CN, (b) EWV, (c) Retardance, and (d) Average DOP of the analyzers.
Fig. 5.
Fig. 5. Difference between the EWV calculated with the fitting polynomial [Eq. (14)] and the EWV data points, normalized by the data points.
Fig. 6.
Fig. 6. Representation on the Poincaré sphere of the optimal analyzers for N = 5. The different trajectories are related with different integrated angle intervals: 0° (outer path), 10°, 20°, 30°, and 40° (inner path). In each of the trajectories the circles indicate the location of a particular set of measuring analyzers. (a) and (b) show different points of view of data in the Poincaré Sphere space.
Fig. 7.
Fig. 7. Optimization results for the RRFP with unrestricted orientations. (a) CN, (b) EWV, (c) Retardance, and (d) Average DOP of the analyzers.
Fig. 8.
Fig. 8. Difference between the EWV calculated with the fitting polynomial [Eq. (15)] and the EWV data points, normalized by the data points.
Fig. 9.
Fig. 9. Optimization results for the RRFP with uniformly spaced angles, and for a fixed retardance value of 90°. (a) CN and (b) EWV.
Fig. 10.
Fig. 10. Representation on the Poincaré sphere of the optimal analyzers for N = 5 when fixing the retardance value to 90°. The different trajectories are related with different integrated angle intervals: 0° (outer path), 10°, 20°, 30°, and 40° (inner path). In each of the trajectories the circles indicate the location of a particular set of measuring analyzers. (a) and (b) show different points of view of data in the Poincaré Sphere space.
Fig. 11.
Fig. 11. Optimization results for the RRFP with uniformly spaced angles, and for a fixed retardance value of 128.1°. (a) CN and (b) EWV.
Fig. 12.
Fig. 12. Non-achromatic zero order retarder with fixed retardance value of 128.1° at 555 nm and 114° at 625 nm. Optimization results at 555 nm for the RRFP with uniformly spaced angles. (a) CN, and (b) average DOP.
Fig. 13.
Fig. 13. Non-achromatic zero order retarder with fixed retardance value of 128.1° at 555 nm and 151° at 470 nm. Optimization results at 555 nm for the RRFP with uniformly spaced angles. (a) CN, and (b) average DOP.
Fig. 14.
Fig. 14. Representation on the Poincaré sphere of the optimal analyzers at 555 nm for N = 11, for a RRFP with uniformly spaced angles and with a non-achromatic zero order retarder with fixed retardance values. The different trajectories are related with different integrated angle intervals: 0° (outer path), 10°, 20°, 30°, and 40° (inner path). In each of the trajectories the circles indicate the location of a particular set of measuring analyzers. (a) Fixed retardances of 128.1° at 555 nm and 114° at 625 nm. (b) Fixed retardances of 128.1° at 555 nm and 151° at 470 nm.
Fig. 15.
Fig. 15. SNR results for the RRFP with uniformly spaced angles and for a fix amount of photons per measurement for, (a) dark shot noise, and (b) read-out noise, obtained as a function of the number of analyzers N and the integrated angle interval $\Delta \theta$ .
Fig. 16.
Fig. 16. SNR results for the RRFP with uniformly spaced angles and for a limited amount of photons, for half a rotation of the retarder, and when the photons are shared by the N measurements, for (a) dark shot noise, and (b) read-out noise, obtained as a function of the number of analyzers N and the integrated angle interval $\Delta \theta$ .

Equations (31)

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I ( φ , θ ( t ) ; S i n ) = A T S = 1 2 { S 0 + ( cos 2 ( 2 θ ( t ) ) + cos ( φ ) sin 2 ( 2 θ ( t ) ) ) S 1  +  ( 1 cos ( φ ) ) cos ( 2 θ ( t ) ) sin ( 2 θ ( t ) ) S 2 sin ( φ ) sin ( 2 θ ( t ) ) S 3 } ,
I ( φ , θ ( t ) ; S ) = A T S = 1 2 { S 0 + ( cos ( φ ) + 1 ( cos ( φ ) 1 ) cos ( 4 θ ( t ) ) 2 ) S 1   + ( 1 cos ( φ ) ) sin ( 4 θ ( t ) ) 2 S 2 sin ( φ ) sin ( 2 θ ( t ) ) S 3 } .
A ( φ , θ ( t ) ) = 1 2 ( 1 cos ( φ ) + 1 ( cos ( φ ) 1 ) cos ( 4 θ ( t ) ) 2 ( 1 cos ( φ ) ) sin ( 4 θ ( t ) ) 2 sin ( φ ) sin ( 2 θ ( t ) ) ) .
cos ( m θ ) Δ θ = sinc ( m Δ θ / Δ θ 2 2 ) cos ( m θ ¯ )
sin ( m θ ) Δ θ = s i n c ( m Δ θ / Δ θ 2 2 ) sin ( m θ ¯ )
sinc ( α ) sin α / sin α α α
f ( θ ) Δ θ = 1 Δ θ θ ¯ Δ θ / 2 θ ¯ + Δ θ / 2 f ( θ ) d θ .
A ( φ , θ ( t ) ) Δ θ = 1 2 ( 1 0.5 ( cos ( φ ) + 1 ) 0.5 ( cos ( φ ) 1 ) cos ( 4 θ ¯ ) sinc ( 2 Δ θ ) 0.5 ( 1 cos ( φ ) ) sin ( 4 θ ¯ ) sinc ( 2 Δ θ ) sin ( φ ) sin ( 2 θ ¯ ) sinc ( Δ θ ) ) .
I = W S ,
S = W + I
W + = ( W T W ) 1 W T
v j = k = 0 N 1 ( W j , k + ) 2 u k ,
E W V = j = 0 3 v j u = j = 0 3 k = 0 N 1 ( W j , k + ) 2 ,
u d a r k = I d a r k Δ t .
E W V ( Δ θ , N ) = ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) / ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) N N ,
E W V ( Δ θ , N ) = ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 ) / ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 ) N N ,
Γ ( λ ) = ( 2 π / 2 π λ λ ) Δ n ( λ ) e
v s u m = j = 0 3 v j = E W V ( φ , θ k ; Δ θ , N ) u ,
S N R S i = S i / S i v s u m v s u m ,
S N R f i x = S i E W V ( φ , θ k ; Δ θ , N ) u ,
S N R f i x , d a r k = S i / S i ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) N I d a r k Δ θ w r e t ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) N I d a r k Δ θ w r e t ,
S N R f i x , d a r k N ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) Δ θ ,
S N R f i x , r e a d N ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) ,
I = Δ θ π W S .
S = π Δ θ W + I ,
v s u m , l i m = ( π Δ θ ) 2 E W V ( φ , θ k ; Δ θ , N ) u ,
v s u m , l i m = ( π Δ θ ) 2 v s u m .
S N R l i m = S i v s u m , l i m ,
S N R l i m = Δ θ π S i E W V ( φ , θ k ; Δ θ , N ) u ,
S N R l i m , d a r k N Δ θ ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) .
S N R l i m , r e a d N Δ θ ( a + b Δ θ 2 + c Δ θ 4 + d Δ θ 6 + e Δ θ 8 ) .

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