Abstract

For some space applications, sensors are sensitive to light polarization and can only be properly calibrated with non-polarized light. Here we propose new optical devices which allow to depolarize light in a spatial process. These devices are thin film multilayers which exhibit polarimetric phase variations in their plane. A zero spatial polarization degree can be reached with high accuracy in a controlled bandwidth.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Optical systems for controlled specular depolarization

Myriam Zerrad, Clément Luitot, Jacques Berthon, and Claude Amra
Opt. Lett. 39(24) 6919-6922 (2014)

Light Waves in Thin Films and Integrated Optics

P. K. Tien
Appl. Opt. 10(11) 2395-2413 (1971)

Spectralon spatial depolarization: towards an intrinsic characterization using a novel phase shift distribution analysis

Jan Dupont, Xavier Orlik, Romain Ceolato, and Thibault Dartigalongue
Opt. Express 25(9) 9544-9555 (2017)

References

  • View by:
  • |
  • |
  • |

  1. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  2. F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49, 683–693 (2010).
    [Crossref] [PubMed]
  3. L. Pouget, J. Fade, C. Hamel, and M. Alouini, “Polarimetric imaging beyond the speckle grain scale,” Appl. Opt. 517345–7356 (2012).
    [Crossref] [PubMed]
  4. S. Ainouz, J. Zallat, A. Martino, and C. Collet, “Physical interpretation of polarization-encoded images by color preview,” Opt. Express 14, 5916–5927 (2006).
    [Crossref] [PubMed]
  5. L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
    [Crossref] [PubMed]
  6. P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).
  7. P. Réfrégier, J. Fade, and M. Roche, “Estimation precision of the degree of polarization from a single speckle intensity image,” Opt. Lett. 32, 739–741 (2007).
    [Crossref] [PubMed]
  8. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).
  9. M. Zerrad, C. Luitot, J. Berthon, and C. Amra, “Optical systems for controlled specular depolarization,” Opt. Lett. 39, 6919–6922 (2014).
    [Crossref] [PubMed]
  10. E. Collett, Field Guide to Polarization (SPIE, 2005).
    [Crossref]
  11. M. Zerrad and C. Amra, “Dépolariseurs spéculaires parfaits,” patent FR1454923 (2014).
  12. A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
    [Crossref] [PubMed]
  13. B. Liu, M. Harman, and M. E. Brezinski, “Variables affecting polarization-sensitive optical coherence tomography imaging examined through the modeling of birefringent phantoms,” J. Opt. Soc. Am. A 22, 262–271 (2005).
    [Crossref]
  14. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
    [Crossref] [PubMed]
  15. Jan Dupont and Xavier Orlik, “Simulation of polarized optical speckle fields: effects of the observation scale on polarimetry,” Opt. Express 24, 11151–11163 (2016).
    [Crossref] [PubMed]
  16. J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34, 2429–2431 (2009).
    [Crossref] [PubMed]
  17. J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19, 21313–21320 (2011).
    [Crossref] [PubMed]
  18. A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22, 14594–14609 (2014).
    [Crossref] [PubMed]
  19. M. Zerrad, A. Ghabbach, G. Soriano, M. Lequime, C. Amra, and J. Berthon, “Depolarizing optical multilayers,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds. (OSA Technical Digest, 2013).
  20. R. M.E. Illing, “Optical and structural performance of the PolZero-Lm time domain polarization scrambler,” presented at the Earth Science Technology Forum, Boulder, USA, 22 Jun. 2010.
  21. J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.
  22. L. Abel-Tibérini, F. Lemarquis, and M. Lequime, “Masking mechanisms applied to thin-film coatings for the manufacturing of linear variable filters for two-dimensional array detectors,” Appl. Opt. 47, 5706–5714 (2008).
    [Crossref] [PubMed]
  23. J. Broky and A. Dogariu, “Correlations of polarization in random electro-magnetic fields,” Opt. Express 19, 15711–15719 (2011).
    [Crossref] [PubMed]
  24. A. V. Tikhonravov, P. W. Baumeister, and K. V. Popov, “Phase properties of multilayers,” Appl. Opt. 36, 4382–4392 (1997).
    [Crossref] [PubMed]
  25. J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
    [Crossref] [PubMed]
  26. E. N. Kotlikov, V. N. Prokashev, V. A. Ivanov, and A. N. Tropin, “Thickness uniformity of films deposited on rotating substrates,” J. Opt. Technol. 76, 100–103 (2009).
    [Crossref]
  27. M. Lequime and C. Amra, De l’Optique électromagnétique à l’Interférométrie - Concepts et illustrations (EDP Sciences, 2013).
  28. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 1996).
  29. H.A. MacLeod and A. MacLeod, Thin Film Optical Filters (Taylor and Francis, 2001).
    [Crossref]
  30. P.W. Baumeister, Optical Coating Technology (SPIE Press Book, 2004).
    [Crossref]
  31. A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
    [Crossref] [PubMed]
  32. M. Bass, Handbook of Optics: Volume IV - Optical Properties of Materials, Nonlinear Optics, Quantum Optics, (McGraw Hill Professional, 2010) Chap. Optical Properties of Films and Coatings.
  33. M. Gross, S. Dligatch, and A. Chtanov, “Optimization of coating uniformity in an ion beam sputtering system using a modified planetary rotation method,” Appl. Opt. 50, C316–C320 (2011).
    [Crossref] [PubMed]
  34. L. Abel-Tiberini, F. Lemarquis, and M. Lequime, “Dedicated spectrophotometer for localized transmittance and reflectance measurements,” Appl. Opt. 45, 1386–1391 (2006).
    [Crossref] [PubMed]
  35. W. D. Shen, M. Cathelinaud, M. Lequime, F. Charpentier, and V. Nazabal, “Light trimming of a narrow bandpass filter based on a photosensitive chalcogenide spacer,” Opt. Express 16, 373–383 (2008).
    [Crossref] [PubMed]
  36. F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).
  37. M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
    [Crossref] [PubMed]
  38. M. Gorman and S.A. Solin, “Transmission Raman and depolarization spectra of bulk a-Se from 13 to 300 cm1,” Solid State Commun. 18, 38–1098 (1976).
  39. N.J. Diorio, M.R. Fisch, and J.L. West, “Filled liquid crystal depolarizers,” J. Appl. Phys. 90(8), 3675–3678 (2001).
    [Crossref]
  40. W. Domañski, “Polarization degree fading during propagation of partially coherent light through retarder,” Opto-Electron. Rev.13 (2005).
  41. O. Polat, Y. Emül, and S. Özharar, “Investigation of the Mueller Matrix elements of the liquid crystal cell illuminated with a broad band light source,” in Optical and Quantum Electronics (Springer, 2017).
  42. O. Polat, “Theoretical study on depolarization of the light transmitted through a non-uniform liquid crystal cell,” Optik 7, 3560–3563 (2016).
    [Crossref]
  43. A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
    [Crossref] [PubMed]

2017 (1)

2016 (2)

O. Polat, “Theoretical study on depolarization of the light transmitted through a non-uniform liquid crystal cell,” Optik 7, 3560–3563 (2016).
[Crossref]

Jan Dupont and Xavier Orlik, “Simulation of polarized optical speckle fields: effects of the observation scale on polarimetry,” Opt. Express 24, 11151–11163 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (4)

2012 (2)

L. Pouget, J. Fade, C. Hamel, and M. Alouini, “Polarimetric imaging beyond the speckle grain scale,” Appl. Opt. 517345–7356 (2012).
[Crossref] [PubMed]

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

2011 (3)

2010 (2)

2009 (3)

2008 (2)

2007 (1)

2006 (2)

2005 (1)

2001 (1)

N.J. Diorio, M.R. Fisch, and J.L. West, “Filled liquid crystal depolarizers,” J. Appl. Phys. 90(8), 3675–3678 (2001).
[Crossref]

1997 (2)

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

A. V. Tikhonravov, P. W. Baumeister, and K. V. Popov, “Phase properties of multilayers,” Appl. Opt. 36, 4382–4392 (1997).
[Crossref] [PubMed]

1993 (1)

1976 (1)

M. Gorman and S.A. Solin, “Transmission Raman and depolarization spectra of bulk a-Se from 13 to 300 cm1,” Solid State Commun. 18, 38–1098 (1976).

Abel-Tiberini, L.

Abel-Tibérini, L.

Ainouz, S.

Ali, J.

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

Alouini, M.

Amra, C.

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22, 14594–14609 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

M. Zerrad, C. Luitot, J. Berthon, and C. Amra, “Optical systems for controlled specular depolarization,” Opt. Lett. 39, 6919–6922 (2014).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19, 21313–21320 (2011).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[Crossref] [PubMed]

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34, 2429–2431 (2009).
[Crossref] [PubMed]

M. Zerrad and C. Amra, “Dépolariseurs spéculaires parfaits,” patent FR1454923 (2014).

M. Zerrad, A. Ghabbach, G. Soriano, M. Lequime, C. Amra, and J. Berthon, “Depolarizing optical multilayers,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds. (OSA Technical Digest, 2013).

M. Lequime and C. Amra, De l’Optique électromagnétique à l’Interférométrie - Concepts et illustrations (EDP Sciences, 2013).

Arnaud, L.

Aziz, M.

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

Bass, M.

M. Bass, Handbook of Optics: Volume IV - Optical Properties of Materials, Nonlinear Optics, Quantum Optics, (McGraw Hill Professional, 2010) Chap. Optical Properties of Films and Coatings.

Baumeister, P. W.

Baumeister, P.W.

P.W. Baumeister, Optical Coating Technology (SPIE Press Book, 2004).
[Crossref]

Bazalgette Courrèges-Lacoste, G.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Bénière, A.

Berthon, J.

M. Zerrad, C. Luitot, J. Berthon, and C. Amra, “Optical systems for controlled specular depolarization,” Opt. Lett. 39, 6919–6922 (2014).
[Crossref] [PubMed]

M. Zerrad, A. Ghabbach, G. Soriano, M. Lequime, C. Amra, and J. Berthon, “Depolarizing optical multilayers,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds. (OSA Technical Digest, 2013).

Bézy, J.L.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Bolshakov, I.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).

Brezinski, M. E.

Broky, J.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Cariou, J.

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

Caron, J.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Cathelinaud, M.

Charpentier, F.

Chtanov, A.

Collet, C.

Collett, E.

E. Collett, Field Guide to Polarization (SPIE, 2005).
[Crossref]

Deumié, C.

Diorio, N.J.

N.J. Diorio, M.R. Fisch, and J.L. West, “Filled liquid crystal depolarizers,” J. Appl. Phys. 90(8), 3675–3678 (2001).
[Crossref]

Dligatch, S.

Dogariu, A.

Domañski, W.

W. Domañski, “Polarization degree fading during propagation of partially coherent light through retarder,” Opto-Electron. Rev.13 (2005).

Dupont, Jan

Elies, P.

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

Emül, Y.

O. Polat, Y. Emül, and S. Özharar, “Investigation of the Mueller Matrix elements of the liquid crystal cell illuminated with a broad band light source,” in Optical and Quantum Electronics (Springer, 2017).

Fade, J.

Fisch, M.R.

N.J. Diorio, M.R. Fisch, and J.L. West, “Filled liquid crystal depolarizers,” J. Appl. Phys. 90(8), 3675–3678 (2001).
[Crossref]

Georges, G.

Gerig, Z.

Gerligand, P.Y.

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

Ghabbach, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 1996).

Gorman, M.

M. Gorman and S.A. Solin, “Transmission Raman and depolarization spectra of bulk a-Se from 13 to 300 cm1,” Solid State Commun. 18, 38–1098 (1976).

Goudail, F.

Gross, M.

Hamel, C.

Harman, M.

Illing, R. M.E.

R. M.E. Illing, “Optical and structural performance of the PolZero-Lm time domain polarization scrambler,” presented at the Earth Science Technology Forum, Boulder, USA, 22 Jun. 2010.

Ismail, F.D.

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

Ivanov, V. A.

Keck, J.

Kotlikov, E. N.

Kruschwitz, J. D. T.

Le Jeune, B.

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

Lemarchand, F.

Lemarquis, F.

Lequime, M.

Liu, B.

Liukaityte, S.

Loiseaux, D.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Lotrian,

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

Luitot, C.

MacLeod, A.

H.A. MacLeod and A. MacLeod, Thin Film Optical Filters (Taylor and Francis, 2001).
[Crossref]

MacLeod, H.A.

H.A. MacLeod and A. MacLeod, Thin Film Optical Filters (Taylor and Francis, 2001).
[Crossref]

Martino, A.

Meynart, R.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Nazabal, V.

Orlik, Xavier

Özharar, S.

O. Polat, Y. Emül, and S. Özharar, “Investigation of the Mueller Matrix elements of the liquid crystal cell illuminated with a broad band light source,” in Optical and Quantum Electronics (Springer, 2017).

Pervak, V.

Polat, O.

O. Polat, “Theoretical study on depolarization of the light transmitted through a non-uniform liquid crystal cell,” Optik 7, 3560–3563 (2016).
[Crossref]

O. Polat, Y. Emül, and S. Özharar, “Investigation of the Mueller Matrix elements of the liquid crystal cell illuminated with a broad band light source,” in Optical and Quantum Electronics (Springer, 2017).

Popov, K. V.

Pouget, L.

Prokashev, V. N.

Réfrégier, P.

Richert, M.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Roche, M.

Sato, K.

Shen, W. D.

Sierk, B.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

Solin, S.A.

M. Gorman and S.A. Solin, “Transmission Raman and depolarization spectra of bulk a-Se from 13 to 300 cm1,” Solid State Commun. 18, 38–1098 (1976).

Soriano, G.

Sorrentini, J.

Southwell, W.

Sugiura, M.

Teeka, C.

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

Tikhonravov, A. V.

Tortel, H.

Tropin, A. N.

Trubetskov, M.

West, J.L.

N.J. Diorio, M.R. Fisch, and J.L. West, “Filled liquid crystal depolarizers,” J. Appl. Phys. 90(8), 3675–3678 (2001).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).

Yuan, W.

Yupapin, P.

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

Zallat, J.

Zerrad, M.

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

M. Zerrad, C. Luitot, J. Berthon, and C. Amra, “Optical systems for controlled specular depolarization,” Opt. Lett. 39, 6919–6922 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22, 14594–14609 (2014).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19, 21313–21320 (2011).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34, 2429–2431 (2009).
[Crossref] [PubMed]

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
[Crossref] [PubMed]

M. Zerrad and C. Amra, “Dépolariseurs spéculaires parfaits,” patent FR1454923 (2014).

M. Zerrad, A. Ghabbach, G. Soriano, M. Lequime, C. Amra, and J. Berthon, “Depolarizing optical multilayers,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds. (OSA Technical Digest, 2013).

Appl. Opt. (8)

A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
[Crossref] [PubMed]

A. V. Tikhonravov, P. W. Baumeister, and K. V. Popov, “Phase properties of multilayers,” Appl. Opt. 36, 4382–4392 (1997).
[Crossref] [PubMed]

L. Abel-Tibérini, F. Lemarquis, and M. Lequime, “Masking mechanisms applied to thin-film coatings for the manufacturing of linear variable filters for two-dimensional array detectors,” Appl. Opt. 47, 5706–5714 (2008).
[Crossref] [PubMed]

L. Abel-Tiberini, F. Lemarquis, and M. Lequime, “Dedicated spectrophotometer for localized transmittance and reflectance measurements,” Appl. Opt. 45, 1386–1391 (2006).
[Crossref] [PubMed]

F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49, 683–693 (2010).
[Crossref] [PubMed]

L. Pouget, J. Fade, C. Hamel, and M. Alouini, “Polarimetric imaging beyond the speckle grain scale,” Appl. Opt. 517345–7356 (2012).
[Crossref] [PubMed]

M. Gross, S. Dligatch, and A. Chtanov, “Optimization of coating uniformity in an ion beam sputtering system using a modified planetary rotation method,” Appl. Opt. 50, C316–C320 (2011).
[Crossref] [PubMed]

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref] [PubMed]

Appl. Phys. (1)

P. Elies, B. Le Jeune, P.Y. Gerligand, J. Cariou, and Lotrian, “Analysis of the dispersion of speckle polarization on the Poincaré sphere,” Appl. Phys. 301285–1292 (1997).

J. Appl. Phys. (1)

N.J. Diorio, M.R. Fisch, and J.L. West, “Filled liquid crystal depolarizers,” J. Appl. Phys. 90(8), 3675–3678 (2001).
[Crossref]

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

J. Opt. Technol. (1)

Opt. Express (11)

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[Crossref] [PubMed]

S. Ainouz, J. Zallat, A. Martino, and C. Collet, “Physical interpretation of polarization-encoded images by color preview,” Opt. Express 14, 5916–5927 (2006).
[Crossref] [PubMed]

J. Broky and A. Dogariu, “Correlations of polarization in random electro-magnetic fields,” Opt. Express 19, 15711–15719 (2011).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19, 21313–21320 (2011).
[Crossref] [PubMed]

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

Jan Dupont and Xavier Orlik, “Simulation of polarized optical speckle fields: effects of the observation scale on polarimetry,” Opt. Express 24, 11151–11163 (2016).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22, 14594–14609 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

W. D. Shen, M. Cathelinaud, M. Lequime, F. Charpentier, and V. Nazabal, “Light trimming of a narrow bandpass filter based on a photosensitive chalcogenide spacer,” Opt. Express 16, 373–383 (2008).
[Crossref] [PubMed]

Opt. Lett. (3)

Optik (1)

O. Polat, “Theoretical study on depolarization of the light transmitted through a non-uniform liquid crystal cell,” Optik 7, 3560–3563 (2016).
[Crossref]

Solid State Commun. (1)

M. Gorman and S.A. Solin, “Transmission Raman and depolarization spectra of bulk a-Se from 13 to 300 cm1,” Solid State Commun. 18, 38–1098 (1976).

World Journal of Modelling and Simulation (1)

F.D. Ismail, M. Aziz, C. Teeka, J. Ali, and P. Yupapin, “Filter design using multi-Bragg reflectors,” World Journal of Modelling and Simulation 8, 205–210 (2012).

Other (14)

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

W. Domañski, “Polarization degree fading during propagation of partially coherent light through retarder,” Opto-Electron. Rev.13 (2005).

O. Polat, Y. Emül, and S. Özharar, “Investigation of the Mueller Matrix elements of the liquid crystal cell illuminated with a broad band light source,” in Optical and Quantum Electronics (Springer, 2017).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).

E. Collett, Field Guide to Polarization (SPIE, 2005).
[Crossref]

M. Zerrad and C. Amra, “Dépolariseurs spéculaires parfaits,” patent FR1454923 (2014).

M. Zerrad, A. Ghabbach, G. Soriano, M. Lequime, C. Amra, and J. Berthon, “Depolarizing optical multilayers,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds. (OSA Technical Digest, 2013).

R. M.E. Illing, “Optical and structural performance of the PolZero-Lm time domain polarization scrambler,” presented at the Earth Science Technology Forum, Boulder, USA, 22 Jun. 2010.

J. Caron, J.L. Bézy, G. Bazalgette Courrèges-Lacoste, B. Sierk, R. Meynart, M. Richert, and D. Loiseaux, “Polarization scramblers in Earth observing spectrometers: lessons learned from Sentinel-4 and 5 phases A/B1,” presented at the International Conference on Space Optics - ICSO, Ajaccio, France, 9–12 Oct. 2012.

M. Lequime and C. Amra, De l’Optique électromagnétique à l’Interférométrie - Concepts et illustrations (EDP Sciences, 2013).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 1996).

H.A. MacLeod and A. MacLeod, Thin Film Optical Filters (Taylor and Francis, 2001).
[Crossref]

P.W. Baumeister, Optical Coating Technology (SPIE Press Book, 2004).
[Crossref]

M. Bass, Handbook of Optics: Volume IV - Optical Properties of Materials, Nonlinear Optics, Quantum Optics, (McGraw Hill Professional, 2010) Chap. Optical Properties of Films and Coatings.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (19)

Fig. 1.
Fig. 1. Example of 1D-transverse variations of the polarimetric phase difference at the surface x–y of the device.
Fig. 2.
Fig. 2. Incident, local and global polarizations plotted on the Poincaré sphere with γ = π/20.
Fig. 3.
Fig. 3. Incident, local and global polarizations plotted on the Poincaré sphere with γ = π/60.
Fig. 4.
Fig. 4. Incident, local and global polarizations plotted on the Poincaré sphere with γ = π/60 for an arbitrary elliptical incident polarization (see text) with β ≠ 1.
Fig. 5.
Fig. 5. Incident, local and global polarizations plotted on the Poincaré sphere with a random phase distribution (For greater clarity, only the polarizations corresponding to the first line of the filter are plot).
Fig. 6.
Fig. 6. Draft on non-uniformity effects at the surface sample (see text).
Fig. 7.
Fig. 7. Optical properties of a quarter-wave mirror at the central wavelength λ0(x) and 45° incidence
Fig. 8.
Fig. 8. Spectral variations of polarization ratio (full lines) in situations where the band-pass condition Eq. (67) is satisfied (blue curve) or not (orange curve). The polarization degree (yellow dashed curve) is also plotted in the case where the bandpass condition is satisfied (see text).
Fig. 9.
Fig. 9. Case where the gradient mirror M0(x) is deposited on a flat mirror Madd (see text).
Fig. 10.
Fig. 10. Intensity spectrum of the total mirror M(x), versus wavelength and x position. We observe that an intensity (horizontal) bandwidth is hold whatever the x-position. The left and right figures are given for TM and TE polarizations, respectively. The oblique bandwidth is that of the gradient mirror M0(x).
Fig. 11.
Fig. 11. Polarimetric phase variations of the total mirror M(x)
Fig. 12.
Fig. 12. Spectral variations of the polarization degree of the total mirror M(x), for different uniformity values which correspond to: Δe/e = 5%, 25%, 50%, 75% and 100%. Total depolarization is reached in the whole mirror band-pass. The reflection spectrum of the gradient mirror is also is plotted in dashed line (see text).
Fig. 13.
Fig. 13. Spectral variations of the polarization degree of a narrow-band filter (see text). The green curve is for the flat coating while the red curve is for the gradient coating.
Fig. 14.
Fig. 14. TE reflected beam versus wavelength and spatial frequency. The left figure is the reference (see text) and the right figure emphasizes additional diffraction effects.
Fig. 15.
Fig. 15. TM reflected beam versus wavelength and spatial frequency. The left figure is the reference (see text) and the right figure emphasizes additional diffraction effects.
Fig. 16.
Fig. 16. TE and TM reflected beams after re-centering, for comparison to Fig. 15 (see text).
Fig. 17.
Fig. 17. Detail of beam alteration at two wavelengths λ1 = 500nm and λ2 = 633nm (see text). The λ1 pattern is quasi-superimposed to the reference, while noticeable differences can be seen for the λ2 pattern plotted in dashed line. The left and right figures are given for TM and TE polarization respectively.
Fig. 18.
Fig. 18. Ratio versus wavelength of reflected energy from the depolarizing device and from the reference. The frequency range of integration is 1/L in the left figure and 3/L in the right figure.
Fig. 19.
Fig. 19. Case of a birefringent substrate.

Equations (90)

Equations on this page are rendered with MathJax. Learn more.

E 0 + = | E 0 s + E o p + = A 0 + exp [ j ( σ 0 . r + α 0 Z ) ] with A 0 + = | A 0 S + exp ( j ϕ S ) A 0 P + exp ( j ϕ P )
σ 0 = 2 π ν 0 = k sin ( i 0 ) x and α 0 = [ k 0 2 σ 2 ] 0.5 = k 0 cos ( i 0 ) with k 0 = 2 π n 0 / λ
r s ( x , y ) = R s ( x , y ) exp [ j δ s ( x , y ) ]
r p ( x , y ) = R p ( x , y ) exp [ j δ p ( x , y ) ]
e r = | e rs e rp = exp [ j ( σ 0 . r + α 0 Z ) ] | A 0 S + R S exp [ j ( ϕ S + δ S ) ] A 0 P + R P exp [ j ( ϕ P + δ P ) ]
DOP 2 = 1 4 [ β / ( 1 + β ) 2 ] [ 1 | μ | 2 ]
β = < | E rp | 2 > / < | E rs | 2 >
μ = < E rs E rp * > / [ < | E rs | 2 > < | E rp | 2 > ] 0.5
E t ( r , z = 0 ) = E 0 + ( r , 0 ) t ( r )
E t ( r , z ) = ν A ( ν ) exp [ j ( 2 π ν . r + α ( ν ) Z ) ] d ν = F . T . [ A ( ν ) exp ( j α ( ν ) Z ) ]
E t ( r , z ) = F . T . [ A ( ν ) ] * r H ( r , Z ) = E t ( r , 0 ) * r H ( r , Z )
H ( r , Z ) = F . T . { exp [ j α ( ν ) Z ] }
E t ( r , 0 ) = t ( r ) E 0 + ( r , 0 ) = t ( r ) exp ( j σ 0 . r ) A 0 +
E t ( r , Z ) = A 0 + t ( r ) exp ( j σ 0 . r ) * r H ( r , Z )
E ^ t ( ν , Z ) = A 0 + t ^ ( ν ν 0 ) exp [ j α ( ν ) Z ]
E r ( r , Z ) = A 0 + r ( r ) exp ( j σ 0 . r ) * r H ( r , Z )
E ^ r ( ν , Z ) = A 0 + r ^ ( ν ν 0 ) exp [ j α ( ν ) Z ]
Φ = | A 0 + | 2 ( 1 / 2 ω μ ) ν α ( ν ) | r ^ ( ν ν 0 ) | 2 d ν
Φ = | A 0 + | 2 ( α 0 / 2 ω μ ) ν | r ^ ( ν ν 0 ) | 2 d ν
Φ = | A 0 + | 2 ( α 0 / 2 ω μ ) r | r ( r ) | 2 d r
β = β 0 ( r | r p ( r ) | 2 d r ) / ( r | r s ( r ) 2 | d r )
μ = r r s ( r ) r p * d r / { ( r | r s ( r ) | 2 d r ) ( r | r p ( r ) | 2 d r ) } 0.5
β 0 = < | A 0 p + | 2 > / < | A 0 s + | 2 >
S 0 = < | E s | 2 + | E p | 2 > S 1 = < | E s | 2 | E p | 2 > S 2 = < E s E p * + E s * E p > S 3 = j < E s E p * E s * E p >
dop 2 = ( 1 / S 0 ) 2 ( S 1 2 + S 2 2 + S 3 2 )
s 0 = 1 s 1 = ( 1 β ) / ( 1 + β ) s 2 = 2 cos ( ψ ) ( β ) / ( 1 + β ) s 3 = 2 sin ( ψ ) ( β ) / ( 1 + β )
ψ = ϕ s ϕ p and β = β 0 = | A 0 p + / A 0 s + | 2
ψ = ( ϕ s ϕ p ) + ( δ s δ p ) and β = β 0 R p / R s
s 0 = 1 s 1 = ( 1 β ) / ( 1 + β ) s 2 = 2 Real ( μ ) ( β ) / ( 1 + β ) s 3 = 2 Im ( μ ) ( β ) / ( 1 + β )
R s = | r s | 2 = R p = | r p | 2
β = 1 DOP = | μ |
μ = r r s ( r ) r p * ( r ) d r / { ( r | r s ( r ) | 2 d r ) ( r | r p ( r ) | 2 d r ) } 0.5
μ = ( 1 / Σ ) x , y exp [ j Δ δ ( x , y ) ] d x d y = < exp [ j Δ δ ( x , y ) ] > x , y
Δ δ ( x , y ) = Δ δ 0 + γ x
μ = exp ( j Δ δ 0 ) sin ( γ L / 2 ) / ( γ L / 2 ) = exp ( j Δ δ 0 ) sinc ( γ L / 2 )
DOP = | sinc ( γ L / 2 ) |
DOP = | sinc ( γ x L x / 2 ) sinc ( γ y L y / 2 ) |
DOP = 1 4 { β 0 / ( 1 + β 0 ) 2 } [ 1 DOP 1 2 ]
DOP min = [ ( 1 β 0 ) / ( 1 + β 0 ) ] 2
Δ δ ( x , y ) = Δ δ 0 + RD ( x , y )
u ( x , y ) = e ( x , y ) / e ( 0 , 0 ) = e ( x , y ) / e 0
e i ( x , y ) = e i ( x ) e i , 0 + x tan ( κ )
u i ( x , y ) = 1 + ( x / e i , 0 ) tan ( κ )
( necos θ ) i = q i λ 0 / 4
M 2 p + 1 = Air / ( HL ) p H / Substrate
( necos θ ) H = ( necos θ ) L = λ 0 / 4
Δ f / f 0 = ( 4 / π ) arcsin [ ( n ˜ H n ˜ L ) / ( n ˜ H + n ˜ L ) ]
n H e H ( x ) cos θ H = u H ( x ) λ / 4 and n L e L ( x ) cos θ L = u L ( x ) λ / 4
u H ( x ) = 1 + ( x / e H ) tan ( κ ) and u L ( x ) = 1 + ( x / e L ) tan ( κ )
u H ( x ) u L ( x ) u ( x )
λ 0 ( x ) = u ( x ) λ 0 = λ 0 [ 1 + ( x / e ) tan ( κ ) ]
DOP 2 = 1 4 [ β / ( 1 + β ) 2 ] [ 1 | μ | 2 ]
μ = x r s ( x ) r p * ( x ) d x / ( [ x | r s ( x ) | 2 d x ] [ x | r p ( x ) | 2 d x ] ) 0.5
β = β 0 [ x | r p ( x ) | 2 d x ] / [ x | r s ( x ) | 2 d x ]
λ 0 ( x ) = u ( x ) λ 0 = λ 0 [ 1 + ( x / e ) tan ( κ ) ]
μ ( λ ) = x r s ( λ , λ 0 ( x ) ) r p * ( λ , λ 0 ( x ) ) d x / ( [ x | r s ( λ , λ 0 ( x ) ) | 2 d x ] [ x | r p ( λ , λ 0 ( x ) ) | 2 d x ] ) 0.5
β = β 0 [ x | r p ( λ , λ 0 ( x ) ) | 2 d x ] / [ x | r s ( λ , λ 0 ( x ) ) | 2 d x ]
r [ λ , λ 0 ( x ) ] = r 0 [ λ ( λ 0 ( x ) λ 0 ) , λ 0 ] = r 0 [ λ ( u ( x ) 1 ) , λ 0 ]
μ ( λ ) = x r 0 s [ λ λ 0 ( x ) ] r 0 p * [ λ λ 0 ( x ) ] d x / ( [ x | r 0 s [ λ λ 0 ( x ) ] | 2 d x ] [ x | r 0 p [ λ λ 0 ( x ) ] | 2 d x ] ) 0.5
β ( λ ) = β 0 [ x | r 0 p [ λ λ 0 ( x ) ] | 2 d x ] / [ x | r 0 s [ λ λ 0 ( x ) ] | 2 d x ]
λ 0 ( x ) = λ 0 ( x / e ) tan ( κ )
λ 0 u ( x ) Δ λ / 2 < λ < λ 0 u ( x ) + Δ λ / 2 for 0 < x < L
λ 0 u ( L ) Δ λ / 2 < λ < λ 0 u ( 0 ) + Δ λ / 2
λ 0 u ( L ) Δ λ / 2 < λ < λ 0 + Δ λ / 2
u ( L ) = 1 + ( L / e ) tan ( κ )
BW = Δ λ λ 0 ( L / e ) tan ( κ ) = Δ λ λ 0 Δ e / e
λ 00 = ( λ 0 / 2 ) [ 1 + ( L / e ) tan ( κ ) ] = ( λ 0 / 2 ) [ 1 + Δ e / e ]
( L / e ) tan ( κ ) = Δ e / e < Δ λ / λ 0
M ( x ) = Air / M 0 ( x ) M add / substrate
r pol ( λ , λ 0 ( x ) ) | r pol ( λ , λ 0 ) | exp [ j δ pol ( x ) ]
DOP = ( 1 / L ) | x exp [ j Δ δ ( x ) ] d x | = | sinc ( γ L / 2 ) |
E ^ r ( λ , ν , z ) = A 0 + r ^ ( λ , ν ν 0 ) e j α ( λ , ν ) z
r ^ ( λ , ν ) = x r pol ( λ , x ) exp ( 2 π ν x ) d x
R ( λ , ν ) = | r ^ ( λ , ν ) | 2
R ( λ , ν ) = R ( λ , ν ) / R max ( λ , ν )
R ref ( λ , ν ) = | sinc ( π ν L ) | 2
R ( λ , ν ) = R ( λ , ν ν 0 ( λ ) )
F ( λ ) = ν R ( λ , ν ) d ν
η ( λ ) = F ( λ ) / F ref ( λ )
t pol ( x ) = t 0 , pol exp [ j ( 2 π / λ ) n pol e 0 ] exp [ j ( 2 π / λ ) n pol x tan ( κ ) ]
Δ δ ( x ) = ( 2 π / λ ) Δ n tan ( κ ) x = γ x
DOP = | sinc ( γ L / 2 ) | with γ = ( 2 π / λ ) Δ n tan ( κ )
Δ n tan ( κ ) > λ / L
E ^ t ( λ , ν , z ) = A 0 + t ^ pol ( λ , ν ν 0 ) e j α ( λ , ν ) z
t pol ( x ) = t 0 , pol exp [ j ( 2 π / λ ) n pol e 0 ] exp [ j ( 2 π / λ ) n pol x tan ( κ ) ]
δ pol = ( 2 π / λ ) n pol tan ( κ ) x = 2 π γ pol x
γ = n pol tan ( κ ) / λ
t pol ( λ , ν ν 0 ) = t 0 , pol exp [ j ( 2 π / λ ) n pol e 0 ] δ [ ν ν 0 γ pol ( λ ) ]
( 2 π / λ ) n pol tan ( κ ) > n pol / ( L Δ n ) = γ min
ν γ min = sin θ / λ γ min = sin θ / λ sin θ sin θ Δ θ = λ γ min = ( λ / L ) ( n / Δ n ) 10 4 / Δ n

Metrics