Systematic errors for a Mueller matrix dual rotating compensator ellipsometer

doi:10.1364/OE.16.008814

Systematic errors for a Mueller matrix dual rotating compensator ellipsometer

Laurent Broch, Aotmane En Naciri, and Luc Johann »View Author Affiliations

Optics Express, Vol. 16, Issue 12, pp. 8814-8824 (2008)
http://dx.doi.org/10.1364/OE.16.008814

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Abstract

The characterization of anisotropic materials and complex systems by ellipsometry has pushed the design of instruments to require the measurement of the full reflection Mueller matrix of the sample with a great precision. Therefore Mueller matrix ellipsometers have emerged over the past twenty years. The values of some coefficients of the matrix can be very small and errors due to noise or systematic errors can induce distored analysis. We present a detailed characterization of the systematic errors for a Mueller Matrix Ellipsometer in the dual-rotating compensator configuration. Starting from a general formalism, we derive explicit first-order expressions for the errors on all the coefficients of the Mueller matrix of the sample. The errors caused by inaccuracy of the azimuthal arrangement of the optical components and residual ellipticity introduced by imperfect optical elements are shown. A new method based on a four-zone averaging measurement is proposed to vanish the systematic errors.

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: March 12, 2008
Revised Manuscript: April 10, 2008
Manuscript Accepted: April 15, 2008
Published: June 2, 2008

Citation
Laurent Broch, Aotmane En Naciri, and Luc Johann, "Systematic errors for a Mueller matrix dual rotating compensator ellipsometer," Opt. Express 16, 8814-8824 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8814

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References

Q1. E. Compain and B. Drevillon, "Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator," Rev. Sci. Instrum. 68, 2671-1680 (1997). [CrossRef]
E. Garcia-Caurel, A. De Martino, and B. Drevillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004). [CrossRef]
R. W. Collins, Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, eds., (William Andrew Publishing & Springer-Verlag, 2005), Chap. 7.3.3, p 546-566.
G. E. JellisonJr, "Spectroscopic ellipsometry data analysis: measured versus calculated quantities," Thin Solid Films 313-314, 33-39 (1998). [CrossRef]
M. Kildemo, I. S. Nerbø, E. Søndergaard, L. Holt, I. Simonsen, and M. Stchakovsky, "Optical response of nanostructured GaSb," Physica Status Solidi (c), in press.
J. S. Tyo, D. L. Golstein, D. B. Chenault, and J. A. Shaw, "Review of passive imaging polarimetry for remote sensing applications," Appl. Opt. 45, 5453-5469 (2006). [CrossRef] [PubMed]
M. H. Smith, "Optimization of dual-rotating-retarder Mueller matrix polarimeter," Appl. Opt. 41, 2488-2493 (2002). [CrossRef] [PubMed]
D. H. Goldstein and R. A. Chipman, "Error analysis of a Mueller matrix polarimeter," J. Opt. Soc. Am. A 7, 693-700 (1990). [CrossRef]
R. Kleim, L. Kuntzler and A. El Ghemmaz, "Systematic errors in rotating-compensator ellipsometry," J. Opt. Soc. Am. A 11, 2550-2558 (1994). [CrossRef]
S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim, "Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry," Thin Solid Films 313-314, 73-78 (1998). [CrossRef]
A. En Naciri, L. Broch, L. Johann, and R. Kleim, "Fixed polarizer, rotating-polarizer and fixed analyzer spectroscopic ellipsometer: accurate calibration method, effcet of errors and testing," Thin Solid Films 406, 103-112 (2002). [CrossRef]
G. Piller, L. Broch, and L. Johann, "Experimental study of the systematic errors for a Mueller matrix double rotating compensator ellipsometer," Physica Status Solidi (c) 5, 1027-1030 (2008). [CrossRef]
R. M. A Azzam and N. M. Bashara, ellipsometry and Polarized Light (North-holland, Amsterdam, 1977).
J. M. M. De Nijs and A. Van Siflhout, "Systematic and random errors in rotating-analyzer ellipsometry," J. Opt. Soc. Am. A 5, 773-781 (1988). [CrossRef]

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[1] Q1. E. Compain and B. Drevillon, "Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator," Rev. Sci. Instrum. 68, 2671-1680 (1997). [CrossRef]

[2] E. Garcia-Caurel, A. De Martino, and B. Drevillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004). [CrossRef]

[3] R. W. Collins, Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, eds., (William Andrew Publishing & Springer-Verlag, 2005), Chap. 7.3.3, p 546-566.

[4] G. E. JellisonJr, "Spectroscopic ellipsometry data analysis: measured versus calculated quantities," Thin Solid Films 313-314, 33-39 (1998). [CrossRef]

[5] M. Kildemo, I. S. Nerbø, E. Søndergaard, L. Holt, I. Simonsen, and M. Stchakovsky, "Optical response of nanostructured GaSb," Physica Status Solidi (c), in press.

[6] J. S. Tyo, D. L. Golstein, D. B. Chenault, and J. A. Shaw, "Review of passive imaging polarimetry for remote sensing applications," Appl. Opt. 45, 5453-5469 (2006). [CrossRef] [PubMed]

[7] M. H. Smith, "Optimization of dual-rotating-retarder Mueller matrix polarimeter," Appl. Opt. 41, 2488-2493 (2002). [CrossRef] [PubMed]

[8] D. H. Goldstein and R. A. Chipman, "Error analysis of a Mueller matrix polarimeter," J. Opt. Soc. Am. A 7, 693-700 (1990). [CrossRef]

[9] R. Kleim, L. Kuntzler and A. El Ghemmaz, "Systematic errors in rotating-compensator ellipsometry," J. Opt. Soc. Am. A 11, 2550-2558 (1994). [CrossRef]

[10] S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim, "Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry," Thin Solid Films 313-314, 73-78 (1998). [CrossRef]

[11] A. En Naciri, L. Broch, L. Johann, and R. Kleim, "Fixed polarizer, rotating-polarizer and fixed analyzer spectroscopic ellipsometer: accurate calibration method, effcet of errors and testing," Thin Solid Films 406, 103-112 (2002). [CrossRef]

[12] G. Piller, L. Broch, and L. Johann, "Experimental study of the systematic errors for a Mueller matrix double rotating compensator ellipsometer," Physica Status Solidi (c) 5, 1027-1030 (2008). [CrossRef]

[13] R. M. A Azzam and N. M. Bashara, ellipsometry and Polarized Light (North-holland, Amsterdam, 1977).

[14] J. M. M. De Nijs and A. Van Siflhout, "Systematic and random errors in rotating-analyzer ellipsometry," J. Opt. Soc. Am. A 5, 773-781 (1988). [CrossRef]

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Systematic errors for a Mueller matrix dual rotating compensator ellipsometer