Current Optics and Photonics

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

Improvement of Calibration Method for a Dual-rotating Compensator Type Spectroscopic Ellipsometer

  • Byeong-Kwan Yang (Jiny Photonics Inc.) ;
  • Jin Seung Kim (Institute of Photonics and Information Technology, Department of Physics, Jeonbuk National University)
  • Received : 2023.04.06
  • Accepted : 2023.06.08
  • Published : 2023.08.25
Download PDF
⟨ Previous Next ⟩

Abstract

The compensators used in spectroscopic ellipsometers are usually assumed to be ideal linear waveplates. In reality, however, they are elliptical waveplates, because they are usually made by bonding two or more linear waveplates of different materials with slight misalignment. This induces systematic error when they are modeled as linear waveplates. We propose an improved calibration method based on an optical model that regards an elliptical waveplate as a combination of a circular waveplate (rotator) and a linear waveplate. The method allows elimination of the systematic error, and the residual error of optic axis measurement is reduced to 0.025 degrees in the spectral range of 450-800 nm.

Keywords

References

  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 1st ed. (North-Holland, Netherlands, 1987). 
  2. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, "Mueller matrix imaging of human colon tissue for cancer diagnostics: How Monte Carlo modeling can help in the interpretation of experimental data," Opt. Express 18, 10200-10208 (2010).  https://doi.org/10.1364/OE.18.010200
  3. M. Foldyna, A. De Martino, E. Garcia-Caurel, R. Ossikovski, C. Licitra, F. Bertin, K. Postava, and B. Drevillon, "Critical dimension of biperiodic gratings determined by spectral ellipsometry and Mueller matrix polarimetry," Eur. Phys. J. Appl. Phys. 42, 351-359 (2008).  https://doi.org/10.1051/epjap:2008089
  4. R. M. A. Azzam, "Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal," Opt. Lett. 2, 148-150 (1978).  https://doi.org/10.1364/OL.2.000148
  5. D. H. Goldstein, "Mueller matrix dual-rotating retarder polarimeter," App. Opt. 31, 6676-6683 (1992).  https://doi.org/10.1364/AO.31.006676
  6. M. H. Smith, "Optimization of a dual-rotating-retarder Mueller matrix polarimeter," Appl. Opt. 41, 2488-2493 (2002).  https://doi.org/10.1364/AO.41.002488
  7. K. M. Twietmeyer and R. A. Chipman, "Optimization of Mueller matrix polarimeters in the presence of error sources," Opt. Express 16, 11589-11603 (2008).  https://doi.org/10.1364/OE.16.011589
  8. P. Hariharan, "Achromatic retarders using quartz and mica," Meas. Sci. Technol. 6, 1078-1079 (1995).  https://doi.org/10.1088/0957-0233/6/7/036
  9. B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, "Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range," Opt. Express 9, 225-235 (2001).  https://doi.org/10.1364/OE.9.000225
  10. H. Gu, S. Liu, X. Chen, and C. Zhang, "Calibration of misalignment errors in composite waveplates using Mueller matrix ellipsometry," Appl. Opt. 54, 684-693 (2015).  https://doi.org/10.1364/AO.54.000684
  11. E. Compain, S. Poirier, and B. Drevillon, "General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers," Appl. Opt. 38, 3490-3502 (1999).  https://doi.org/10.1364/AO.38.003490
  12. C. Macias-Romero and P. Torok, "Eigenvalue calibration methods for polarimetry," J. Eur. Opt. Soc.: Rapid Publ. 7, 12004 (2012). 
  13. K. Y. Bang, J. S. An, I. An, and R. W. Collins, "Self-calibrated Mueller matrix spectroscopic ellipsometry," J. Korean Phys. Soc. 45, 185-188 (2004). 
  14. C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, "Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle," Thin Solid Films 455-456, 14-23 (2004).  https://doi.org/10.1016/j.tsf.2003.11.191
  15. J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films," Rev. Sci. Instrum. 72, 1742-1754 (2001).  https://doi.org/10.1063/1.1347969
  16. J. Lee, P. I. Rovira, I. An, and R. W. Collins, "Alignment and calibration of the MgF2 biplate compensator for applications in rotating-compensator multichannel ellipsometry," J. Opt. Soc. Am. A 18, 1980-1985 (2001).  https://doi.org/10.1364/JOSAA.18.001980
  17. H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, "Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes," J. Opt. 18, 025702 (2016). 
  18. D. H. Goldstein and R. A. Chipman, "Error analysis of a Mueller matrix polarimeter," J. Opt. Soc. Am. A 7, 693-700 (1990).  https://doi.org/10.1364/JOSAA.7.000693
  19. H. Gu, X. Chen, Y. Shi, H. Jiang, C. Zhang, P. Gong, and S. Liu, "Comprehensive characterization of a general composite waveplate by spectroscopic Mueller matrix polarimetry," Opt. Express 26, 25408-25425 (2018).  https://doi.org/10.1364/OE.26.025408
  20. H. Hurwitz Jr. and R. C. Jones, "A new calculus for the treatment of optical systems II. Proof of three general equivalence theorems," J. Opt. Soc. Am. 31, 493-499 (1941).  https://doi.org/10.1364/JOSA.31.000493
  21. S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and K. Singh, "Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry," Opt. Express 14, 190-202 (2006).  https://doi.org/10.1364/OPEX.14.000190
  22. S.-Y. Lu and R. A. Chipman, "Interpretation of Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996). https://doi.org/10.1364/JOSAA.13.001106