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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 1 — Jan. 1, 2007
  • pp: 95–105

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators

Gabriel Milewski, David Engström, and Jörgen Bengtsson  »View Author Affiliations

Applied Optics, Vol. 46, Issue 1, pp. 95-105 (2007)

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Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace–interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 × 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of 2 π   rad could be obtained, accompanied by an intensity modulation depth as high as > 95 % .

© 2007 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(090.1760) Holography : Computer holography
(100.5090) Image processing : Phase-only filters
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Optical Devices

Original Manuscript: May 10, 2006
Revised Manuscript: July 26, 2006
Manuscript Accepted: September 4, 2006

Gabriel Milewski, David Engström, and Jörgen Bengtsson, "Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators," Appl. Opt. 46, 95-105 (2007)

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  1. J. Sampsell, "Digital micromirror device and its application to projection displays," J. Vac. Sci. Technol. B 12, 3242-3246 (1994). [CrossRef]
  2. A. Gehner, W. Doleschal, A. Elgner, R. Kauert, D. Kunze, and M. Wildenhain, "Active-matrix-addressed micromirror array for wavefront correction in adaptive optics," in MOEMS and Miniaturized Systems II, M. E. Motamedi and R. Goering, eds., Proc. SPIE 4561, 265-275 (2001). [CrossRef]
  3. J. L. Pezzaniti and R. A. Chipman, "Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states," Opt. Lett. 18, 1567-1569 (1993). [CrossRef] [PubMed]
  4. B. Löfving, "Self-adjusting dynamic binary phase holograms," Appl. Opt. 36, 2347-2352 (1997). [CrossRef] [PubMed]
  5. Z. Zhang, G. Lu, and F. Yu, "Simple method for measuring phase modulation in liquid crystal televisions," Opt. Eng. 33, 3018-3022 (1994). [CrossRef]
  6. D. Engström, G. Milewski, J. Bengtsson, and S. Galt, "Diffraction-based determination of the phase modulation for general spatial light modulators," Appl. Opt. 45, 7195-7204 (2006). [CrossRef] [PubMed]
  7. D. Prongue, H. Herzig, R. Dandliker, and M. Gale, "Optimized kinoform structures for highly efficient fan-out elements," Appl. Opt. 31, 5706-5711 (1992). [CrossRef] [PubMed]
  8. M. W. Farn, "New iterative algorithm for the design of phase-only gratings," in Computer and Optically Generated Holographic Optics; 4th in a Series, I. Cindrich and S. H. Lee, eds., Proc. SPIE 1555, 34-42 (1991). [CrossRef]
  9. G.-Z. Yang, B.-Z. Dong, B.-Y. Gu, J.-Y. Zhuang, and O. Ersoy, "Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison," Appl. Opt. 33, 209-218 (1994). [CrossRef] [PubMed]
  10. J. Bengtsson, "Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method," Appl. Opt. 36, 8435-8444 (1997). [CrossRef]
  11. T. Chang, "Proximity effect in electron-beam lithography," J. Vac. Sci. Technol. 12, 1271-1275 (1976). [CrossRef]
  12. G. Owen, "Methods for proximity effect correction in electron lithography," J. Vac. Sci. Technol. B 8, 1889-1892 (1990). [CrossRef]
  13. F. Nikolajeff, J. Bengtsson, M. Larsson, M. Ekberg, and S. Hard, "Measuring and modeling the proximity effect in direct-write electron-beam lithography kinoforms," Appl. Opt. 34, 897-903 (1995). [CrossRef] [PubMed]
  14. A. M. C. Iemmi, I. Moreno, J. Campos, and M. Yzuel, "Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays: optimization of the modulation diffraction efficiency," Opt. Express 13, 2111-2119 (2005). [CrossRef] [PubMed]
  15. I. Moreno, J. Campos, C. Gorecki, and M. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Appl. Opt. 34, 6423-6432 (1995).
  16. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, "Synthesis of digital holograms by direct binary search," Appl. Opt. 26, 2788-2798 (1987). [CrossRef] [PubMed]
  17. C. Stolz, L. Bigué, and P. Ambs, "Implementation of high-resolution diffractive optical elements on coupled phase and amplitude spatial light modulators," Appl. Opt. 40, 6415-6424 (2001). [CrossRef]
  18. N. N. Yoshikawa and T. Yatagai, "Phase optimization of a kinoform by simulated annealing," Appl. Opt. 33, 863-868 (1994). [CrossRef] [PubMed]
  19. N. Yoshikawa, M. Itoh, and T. Yatagai, "Quantized phase optimization of two-dimensional Fourier kinoforms by a genetic algorithm," Opt. Lett. 20, 752-754 (1995). [CrossRef] [PubMed]
  20. M. Gruneisen, L. DeSandre, J. Rotge, R. Dymale, and D. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004). [CrossRef]
  21. J. E. Stockley, D. Subacius, and S. A. Serati, "Influence of the interpixel region in liquid crystal diffraction gratings," in Liquid Crystal Materials, Devices, and Applications VII, R. Shashidhar, ed., Proc. SPIE 3635, 127-136 (1999). [CrossRef]
  22. X. Xun and R. W. Cohn, "Phase calibration of spatially nonuniform spatial light modulators," Appl. Opt. 43, 6400-6406 (2004). [CrossRef] [PubMed]
  23. J. Bengtsson, "Direct inclusion of the proximity effect in the calculation of kinoforms," Appl. Opt. 33, 4993-4996 (1994). [CrossRef] [PubMed]

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