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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 19 — Sep. 15, 2008
  • pp: 14853–14861
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Hologram optimization for SLM-based reconstruction with regard to polarization effects

C. Kohler, T. Haist, X. Schwab, and W. Osten  »View Author Affiliations


Optics Express, Vol. 16, Issue 19, pp. 14853-14861 (2008)
http://dx.doi.org/10.1364/OE.16.014853


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Abstract

We report on first results obtained with two modified hologram optimization algorithms. These algorithms take into account the complex modulation characteristic of the spatial light modulators employed for hologram reconstruction. To this end the Jones matrices of the modulator as well as all other components of the setup are used within a modified direct binary search and an iterative Fourier transform algorithm. Geometrical phase effects are included in the optimization. Elimination of the analyzer behind the spatial light modulator is possible by that approach and for typical setups using twisted-nematic liquid crystal modulators an enhanced overall diffraction efficiency is achieved. Possible applications are the comparative digital holography and optical tweezers. Experimental results for the reconstructions of holograms with a Holoeye LC-R 3000 modulator are presented.

© 2008 Optical Society of America

1. Introduction

Liquid Crystal Displays (LCDs) are widely used in optical measurement systems e.g. for fringe projection [1

1. K.-P. Proll, J.-M. Nivet, K. Körner, and H. J. Tiziani, “Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays,” Appl. Opt. 42, 1773–1778 (2003). [CrossRef] [PubMed]

], optical tweezers [2

2. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000). [CrossRef]

], or digital holography [3

3. W. Osten, T. Baumbach, and W. Jüptner, “Comparative digital holography,” Opt. Lett. 27, 1764–1766 (2002). [CrossRef]

, 4

4. Kyongsik Choi, Hwi Kim, and Byoungho Lee, “Full-color autostereoscopic 3D display system using color-dispersion-compensated synthetic phase holograms,” Opt. Express 12, 5229–5236 (2004). [CrossRef] [PubMed]

]. Most of the commercially available devices have been developed for projection applications. Therefore, theses devices are optimized to achieve high contrast amplitude modulation. Most of these devices are constructed as twisted-nematic LCDs and phase modulation of the elements is only a side effect. Nevertheless by proper addressing phase-only or at least phase-mostly modulation is possible if the display is well controlled [5

5. 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]

, 6

6. L. G. Neto, D. Roberge, and Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995). [CrossRef] [PubMed]

, 7

7. J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998). [CrossRef]

, 8

8. I. Moreno, P. Velasquez, C. R. Fernandez-Pousa, M. M. Sanchez-Lopez, and F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 943697–3702 (2003). [CrossRef]

].

One well known technique is to use polarization eigenvectors [5

5. 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]

, 7

7. J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998). [CrossRef]

, 9

9. J. E. Bigelow and R. A. Kashnow, “Poincare sphere analysis of liquid crystal optics,” Appl. Opt. 16, 2090–2096 (1977). [CrossRef] [PubMed]

, 10

10. J. A. Davis, J. Nicols, and A. Marquez, “Phasor analysis of eigenvector generated in liquid-crystal displays,” Appl. Opt. 41, 4579–4584 (2002). [CrossRef] [PubMed]

, 11

11. M. Yamauchi, A. Marquez, J. A. Davis, and D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000). [CrossRef]

, 12

12. V. Durán, J. Lancis, E. Tajahuerce, and M. Fernndez-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607–5616 (2006). [CrossRef] [PubMed]

, 13

13. X. Zhu, Q. Hong, Y. Huang, and S.-T. Wu, “Eigenmodes of a reflective twisted-nematic liquid-crystal cell,” J. Appl. Phys. 94, 2868–2873 (2003). [CrossRef]

]. If such an “eigenmode” is modulated by the LCD only the complex scalar amplitude of the light is changed. The polarization remains unchanged. Therefore, by proper selection of the input polarization one can avoid problems due to geometric phase. However, one has to consider that the eigenmodes change with the addressing graylevel so one can only use some sort of average eigenvector. Theoretical predictions using typical LCD models [14

14. B. E. A. Saleh : “Theory and Design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Express 29, 240–246 (1990).

, 15

15. P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507- (1982). [CrossRef]

, 16

16. F. H. Yu and H. S. Kwok, “Comparison of extended Jones matrices for twisted nematic liquid-crystal displays at oblique angles of incidence,” J. Opt. Soc. Am. 16, 2772–2780 (1999). [CrossRef]

, 17

17. A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Express 39, 3301–3307 (2000).

, 18

18. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative predict of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001). [CrossRef]

] as well as measurement [5

5. 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]

] of such eigenvectors is possible.

Nevertheless in most setups optimum results are not achieved [18

18. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative predict of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001). [CrossRef]

, 19

19. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006). [CrossRef] [PubMed]

]. Polarization of the output light for twisted-nematic liquid crystal displays (TN-LCDs) dramatically varies with the addressed gray level. This leads to a change of the so-called geometric or Pancharatnam phase [20

20. P. Hariharan, H. Remachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: A demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997). [CrossRef]

, 21

21. G. Wernicke, M. Dürr, H. Gruber, A. Hermerschmidt, S. Krüger, and A. Langner, “High resolution optical reconstruction of digital holograms,” Proc. Fringe 2005, 480–487, Springer (2005).

, 22

22. V. Duran, J. Lancis, E. Tajahuerce, and V. Climent, “Poincare sphere method for optimizing the phase modulation response of a twisted nematic liquid crystal display,” J. Display Technol. 3, 9–14 (2007). [CrossRef]

]. Consequently, the overall phase change is the sum of the conventional dynamic phase change and the geometric phase. The additional geometric phase results in a quite complicated hologram reconstruction because of a non-transitive overall phase change [23

23. H. Schmitzer, S. Klein, and W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993). [CrossRef] [PubMed]

].

We want to clarify this by a small example:We denote the phase difference between the phase due to the arbitrary gray level GN with the phase due to the gray level G0 = 0 by ϕ (GN,G0). Normally one would expect that ϕ (G1,G0)-ϕ (G2,G0) equals the phase difference of the phases of two pixels addressed by the gray levels G1 and G2. Unfortunately this is not true due this additional polarization dependent effect. Mathematically we have

ϕ(G1,G0)ϕ(G2,G0)ϕ(G1,G2)
(1)

Such complications normally are avoided by using a linear polarizer behind the modulator because then the polarization is constant for all gray levels [6

6. L. G. Neto, D. Roberge, and Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995). [CrossRef] [PubMed]

]. Especially if the modulators are used for the reconstruction of digital or computer-generated holograms a closer look on the setup shows that there is potential for increasing the overall efficiency. Most important, the linear analyzer behind the display will lead to loss of light. Omitting this linear analyzer will not only reduce the loss of light but also possible aberrations, unwanted interferences, and the overall cost of the system.

In the following we suggest two advanced algorithms for hologram optimization based on a combination of the vectorial Jones calculus with traditional methods of hologram optimization. The approach is quite general and it is demonstrated for two well known hologram optimization algorithms but it is likely to work with other optimization methods as well, e.g. simulated annealing [24

24. N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoform using simulated annealing,” Appl. Opt. 33, 863–868 (1994). [CrossRef] [PubMed]

] or genetic algorithms [25

25. 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]

]. The incorporation of the Jones calculus into the hologram optimization step goes beyond the use of the modulator’s complex transmission as already presented (e.g. in [26

26. T. Haist, T. M. Schönleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997). [CrossRef]

, 27

27. 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]

]), where a linear polarizer behind the spatial light modulator (SLM) has been used and the effects of the nonlinear geometric phase and complex interference contrast therefore have not been present.

2. Hologram optimization algorithms

The core idea to incorporate the influence of the geometric phase into the optimization is the usage of the modulator’s Jones matrix during optimization. Therefore, as a mandatory step it is necessary to first perform a detailed characterization of the SLM. Different methods were introduced for the measurement of the modulators Jones-Matrix e.g. the model-based approaches presented in [14

14. B. E. A. Saleh : “Theory and Design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Express 29, 240–246 (1990).

, 5

5. 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]

, 31

31. C. Soutar and K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Express 33, 2704–2712 (1994).

, 6

6. L. G. Neto, D. Roberge, and Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995). [CrossRef] [PubMed]

, 18

18. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative predict of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001). [CrossRef]

], as well as other characterizations, e.g presented in [32

32. Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Express 33, 3018–3022 (1994).

, 33

33. G. Bader, R. Brkle, E. Lueder, N. Fruehauf, and C. Zeile, “Fast and accurate techniques for measuring the complex transmittance of liquid crystal valves,” Proc. SPIE 3015, 93–104 (1997). [CrossRef]

, 34

34. A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144152 (2005).

].

We used polarimetric measurements in order to first obtain the phase-reduced Jones matrix. Then additional phase measurements with a modified double-slit method [35

35. G. O. ReynoldsJ. B. DeVelisG. B. ParrentB. J. Thompson “The New Physical Optics Notebook: Tutorials in Fourier Optics,” SPIE Press (1989).

] lead to the full Jones matrix with eight parameters. A general description of the modulator used, not in including the measurement of the Jones-Matrix, can be found in [19

19. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006). [CrossRef] [PubMed]

]. For the measurement of the modulators Jones-Matrix we refer to [16

16. F. H. Yu and H. S. Kwok, “Comparison of extended Jones matrices for twisted nematic liquid-crystal displays at oblique angles of incidence,” J. Opt. Soc. Am. 16, 2772–2780 (1999). [CrossRef]

, 17

17. A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Express 39, 3301–3307 (2000).

]. A detailed description about the setup used at our institute will be presented shortly within a doctoral thesis. Apart from the Jones matrix of the modulator also the Jones matrices of the other elements used in the setup should be known. For the results presented here only the Jones matrix of the modulator was measured. For all the other elements, as an approximation, the theoretical Jones matrices were used.

The basic procedure is the same in first approximation for both algorithms. We start with the illumination represented by the Jones vector of the illuminating wave front. All following elements are considered by multiplication of the illumination Jones vectors with the Jones matrices of the optical elements passed in their physical order. For each pixel of the SLM the Jones matrix corresponding to the gray value written into the SLM at that pixel is used. The simulation of the hologram reconstruction is then done separately for the x- and y-component of the electrical field transmitted by the SLM.

In the examples shown below only Fourier or quasi-Fourier holograms were computed. Because we are interested in the reconstruction with low numerical aperture the reconstructed field can be obtained simply by performing Fourier transforms separately for the x and y components of the electrical field. Of course, it is possible to extend this to any other hologram reconstruction geometry by using Fresnel- or Rayleigh-Sommerfeld propagation [36

36. W. Freude and G. K. Grau, “Rayleigh-Sommerfeld and Helmholtz-Kirchhoff Integrals: Application to the Scalar and Vectorial Theory of Wave Propagation and Diffraction,” J. Lightwave Technol. 13, 24–32 (1995). [CrossRef]

] or even rigorous methods [37

37. W. Singer, M. Totzeck, and H. Gross, Handbook of optical systems 2: physical image formation (Wiley-VCH, Weinheim, 2005).

].

By employing this simulation of the LCD-based hologram reconstruction it becomes possible to optimize the holograms even if no analyzer behind the LCD is used. The procedures of the two advanced hologram optimization algorithms are shown in Fig. 1 and Fig. 2.

The implementation of the advanced DBS optimization is straight forward because DBS is directly based on the minimization of a chosen error metric based on the simulated reconstruction. Arbitrary modifications within the forward simulation of the hologram reconstruction can be implemented. Provided that the simulation is realistic and that it takes into account geometrical phases we therefore can optimize holograms for setups with arbitrary polarization components.

For the advanced IFTA optimization the procedure is more complicated. In the reconstruction plane the reconstructed amplitudes have to be be replaced by the target amplitudes. This is done, as shown in Fig. 2, by scaling the amplitude of the Jones vector J(x,y) of each pixel in the reconstruction plane. The second and more difficult problem is the transformation of the newly calculated phase and amplitude in the hologram plane into a corresponding gray value of the display. We use a minimization of the magnitude of the complex difference vector between the modulator output and the desired complex light field at a certain pixel |J(x,y)-J(GN)|. In the case of the IFT algorithm the polarization behavior of the modulator is incorporated by the magnitude of the difference vector for the replacement of the gray values written to the newly calculated hologram. This heuristic incorporation of the polarization leads to improved results and we have only minor differences compared to the DBS-based optimization. Since the method of optimization is independent of the modulator’s capabilities a change of the input polarization is not analyzed here. Though, of course, in cases where the chosen input polarization causes less changes in the output polarization the optimization is easier and will give probably better results. The extremal case would be the use of the Jones calculus enhanced hologram optimization with a planar nematic liquid crystal display. In this case there is no polarization modulation if linear input polarization is used and therefore conventional hologram optimization is adequate.

Fig. 1. Procedure of the advanced DBS hologram optimization. SchemaDBS.eps

Both methods can be of course used for correcting additional aberrations. One way is to measure the wavefront of the optical system. For the DBS optimization it is sufficient to subtract the measured phase distribution during iteration from the hologram before reconstruction. In case of the IFTA optimization the aberration can be subtracted from the phase during iteration before the computation of the gray values.

3. Results of the optimization

For different setups simulations have been done. Setups with both polarizer and analyzer, with a polarizer, an analyzer and two additional quarter wave plates and with a polarizer only have been considered.

3.1. Simulation results

Simulations were performed to compare the Jones matrix-enhanced optimization with the conventional methods. Holograms reconstructing three single spots, each having a size of one single pixel in the reconstruction plane, were optimized. The simulations were done first for an “ideal linear phase modulator” (0 to 2π) without change of polarization and second for a modulator with the measured graylevel-dependent Jones matrices. In order to achieve a meaningful comparison of the two cases the “ideal linear phase modulator” was implemented using a unity Jones matrix with a different global linear phase factor for each of the gray values. Accordingly, the angles of the polarizer and analyzer within our simulation program should not have any influence on the simulated hologram reconstruction with the ideal phase modulator. Anyway, we used exactly the same simulation steps (including the polarizers) in order to be sure that we do not obtain different results due to numeric problems (inaccuracies caused by different implementations).

Fig. 2. Procedure of the advanced IFTA hologram optimization. SchemaIFTAJones.eps

The optimization was done for different polarizer and analyzer settings. Table 1 shows the results of the simulation. As expected the linear 2π phase shift (setup #7) yields the highest diffraction efficiency but the hologram optimized for the measured characteristic curve of the modulator without an analyzer leads to almost the same efficiency (setup #6).

Only small differences between the optimizations with the phase-only mode and the phase-mostly mode, in which no quarter wave plates were used, exist. The reconstruction of the hologram optimized for the linear phase shift with the measured Jones matrix shows always a reduced diffraction efficiency. This is as expected, because the characteristic curve used for the reconstruction does not match the one used for the optimization.

The error of the simulation is mainly caused by two aspects: by the error of the Jones Matrices used and by errors caused by effects not included in the model used, e.g. pixel cross talk or surface reflections on the SLM’s cover glass. As the error is depending on the gray level, i.e. the addressing voltage for each pixel it is difficult to give a general measure for the error. We estimate the error to be about 10%.

Table 1. Simulated diffraction efficiencies for the IFTA optimized holograms reconstructing three spots. The angles are given relative to the modulators frame. Where 0 equals the vertical axis i.e. the modulator’s shorter side. Positive angles are given counterclockwise in the direction with the positive z-axis pointing in the light direction.

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3.2. Measurement results

Table 2. Measured transmittance of the setup using different experimental settings of polarization elements (normalized to setup #3), as well as the estimated transmittance with an lossless crystal polarizer.

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The reconstructions were performed with three different settings: 1. phase mostly mode with a linear polarizer in front of and behind the display, 2. in an almost phase only mode with a linear polarizer and quarter wave plate each in front of and behind the modulator, and 3. with a single linear polarizer in front of the display. Table 2 lists the orientations of the polarizing elements, the amplitude contrasts, and the achieved phase modulations. The employed modulator Holoeye LCR-3000 is a twisted-nematic LCOS display with 1920×1200 pixels and a pixel pitch of 9.5 µm. Additional specifications can be found e.g. in [19

19. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006). [CrossRef] [PubMed]

, 38

38. C. Kohler, X. Schwab, W. Osten, and T. Baumbach, “Characterization of liquid crystal spatial light modulators for the reconstruction of digital holograms (in german: Charakterisierung von Flssigkristalllichtmodulatoren für die Rekonstruktion digitaler Hologramme),” Technisches Messen 73, 157–165 (2006). [CrossRef]

] and in the documentation of the manufacturer.

The results of the achieved overall light throughput are listed in table 2. For the settings with polarization elements behind the display the measured light throughput is given for a gray value of zero. This leads to maximum transmission in this configuration. Due to the remaining amplitude modulation in practice the achieved throughput is further reduced and the amount of reduction depends on the gray value distribution of the hologram. Anyway, the loss of light compared to the system without a linear polarizer behind the display is significant, as even the employed linear polarizer (B&W Filter, type KS-MIK) illuminated with the correct linear polarization causes about 10% loss of light.

Table 3 shows the measured diffraction efficiencies of the reconstructed holograms. Although the achieved diffraction efficiency with an analyzer is not maximum the overall light throughput (see #3, table 1) yields a noticeable improvement compared to the simple phase only setup (setup #2) which yields the best diffraction efficiency. Therefore, a trade off has to be made. For applications where a maximum diffraction efficiency is needed the phase only setup is best suited and for applications where a slightly reduced diffraction efficiency is not harmful but where a maximum light transmittance is demanded the setup omitting the analyzer yields the best properties.

Table 3. Diffraction efficiencies achieved with the setups (@532 nm) not taking into account the transmittance (compare table 2).

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Based on the transmission of the different setups given in table 2 and the measured diffraction efficiencies shown in table 3 the overall light efficiencies for a blazed grating written into the SLM can be calculated as follows. For setup # 1 using lossless crystal polarizers we obtain an overall efficiency of 82%·69.2% = 56.7%. For setup # 2 the achieved effiency is slightly lower 69%·75.7% = 52.1%. As expected, the best overall efficiency can be reached with the setup without polarizers and advanced hologram optimization, namely 100%·65% = 65%.

Fig. 3. Reconstructed ITO-Logos: (a) without analyzer (setup #3), (b) optimal setting, display in phase-only mode (setup #2, table 1).

4. Summary

Acknowledgment

We thank the Deutsche Forschungsgemeinschaft (DFG) for financial support under the grant number OS-111/23-1.

References and links

1.

K.-P. Proll, J.-M. Nivet, K. Körner, and H. J. Tiziani, “Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays,” Appl. Opt. 42, 1773–1778 (2003). [CrossRef] [PubMed]

2.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000). [CrossRef]

3.

W. Osten, T. Baumbach, and W. Jüptner, “Comparative digital holography,” Opt. Lett. 27, 1764–1766 (2002). [CrossRef]

4.

Kyongsik Choi, Hwi Kim, and Byoungho Lee, “Full-color autostereoscopic 3D display system using color-dispersion-compensated synthetic phase holograms,” Opt. Express 12, 5229–5236 (2004). [CrossRef] [PubMed]

5.

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]

6.

L. G. Neto, D. Roberge, and Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995). [CrossRef] [PubMed]

7.

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998). [CrossRef]

8.

I. Moreno, P. Velasquez, C. R. Fernandez-Pousa, M. M. Sanchez-Lopez, and F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 943697–3702 (2003). [CrossRef]

9.

J. E. Bigelow and R. A. Kashnow, “Poincare sphere analysis of liquid crystal optics,” Appl. Opt. 16, 2090–2096 (1977). [CrossRef] [PubMed]

10.

J. A. Davis, J. Nicols, and A. Marquez, “Phasor analysis of eigenvector generated in liquid-crystal displays,” Appl. Opt. 41, 4579–4584 (2002). [CrossRef] [PubMed]

11.

M. Yamauchi, A. Marquez, J. A. Davis, and D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted nematic liquid crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000). [CrossRef]

12.

V. Durán, J. Lancis, E. Tajahuerce, and M. Fernndez-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607–5616 (2006). [CrossRef] [PubMed]

13.

X. Zhu, Q. Hong, Y. Huang, and S.-T. Wu, “Eigenmodes of a reflective twisted-nematic liquid-crystal cell,” J. Appl. Phys. 94, 2868–2873 (2003). [CrossRef]

14.

B. E. A. Saleh : “Theory and Design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Express 29, 240–246 (1990).

15.

P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507- (1982). [CrossRef]

16.

F. H. Yu and H. S. Kwok, “Comparison of extended Jones matrices for twisted nematic liquid-crystal displays at oblique angles of incidence,” J. Opt. Soc. Am. 16, 2772–2780 (1999). [CrossRef]

17.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Express 39, 3301–3307 (2000).

18.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative predict of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001). [CrossRef]

19.

C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006). [CrossRef] [PubMed]

20.

P. Hariharan, H. Remachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: A demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997). [CrossRef]

21.

G. Wernicke, M. Dürr, H. Gruber, A. Hermerschmidt, S. Krüger, and A. Langner, “High resolution optical reconstruction of digital holograms,” Proc. Fringe 2005, 480–487, Springer (2005).

22.

V. Duran, J. Lancis, E. Tajahuerce, and V. Climent, “Poincare sphere method for optimizing the phase modulation response of a twisted nematic liquid crystal display,” J. Display Technol. 3, 9–14 (2007). [CrossRef]

23.

H. Schmitzer, S. Klein, and W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993). [CrossRef] [PubMed]

24.

N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoform using simulated annealing,” Appl. Opt. 33, 863–868 (1994). [CrossRef] [PubMed]

25.

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]

26.

T. Haist, T. M. Schönleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997). [CrossRef]

27.

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]

28.

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]

29.

B. B. Chhetri, S. Yang, and T. Shimomura, “Stochastic approach in the efficient design of the direct-binary-search algorithm for hologram synthesis,” Appl. Opt. 39, 5956–5964 (2000). [CrossRef]

30.

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. 5, 1058–1065 (1988). [CrossRef]

31.

C. Soutar and K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Express 33, 2704–2712 (1994).

32.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Express 33, 3018–3022 (1994).

33.

G. Bader, R. Brkle, E. Lueder, N. Fruehauf, and C. Zeile, “Fast and accurate techniques for measuring the complex transmittance of liquid crystal valves,” Proc. SPIE 3015, 93–104 (1997). [CrossRef]

34.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144152 (2005).

35.

G. O. ReynoldsJ. B. DeVelisG. B. ParrentB. J. Thompson “The New Physical Optics Notebook: Tutorials in Fourier Optics,” SPIE Press (1989).

36.

W. Freude and G. K. Grau, “Rayleigh-Sommerfeld and Helmholtz-Kirchhoff Integrals: Application to the Scalar and Vectorial Theory of Wave Propagation and Diffraction,” J. Lightwave Technol. 13, 24–32 (1995). [CrossRef]

37.

W. Singer, M. Totzeck, and H. Gross, Handbook of optical systems 2: physical image formation (Wiley-VCH, Weinheim, 2005).

38.

C. Kohler, X. Schwab, W. Osten, and T. Baumbach, “Characterization of liquid crystal spatial light modulators for the reconstruction of digital holograms (in german: Charakterisierung von Flssigkristalllichtmodulatoren für die Rekonstruktion digitaler Hologramme),” Technisches Messen 73, 157–165 (2006). [CrossRef]

OCIS Codes
(090.0090) Holography : Holography
(090.2890) Holography : Holographic optical elements
(230.4110) Optical devices : Modulators
(230.6120) Optical devices : Spatial light modulators
(090.1995) Holography : Digital holography
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Holography

History
Original Manuscript: June 19, 2008
Revised Manuscript: August 29, 2008
Manuscript Accepted: August 31, 2008
Published: September 5, 2008

Virtual Issues
Vol. 3, Iss. 11 Virtual Journal for Biomedical Optics

Citation
C. Kohler, T. Haist, X. Schwab, and W. Osten, "Hologram optimization for SLM-based reconstruction with regard to polarization effects," Opt. Express 16, 14853-14861 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-19-14853


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References

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  26. T. Haist, T. M. Sch¨onleber and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997). [CrossRef]
  27. C. Stolz, L. Bigu???e 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]
  28. 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]
  29. B. B. Chhetri, S. Yang and T. Shimomura, "Stochastic approach in the efficient design of the direct-binary-search algorithm for hologram synthesis," Appl. Opt. 39, 5956-5964 (2000). [CrossRef]
  30. F. Wyrowski and O. Bryngdahl, "Iterative Fourier-transform algorithm applied to computer holography," J. Opt. Soc. Am. 5, 1058-1065 (1988). [CrossRef]
  31. C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Express 33, 2704-2712 (1994).
  32. Z. Zhang, G. Lu and F. T. S. Yu, "Simple method for measuring phase modulation in liquid crystal televisions," Opt. Express 33, 3018-3022 (1994).
  33. G. Bader, R. Brkle, E. Lueder, N. Fruehauf and C. Zeile, "Fast and accurate techniques for measuring the complex transmittance of liquid crystal valves," Proc. SPIE 3015, 93-104 (1997). [CrossRef]
  34. A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, "Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator," Proc. SPIE 5776, 144152 (2005).
  35. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr. and B. J. Thompson: The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE Press, 1989).
  36. W. Freude and G. K. Grau, "Rayleigh-Sommerfeld and Helmholtz-Kirchhoff Integrals: Application to the Scalar and Vectorial Theory of Wave Propagation and Diffraction," J. Lightwave Technol. 13, 24-32 (1995). [CrossRef]
  37. W. Singer, M. Totzeck and H. Gross, Handbook of optical systems 2: physical image formation (Wiley-VCH, Weinheim, 2005).
  38. C. Kohler, X. Schwab, W. Osten and T. Baumbach, "Characterization of liquid crystal spatial light modulators for the reconstruction of digital holograms (in german: Charakterisierung von Flssigkristalllichtmodulatoren f¨ur die Rekonstruktion digitaler Hologramme)," Technisches Messen 73, 157-165 (2006). [CrossRef]

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