## Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection

Applied Optics, Vol. 48, Issue 30, pp. 5834-5841 (2009)

http://dx.doi.org/10.1364/AO.48.005834

Acrobat PDF (801 KB)

### Abstract

A technique is proposed theoretically and verified experimentally to eliminate a zero-order beam caused by a pixelated phase-only spatial light modulator (SLM) for holographic projection. The formulas for determination of the optical field in the Fourier plane are deduced, and the influence of the pixelated structure of a SLM on the intensity of the zero-order beam is numerically investigated. Two currently existing techniques are studied and a new one is presented. These three techniques are used separately to eliminate the zero-order interruption, and the optical performances of the reconstructed patterns are compared. The new technique results in higher reconstruction quality and diffraction efficiency. A short animated movie is illuminated for holographic projection display. The experimental results show that the zero-order beam can be efficiently eliminated by the new technique. It is believed that this technique can be used in various optical systems that are based on pixelated phase-only SLMs, such as holographic optical tweezers and optical testing systems.

© 2009 Optical Society of America

## 1. Introduction

1. H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. **3**, 312–315 (1971). [CrossRef]

3. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. **3**, 27–29 (1978). [CrossRef] [PubMed]

4. B. Gu, G. Yang, and B. Dong, “General theory for performing an optical transform,” Appl. Opt. **25**, 3197–3206 (1986). [CrossRef] [PubMed]

5. S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Opti mization by simulated annealing,” Science **220**, 671–680 (1983). [CrossRef] [PubMed]

6. A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. **10**, 035302 (2008). [CrossRef]

7. A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. **47**, 4793–4803 (2008). [CrossRef] [PubMed]

8. H. Melville, G. Milne, G. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic holograms,” Opt. Express **11**, 3562–3567 (2003). [CrossRef] [PubMed]

9. Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express **13**, 1059–1065 (2005). [CrossRef] [PubMed]

10. 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**, 144–152 (2005). [CrossRef]

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

12. J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. **45**, 6374–6380 (2006). [CrossRef] [PubMed]

13. X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. **43**, 6400–6406 (2004). [CrossRef] [PubMed]

14. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. **46**, 5667–5679 (2007). [CrossRef] [PubMed]

*et al.*analyzed the diffraction efficiency produced by the pixelated SLM with a limited fill factor and absorbing dead space areas [15

15. V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. **160**, 207–213 (1999). [CrossRef]

16. D. Palima and V. R. Daria, “Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms,” Appl. Opt. **45**, 6689–6693 (2006). [CrossRef] [PubMed]

17. D. Palima and V. R. Daria, “Holographic projection of arbitrary light patterns with a suppressed zero-order beam,” Appl. Opt. **46**, 4197–4201 (2007). [CrossRef] [PubMed]

*et al.*proposed a method in which the zero-order beam is actively removed by forcing some of the light from the active regions of the pixels to fall and destructively interfere with the light resulting from the dead spaces [18

18. G. Milewski, D. Engström, and J. 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). [CrossRef]

## 2. Theory and Methods

### 2A. Optical Characteristic of the Pixelated Phase-Only Spatial Light Modulator

*XOY*coordinate system is in the center of the phase-only SLM. The transmittance function of the pixelated SLM can be described as where the transmittance from the active areas of the SLM is the transmittance from the dead space areas of the SLM is where

*μ*is defined as The complex amplitude distribution in the reconstruction plane can be calculated as the Fourier transform of

*δ*function because

*μ*,

*μ*.

18. G. Milewski, D. Engström, and J. 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). [CrossRef]

19. 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]

*l*to describe the phase modulation of the dead space areas, that is, where

*ε*and

*ε*increases as

### 2B. Methods for Eliminating the Zero-Order Beam

#### 2B1. Spherically Loaded Phase Technique

*f*is the focal length of the Fourier lens. By adding the phase information of spherical wave

*λ*is the wavelength,

*r*is the distance from the SLM to the center of the divergent spherical wave. The sign on the right-hand side of Eq. (8) is determined by the type of phase-only SLM. If a transmissive SLM is used, there should be a plus sign, and if a reflective one is used there should be a minus sign. The schematic of this technique is shown in Fig. 4a. The reconstruction plane and the focal plane of the Fourier lens are separated along the optical axis. The distance between the reconstruction plane and the focal plane of the Fourier lens can be expressed as The real image of the reconstruction pattern can be obtained when

#### 2B2. Linearly Loaded Phase Technique

13. X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. **43**, 6400–6406 (2004). [CrossRef] [PubMed]

*θ*is the obliquity of the added linear phase ramp, and Figure 4b shows the optical arrangement of the linearly loaded phase technique. The zero-order distortion from the dead space areas is focused to a fixed spot in the focal plane of the Fourier lens. The reconstructed pattern is shifted away from the optical axis because of the additional linear phase ramp loaded on the SLM. The distance between the center of the reconstructed pattern and the focus of the Fourier lens is given by It is not necessary to add any filter to the light path, which would simplify the entire system. However, the zero-order illumination and the reconstructed pattern are still in the same plane, which is a limiting factor in the vision system. At the same time, the zero-order beam and the reconstructed pattern interfere with each other. The optical quality of the reconstructed pattern will weaken.

### 2C. Combination of Spherically and Linearly Loaded Phase Technique

*M*and

*N*are the pixel numbers of the reconstructed and original patterns.

## 3. Experimental Results

*XY*PhaseFlat of liquid crystal on a silicon SLM (Boulder Nonlinear Systems, Lafayette, Colorado, USA), which is a pure phase modulator that consists of

*in vivo*, we show a short animated movie for dynamic holographic projection, and one frame of it is shown in Fig. 6 (Media 1). It can be clearly seen that our technique can eliminate the zero-order beam successfully in a dynamic holographic projection system.

## 4. Discussion and Conclusion

*ξ*and

*η*as the coordinate system of the image plane. The spatial frequency spectrum of

*ξ*axis direction is shown in Fig. 7 (solid line), and it is obvious that it is an impulse function. As

*θ*increases, the pulse position moves laterally. Also, the pulse width will gradually expand because of the discrete expression of

*θ*is

*ξ*axis when

*r*should be larger than

*ξ*axis when

*ξ*axis when

1. | H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. |

2. | R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) |

3. | J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. |

4. | B. Gu, G. Yang, and B. Dong, “General theory for performing an optical transform,” Appl. Opt. |

5. | S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Opti mization by simulated annealing,” Science |

6. | A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. |

7. | A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. |

8. | H. Melville, G. Milne, G. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic holograms,” Opt. Express |

9. | Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express |

10. | 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 |

11. | C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. |

12. | J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. |

13. | X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. |

14. | J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. |

15. | V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. |

16. | D. Palima and V. R. Daria, “Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms,” Appl. Opt. |

17. | D. Palima and V. R. Daria, “Holographic projection of arbitrary light patterns with a suppressed zero-order beam,” Appl. Opt. |

18. | G. Milewski, D. Engström, and J. Bengtsson, “Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators,” Appl. Opt. |

19. | 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. |

20. | J. Christmas, N. Collings, and A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UKpatentGB2438458 (28 November 2007). |

**OCIS Codes**

(090.1760) Holography : Computer holography

(090.2870) Holography : Holographic display

**ToC Category:**

Holography

**History**

Original Manuscript: June 9, 2009

Revised Manuscript: September 3, 2009

Manuscript Accepted: September 30, 2009

Published: October 16, 2009

**Virtual Issues**

Vol. 4, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

Hao Zhang, Jinghui Xie, Juan Liu, and Yongtian Wang, "Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection," Appl. Opt. **48**, 5834-5841 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-48-30-5834

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### References

- H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971). [CrossRef]
- R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).
- J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27-29 (1978). [CrossRef] [PubMed]
- B. Gu, G. Yang, and B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197-3206 (1986). [CrossRef] [PubMed]
- S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983). [CrossRef] [PubMed]
- A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008). [CrossRef]
- A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793-4803 (2008). [CrossRef] [PubMed]
- H. Melville, G. Milne, G. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic holograms,” Opt. Express 11, 3562-3567 (2003). [CrossRef] [PubMed]
- Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express 13, 1059-1065 (2005). [CrossRef] [PubMed]
- 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, 144-152 (2005). [CrossRef]
- C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960-967 (2006). [CrossRef] [PubMed]
- J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45, 6374-6380 (2006). [CrossRef] [PubMed]
- X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400-6406(2004). [CrossRef] [PubMed]
- J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46, 5667-5679 (2007). [CrossRef] [PubMed]
- V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999). [CrossRef]
- D. Palima and V. R. Daria, “Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms,” Appl. Opt. 45, 6689-6693 (2006). [CrossRef] [PubMed]
- D. Palima and V. R. Daria, “Holographic projection of arbitrary light patterns with a suppressed zero-order beam,” Appl. Opt. 46, 4197-4201 (2007). [CrossRef] [PubMed]
- G. Milewski, D. Engström, and J. 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). [CrossRef]
- 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]
- J. Christmas, N. Collings, A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UK patent GB2438458 (28 November 2007).

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