## Approach to improve beam quality of inter-satellite optical communication system based on diffractive optical elements

Optics Express, Vol. 17, Issue 8, pp. 6311-6319 (2009)

http://dx.doi.org/10.1364/OE.17.006311

Acrobat PDF (736 KB)

### Abstract

For inter-satellite optical communication transmitter with reflective telescope of two-mirrors on axis, a large mount of the transmitted energy will be blocked by central obscuration of the secondary mirror. In this paper, a novel scheme based on diffractive optical element (DOE) is introduced to avoid it. This scheme includes one diffractive beam shaper and another diffractive phase corrector, which can diffract the obscured part of transmitted beam into the domain unobscured by the secondary mirror. The proposed approach is firstly researched with a fixed obscuration ratio of 1/4. Numerical simulation shows that the emission efficiency of new figuration is 99.99%; the beam divergence from the novel inter-satellite optical communication transmitter is unchanged; and the peak intensity of receiver plane is increased about 31% compared with the typical configuration. Then the intensity patterns of receiver plane are analyzed with various obscuration ratio, the corresponding numerical modelling reveals that the intensity patterns with various obscuration ratio are nearly identical, but the amplify of relative peak intensity is getting down with the growth of obscuration ratio. This work can improve the beam quality of inter-satellite optical communication system without affecting any other functionality.

© 2009 Optical Society of America

## 1. Introduction

2. P. Henneberg and H. Schubert, “A new telescope concept for space communication,” Proc. SPIE **1218**, 153–159 (1990). [CrossRef]

6. W. N. Peters and A. M. Ledger, “Techniques for matching laser TEM00 mode to obstructed circular aperture,” Appl. Opt . **9**, 1435–1442 (1970). [CrossRef] [PubMed]

7. B. J. Klein and J. J. Degnan,“Optical antenna gain 1 : transmitting antennas,” Appl. Opt . **13**, 2134–2141 (1974). [CrossRef] [PubMed]

10. H. Hemmati and N. Page, “Approaches for efficient coupling of lasers to telescope with secondary mirror and baffle obscuration,” Proc. SPIE **4635**, 288–294 (2002). [CrossRef]

12. R. N. Smartt and E. W. Cross, “Advances in spherical-mirror telescopic systems design: application to large-aperature solar coronagraphs,” Opt. Eng . **41**, 2055–2058 (2002). [CrossRef]

13. Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett . **32**, 2076–2078 (2007). [CrossRef] [PubMed]

14. Z. Liu, J. Dai, X. Sun, and S. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express **16**, 19926–19933 (2008). [CrossRef] [PubMed]

## 2. Improved inter-satellite optical communication transmitter configuration

## 3. Design of DOE and beam transformation

### 3.1. Design of DOE

*A*and

*B*are assigned to these two planes, respectively.To begin, a random phase distribution

*φ*

_{0}is generated to serve as the initial phase estimate and combined with the corresponding sampled amplitude function

*A*to form input wave function

*E*(

_{in}*x*

_{1},

*y*

_{1}). Then, this synthesized complex discrete function is done by means of the Fast Fourier Transform (FFT) algorithm. The phase portion

*ϕ*′ of the complex wave function

*E*′(

_{out}*x*

_{2},

*y*

_{2}) resulting from this transformation are computed and reserved, and it is combined with the corresponding sampled amplitude function

*B*. This new complex function

*E*(

_{out}*x*

_{2},

*y*

_{2}) is then done by Inverse Fast Fourier Transform (IFFT), the phases

*φ*′ of the sample points are calculated and combined with the known sampled amplitude function

*A*to form a new estimate of the complex sampled input plane, and the iteration process is repeated.

20. B. Lin and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt . **13**, 2470–2471 (1974). [CrossRef]

*ℱ*represents FFT,

*ζ*is an infinitesimal. Finally, the phase mapping representing the DOE data will be obtained across a subtraction between calculated phase mapping and initial phase of input plane-wave.

### 3.2. Beam transformation

*E*represents the total beam energy emitting from light source, and

*E*′ represents the beam energy emitting from the exit pupil pupil.

*k*= 2

*π*/

*λ*represents wavenumber,

*z*is transmitted distance,

*f*,

_{x}*f*are spatial frequency of receiver plane along

_{y}*x*-direction and

*y*-direction, respectively.

*η*:

_{P}*I*

_{4max}and

*I*

_{4max}′ are the peak energy of far field with and without DOE, respectively.

## 4. Numerical simulations

*T*. Obviously, the inner diameter of HGB in exit pupil plane varies with

*T*, so the intensity patterns of far-field are also varied with

*T*. This variation prompts us to investigate the far-field intensity patterns with various obscuration ratio.

*r*

_{3m},

*ω*

_{03}, and

*r*

_{30}=

*r*

_{3m}·

*T*represent the outer radius, beam waist, and inner radius of required HGB profile, respectively.

*λ*= 800

*nm*; the radius of exit pupil plane

*r*

_{3m}= 10

*mm*, corresponding beam waist

*ω*

_{03}=

*r*

_{3m}/√2; the transmitted distance between inter-satellite optical communication transmitter and inter-satellite optical communication receiver

*z*= 5 × 10

^{7}

*m*.

### 4.1. Design of DOE with fixed obscuration ratio

*T*= 1/4, when the amplitude function of exit pupil plane has been given, the amplitude function of plane P2 and plane P1 in Fig. 2 can be determined by

*r*

_{2m}=

*r*

_{3m}·

*T*,

*ω*

_{02}=

*ω*

_{03}·

*T*, and

*r*

_{20}=

*r*

_{30}·

*T*represent the outer radius, beam waist, and inner radius of desired HGB profile in plane P2, respectively.

*c*

_{2}is an amplitude profile coefficient, which makes a relation of conservation of energy between the waves of plane P2 and P3:

*r*

_{1}∈ [0,

*r*

_{1m}], and

*r*

_{1m}=

*r*

_{2m}is the maximal spot radius of plane P1 in Fig. 2,

*ω*

_{01}=

*r*

_{1m}/√2 is the corresponding beam waist. The action of c1 is similar to

*c*

_{2}, which ensures the energy conservation between plane P1 and P2.

*η*is 31.5%. Furthermore, these two distribution curves are kept with a same width of main lobe, which indicates that the PAT (pointing, acquisition, and tracking) mechanism of inter-satellite optical communication system won’t be influenced.

_{P}### 4.2. Design of DOE with varying obscuration ratio

*T*. When

*T*equal to 1/4, 1/6, 1/8, and 1/10, the corresponding

*η*are 31.5%, 13.7%, 8.1%, and 5.5%, respectively.

_{P}## 5. Conclusion

## References and links

1. | M. Katzman, ed., Laser Satellite Communications, (Englewood Cliffs, N.J., Prentice-Hall, 1987). |

2. | P. Henneberg and H. Schubert, “A new telescope concept for space communication,” Proc. SPIE |

3. | A. Yamamoto, T. Hori, T. Shimizu, and K. Nakagawa, “Japanese first optical inter-orbit communications engineering test satellite (OICETS),” Proc. SPIE |

4. | H. Hemmati and N. Page, “Preliminary opto-mechanical design for the X2000 transceiver,” Proc. SPIE |

5. | M. Knapek, J. Horwath, N. Perlot, and B. Wilkerson, “The DLR ground station in the optical payload experiment (STROPEX) - results of the atmospheric measurement instruments,” Proc. SPIE |

6. | W. N. Peters and A. M. Ledger, “Techniques for matching laser TEM00 mode to obstructed circular aperture,” Appl. Opt . |

7. | B. J. Klein and J. J. Degnan,“Optical antenna gain 1 : transmitting antennas,” Appl. Opt . |

8. | O. D. Christy, “Dual-secondary mirror Cassegrain optical system,” U. S. Patent 4,439,012, Mar 27 (1984). |

9. | X. L. Kong and P. M. Hao, “New method to remove central shade for reflecting laser beam expander,” Chin. J. Quantum Electron . |

10. | H. Hemmati and N. Page, “Approaches for efficient coupling of lasers to telescope with secondary mirror and baffle obscuration,” Proc. SPIE |

11. | C. W. Chen, “Re-imaging optical system including refractive and diffractive optical elements,” U. S. Patent 5,287,218, Feb 15 (1994). |

12. | R. N. Smartt and E. W. Cross, “Advances in spherical-mirror telescopic systems design: application to large-aperature solar coronagraphs,” Opt. Eng . |

13. | Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett . |

14. | Z. Liu, J. Dai, X. Sun, and S. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express |

15. | W. B. Veldkamp and T. J. McHugh, “Binary optics,” Sci. Am. May , |

16. | R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik |

17. | J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt . |

18. | G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express |

19. | C. Rydberg and J. Bengtsson, “Numerical algorithm for the retrieval of coherent beams from transverse intensity measurements,” Opt. Express |

20. | B. Lin and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt . |

21. | J. W. Goodman, Introduction to Fourier Optics, Second Edition, (New York, McGraw-Hill, 2006). |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: December 4, 2008

Revised Manuscript: February 25, 2009

Manuscript Accepted: March 20, 2009

Published: April 2, 2009

**Citation**

Liying Tan, Jianjie Yu, Jing Ma, Yuqiang Yang, Mi Li, Yijun Jiang, Jianfeng Liu, and Qiqi Han, "Approach to improve beam quality of inter-satellite optical communication system based on diffractive optical elements," Opt. Express **17**, 6311-6319 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6311

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### References

- M. Katzman, ed., Laser Satellite Communications, (Englewood Cliffs, N.J., Prentice-Hall, 1987).
- P. Henneberg and H. Schubert, "A new telescope concept for space communication," Proc. SPIE 1218, 153-159 (1990). [CrossRef]
- A. Yamamoto, T. Hori, T. Shimizu, and K. Nakagawa, "Japanese first optical inter-orbit communications engineering test satellite (OICETS)," Proc. SPIE 2210, 30-38 (1994). [CrossRef]
- H. Hemmati and N. Page, "Preliminary opto-mechanical design for the X2000 transceiver," Proc. SPIE 3615, 206-211 (1999). [CrossRef]
- M. Knapek, J. Horwath, N. Perlot, and B. Wilkerson, "The DLR ground station in the optical payload experiment (STROPEX) - results of the atmospheric measurement instruments," Proc. SPIE 6304, 63041U (2006). [CrossRef]
- W. N. Peters and A. M. Ledger, "Techniques for matching laser TEM00 mode to obstructed circular aperture," Appl. Opt. 9, 1435-1442 (1970). [CrossRef] [PubMed]
- B. J. Klein and J. J. Degnan, "Optical antenna gain 1: transmitting antennas," Appl. Opt. 13, 2134-2141 (1974). [CrossRef] [PubMed]
- O. D. Christy, "Dual-secondary mirror Cassegrain optical system," U. S. Patent 4,439,012, Mar. 27 (1984).
- X. L. Kong and P. M. Hao, "New method to remove central shade for reflecting laser beam expander," Chin. J. Quantum Electron. 19, 205-209 (2002).
- H. Hemmati and N. Page, "Approaches for efficient coupling of lasers to telescope with secondary mirror and baffle obscuration," Proc. SPIE 4635, 288-294 (2002). [CrossRef]
- C. W. Chen, "Re-imaging optical system including refractive and diffractive optical elements," U. S. Patent 5,287,218, Feb. 15 (1994).
- R. N. Smartt and E. W. Cross, "Advances in spherical-mirror telescopic systems design: application to largeaperature solar coronagraphs," Opt. Eng. 41, 2055-2058 (2002). [CrossRef]
- Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, "Generation of hollow Gaussian beams by spatial filtering," Opt. Lett. 32, 2076-2078 (2007). [CrossRef] [PubMed]
- Z. Liu, J. Dai, X. Sun, and S. Liu, "Generation of hollow Gaussian beam by phase-only filtering," Opt. Express 16, 19926-19933 (2008). [CrossRef] [PubMed]
- W. B. Veldkamp and T. J. McHugh, "Binary optics," Sci. Am. 266, 50-55 (1992).
- R.W. Gerchberg and W. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane picture," Optik 35, 227-246 (1972).
- J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 15, 2758-2769 (1982). [CrossRef]
- G. R. Brady and J. R. Fienup, "Nonlinear optimization algorithm for retrieving the full complex pupil function," Opt. Express 14, 474-486 (2006). [CrossRef] [PubMed]
- C. Rydberg and J. Bengtsson, "Numerical algorithm for the retrieval of coherent beams from transverse intensity measurements," Opt. Express 15, 13613-13623 (2007). [CrossRef] [PubMed]
- B. Lin and N. C. Gallagher, "Convergence of a spectrum shaping algorithm," Appl. Opt. 13, 2470-2471 (1974). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics, Second Edition, (New York, McGraw-Hill, 2006).

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