## Microlens diffusers for efficient laser speckle generation

Optics Express, Vol. 15, Issue 22, pp. 14573-14579 (2007)

http://dx.doi.org/10.1364/OE.15.014573

Acrobat PDF (189 KB)

### Abstract

Laser Speckle is the optical phenomena resulting from the random interference of coherent light. This phenomenon can be utilized to measure the Modulation Transfer Function (MTF) of detector arrays. Common devices used for speckle generation, such as integrating spheres and ground glass, suffer from low efficiencies less than 20%. Microlens diffusers are shown to be more efficient alternatives for speckle generation. An analysis of the statistical behavior of microlens diffusers is presented with emphasis on their application to MTF testing of detector arrays in the visible spectrum.

© 2007 Optical Society of America

## 1. Introduction

^{TM}, are available from RPC Photonics[1

01. RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com.

01. RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com.

01. RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com.

## 2. Polarization preservation

*θ*= tan

^{-1}(

*P*

_{min}/

*P*

_{max}). These measurements were repeated ten times and the results averaged. The measured ellipticity was 0.12 or effectively linearly polarized. The angular difference between the input angle and the angle of polarization was less than 1%. This measurement demonstrates that the HiLAM microlens diffuser preserves the input polarization. It has been demonstrated that an integrating sphere completely randomizes the polarization of the generated laser speckle [7

07. G. Boreman, Y. Sun, and A. James, “Generation of laser speckle with an integrating sphere,” Opt. Eng. **29**, 339–342 (1990). [CrossRef]

## 3. First-order statistics

### 3.1 Theoretical calculation

*M*, can be calculated from the aperture area, S

_{m}, and the speckle correlation area, S

_{c}. For a uniform square scattering spot of size, L, the correlation parameter,

*M*, can be calculated as,

_{m}= w

^{2}the correlation area, S

_{c}, is,

### 3.2 Measurement

## 4. Second-order statistics

### 4.1 Theoretical calculation

07. G. Boreman, Y. Sun, and A. James, “Generation of laser speckle with an integrating sphere,” Opt. Eng. **29**, 339–342 (1990). [CrossRef]

*x*) = 1 - ∣

*x*∣ for ∣

*x*∣ ≤ 1, zero otherwise. The fixed variables are: distance,

*z*, from the aperture to the measurement plane, the wavelength,

*λ*, and dimensions of the square aperture,

*L*. This theoretical PSDinput, theo will be used to determine the MTF of the array following the method employed by Boreman [7

07. G. Boreman, Y. Sun, and A. James, “Generation of laser speckle with an integrating sphere,” Opt. Eng. **29**, 339–342 (1990). [CrossRef]

### 4.2 Measurement

*w*in this case represents the detector width and equivalent sampling spacing of 5.6 um.

_{meas}for the CCD array using Eq. 6 is shown in Fig. 6 as “Measured MTF.” The “Measured MTF” is the result of dividing the “Output PSD” by the “Input PSD” from Fig. 5. The “Measured MTF” ends prematurely at 85 cycles/mm rather than extending to 90 cycles/mm. This is a result of a processing artifact where the division of the output by the input PSDs yields values greater than the expected “Theoretical MTF.” These values have been discarded from the “Measured MTF” shown in Fig. 6.

_{input}. This would be evaluated as;

_{input,actual}will be influenced by the MTF of the detector array since a difference between the MTF

_{meas}and MTF

_{Theo,CCD}is expected. For completeness, this comparison is provided in Fig. 7.

_{Theo,CCD}and MTF

_{meas}using the theoretical PSD

_{input}to would be sufficient (as shown in Fig. 6). Ultimately, an independent measurement of the MTF of the detector array could be used. This information was not available for this analysis.

## 5. Summary

## References and links

01. | RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com. |

02. | A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. |

03. | G. D. Boreman and E. L. Dereniak, “Method for measuring modulation transfer function of charge-coupled devices using laser speckle,” Opt. Eng. |

04. | A. M. Pozo and M. Rubi˜o, “Optical characterization of ophthalmic lenses by means of modulation transfer function determination from a laser speckle pattern,” Appl. Opt. |

05. | M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, “Modulation transfer function testing of detector arrays using narrow-band laser speckle,” Opt. Eng. |

06. | A. M. Pozo and M. Rubi˜o, “Comparative analysis of techniques for measuring the modulation transfer functions of charge-coupled devices based on the generation of laser speckle,” Appl. Opt. |

07. | G. Boreman, Y. Sun, and A. James, “Generation of laser speckle with an integrating sphere,” Opt. Eng. |

08. | J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 15–1119. |

09. | J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 46–54. |

10. | J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, p. 40. |

11. | J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics, (John Wiley & Sons, 1978), Chap. 3. |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(110.4100) Imaging systems : Modulation transfer function

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: July 3, 2007

Revised Manuscript: August 13, 2007

Manuscript Accepted: August 17, 2007

Published: October 19, 2007

**Citation**

Alfred D. Ducharme, "Microlens diffusers for efficient laser speckle generation," Opt. Express **15**, 14573-14579 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-22-14573

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### References

- RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com>.
- A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34, 860-868 (1995). [CrossRef]
- G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25, 148-150 (1986).
- A. M. Pozo and M. Rubiño, "Optical characterization of ophthalmic lenses by means of modulation transfer function determination from a laser speckle pattern," Appl. Opt. 44, 7744-7748 (2005). [CrossRef] [PubMed]
- M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32, 395-400 (1993). [CrossRef]
- A. M. Pozo and M. Rubiño, "Comparative analysis of techniques for measuring the modulation transfer functions of charge-coupled devices based on the generation of laser speckle," Appl. Opt. 44, 1543-1547 (2005). [CrossRef] [PubMed]
- G. Boreman, Y. Sun, and A. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29, 339-342 (1990). [CrossRef]
- J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 15-19.
- J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 46-54.
- J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, p. 40.
- J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics, (John Wiley & Sons, 1978), Chap. 3.

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