## A liquid crystal atmospheric turbulence simulator

Optics Express, Vol. 14, Issue 25, pp. 11911-11918 (2006)

http://dx.doi.org/10.1364/OE.14.011911

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### Abstract

In the paper, a method to calculate the time evolution turbulence wavefronts based on the covariance method is theoretically presented in detail. According to it, the time-evolution wavefronts disturbed by atmospheric turbulence were experimentally generated by our LC atmospheric turbulence simulator (ATS) based on liquid crystal on silicon (LCOS) with high pixel density, and measured with a wavefront sensor. The advantage of such a LC ATS over a conventional one is that it is flexible with considering the weather parameters of wind speed and

© 2006 Optical Society of America

## 1. Introduction

8. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. **66**, 207–211 (1976). [CrossRef]

8. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. **66**, 207–211 (1976). [CrossRef]

9. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. **29**, 1174–1180 (1990). [CrossRef]

## 2. Generation of dynamic turbulence wavefronts

8. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. **66**, 207–211 (1976). [CrossRef]

9. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. **29**, 1174–1180 (1990). [CrossRef]

**66**, 207–211 (1976). [CrossRef]

*E*between them due to the fact that the Zernike polynomials are not statistically independent. The independent random Karhunen-Loève coefficients can be computed, then, converted to Zernike coefficients according to the Karhunen-Loève Zernike expansion [9

9. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. **29**, 1174–1180 (1990). [CrossRef]

*N*) of turbulence phase simulation for large N could be calculated as:

*R*

_{z}/

*r*

_{0}),

*R*

_{z}is the diameter of simulated area, the rms as a function of N is shown in Fig. 1 for wavelength λ of 632.8nm. For example, it could be seen that rms will be 0.07λ for scaling factor of 10 and N of 120. Larger

*R*

_{z}/

*r*

_{0}will lead to larger N to obtain the same rms values of 0.07λ. In addition, because the target error should be smaller than 0.07λ, for lab testing of AO systems, this limit would bias the results toward better performance since it would leave out higher spatial frequency components. The calculation speed should be improved and decrease the rms for a real-time calculation of turbulence wavefronts. If the real-time calculation is not possible, another way is to calculate a series of turbulence wavefronts before testing an AO system, and save them to BMP files. Finally display these BMP files orderly on LCOS when testing an AO system.

*R*

_{z}/

*r*

_{0}) as a constant without taking into account parameters, such as altitude

*h*, zenith angle

*β*and wind speed. We could calculate

*r*

_{0}with the real-world parameters to generate the turbulence phase. And

*r*

_{0}is widely used to characterize the level of turbulence at a particular site and could be calculated as [11

11. F. Roddier, *Adaptive optics in astronomy*, (Cambridge, Cambridge University Press, 1999), pp. 9–56. [CrossRef]

*β*is the zenith angle. Its value varies from a few meters in very good seeing conditions to a few centimeters in difficult seeing at visible wavelengths.

^{-14}m

^{-2/3}to 10

^{-18}m

^{-2/3}. Usually, Hufnagel-Valley Boundary model is often used to predict the

*h*is the altitude in kilometers,

*v*is the wind speed in m/s. And

*l*

_{0}is zero and the outer scale

*L*

_{0}is infinity. Therefore, it is reasonable to define a radius

*R*

_{z}of the produced wavefront.

*R*

_{z}should be large enough and smaller than

*L*

_{0}, so as to generate turbulence wavefront and decrease its periodic phenomenon as possible.

*L*/

*v*, where

*L*is the length of the chosen route. The time step Δ

*T*should be chosen reasonably so that the simulated turbulence seems fluent. It should be noted that

*L*

_{A}and

*L*

_{B}are the length of route A and B, respectively. First, we calculate a large wavefront ϕ

_{total}on the area with diameter of

*R*

_{z}. Second, a part wavefront ϕ

_{1}of ϕ

_{total}on the rectangle sub-area with size of 1.33D×D was read, interpolated with available interpolating program and converted to gray map on LCOS with grid of 1024×768. It should be noted that D is the diameter of an optical system, such as a telescope. In the paper, D is defined as 1m. Third, next wavefront ϕ

_{2}with the same size was read from the calculated wavefront at a distance away from the first one. The distance could be obtained with wind speed

*v*multiplied by spacing time Δ

*T*. Repeat the third step to generate followed wavefronts. Therefore, we could simulate a dynamic turbulence with our LC ATS.

*R*

_{z}/

*r*

_{0})

^{2}. For a LC device, the phase wrapping level is 8 at least for a high diffraction efficient. Therefore, the grid number is at least equal to 64(

*R*

_{z}/

*r*

_{0})

^{2}so as to generate turbulence wavefront with enough spatial frequency. In addition, actual optical system size D must be smaller than R

_{z}. The area with the diameter of D is corresponding to an inscribed circle on LCOS. Considering that the aspect ratio of LCOS is about 1.3, we set the grid is 11(D/

*r*

_{0}) ×8(D/

*r*

_{0}). Then, the phase grid is interpolated to for the LCOS.

## 3. LC screen and experiment

## 4. Results and discussion

*R*

_{z}of 1m. Its size is relatively small. But it is enough to demonstrate the procedure to generate dynamic turbulence wavefronts. The diameter D of actual aperture of optical system is 0.6 m. Therefore, the physical size of turbulence wavefront corresponding to the LCOS is 0.8×0.6 m

^{2}, and its grid is 96×72, which is a little less dense than that defined in table 1. The parameters used to simulate the turbulence wavefront are listed in table 3. For simplification, we select route B because only 4 wavefronts will be calculated. But for a long duration turbulence simulation, we should enlarge the size of

*R*

_{z}and select route A. The wind speed is 6m/s. And the refractive index structure constant at ground,

^{-15}m

^{-2/3}. The object distance is 300km above which the effects of turbulence could be ignored. The Monte Carlo analysis was conducted to evaluate the obtained turbulence wavefronts according to the phase structure function’s 5/3 power. The obtained powers are shown in Fig. 5 for phase structure function of 1000 independent wavefronts corresponding to area with diameter of

*R*

_{z}. Their mean value is 1.56 that is very close to 5/3, which indicates that our results are very good and close to the Kolmogorov theory.

_{0}is about 0.10m according to Eq. (2) and the diameter of simulated area is 1m, the R

_{z}/r

_{0}is 10. Therefore, to choose 120 Zernike modes is optimum in calculating speed and turbulence simulation precision according to our discussion in section 2. Pre-120 Zernike modes coefficients is used and also shown right in Fig. 6. It could be seen that tip and tilt aberrations dominate the turbulent wavefront, which accords with practical situations.

^{2}with grid of 72×96 that is interpolated to for the LCOS. The time step between two neighbor wavefronts in calculation program is 10ms, that is, the next wavefront is sampled at a distance of wind speed 6m/s multiplied by 10ms away from our selected area, that is, 0.06m. Therefore, we simulated four phase screens along x axis with total time of 40ms and time step of 10ms. Then, the gray maps of the generated timeevolution turbulence wavefronts were calculated with the phase vs voltage (gray level) curve in Fig. 3. Then, they were sent to the LC screen. The turbulence wavefronts were measured with a wavefront sensor, HASO 32 of Imagine optic Ltd. Co. To minimize the effects of the aberration,

*φ*

_{LC}, of the LC screen, we measured it with a gray level of zero on the whole screen. Secondly, to minimize the diffractive effects of the regular pixel structure of the LC screen, we could introduce a tilt,

*φ*

_{T}, on the whole screen and filter the first order. Therefore, we could overcome their effects by calculating the gray level with sum of the turbulence wavefronts,

*φ*,

*φ*

_{LC}and

*φ*

_{T}. As an example, the measured results of time series of 4 Kolmogorov turbulence wavefronts are shown in the Fig. 7. It should be noted that the pixilation in Fig. 6 corresponds to HASO 32 that is used to measure the wavefront. In the experiment, the L2 and L3 result that the area of LCOS is corresponding to a part of HASO 32’s microlens 32×32 array due to compression effects of lens L2 and L3, the effective microlens array is 19×25 in the experiment.

## 5. Conclusion

## Acknowledgments

## References and Links

1. | K. J. Gamble, A. R. Weeks, H. R. Myler, and W. A. Rabadi, “Results of two-dimensional time-evolved phase screen computer simulations,” in |

2. | T.-L. Kelly, D. F. Buscher, P. Clark, C. Dunlop, G. Love, R. M. Myers, R. Sharples, and A. Zadrozny, “Dual-conjugate wavefront generation for adaptive optics,” Opt. Express |

3. | T. S. Taylor and D. A. Gregory, “Laboratory simulation of atmospheric turbulence-induced optical wavefront distortion,” Opt. Laser Technol. |

4. | S. Thomas, “A simple turbulence simulator for adaptive optics,” in |

5. | M. K. Giles, A. Seward, M. A. Vorontsov, J. Rha, and R. Jimenez, “Setting up a liquid crystal phase screen to simulate atmospheric turbulence,” in |

6. | M. A. A. Neil, M. J. Booth, and T Wilson, “Dynamic wave-front generation for the characterization and testing of optical systems,” Opt. Lett. |

7. | D. J. Cho, S. T. Thdurman, J. T. Donner, and G. M. Morris, “Characteristics of a 128×128 liquid-crystal spatial light modulator for wave-front generation,” Opt. Lett. |

8. | R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. |

9. | N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. |

10. | M. C. Roggemann, B. M. Welsh, D. Montera, and T. A. Rhoadarmer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Appl. Opt. |

11. | F. Roddier, |

**OCIS Codes**

(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(160.3710) Materials : Liquid crystals

(230.6120) Optical devices : Spatial light modulators

**ToC Category:**

Atmospheric and ocean optics

**History**

Original Manuscript: September 5, 2006

Revised Manuscript: November 8, 2006

Manuscript Accepted: November 15, 2006

Published: December 11, 2006

**Citation**

Lifa Hu, Li Xuan, Zhaoliang Cao, Quanquan Mu, Dayu Li, and Yonggang Liu, "A liquid crystal atmospheric turbulence simulator," Opt. Express **14**, 11911-11918 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-11911

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### References

- K. J. Gamble, A. R. Weeks, H. R. Myler, and W. A. Rabadi, "Results of two-dimensional time-evolved phase screen computer simulations," in Atmospheric Propagation and Remote Sensing IV, J. Christopher Dainty, ed., Proc. SPIE 2471, 170-180 (1995). [CrossRef]
- T.-L. Kelly, D. F. Buscher, P. Clark, C. Dunlop, G. Love, R. M. Myers, R. Sharples, and A. Zadrozny, "Dual-conjugate wavefront generation for adaptive optics," Opt. Express 17, 368-374 (2000). [CrossRef]
- T. S. Taylor and D. A. Gregory, "Laboratory simulation of atmospheric turbulence-induced optical wavefront distortion," Opt. Laser Technol. 34, 665-669 (2002). [CrossRef]
- S. Thomas, "A simple turbulence simulator for adaptive optics," in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, R. Ragazzoni, eds., Proc. SPIE 5490, 766-773 (2004). [CrossRef]
- M. K. Giles, A. Seward, M. A. Vorontsov, J. Rha, and R. Jimenez, "Setting up a liquid crystal phase screen to simulate atmospheric turbulence," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE 4124, 89-97 (2000). [CrossRef]
- M. A. A. Neil, M. J. Booth, and T. Wilson, "Dynamic wave-front generation for the characterization and testing of optical systems," Opt. Lett. 23,1849-1851 (1998). [CrossRef]
- D. J. Cho, S. T. Thdurman, J. T. Donner, and G. M. Morris, "Characteristics of a 128×128 liquid-crystal spatial light modulator for wave-front generation," Opt. Lett. 23, 969-971 (1998). [CrossRef]
- R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976). [CrossRef]
- N. Roddier, "Atmospheric wavefront simulation using Zernike polynomials," Opt. Eng. 29, 1174-1180 (1990). [CrossRef]
- M. C. Roggemann, B. M. Welsh, D. Montera, and T. A. Rhoadarmer, "Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions," Appl. Opt. 34, 4037-4051 (1995). [CrossRef] [PubMed]
- F. Roddier, Adaptive optics in astronomy, (Cambridge, Cambridge University Press, 1999), pp. 9-56. [CrossRef]

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