## Dual-conjugate wavefront generation for adaptive optics

Optics Express, Vol. 7, Issue 11, pp. 368-374 (2000)

http://dx.doi.org/10.1364/OE.7.000368

Acrobat PDF (191 KB)

### Abstract

We present results of the isoplanatic performance of an astronomical adaptive optics system in the laboratory, by using a dual layer turbulence simulator. We describe how the performance of adaptive correction degrades with off-axis angle. These experiments demonstrate that it is now possible to produce quantifiable multi-layer turbulence in the laboratory as a precursor to constructing multi-conjugate adaptive optics.

© Optical Society of America

## 1 Introduction

2. B. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,”J. Opt. Soc. Am. A **11**, 783–805 (1994) [CrossRef]

3. R. Ragazzoni, E. Marchetti, and G. Valente, “Adaptive-optics corrections available for the whole sky,”Nature (London) **403**, 54–56 (2000) [CrossRef]

4. D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,”J. Opt. Soc. Am. A **11**394–408 (1994) [CrossRef]

*θ*

_{0}.

2. B. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,”J. Opt. Soc. Am. A **11**, 783–805 (1994) [CrossRef]

3. R. Ragazzoni, E. Marchetti, and G. Valente, “Adaptive-optics corrections available for the whole sky,”Nature (London) **403**, 54–56 (2000) [CrossRef]

4. D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,”J. Opt. Soc. Am. A **11**394–408 (1994) [CrossRef]

*et al*.[5

5. 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]

## 2 The turbulence generator

5. 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]

5. 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*/

*r*

_{0}=30, where

*D*is the telescope pupil diameter, and r0 is the Fried parameter. The optical throughput of the system is also limited by the holographic technique (40.5% theoretical maximum per layer, or a few % in reality), but this is not important in the laboratory.

*µ*m×15

*µ*m. The LC SLMs can operate at speeds up to 2.5kHz, allowing turbulence generation at rates similar to atmospheric wind speeds, and significantly faster than analogue nematic LC SLMs. To simulate an AO system which uses a natural guide star to correct an off—axis object, a second light source is introduced into the optical setup via a pellicle beamsplitter BS and 2 mirrors M1 and M2. The imaging between the two turbulent layers is controlled by lenses L1 and L2, and is arranged so that emerging light from both the on— and off—axis beams overlap at the lower SLM whereas they are displaced on the upper SLM with the correct pupil shear. The amount of shear, or the equivalent height of the upper SLM, is controlled by the distance of the lower SLM from the image of the upper SLM. If this distance is given by Δ

*z*in real space, then the spacing of the equivalent layers in the (virtual) atmosphere is given by Δ

*z*(

*D*/

*d*)

^{2}, where

*D*is the telescope pupil size, and

*d*is the SLM size (=3.84mm). We initially designed the system to model a 1m telescope, with the lower turbulent layer at the telescope pupil and the upper turbulent layer at an altitude of 3.4km. It is very difficult to reproduce accurately the optics of a large telescope using small optics, because the angle of the off—axis beam is magnified by a factor of

*D*/

*d*, which means that the off axis angles in the system become unfeasible (e.g. 35° for an 8m aperture and a 1arcmin off—axis angle). However, when simulating a system it is the off—axis angle normalised by the isoplanatic patch size which is of interest. Therefore we can model the performance of large apertures by effectively assuming that that the turbulence is at a very high altitude.

*θ*

_{0}. Simple Kolmogorov theory states the size of the isoplanatic patch is given by

*θ*

_{0}, where

*ħ*is the average height of turbulence. As we have only 2 layers, one of which is effectively at the telescope pupil, we can replace (

*ħ*) with

*h*, as long as

*r*

_{0}is replaced with the

*r*

_{0}of only the upper layer. Alternatively the total

*r*

_{0}can be used,

*r*is calculated from the

_{i}*D*/

*r*

_{0}values for each layer, and the

*ħ*can be calculated using

*α*, will be magnified with respect to the angle at the lower SLM,

*β*. At the same time, the off—axis beam should not be vignetted by the SLMs, spatial filters, lens apertures or other optical components. The aperture size of the lenses L1 and L2 place an additional constraint on the maximum values of

*α*and

*β*, as does the effective separation of the SLMs, Δ

*z*. Therefore the lenses must be chosen carefully for focal length, aperture size, magnification and

*f*/#.

## 3 Experiment

*M*=2.5. Lenses L3 and L4 are identical 100 mm focal length lenses with apertures of 25 mm. The off—axis beam is produced via the pellicle beamsplitter BS and the two mirrors M1 and M2. The spatial filters were slits, rather than pinholes, to allow both the on— and off—axis beams to propagate through the system. The off—axis angle can be varied by adjusting either M1 or M2.

*D*=1 m telescope). The turbulence applied to the upper SLM was actually 2.5 times the desired turbulence, to account for the magnification of the upper layer with respect to the lower layer. The parameters of turbulence generated were

*D*/

*r*

_{0}=6

*D*/

*r*

_{0}=7.7.

*D*/

*r*

_{0}=6, and the upper layer with

*D*/

*r*

_{0}=4, which is equivalent to a total turbulence of

*D*/

*r*

_{0}=7.7.

*D*/

*r*

_{0}=6 (equivalent to a total turbulence

*D*/

*r*

_{0}=9.1)

*θ*

_{0}) could be increased by using a higher resolution camera, or by changing the turbulence to decrease

*θ*

_{0}. The minimum allowable off—axis angle we could simulate was determined by leakage of light from the off—axis beam into the wavefront sensor.

## 4 Results

8. N. Doble, G.D. Love, D.F. Buscher, R.M. Myers, and A. Purvis, “The use of image quality metrics for correction of non-common path errors in the ELECTRA adaptive optics system,”Proc. SPIE **3749**785, ICO 18th Congress (1999) [CrossRef]

*D*/

*r*

_{0}=6. The left column is the PSF of the on—axis beam, while the right column is the off—axis beam. Fig 3 shows similar plots for dual layer turbulence, both upper and lower layers with

*D*/

*r*

_{0}=6. For both Figs 2 and 3, the off—axis angle is approximately 13 arcsecs for a

*D*=1m telescope. In both cases, the on axis beam is well-corrected, but the off—axis correction is much better for the single layer turbulence than for the dual-layer turbulence.

*R*/

*h*where

*R*is the telescope aperture radius and

*h*is the height of the turbulence. For a 1m telescope, and turbulence at 3.4km, this scale would have a range from 0 to 20 arcseconds. The experimental results show that …

*S*should then show the following dependence with off—axis angle,

*θ*, using the Maréchal approximation (

*S*=exp(-

*σ*

^{2})),

*y*=

*A*exp(

*Bx*) +

^{C}*D*(similarly to Eqn 4) for turbulence 3 and 4. The exponent (C) for turbulence 3 was 1.37±0.05 and for turbulence 4 it was 1.63±0.09, indicating that the experimental data more closely follow an exponent of 5/3 rather than an exponent of 2. However, the experimental data are sparse for small off—axis angles because of light leakage into the wavefront sensor as explained above. Our results are also complicated by the fact that our turbulence had no tip—tilt included. We are currently performing a more complete theoretical analysis of our system to include these effects.

## 5 Conclusion

## References and links

1. | J. M. Beckers, “Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics,” in |

2. | B. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,”J. Opt. Soc. Am. A |

3. | R. Ragazzoni, E. Marchetti, and G. Valente, “Adaptive-optics corrections available for the whole sky,”Nature (London) |

4. | D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,”J. Opt. Soc. Am. A |

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

6. | R. J. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,”Waves Random Media |

7. | A. Zadrozny, M.P.J.L. Chang, D.F. Buscher, R.M. Myers, A.P. Doel, C.N. Dunlop, R.M. Sharples, and R.L. Arnold. In ESO/SPIE Topical Meeting on Astronomy with Adaptive Optics, ed. D. Bonaccini. (1999) |

8. | N. Doble, G.D. Love, D.F. Buscher, R.M. Myers, and A. Purvis, “The use of image quality metrics for correction of non-common path errors in the ELECTRA adaptive optics system,”Proc. SPIE |

9. | F. Roddier, M.J. Northcott, J.E. Graves, and D.L. McKenna. “One-dimensional spectra of turbulence-induced Zernike aberrations: time delay and isoplanicity error in partial adaptive compensation,” J. Opt. Soc. Am. A |

**OCIS Codes**

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

(230.6120) Optical devices : Spatial light modulators

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 31, 2000

Published: November 20, 2000

**Citation**

Thu-Lan Kelly, David F. Buscher, Paul Clark, Colin Dunlop, Gordon Love, Richard M. Myers, Ray Sharples, and Andrew Zadrozny, "Dual-conjugate wavefront generation for adaptive optics," Opt. Express **7**, 368-374 (2000)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-11-368

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### References

- J. M. Beckers, "Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics, in ESO Symposium on Large Telescopes and Their Instrumentation M.-H. Ulrich, ed. (ESO Proc, Garching) 693-703 (1988)
- B. Ellerbroek, "First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes, J. Opt. Soc. Am. A 11, 783-805 (1994) [CrossRef]
- R. Ragazzoni, E. Marchetti and G. Valente, "Adaptive-optics corrections available for the whole sky, Nature (London) 403, 54-56 (2000) [CrossRef]
- D. C. Johnston and B. M. Welsh, "Analysis of multiconjugate adaptive optics, J. Opt. Soc. Am. A 11 394-408 (1994) [CrossRef]
- M. A. A. Neil, M. J. Booth, T. Wilson, "Dynamic wave-front generation for the characterization and testing of optical systems, Opt. Lett. 23 1849-1851 (1998) [CrossRef]
- R. J. Lane, A. Glindemann, J. C. Dainty, "Simulation of a Kolmogorov phase screen, Waves Random Media 2, 209-224 (1992) [CrossRef]
- A. Zadrozny, M. P. J. L. Chang, D. F. Buscher, R. M. Myers, A. P. Doel, C. N. Dunlop, R. M. Sharples and R. L. Arnold, In ESO/SPIE Topical Meeting on Astronomy with Adaptive Optics, ed. D. Bonaccini (1999)
- N. Doble, G. D. Love, D. F. Buscher, R. M. Myers and A. Purvis, "The use of image quality metrics for correction of non-common path errors in the ELECTRA adaptive optics system, Proc. SPIE 3749 785, ICO 18th Congress (1999) [CrossRef]
- F. Roddier, M. J. Northcott, J. E. Graves, and D. L. McKenna. "One-dimensional spectra of turbulence-induced Zernike aberrations: time delay and isoplanicity error in partial adaptive compensation, J. Opt. Soc. Am. A 10 957-965 (1993) [CrossRef]

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