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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 1, Iss. 11 — Nov. 24, 1997
  • pp: 338–346
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Adaptive optics using a liquid crystal phase modulator in conjunction with a Shack-Hartmann wave-front sensor and zonal control algorithm

David Dayton, Steve Sandven, John Gonglewski, Steve Browne, Samuel Rogers, and Scot McDermott  »View Author Affiliations


Optics Express, Vol. 1, Issue 11, pp. 338-346 (1997)
http://dx.doi.org/10.1364/OE.1.000338


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Abstract

Multi-segment liquid crystal spatial light modulators have received much attention recently for use as high-precision wavefront control devices for use in astronomical and non-astronomical applications. They act much like piston only segmented deformable mirrors. In this paper we investigate the use of these devices in conjunction with a Shack-Hartmann wave-front sensor. Previous investigators have considered Zernike modal control algorithms. In this paper we consider a zonal algorithm in order to take advantage of high speed matrix multiply hardware which we have in hand.

© Optical Society of America

1. Introduction

When used with polarized light, the device can be made to act like a multi-segment piston-only deformable mirror. In order to form a closed loop adaptive optics system, the device must be used in conjunction with a wavefront sensor. Although a number of different types of wave-front sensors exist, the Shack-Hartmann sensor has the advantage that it is simple, easy to build and can be operated at a high temporal bandwidth when only the centroids of the sub-aperture spots are used to determine the average wave-front tilt across the sub-aperture.

Because the SLM can only perform piston wave-front correction, it can introduce waffle modes into the wavefront that are not observable by the Shack-Hartmann sensor. In addition, the multiple segments may introduce high order diffraction patterns into the spots produced by the individual Shack-Hartmann sub-apertures. These effects limit the operable configurations of the SLM/wave-front sensor combination.

The purpose of this paper is to discuss experiments and analysis using the Meadowlark hexagonal 127 element liquid crystal array in conjunction with a hexagonal Shack-Hartmann wave-front sensor. These experiments were performed in an attempt to understand and quantify the effects associated with this combination.

2. Higher order diffraction modes and waffle

Because the SLM acts like a piston only adaptive optic we must be concerned with the diffraction effects associated with the interference of light passing through adjacent SLM segments. Figure 1 shows a computer simulated one-dimensional cross-section of a Shack-Hartmann spot produced when the phase delays of two adjacent segments are displaced with respect to each other. We can see from the plots that for small phase differences each Shack-Hartmann lenslet will produce a well defined spot. However as the relative displacement increases, the intensity of one of the side lobes increases. As the displacement reaches one half wave, the spot breaks in two. This effect cannot be detected by a simple centroid operation.

Although high order aberrations can be calculated in the Shack-Hartmann spots, most wave-front sensors only work with the spot centroids. As the side-lobes in the diffraction pattern become significant, the error in the estimation of the centroid location increases. Figure 2 shows the percent error in the centroid calculations as a function of SLM segment displacement. It is seen that as the displacement approaches one half wave, the error approaches one hundred percent due to the bi-modal spot. This error introduces an ambiguity into the wave-front measurements that can lead to waffle modes developing in the SLM segments when we operate it as a closed-loop adaptive optic. In order to mitigate this problem, the commands applied to the SLM segments must be constrained such that the relative inter-segment displacements are less than one-half wave.

Fig. 1 Simulated one dimensional cross sections of Shack-Hartmann spot
Fig. 2 Shack-Hartmann centroid error as a function of segment displacement

3. Zonal control of the spatial light modulator

Large aperture adaptive optics designed to work in the visible typically encounter turbulence with D/r0 greater than ten. In order to obtain near full order correction for such systems, a controller employing several hundred zernike modes would be required. In such instances zonal control algorithms, using a multi-input multi-output (MIMO) control algorithm are often used [4

4. W. Wild, E. Kibblewhite, and R. Vuilleumier, “Sparse matrix wave-front estimators for adaptive-optics system for large ground-based telescopes,” Opt. Lett. 20 (9), 995–957 (1995). [CrossRef]

] in order to take advantage of high speed matrix multiply hardware. In this paper we investigate the use of a zonal control algorithm with the SLM similar to one used with a continuous face hexagonal deformable mirror.

Fig. 3 Arrangement of SLM Elements With Respect to Shack-Hartmann Sub-Apertures

The effect of the phase discontinuity is illustrated in Figure 4 which shows an image of several Shack-Hartmann spots with varying amounts of phase piston displacement on a single SLM segment. Figures 4a and 4b show that for small displacements of the segment, the three surrounding spots move outward as desired. Figure 4c shows that as the segment displacement approaches one-half wave, the three spots become bi-modal. The side-lobes from these three spots coalesce to form a spot at the center of the SLM segment location. This effect causes errors in the centroid calculation for each of the three Shack-Hartmann spots and is detrimental to control system performance. The effect limits the relative displacement that can be allowed between two adjacent SLM segments.

Fig. 4 Effect of SLM segment displacement on Shack-Hartmann Spots

We assume that for small displacements of adjacent segments, we can treat the control problem in the same way as for a continuous mirror. Referring to the three segment basic cell shown in the right hand side of Figure 3, an approximate relationship between the piston in the SLM segments and the spot displacement seen by the Shack-Hartmann sensor can be given as follows.

ϕx=32(ab)
(1)
ϕy=ca+b2
(2)

We then follow the standard least squares MIMO control approach [4

4. W. Wild, E. Kibblewhite, and R. Vuilleumier, “Sparse matrix wave-front estimators for adaptive-optics system for large ground-based telescopes,” Opt. Lett. 20 (9), 995–957 (1995). [CrossRef]

] and put equations (1) and (2) in matrix form.

Φ=ΓX
(3)

where Φ is the Shack-Hartmann phase gradient measurement vector, and X is the SLM segment displacement vector.

Φ=[ϕx11ϕx12··ϕy11ϕy12··]
(4)
X=[x11x12··x21x22··]
(5)

The matrix Γ is given by

Γ=[3232000·0323200·······1212·10·01212·1·]
(6)

The MIMO control matrix, H, is then formed using the pseudo inverse operation.

H=ΓT(ΓTΓ)1
(7)

The H matrix is incorporated in a summation control algorithm, which attempts to drive the wave-front centroid errors to zero. The commands to the SLM segments can be described by:

Ck=Ck1gH(ΦΦ0)
(8)

Where Φ0 is a set of nominal centroid offsets obtained from a wave-front sensor calibration. The term Ck represents SLM segment commands at time step k, and g represents the loop gain.

The closed loop feedback control system is shown in the following block diagram.

Fig. 5 Block Diagram Zonal Control of Spatial Light Modulator

4. Experimental results

In this section we describe results of experimentation with the SLM configured in the zonal feedback control loop discussed previously. Figure 6 shows the optical layout of the experiment.

We first show results with a static aberration. Approximately one wave peak-to-valley of defocus and astigmatism was applied to the wave-front using a plate aberrator. The open and closed loop focal plane spots are shown in Figure 7. The open loop Strehl ratio was approximately .16 while the closed loop was .25.

Fig. 6 Experimental Layout for Closed Loop Tests
Fig. 7 Open and Closed Loop results with a Static Aberration

Fig. 8 Dynamic Closed Loop Control [Media 1]

The animation represents about one-half second of data at one hundred frames per second. It shows that the closed loop configuration was able to correct small fluctuations in the aberration with a band-width of several hertz. Further study is required to determine exactly the closed loop disturbance rejection band-width of the system.

5. Conclusions

The liquid crystal spatial light modulator is a compact low cost alternative to deformable mirrors for adaptive optics systems. When used with polarized light, it acts like a piston only segmented deformable mirror. High order aberrations, produced by the discontinuities at the segment boundaries, can have an adverse effect when used with a Hartmann sensor. Special care must be exercised to mitigate this effect.

The experimental results show that under the constraints discussed, a zonal control algorithm, similar to one used with a continuous face sheet hexagonal deformable mirror, can be used to control the SLM with a closed loop band-width of several hertz. The experimentation used one Shack-Hartmann sub-aperture per SLM segment. The Shack-Hartmann sub-apertures were off-set from the SLM segments by half a row and half a column. This allowed control of all 127 degrees of freedom possible with the corrector. The disturbance wave-front had only about one wave peak-to-valley distortion. Thus the displacements between SLM segments required to correct the wave-front were small and we did not have problems with the Shack-Hartmann spots breaking up. In addition the SLM segments have a maximum throw of only a little more than one wave, so the system can’t correct for larger distortions. In future experiments we plan to investigate a double pass configuration to increase the throw of each segment.

References and links

1.

G.D. Love, “Wavefront correction and production of Zernike modes with a liquid crystal SLM”, Appl. Opt. , 36, 1517–1524 (1997). [CrossRef] [PubMed]

2.

J. Gourlay, G.D. Love, P.M. Birch, R.M. Sharples, and A. Purvis, “A real-time closed-loop liquid crystal adaptive optics system: first results”, Opt. Commun. 137, 17–21 (1997). [CrossRef]

3.

A. Kudryashov, J. Gonglewski, S. Browne, and R. Highland, “Liquid crystal phase modulator for adaptive optics. Temporal performance characterization”, Opt. Commun. 141, 247–253 (1997). [CrossRef]

4.

W. Wild, E. Kibblewhite, and R. Vuilleumier, “Sparse matrix wave-front estimators for adaptive-optics system for large ground-based telescopes,” Opt. Lett. 20 (9), 995–957 (1995). [CrossRef]

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(230.3720) Optical devices : Liquid-crystal devices
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Focus Issue: Signal collection and recovery

History
Original Manuscript: September 2, 1997
Published: November 24, 1997

Citation
David Dayton, Steve Sandven, John Gonglewski, Stephen Browne, Sam Rogers, and Scott Mcdermott, "Adaptive optics using a liquid crystal phase modulator in conjunction with a Shack-Hartmann wave front sensor and zonal control algorithm," Opt. Express 1, 338-346 (1997)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-1-11-338


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References

  1. G.D. Love, "Wavefront correction and production of Zernike modes with a liquid crystal SLM", Appl. Opt., 36, 1517-1524 (1997). [CrossRef] [PubMed]
  2. J. Gourlay, G.D. Love, P.M. Birch, R.M. Sharples, A. Purvis, A real-time closed-loop liquid crystal adaptive optics system: first results, Opt. Commun. 137, 17-21 (1997). [CrossRef]
  3. A. Kudryashov, J. Gonglewski, S. Browne, R. Highland, Liquid crystal phase modulator for adaptive optics. Temporal performance characterization, Opt. Commun. 141, 247-253 (1997). [CrossRef]
  4. W. Wild, E. Kibblewhite, R. Vuilleumier, "Sparse matrix wave-front estimators for adaptive-optics system for large ground-based telescopes," Opt. Lett. 20 (9), 995-957 (1995). [CrossRef]

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