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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 9 — May. 2, 2005
  • pp: 3491–3499
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Common path interferometric wavefront sensor for extreme adaptive optics

Gordon D. Love, Thomas J. D. Oag, and Andrew K. Kirby  »View Author Affiliations


Optics Express, Vol. 13, Issue 9, pp. 3491-3499 (2005)
http://dx.doi.org/10.1364/OPEX.13.003491


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Abstract

We describe a method of implementing a common-path phase-shifting point diffraction interferometric wavefront sensor suitable for extreme adaptive optics. The sensor simultaneously gives two phase-shifted outputs which can be used to drive a phase-only wavefront corrector. The device can also give a null output which can be used to calibrate any scintillation. Simulations are performed showing the utility of the device and experimental results of a high speed single channel closed loop system are presented.

© 2005 Optical Society of America

1. Introduction

The current generation of astronomical adaptive optics (AO) systems have ~102–103 actuators and results on large telescopes have largely been confined to the infrared, where atmospheric turbulence is relatively benign. Much higher order wavefront correction, known as extreme adaptive optics (XAO) is needed for applications ranging from visible correction on 8m class telescopes and exoplanet detection, up to wavefront correction on future extremely large telescopes. The number of required actuators can be as large as 105–106. There are no currently available wavefront corrections technologies with such specifications, but likely candidates (for systems with a small field of view) are MEMS and liquid crystal (LC) devices.

In an AO system it is advantageous for the control if the wavefront sensor measures the typical wavefront deformations produced by the wavefront corrector, e.g. a bimorph mirror is matched well to a curvature sensor and a segmented deformable mirror is matched well to a Shack Hartmann wavefront sensor. Some MEMS and LC devices typically have piston-only influence functions, and therefore a wavefront sensor which measures phase directly, such as an interferometer is desirable. This has the advantage that it will be possible to produce a “reconstructor-free” control system, whereby the control of each actuator is independent of the other actuators, and therefore the complexity of the control will scale linearly with the number of actuators. Such systems were proposed, in the context of XAO some time ago1, although there is recent revised interest2–5 in them as practical advances towards XAO are beginning to be made.

This letter has two aims. First we describe an alternative configuration of a common-path point diffraction interferometer (PDI) which gives simultaneously two phase-shifted fringe patterns, and which also allows for calibration of scintillation. The interferometric arrangements based in refs. 2–4 are based on a Mach-Zhender configuration, and therefore do not have the stability advantages associated with common-path operation described here. LCs have previously been used to produce phase-shifting PDIs6,7. Here we just use the fact that they are birefringent to produce two phase-shifted fringe patterns simultaneously using incident unpolarized light (and therefore without wasting any light by the use of a polarizer as is often the case when LCs are used). The second aim is to describe the use of the PDI to control a high-speed dual frequency LC cell to produce a single-channel laboratory AO system. The key point is that this system is linearly scalable in terms of the number of actuators.

2. The liquid crystal point diffraction interferometer

The key element in the wavefront sensor is a ferroelectric liquid crystal (FLC) cell (which acts as an electrically rotatable half-wave plate (HWP)) that has small circle, 20µm in diameter, removed from one of the control electrodes. Phase-only modulation with the FLC is achieved8 by placing the device between two co-aligned quarter-wave plates (QWPs), as shown in figure 1.

Light which is incident linearly polarized at 45° to the QWP’s crystal axes is phase modulated by an amount , where θ is the switching angle of the FLC (which is normally twice the tilt angle). When the FLC is turned on, it acts like a phase plate with a small phase discontinuity, where there is no electrode in the center, of magnitude 2θ=90° (since the FLC switching angle is 45°). An orthogonally polarized component experiences a similar phase plate, but with a phase shift of -2θ=-90°. If the wavefront sensor is therefore used with unpolarized light, which can be considered as an incoherent sum of two orthogonally polarized linear states, then two, orthogonally polarized, fringe patterns will be produced. These can be separated by a polarizing beam splitter (the device could also be used in non-astronomical situations using linearly polarized light of the azimuth was set appropriately). The resultant fringe patterns are therefore differing in phase by 180°. When the FLC is in the off state, then the molecules throughout the whole cell are aligned, and no interferogram is observed. The device acts, effectively, like an isotropic plate.

Fig. 1. Concept for a common path point diffraction interferometer based on a ferroelectric liquid crystal (FLC) phase shifter. The FLC is essentially a switchable half-wave plate placed between two quarter-wave plates (QWP). The devices works with unpolarized input light to give two simultaneous interferograms which are orthogonally polarized, phase shifted by half a wave, and which are then separated by a polarizing beamsplitter.

The observed interferograms will be of the form,

IA,B=I0[1+γcos(ϕ(x,y)ϕ¯±π2)],

where IA and IB are the two observed intensity patterns (which will be a function of the position, (x,y)), I0 is the normalization intensity, γ is the fringe visibility, ϕ(x,y)is the phase of the wavefront, and ϕ̄ is the average phase across the wavefront. This latter term arises because in this kind of PDI the reference wavefronts are produced directly from the test wavefronts. The final ±π2 arises from the phase shifter for each of the outputs, A and B. If the wavefront sensor was to be used for metrology, then it would be usual to record at least 3 fringe patterns in order to determine the three unknowns; I0, γ, and ϕ(x,y). ϕ̄ is not needed because constant phase shifts over the whole beam can usually be ignored. When controlling an AO system an output which is proportional to the phase, instead of equal to the exact value, is required and therefore fewer interferograms are needed. We therefore calculate, using approximations, a value for the measured phase, ϕm, using a number of approximations as described below.

Expanding the cosine term in the above equation gives,

IA,B=I0[1γsin(φ(x,y)φ¯)],

and therefore the required measured phase, ϕmϕ(x,y)-ϕ̄ is given by,

sinφm=1γ[IBIAIB+IA].

For small values of ϕm then the approximation sinϕmϕm can be used, and assuming unit visibility fringes, then,

ϕm=IBIAIB+IA.
(1)
Fig. 2. Simulation results of the residual rms wavefront error from measurements of aberrated wavefronts. The test wavefronts were pure Zernike modes, as indicated on the x-axis and the amplitude of the applied mode is shown on the y-axis. It can be seen that measurement quality decreases with increasing amplitude, as is expected.

A noiseless computer simulation was produced of the system and aberrated test wavefronts were generated using Zernike polynomials. The wavefronts were reconstructed using the above approximation for ϕm and compared to the original wavefronts. The results are shown in Fig. 2, which shows the residual rms wavefront error plotted versus mode number and the amplitude of the mode. The simulation demonstrates the utility of the technique for small amplitude aberrations.

φm=(IBU)(IAU)(IBU)+(IAU)=IBIAIB+IA2U.

The results are shown in Fig. 3. for the 8th Zernike mode (which here is second-order astigmatism). The reconstructed phase was subtracted from the original phase to give the residual error, and the figure shows a slice through this data. The numerical residual errors are shown in Table 1.

Fig. 3. Simulation results showing the effect of calibration for scintillation. The red line shows a scan through the residual phase error if no attempt is made to correct for scintillation. The phase was reconstructed using equation 1. The blue line shows the residual phase error when the phase was reconstructed using equation 2.

Table 1. Simulated residual wavefront errors showing that errors can be reduced by accounting for the scintillation by also measuring the pupil intensity. In the system described here this can be done without non-common path errors by recording data when the FLC is off.

table-icon
View This Table

The description so far, and the simulations, have assumed the use of monochromatic light. In general, broadband light must be used. The QHQ is similar in design to a broadband waveplate (which are made from a series of individual wavplates) and its performance is approximately achromatic9. However, how the precise affect of this on the total system performance awaits a full closed loop broadband simulation.

3. Closed loop high speed single channel system

In order to demonstrate the wavefront sensor in closed loop operation a single channel system was constructed as shown in Fig. 4.

Fig. 4. Diagram of the closed loop system. Unpolarized light from the laser passes through the turbulence generator, followed by the LC wavefront corrector. The wavefront sensor, formed by the two quarter-wave plates (QWPs) and the FLC half-wave plate (HWP) followed by the polarizing beamsplitter, produces 2 signals on the photodiodes. Pinholes before the photodiodes ensure that the correct pixel on the wavefront corrector is being imaged onto the detectors. The differential signal from the photodiodes (which is the wavefront sensor output) is then compared with a reference DC signal in a comparator, which is used to control an analogue switch which supplies the wavefront corrector with a high voltage low or high frequency voltage.

First, the loop was not closed, the turbulence generator turned off, and the LC wavefront corrector was set to oscillate between phase values of 0 and 2π, and the output of the wavefront sensor (after the differential amplifier) was measured, and is shown in Fig. 5.

Fig. 5. Wavefront sensor output, measured after the differential amplifier (in fig. 4.), with the loop not closed, and an alternating signal of 1 wave being applied to the wavefront corrector.

The power spectra of these data are shown in Fig. 7. The spectra were smoothed to make the general trend clearer. It can be seen that the crossover frequency, when the system begins to add noise is about 700Hz.

Fig. 6. Calibrated wavefront sensor output without (left) and with (right) the loop closed. The turbulence was severe (from a hot air blower). The uncorrected and corrected phase variances are 2.44 rad2 0.40 rad2 respectively.

The noise performance of the system could be improved by potentially including hysteresis in the comparator stage of the control system. In principle, the system could also be improved by adopting a proportional control, rather than a bang-bang type, although the latter was chosen because it particularly lends itself to the control of dual frequency LCs.

Fig. 7. Power spectrum of the wavefront sensor output with the loop not closed (red line) and closed (blue line). The system is reducing wavefront aberrations up to a crossover frequency of about 700Hz.

4. Discussion

Acknowledgments

Thanks to Alexander Naumov (Physical Optics Corp, Ca.), for his work on controlling dual frequency liquid crystals and to anonymous referee for pointing out a number of issues.. David Buscher (Cambridge, U.K.) and Tony Roberts (Sony Europe GmbH, Germany) helped in the early conceptualization of this work. Thomas Oag acknowledges a studentship funded by the UK Particle Physics and Astronomy Research Council (PPARC).

References and Links

1.

J. R. P. Angel. “Ground-based imaging of extrasolar planes using adaptive optics,” Nature 368, 203–207, (1994) [CrossRef]

2.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, P. E. Young, D. T. Gavel, J. W. Tucker, D. A. Silva, and S. S. Olivier. “Open- and closed-loop aberration correction by use of a quadrature interferometric wave-front sensor,” Opt. Lett. 29, 47–49, 2004 [CrossRef] [PubMed]

3.

K.L. Baker, E.A. Stappaerts, D. Gavel, S.C. Wilks, J. Tucker, D.A. Silva, J. Olsen, S.S. Olivier, P.E. Young, M.W. Kartz, L.M. Flath, P. Krulevitch, J. Crawford, and O. Azucena. “Breadboard testing of a phase-conjugate engine with an interferometric wave-front sensor and a microelectromechanical systems-based spatial light modulator,” Appl. Opt. 43, 5585–5593, (2004) [CrossRef] [PubMed]

4.

M. Langlois, R. Angel, M. Lloyd-Hart, F. Wildi, G.D. Love, and A. Naumov. “High Order Reconstructor Free Adaptive Optics for 6–8 metre class telescopes” Proceedings of the ESO Conference on Beyond Conventional Adaptive Optics, May 7–10, Venice (2001)

5.

E. E. Bloemhof and J. K. Wallace, “Simple broadband implementation of a phase contrast wavefront sensor for adaptive optics,” Opt. Express 12, 6240–6245, (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6240 [CrossRef] [PubMed]

6.

H. Kadono, M. Ogusu, and S. Toyooka. “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Commun , 110, 391–400 (1994) [CrossRef]

7.

C. R. Mercer and K. Creath. “Liquid crystal point diffraction interferometer for wave-front measurements,” Appl. Opt. 35, 1633–1642 (1996). [CrossRef] [PubMed]

8.

G.D. Love and R. Bhandari. “Optical properties of a QHQ ferroelectric liquid crystal phase modulator,” Opt. Commun. 110, 475–478 (1994) [CrossRef]

9.

R. Bhandari and G. D Love. “Polarization eigenmodes of a QHQ retarder—some new features,” Opt. Commun. 110, 479–484 (1994). [CrossRef]

10.

Meadowlark Optics, 5964 Iris Parkway, Frederick, CO 80530-1000, USA. http://www.meadowlark.com

11.

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

12.

G.D. Love. “Liquid crystal phase modulator for unpolarized light,” Appl. Opt. 32:2222–2223 (1993).

13.

S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos, and M. Shilko. “On the use of dual frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,” Opt. Express 6, 2–6 (1999) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-1-2 [CrossRef]

14.

V. A. Dorezyuk, A.F. Naumov, and V.I. Shmal’gauzen, “Control of liquid crystal correctors in adaptive optical systems”, Sov. Tech. Phys. 34, 1389–1392 (1989).

15.

A.K. Kirby and G.D. Love. “Fast, large and controllable phase modulation using dual frequency liquid crystals,” Opt. Express 12, 1470–1475 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1470 [CrossRef] [PubMed]

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(350.1260) Other areas of optics : Astronomical optics

ToC Category:
Research Papers

History
Original Manuscript: March 15, 2005
Revised Manuscript: April 19, 2005
Published: May 2, 2005

Citation
Gordon Love, Thomas Oag, and Andrew Kirby, "Common path interferometric wavefront sensor for extreme adaptive optics," Opt. Express 13, 3491-3499 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3491


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References

  1. J. R. P. Angel. �??Ground-based imaging of extrasolar planes using adaptive optics,�?? Nature 368, 203-207, (1994) [CrossRef]
  2. K. L. Baker, E. A. Stappaerts, S. C. Wilks, P. E. Young, D. T. Gavel, J. W. Tucker, D. A. Silva and S. S. Olivier. �??Open- and closed-loop aberration correction by use of a quadrature interferometric wave-front sensor,�?? Opt. Lett. 29, 47-49 , 2004 [CrossRef] [PubMed]
  3. K.L. Baker, E.A. Stappaerts, D. Gavel, S.C. Wilks, J. Tucker, D.A. Silva, J. Olsen, S.S. Olivier, P.E. Young, M.W. Kartz, L.M. Flath, P. Krulevitch, J. Crawford, O. Azucena. �??Breadboard testing of a phase-conjugate engine with an interferometric wave-front sensor and a microelectromechanical systems-based spatial light modulator,�?? Appl. Opt. 43, 5585-5593, (2004) [CrossRef] [PubMed]
  4. M. Langlois, R. Angel, M. Lloyd-Hart, F. Wildi, G.D. Love and A. Naumov. �??High Order Reconstructor Free Adaptive Optics for 6-8 metre class telescopes�?? Proceedings of the ESO Conference on Beyond Conventional Adaptive Optics, May 7-10, Venice (2001)
  5. E. E. Bloemhof and J. K. Wallace, �??Simple broadband implementation of a phase contrast wavefront sensor for adaptive optics,�?? Opt. Express 12, 6240-6245, (2004) <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6240">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6240</a> [CrossRef] [PubMed]
  6. H. Kadono, M. Ogusu and S. Toyooka. �??Phase shifting common path interferometer using a liquid-crystal phase modulator,�?? Opt. Commun, 110, 391-400 (1994) [CrossRef]
  7. C. R. Mercer and K. Creath. �??Liquid crystal point diffraction interferometer for wave-front measurements,�?? Appl. Opt. 35, 1633-1642 (1996). [CrossRef] [PubMed]
  8. G.D. Love and R. Bhandari. �??Optical properties of a QHQ ferroelectric liquid crystal phase modulator,�?? Opt. Commun. 110, 475-478 (1994) [CrossRef]
  9. R. Bhandari and G. D Love. "Polarization eigenmodes of a QHQ retarder�??some new features,�??�?? Opt. Commun. 110, 479-484 (1994). [CrossRef]
  10. Meadowlark Optics, 5964 Iris Parkway, Frederick, CO 80530-1000, USA. Meadowlark Optics, 5964 Iris Parkway, Frederick, CO 80530-1000, USA. <a href= "http://www.meadowlark.com">http://www.meadowlark.com</a>
  11. G.D. Love, �??Wavefront correction and production of Zernike modes with a liquid crystal SLM.�?? Appl. Opt. 36, 1517-1524 (1997). [CrossRef] [PubMed]
  12. G.D. Love. �??Liquid crystal phase modulator for unpolarized light,�?? Appl. Opt. 32:2222-2223 (1993).
  13. S.R. Restaino, D. Dayton, S. Browne, J. Gonglewski, J. Baker, S. Rogers, S. McDermott, J. Gallegos and M. Shilko. �??On the use of dual frequency nematic material for adaptive optics systems: first results of a closed-loop experiment,�?? Opt. Express 6, 2-6 (1999) <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-1-2">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-1-2</a> [CrossRef]
  14. V. A. Dorezyuk, A.F. Naumov, V.I. Shmal�??gauzen, �??Control of liquid crystal correctors in adaptive optical systems�??, Sov. Tech. Phys. 34, 1389-1392 (1989).
  15. A.K. Kirby & G.D. Love. �??Fast, large and controllable phase modulation using dual frequency liquid crystals,�?? Opt. Express 12, 1470-1475 (2004) <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1470">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1470</a> [CrossRef] [PubMed]

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