interferometer with application to large scale AO. Andrew ... ref 1) a novel method of implementing a common-path phase-shifting point diffraction interferometric ...
Proc. SPIE 6306: 630601 (2006)
Direct wavefront phase measurement using a point diffraction interferometer with application to large scale AO Andrew K. Kirby, Thomas J.D. Oag, and Gordon D. Love. Durham University, Rochester Building, Dept. of Physics, Durham, DH1 3LE, UK ABSTRACT Interferometric techniques are attractive in wavefront sensing because they give a direct measure of the phase (as opposed to the first or second derivative) which means they are useful for use with a piston-only wavefront corrector (such as a liquid crystal spatial light modulator, or some MEMS mirrors). In this paper we describe (also described in ref 1) a novel method of implementing a common-path phase-shifting point diffraction interferometric wavefront sensor suitable. 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. Keywords: Point diffraction, liquid crystal, extreme adaptive optics, reconstructor-free
INTRODUCTION In an AO system it is advantageous for the control if the wavefront deformation measured by the wavefront sensor matches the deformation produced by the wavefront controller, e.g. a curvature sensor with a bimorph mirror, or a Shack-Hartmann sensor with a segmented deformable mirror. Some MEMS and LC devices have piston-only influence functions, and so it is desirable to use a wavefront sensor which measures phase directly, such as an interferometer. This will make a “reconstructor-free” control system possible, in which the control of each actuator is independent of the other actuators, and the complexity of the control will scale linearly with the number of actuators. Such systems were proposed some time ago2, although there is recent renewed interest2-6 in them as practical advances are being made. QWP
QWP
Polarizing beamsplitter
Output A (Camera or photodetector) Incident unpolarized beam FLC Output B (Camera or photodetector)
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.
We describe here an alternative configuration of a common-path point diffraction interferometer (PDI) which gives simultaneously two phase-shifted fringe patterns, and which allows for calibration of scintillation. The interferometric arrangements based in refs. 3-5 are based on a Mach-Zhender configuration, and do not have the stability advantages
Proc. SPIE 6306: 630601 (2006)
associated with common-path operation we describe. LCs have previously been used to produce phase-shifting PDIs7,8. In our work, we use the fact that they are birefringent to produce two phase-shifted fringe patterns simultaneously using incident unpolarized light. We also 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 the complexity of this type of control system scales linearly with number of actuators used.
THE LIQUID CRYSTAL POINT DIFFRACTION INTERFEROMETER The most important element is a ferroelectric liquid crystal (FLC) cell, which acts as an electrically rotatable half-wave plate (HWP), and which has small circle, 20µm in diameter, removed from one of the control electrodes. By placing the device between two co-aligned quarter-wave plates (QWPs), as shown in figure 1, we can achieve8 phase-only modulation. Linearly polarized light which is incident at 45o to the QWP crystal axes is phase modulated by an amount 2θ, 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 = 90o (since the FLC switching angle is 45o). The orthogonally polarized component experiences a similar phase plate, but with a phase shift of -2θ = −90o. If the wavefront sensor is therefore used with unpolarized light, i.e. the 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 resultant fringe patterns differ in phase by 180o. 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. The interferometer also has a “null output” which can be used to measure the intensity of the beam when the phase shifter is not activated (i.e. the FLC is switched ‘off’). Of course, this could also be implemented in any of the systems described in refs 2-4 simply by placing a beamsplitter before the wavefront sensor and imaging the pupil onto another detector. However, using this method, there are no non-common path errors caused by differences in optics or detectors between the wavefront sensor and the intensity detector. We produced a computer simulation1 of the device to show that the PDI can measure phase, and can be used to reduce the effects of simulation.
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 figure 2 A collimated HeNe (633nm) laser beam was passed through a hot-air turbulence generator and onto the wavefront corrector. The wavefront corrector was a Meadlowlark Optics10 nematic liquid crystal device11 which has 127 phase-only correction elements. The device operates with unpolarized light by using a QWP between the LC and a mirror12. The device uses high speed dual frequency LC material and has a much faster response time than conventional LC devices. Previous work has demonstrated the use of such devices in a closed loop system using a Shack-Hartman wavefront sensor13, however, as the authors acknowledge in their papers, the Shack-Hartman is not an ideal wavefront sensor for a piston-only wavefront corrector. Here, the output of the wavefront sensor is used in a control system specially designed for operation with dual frequency LCs14,15. The optics were arranged so that a single pixel of the wavefront corrector was imaged onto a pinhole in front of a photodiode in each of the detector arms, in order to produce the two required signals, IA and IB. A ‘bang-bang’ type control system was implemented. The two signals from the photodetectors were input to a differential amplifier to give a voltage, Vdet, which is proportional to IA - I B. A comparator compares Vdet and a set-point voltage, Vref, and operates an analogue switch to controls the signal fed, via a high-voltage (HV) amplifier, to the LC wavefront corrector. If Vdet > Vref then a high frequency (~30KHz) drive signal is selected. If Vdet < Vref then a low frequency (~1KHz) drive signal is selected. Since the comparator used in this implementation had no hysteresis, the operation of this system is such that, if the measured phase differs in either direction from the set-point, then the wavefront corrector applies the maximum compensating signal. This means that the dual frequency LC in the wavefront corrector is always either turning on or turning off. Operating in open-loop mode, with the turbulence generator turned off, 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 figure 3. Operating in closed loop mode, the reference DC signal was adjusted to select the desired set-point phase shift. Figure 4 shows a comparison of the output of the wavefront sensor with the system
Proc. SPIE 6306: 630601 (2006)
operating in open- and closed- loop modes, with the turbulence generator switched on. The results have been converted to waves, using the data in figure 3 as calibration. It can be seen that the phase variance has been considerably reduced (from 2.44 to 0.40 rad2). If we make the assumption that all the pixels in a full AO system behaved similarly then the Maréchel approximation could be used to assign Strehl ratios to these variances of 0.09 and 0.67. The power spectra of these data are shown in Fig. 5. The spectra were smoothed to make the general trend clearer. It can be seen that the crossover frequency, at which the system begins to add noise, is about 700Hz.
DISCUSSION An alternative form of point diffraction interferometer has been described, which has the advantage of giving phase shifted outputs and common path operation, as well as having an option for reducing scintillation. The interferometer allows for piston-only phase measurement, and is thus well matched to wavefront controllers which operate by pistononly phase modulation, potentially allowing for reconstructor-free large scale AO wavefront control.
Turbulence generator HeNe Laser (unpolarized)
Polarizing Beamsplitter
QWP
QWP
FLC HWP
Pinhole
LC wavefront corrector
Photodiodes Comparator and analogue switch
Oscilloscope
HV Amplifier
Vdet Differential amplifier
Vref
DC reference source High frequency signal generator
Low frequency signal generator
Fig. 2. Diagram of the single channel 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 quarterwave 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 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.
Proc. SPIE 6306: 630601 (2006)
Figure 3. Wavefront sensor (WFS) output, measured after the differential amplifier (in fig. 2) with the loop not closed, and an alternating signal of 1 wave being applied to the wavefront corrector.
Figure 4. Calibrated wavefront sensor output in open- (left) and closed- (right) loop modes. The turbulence was severe. The uncorrected and corrected phase variances are 2.44 rad2 0.40 rad2 respectively.
Proc. SPIE 6306: 630601 (2006)
Figure 5. Power spectrum of the wavefront sensor output for open-loop (dashed line) and closed-loop (solid line) operation. The system reduces wavefront aberrations up to a frequency of about 700Hz.
Closed-loop operation was demonstrated for a single channel, using a high-speed dual frequency LC phase modulator, and giving a reduction in wavefront aberration up to a frequency of approximately 700Hz. It is likely that some of the noise contributions at frequencies above 700Hz are due to the simple bang-bang type of control system used, and the use of more sophisticated proportional control would reduce the noise, allow the use of larger driving voltages and hence increase the closed-loop bandwidth of the control system.
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