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Simple broadband implementation of a phase contrast wavefront sensor for adaptive optics

E. E. Bloemhof and J. K. Wallace

Open Access Open Access

Abstract

The most critical element of an adaptive optics system is its wavefront sensor, which must measure the closed-loop difference between the corrected wavefront and an ideal template at high speed, in real time, over a dense sampling of the pupil. Most high-order systems have used Shack-Hartmann wavefront sensors, but a novel approach based on Zernike’s phase contrast principle appears promising. In this paper we discuss a simple way to achromatize such a phase contrast wavefront sensor, using the π/2 phase difference between reflected and transmitted rays in a thin, symmetric beam splitter. We further model the response at a range of wavelengths to show that the required transverse dimension of the focal-plane phase-shifting spot, nominally λ/D, may not be very sensitive to wavelength, and so in practice additional optics to introduce wavelength-dependent transverse magnification achromatizing this spot diameter may not be required. A very simple broadband implementation of the phase contrast wavefront sensor results.

©2004 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. Schematic of the phase contrast filter as a real-time wavefront sensor for adaptive optics. Light from an unresolved guide star enters the telescope with atmospherically-induced errors represented by a phase function across the pupil, φ(ξ,η). The telescope, represented here by a single lens, brings the light to a focus on a Zernike focal-plane filter, a dielectric mesa that imparts an additional phase of π/2 to the central ~λ/D portion of the beam compared to the air path traversed by off-axis rays. When the pupil plane is reimaged, it provides a phase map proportional to 1±2φ, where φ is the phase across the input pupil. This literal implementation, with a quarter-wavelength extra phase shift within the central diffraction-limited spot size, is implicitly monochromatic.

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Fig. 2.
Fig. 2. Schematic broadband implementation of the phase contrast filter as an adaptive optic wavefront sensor, based on the π/2 phase relationship between transmitted and reflected rays in an ideal beam splitter. The incident beam, converging from the telescope at typically f/16, first strikes a 50:50 beam splitter that imparts a π/2 relative phase shift between transmitted and reflected beams. These beams traverse equal pathlengths to mirror M2, where they come to a focus. A pinhole in M2 transmits the central ~λ/D portion of one beam, while reflecting the outer portion of the other beam (λ is chosen at the center wavelength of the passband: a moderate range of pinhole diameters measured as multiples of different wavelengths may be tolerable, according to simulations, as discussed in the text). The required phase shift between undiffracted central rays and off-axis rays (phase signal) has now been accomplished over a broad spectral band. Each output port nominally contains 50% of the total guide star light, and each provides a map of incident pupil phase proportional to 1±2φ.

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Fig. 3.
Fig. 3. Simulated response of phase contrast wavefront sensor for a range of wavelengths. The bold curve is a one-dimensional cut through the input phase function φ(ξ,η), modeled for a wavefront with Strehl ratio S=0.9 and DM actuator density D/a=16. The three lighter, dashed curves (identically scaled and offset vertically) are wavefront sensor outputs for 3 different choices of the diameter of the focal-plane phase-shifting spot equal to 0.75 λ/D, λ/D, and 1.25 λ/D, assuming a perfect phase shift of π/2 in each case. The response is a replica of the input pupil phase, relatively insensitive to the phase-shifting spot diameter in wavelengths, over a wavelength span of 1:1.67, comparable to the optical bandwidth of the current Shack-Hartmann used in the Palomar adaptive optics system. RMS departures of the three outputs from the input are 0.17, 0.10, and 0.16 radians, respectively; RMS input phase variation is 0.36 radians.

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Equations (2)

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Δ φ x ∼ 3 π 2 8 1 SNR ∼ 3.7 SNR ,
Δ φ ∼ 0.5 SNR .
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