Adaptive optics

An adaptive optics system has three parts. A wavefront sensor measures how a reference beam, from a star, a laser guide star or a point in the sample, departs from a flat wavefront; the most common is the Shack-Hartmann sensor, a lenslet array whose spot displacements give the local wavefront slope. A deformable mirror, a thin reflective face sheet pushed by an array of actuators, takes a shape that cancels the error; because reflection doubles a surface deformation, its surface moves by only half the wavefront error. A control computer closes the loop, updating the mirror hundreds to thousands of times per second so that the correction keeps up with the changing error. The result is judged by the Strehl ratio of the corrected image.

Astronomy is the original application. Atmospheric turbulence limits a ground-based telescope's resolution to that of an aperture the size of the Fried parameter $r_0$, typically 10 to 20 cm at 500 nm at a good site, whatever the telescope's diameter. Because $r_0$ grows as $\lambda^{6/5}$, an atmosphere with $r_0 = 10$ cm at 500 nm gives 59 cm at 2.2 µm, and correction is much easier in the near infrared, where most astronomical adaptive optics works. The number of corrected elements needed scales roughly as $(D/r_0)^2$: 6400 for an 8 m telescope at 500 nm, far fewer in the infrared. Bright reference stars are rare, so laser guide stars, sodium-layer fluorescence excited by a 589 nm laser, provide an artificial reference anywhere in the sky.

The same principle corrects other media. In ophthalmology, adaptive optics removes the eye's own aberrations and resolves individual photoreceptors in the living retina. In microscopy it corrects the aberrations introduced by refractive-index variations in thick tissue, recovering resolution and signal at depth. In free-space optical communication it corrects turbulence so that received light can be coupled into single-mode fiber, and in high-power lasers it compensates thermally induced distortion.

Performance is limited by the number of actuators, the sensor's noise and the loop's speed relative to the rate at which the error changes; each residual is usually expressed as an rms wavefront error and combined, in quadrature, into an error budget. Wavefront errors are commonly decomposed into Zernike polynomials, which separate correctable low-order terms from the high-order residual.

References: J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, 1998); R. Davies, M. Kasper, Annu. Rev. Astron. Astrophys. 50, 305 (2012).