Wave-front reconstruction using a Shack–Hartmann sensor

Abstract

An analysis of the problem of wave-front reconstruction from Shack-Hartmann measurements is presented. The wave-front aberration is assumed to result from passage of the wave front through Kolmogorov turbulence. Limitations of using Zernike polynomials as an orthogonal basis for wave-front reconstruction are highlighted, and the advantage of using the Karhunen-Loeve functions for computing the higher-order modes of the wave front is shown.

Conceptual design of a phase-shifting telescope-interferometer

“…Figure 5 shows different possible arrangements of the reference facet on the primary mirror, for both segmented and diluted-aperture geometry. The reader will easily verify that the whole set of equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) leading to the final phase retrieval formulae remains valid when the reference pupil is decentred of a given amount with respect to the main pupil: in that case Eq. [16] will simply generate a laterally-shifted pupil map without any information loss.…”

“…Unfortunately, the most familiar and efficient Wavefront Sensors (WFS) employed in Adaptive Optics are not well matched to that purpose, because they are all based upon WFE slopes or curvature measurements (then reconstructing the wavefronts digitally). Typical examples are the Shack-Hartmann [1], the shearing interferometer [2], the curvature sensor [3] and the most recently proposed pyramidal WFS [4]. Piston evaluation is hardly achievable from these devices, therefore direct phase measurement techniques should be preferred.…”

Hybrid Atmospheric Compensation in Free-Space Optical Communication

“…On the other hand, the mean local gradient of the distorted wave front in the mth (m=1, 2,…, M) subaperture is regarded as the mean of the partial derivative of the wave front φ (x, y) in the area Sm, which is the local area of the m th subaperture [6]. Based on Eq.…”

“…Adaptive optical (AO) systems have been successfully applied to FSO to compensate the distorted wave front [3][4][5][6][7][8][9]. Based on the phase-conjugation principle, traditionally there are two main branches.…”

“…Based on the phase-conjugation principle, traditionally there are two main branches. One in [6] is based on a wave-front sensor, such as the SH-WFS, to detect the local slope of the wave front and reconstruct the wave front in the Zernike or some other model. With a model, a deformable mirror (DM) can be controlled to construct a conjugated wave front, to offset the aberrations and obtain an approximately planar wave.…”