Evaluation of the performance of Hartmann sensors in strong scintillation

Abstract

A simulation study is presented that evaluates the performance of Hartmann wave-front sensors with measurements obtained with the Fried geometry and the Hutchin geometry. Performance is defined in terms of the Strehl ratio achieved when the estimate of the complex field obtained from reconstruction is used to correct the distorted wave front presented to the wave-front sensor. A series of evaluations is performed to identify the strengths and the weaknesses of Hartmann sensors used in each of the two geometries in the two-dimensional space of the Fried parameter r0 and the Rytov parameter. We found that the performance of Hartmann sensors degrades severely when the Rytov number exceeds 0.2 and the ratio l/r0 exceeds 1/4 (where l is the subaperture side length) because of the presence of branch points in the phase function and the effect of amplitude scintillation on the measurement values produced by the Hartmann sensor.

Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry

“…22 In general, the applications are abundant. 23,24 With wavefront-sensing applications in mind, the presence of deep turbulence tends to be the "Achilles' heel" to modern-day solutions [e.g., the Shack-Hartmann wavefront sensor (WFS), 25 which provides access to localized wavefront slope estimates]. This is said because coherentlight propagation through deep turbulence causes scintillation, which manifests as time-varying constructive and destructive interference between the object and receiver planes.…”

Least-squares phase estimation with wrapped measurements and branch points

“…Let cx; y be the curl of the vector field ψx; y, i.e., cx; y ∇ y ψ x x; y − ∇ x ψ y x; y; (11) and let ϕx; y, vx; y be the scalar and vector potentials as in Eq. (4).…”

“…It is well known that Fried derivatives are good models for Shack-Hartmann sensors, which measure local phase gradients. However, Barchers demonstrated that the Fried geometry performance degrades in high scintillation when compared to Hudgin geometry [11]. When branch points causing phase wrapping are present, it is imperative to properly embed the wrapping operation within the Fried gradients computations.…”

“…The Shack-Hartmann sensor degrades from random apodization in the subapertures as the Rytov number increases [11], and a shearing or point diffraction interferometer may be a better choice [12]. The algorithm presented in this paper does not cover the effects of scintillation on the physics of the wavefront sensor; however, the algorithm presented here does cover the effects of branch points on the reconstruction algorithm.…”

Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets

“…The initial guess, (0) h , used in the algorithm is a 4x4 block-integrated surface (the x and y-slope maps are combined and locally integrated using the Fried algorithm 8 ) where the shape of each block is determined by integration of the normal data. The center-height of each block is set to the average height over the region as measured by structured light analysis.…”