Biomedical subjects

Erez N Ribak

Publications and source records attributed to Erez N Ribak.

5 recordsLinked to original sources

PubMed2007

Adaptive optics implementation with a Fourier reconstructor.

Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.

Journal Article↗

PubMed2006

Wavefront reconstruction from its gradients.

Wavefronts reconstructed from measured gradients are composed of a straightforward integration of the measured data, plus a correction term that disappears when there are no measurement errors. For regions of any shape, this term is a solution of Poisson's equation with Dirichlet conditions (V = 0 on the boundaries). We show that for rectangular regions, the correct solution is not a periodic one, but one expressed with Fourier cosine series. The correct solution has a lower variance than the periodic Fourier transform solution. Similar formulas exist for a circular region with obscuration. We present a near-optimal solution that is much faster than fast-Fourier-transform methods. By use of diagonal multigrid methods, a single iteration brings the correction term to within a standard deviation of 0.08, two iterations, to within 0.0064, etc.

Algorithms↗

PubMed2004

Reduction of laser spot elongation in adaptive optics.

Adaptive optics systems measure the wave front to be corrected by use of a reference source, a star, or a laser beacon. Such laser guide stars are a few kilometers long, and when observed near the edges of large telescopes they appear elongated. This limits their utility significantly. However, with more sophisticated launch optics their shape and length can be controlled. We propose to string around the rim of a telescope a number of small telescopes that will add laser beams in the scattering medium to create a compact spot. The method could also be adapted for ocular adaptive optics.

Journal Article↗

PubMed2004

Direct demodulation of Hartmann-Shack patterns.

Hartmann-Shack wave-front sensors produce a distorted grid of spots whose deviation from perfection is linear with the wave-front gradient. Usually, the centroid of each spot is calculated to provide that deviation, but it is also possible to perform the calculation by Fourier demodulation of the spot pattern [Opt. Commun. 215, 285, 2003]. We show that this demodulation can be performed directly on the grid, without reverting to Fourier transforms. Tracking the motion of each centroid individually is limited to well-defined spots with motions smaller than their pitch. In contrast, our method treats the image as a whole, is not limited to non-overlapping or sharp spots, and allows large spot motions. By replicating the array of spots slightly beyond the edge of the aperture, we reduce the chance for boundary phase dislocations in the reconstruction of the wave front. The method is especially suited to very large arrays.

Journal Article↗

PubMed2003

Separating atmospheric layers in adaptive optics.

Several optical schemes have been proposed to measure the separate contributions of atmospheric layers for astronomical adaptive optics. I show here that simple conjugation of the wave-front sensors to the layers is sufficient. Although a larger camera is required for a larger field of view, only the pixels that sense stars are being read out. The nearly periodic Hartmann data are analyzed by Fourier filtering so that the signals from all stars are added up while most of the noise is excluded. Acoustic Hartmann wave-front sensors [Opt. Lett. 26, 1834 (2001)1 that switch between layers improve flexibility and sensitivity.

Journal Article↗