Darryl J. Sanchez

Adaptive gain in closed-loop tilt control and adaptive optics

The performance of closed-loop tilt-control and adaptive-optics systems suffers when conditions change. Examples of changing conditions are angular extent of the object, signal-to-noise ratio, and characteristics of the disturbance. A simple learning algorithm motivated by neural network theory is developed to change the closed-loop gain in real-time to adapt quickly to changing conditions. This technique finds the correct loop gain within seconds with no operator intervention, which saves several minutes for each observation. Simulation and experimental results show improvement for both tilt-control and adaptive-optics systems.

Stabilization of the sodium beacon: a proposal to achieve full-sky coverage for laser guidestar adaptive optics

This document proposes a method to achieve full-sky adaptive optic coverage using a laser guidestar (LGS) adaptive optics (AO) system. This is done by stabilizing the sodium beacon by using information from the uplink beam so that the downlink tilt, i.e. the atmospheric tilt, can be measured. It is commonly known that tilt cannot be measured from a laser guidestar beacon because the uplink and downlink beams experience the same atmospheric tilt. This is true in itself, but disregards information that can be obtained from the uplink beam. Because the atmospheric structure function is a maximum near the exit aperture and decreases exponentially with altitude, the uplink beam accumulates most of its tilt near the exit aperture. For instance, when using the Hufnagel-Valley atmospheric model with A = 1.7 x 10-14 and W = 21, ≳ 92% of uplink atmospheric tilt occurs at altitudes below 5Km and 97% by ∼ 20Km. So, the instantaneous position of the uplink beam along the uplink path can be a predictor of the instantaneous position of the sodium beacon; this is this papers main result. Further, a means of measuring tilt from the uplink beam from its Rayleigh backscatter is presented and for some of the parameters and geometries considered, it is shown that the uplink tilt can be measured at sufficiently high altitudes and camera frames rates that a control system can stabilize the uplink beam, which in-turn stabilizes the sodium beacon, thus allowing atmospheric downlink tilt to be measured. Assuming that such a control loop can be implemented, such stabilization would allow for full sky laser guide star operation with AO performance similar to current LGS AO systems using off-axis natural guide stars.

Use of the analyticity of the generalized Fourier spectrum in object reconstruction

The analyticity of the generalized Fourier spectrum is used to estimate unmeasured visibilities with data obtained from an amplitude–phase optical interferometer. According to the Van Cittert–Zernike theorem, the complex visibilities are a scaled version of the spatial spectrum of the object. Hence an image of the object can be reconstructed from this measurement. However, since interferometers sparsely sample the object’s frequency spectrum, estimation of the unmeasured visibilities is crucial to obtaining a good spatial description of the object. This paper presents two techniques derived from the analyticity of the generalized Fourier spectrum that implement the estimation process. Both techniques are tailored specifically to interferometric data in that (1) all measured data is kept and used and (2) the sparseness of the sampling is taken into account.

Minimum uncertainty relations on a finite interval

A set of functions, cn(x), is presented that minimize beam dispersion for a fixed-size exit aperture. The root-mean-square deviation of the set of functions and their Fourier transforms are calculated and compared with Gaussian Fourier transform pairs. It is shown for Cn(k), the Fourier transforms of the cn(x), that as n increases, the energy in the central lobe of Cn(k) increases, given that the cn(x) are defined such that each is smoother than the previous one. It is also shown that the cn(x) become narrower and the Cn(k) become broader as n increases. When the root mean square is used as the measure of the width of the functions, for n → ∞ the product of the variances of cn(x) and Cn(k) approaches 1/2. Additionally, it is shown that the cn(x) span the [−1, 1] Hilbert space.