Compensated Imaging System Research Articles

Smart adaptive optic systems using spatial light modulators

Many factors contribute to the aberrations induced in an optical system. Atmospheric turbulence between the object and the imaging system, physical or thermal perturbations in optical elements degrade the system's point spread function, and misaligned optics are the primary sources of aberrations that affect image quality. The design of a nonconventional real-time adaptive optic system using a micro-mirror device for wavefront correction is presented. The unconventional compensated imaging system presented offers advantages in speed, cost, power consumption, and weight. A pulsed-coupled neural network is used to as a preprocessor to enhance the performance of the wavefront sensor for low-light applications. Modeling results that characterize the system performance are presented.

Rapid evaluation of d_0: the effective diameter of a laser-guide-star adaptive-optics system

The Kolmogorov theory is used to illustrate that the mean-square wave-front error E2, which results when the wave-front distortion associated with an artificial guide-star reference is used to compensate a telescope aperture of diameter D, for imaging an object at infinity is given by E2 = (D/d0)5/3. The quantity d0 is a measure of the effective diameter of the compensated imaging system (i.e., a telescope with a diameter equal to d0 will have 1 rad of rms wave-front error) and is expressed as an integral over the Cn2 profile. The Cn2-weighting function is expressed in terms of hypergeometric functions whose series representation converges very rapidly. (Typically only a few terms are required). As a result d0 can be evaluated quite quickly on a microcomputer or a scientific calculator. In this study the quantity d0 is evaluated for six Cn2 profiles of interest, illustrating the importance of including the altitude weighting in the theoretical formulation of d0. In addition, this study illustrates the importance of removing the piston and the tilt from the wave-front distortion when assessing the performance of an imaging system.

Linear reconstruction of compensated images: theory and experimental results

Linear image reconstruction techniques are proposed for postprocessing astronomical images measured with compensated imaging systems. Linear techniques use averaging to overcome the effects of noise and deconvolution to remove system effects. Experimental results from compensated image measurements of four single stars and one binary star at visible wavelengths are reported for the first time, to our knowledge, and a previously derived analytic expression relating the statistics of the compensated optical transfer function to the compensated image spectrum signal-to-noise ratio is verified. The performance of deconvolution on a bright binary star with angular subtense previously estimated to be 0.52 arcsec (2.52 microrad) is demonstrated.

Anisoplanatism in adaptive optics

We examine the consequences for an adaptive-optics system of the fact that the turbulence-induced wave-front distortion for two propagation paths with only slightly different propagation directions can be significantly different. We consider the implications of this fact for a compensated imaging system and for an adaptive-optics laser transmitter. Theory and numerical results are presented. The basic results are presented in terms of the average optical transfer function of a compensated imaging system and in terms of the average antenna gain of an adaptive-optics laser transmitter, each expressed as a function of the angular separation ϑ between the propagation path along which the reference signal arrives and the propagation path along which the adaptive-optics system is to provide performance. It is shown that for high spatial frequencies (for the compensated imaging system) and for large-aperture diameters (for the adaptive-laser optics transmitter), i.e., large compared with r0/λ and with r0, respectively, the magnitude of the anisoplanatism effect can be characterized by an isoplanatic patch angular size, which we denote by ϑ0. If the angular separation between the two propagation paths is ϑ, it is shown that the optical transfer function and the antenna gain are each reduced by a factor of exp[−(ϑ/ϑ0)5/3]. This simply expressed performance-reduction factor represents an asymptotic limit for high spatial frequencies and for large transmitter diameters. For lower spatial frequencies and smaller transmitter diameters the reduction factor is not so severe. Numerical results are presented to illustrate this.

Minimizing atmospheric dispersion effects in compensated imaging

A compensated imaging system that corrects optical path length distortions due to atmospheric turbulence by means of an achromatic corrector will have residual errors caused by the dispersion of the atmosphere. These errors become significant for astronomical objects at large zenith angles, but they may be minimized by special dispersion correctors.

Optimal wave-front estimation

In a compensated imaging (CI) system the wave-front distortion is changing randomly in time and the data processing must follow the changes and even, to some extent, predict them. Furthermore, the system is not infinitely fast; it has time delays and bandwidth limitations which can be quite significant. Couple to this the substantial photon noise in the wave-front measurements, and it becomes desirable to find the optimal data processing to use for system control. This paper derives the optimal linear control algorithm assuming the aberration and noise statistics are known for a compensated imaging system, and discusses the properties of this algorithm.