Curvature sensors, adaptive optics, and Neumann boundary conditions.

We consider the Neumann boundary-value problem for curvature adaptive optics systems. We show that, because curvature sensors average over extended regions of the wave front, inconsistent data for the solution of the Neumann problem result when the measurements are treated as local. Because this inconsistency is generally resolved passively in the adaptive mirror itself, it can be interpreted as an uncontrolled degree of freedom of the system. We offer several procedures for treating the data in a more consistent fashion.

Field-of-view limitations of phased telescope arrays.

The optical performance of imaging phased telescope arrays is degraded by various design, manufacturing, and operational errors. Perhaps the most basic and fundamental of these error sources are the residual aberrations of the optical design chosen for the individual telescopes. We show that third-order field curvature and distortion, which are rather benign aberrations in a conventional telescope, result in relative phase and tilt errors between the individual telescopes making up the array. The field-dependent image degradation caused by these relative phase and tilt errors is then predicted for different subaperture configurations and telescope design parameters. For phased arrays made up of simple two-mirror telescopes, distortion limits the field of view to less than 5 arcmin for small subapertures (D < 0.5 m), and field curvature limits the field of view to less than 1 arcmin for subaperture diameters greater than 2 m. Quantitative parametric results yielding tolerances for residual field curvature as the phased array is scaled up in size are presented graphically. If a 0.5-deg field of view is desired for telescope diameters greater than 2 m, complex telescope configurations are necessary to satisfy the rather tight tolerances on both field curvature and distortion.

Diffraction effects of telescope secondary mirror spiders on various image-quality criteria.

Diffraction from secondary mirror spiders can significantly affect the image quality of optical telescopes; however, these effects vary drastically with the chosen image-quality criterion. Rigorous analytical calculations of these diffraction effects are often unwieldy, and virtually all commercially available optical design and analysis codes that have a diffraction-analysis capability are based on numerical Fourier-transform algorithms that frequently lack an adequate sampling density to model narrow spiders. The effects of spider diffraction on the Strehl ratio (or peak intensity of the diffraction image), full width at half-maximum of the point-spread function, the fractional encircled energy, and the modulation transfer function are discussed in detail. A simple empirical equation is developed that permits accurate engineering calculations of fractional encircled energy for an arbitrary obscuration ratio and spider configuration. Performance predictions are presented parametrically in an attempt to provide insight into this sometimes subtle phenomenon.

On-orbit performance of the Hubble Space Telescope optical control system.

On-orbit data are used to examine the performance of the Hubble Space Telescope optical control system. The precision, relative accuracy, and absolute accuracy of the off-axis Wavefront-Sensor measurements are evaluated and compared with design requirements. The internal stability of the sensors is better than 0.006 microm rms over five years, including launch. Random errors are estimated to be within 0.01 microm rms. Systematic errors are present in the estimates of focus, spherical, and coma aberrations, but none has been identified for astigmatism. Primary-mirror spherical aberration is believed to be the probable cause of all subspecification performances.

Hubble Space Telescope fine-guidance-sensor transfer function and its impact on telescope alignment and guidance.

We describe the use of Hubble Space Telescope Fine Guidance Sensor transfer scans to characterize telescope alignment. To accomplish this we developed a software system to extract the aberration content from the observed transfer scans. The transfer scans show large aberration levels that do not originate in the telescope. The appearance of significant coma in the transfer scans has been identified as resulting from the shearing of spherical aberration caused by a beam misalignment within the Fine Guidance Sensors themselves.