Wavefront Sensor Measurements Research Articles

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.

Estimating the contribution of different parts of the atmosphere to optical wavefront aberration

Current adaptive optical telescope designs use a single deformable mirror (DM), usually conjugated to the aperture plane, to compensate for the cumulative effects of optical turbulence. The corrected field of view (FOV) of an adaptive optics system could theoretically be increased through the use of multiple DMs conjugated to a like number of corresponding planes which sample the turbulence region in altitude. Often, the atmospheric turbulence responsible for the degradation of long-exposure telescope images is concentrated in several relatively strong layers. The logical location for the planes of correction in a multiconjugate adaptive optics (MCAO) system would be the same as these “seeing layers.” Each DM would correct for the component of the total wavefront contributed by its associated turbulent layer. However, there is no known method of isolating a particular layer so that its component may be measured. Somehow, the individual components must be estimated using available measurements of the cumulative wavefront at the aperture of the telescope. This paper presents a theoretical analysis of a signal processing technique for determining these phase contributions. The method takes advantage of the spatial diversity of wavefront sensor (WFS) measurements from two or more reference sources. These separate wavefront sensor measurements are processed via minimum mean square error filtering to yield an estimate of the phase perturbation caused by a particular turbulent layer of the atmosphere. Our results indicate that multiple wavefront corrector adaptive optics systems will require much brighter reference sources than single wavefront corrector systems.

Coherent image synthesis from wave-front sensor measurements of a nonimaged laser speckle field: a laboratory demonstrations

We report what are to our knowledge the first coherent images recovered in the laboratory from measurements made with a Shack-Hartmann wave-front sensor of the phase and amplitude of a laser speckle wave front. We discuss the design of our wave-front sensor, which can obtain the phase and amplitude of an optical field with a single intensity measurement, and we point out a particular type of phase jump that cannot be detected by the Shack-Hartmann sensor. We also discuss implementations of this technique that may permit near-diffraction-limited imaging through turbulent media.

Image synthesis from wave-front sensor measurements of a coherent diffraction field

We demonstrate that images of laser-illuminated objects can be formed from measurements of the wave-front slope (gradient) associated with the backscattered, coherent laser-speckle field. A digital wave-front recovery and image synthesis procedure is described, and the results of computer-simulation experiments are presented in which coherent images are reconstructed from digitally simulated Fourier-plane laser-speckle measurements. Images are recovered from noisy wave-front-difference data to illustrate the effect that measurement noise has on recovered image quality.

Wavefront sensor noise reduction and dynamic range expansion by means of optical image intensification

A Hartmann wavefront sensor measures optical wavefront aberrations by using a lens array to break the input sample into subapertures. The lens in each subaperture produces an image whose centroid position depends on the average phase front tilt in the subaperture. The simplest measurement implementation, a quad cell detector, is limited in tilt dynamic range to 1 wave because the (diffraction-limited) image has a radius equivalent to 1 wave of tilt. For greater tilts, the image is off-null and no positional information is available. Dynamic range can be increased by defocusing the spot but only at the expense of increased centroid variance. However, if the spot image is optically intensified before being detected, the intensified image can be defocused without increasing the centroid variance. A theoretical derivation of sensor performance with and without intensification is given. Results of simulations and laboratory experiment are presented showing good agreement with theory. The use of this technique may greatly extend the capabilities of wavefront sensor systems at modest increase in cost or complexity.

Cramer-Rao Lower Bound On Wavefront Sensor Error

Wavefront sensors that can operate at low light levels, be built from present technology components, and provide accurate wavefront phase estimates in real time are required for use with adaptive optics systems. The use of estimation theory makes possible the evaluation of wavefront sensors without specification of the wavefront phase estimation algorithms. The Cramer-Rao method was used to find a lower bound on integrated rms wavefront sensor estimation error. In addition to an analysis of the general case, the error lower bound was numerically evaluated for the shearing interferometer wavefront sensor. Computer simulations of the atmosphere and wavefront sensor measurements including noise were performed. Using an appropriate algorithm, the phase was estimated and the resulting phase error was compared with the lower bound. The results support the validity of using the Cramer-Rao lower bound to evaluate wavefront sensor performance.