An overview of modeling, analysis and demonstrations of optical wavefront control implemented with a reconfigurable diffractive optic is presented. This includes, analytic modeling of the wavelength-dependent diffraction efficiency and wavefront errors associated with modulo-<i>Nλ<sub>0</sub></i> optical path control and analysis of the effects of discrete-element addressing and fill factor on diffraction efficiency. More than 200 waves of 2-D wavefront control are demonstrated with a 640x480-element optical path modulator. Wavefront steering together with field-angle-dependent aberration compensation is demonstrated as a technique for acquiring extended field-of-regard mosaic images. The effects of diffraction phenomena on image quality are analyzed.
This paper builds upon past work demonstrating the integrated performance of a programmable diffractive element of large pixel count with a telescope system. More specifically, a liquid-crystal-based spatial light modulator is used as a reconfigurable diffractive optical element in a telescope system to extend the systems field of regard by compensating large aberrations associated with off-axis orientation of the primary mirror and by steering object light over angles greater than the instantaneous field of view.
This paper presents an analytic treatment of the wavelength dependences associated modulo λ<sub>r</sub> optical path control, treating the case where the reset wavelength λ<sub>r</sub> is allowed to be an integer multiple of a nominal operating wavelength λ<sub>0</sub>, λ<sub>r</sub>=Nλ<sub>0</sub>. Equations for the wavelength dependences associated with modulo Nλ<sub>0</sub> optical path modulation are derived using both a Strehl ratio analysis approach and a Fourier analysis approach. Geometrical analysis of the transmitted wavefront yields expressions for the Strehl ratio and angular dispersion that are in agreement with the N<sup>th</sup>-order diffraction efficiency and angular dispersion relationships derived by Fourier analysis. The Fourier analysis approach yields additional expressions for the diffraction efficiency and wavefront characteristics associated with all diffracted orders.
Image metric optimization is an attractive alternative to conventional wavefront sensing for optical systems that are constrained by weight, cost, size, and power consumption and required to operate using light from extended object scenes. For these optical systems, an image metric optimizer must be able to function in the presence of potentially large system aberrations. This paper examines the usefulness of image entropy as a metric for measuring changes in image quality in the presence of large aberrations. In our experiment, we use a liquid-crystal spatial light modulator as a programmable diffractive optic to compensate for roughly 40 waves of peak-to-valley aberration introduced by using a parabolic mirror tilted 5 degrees off the optic axis. The results of our experiment show that image entropy does function well as a metric for measuring changes in image quality for 20 waves of aberration or less. For aberrations greater than 20 waves peak-to-valley the total optical power incident on the camera is a better metric.