Wavefront error estimation derived from observation of arbitrary unknown extended scenes

A cross-correlation, extended scene, wavefront sensing method for use with an adaptive system for determining and correcting system wavefront errors from observations of extended scenes, and wherein the adaptive system comprises a receiver, detection means coupled to the receiver, and processing means coupled to the detection means for producing signals that are adapted to correct for system wavefront errors, said wavefront sensing method comprising the steps of:

• processing measured intensity distributions derived from signals received by the receiver and detection means to produce a transmitted intensity, I.sub.m+ (R, t), and a reflected intensity, I.sub.m- (R, t);
• differencing the measured intensity distributions to form intensity difference signals .DELTA.I.sub.m (R, t), and differencing the intensity distributions to form intensity difference signals .DELTA.I.sub.m (R, t);
• generating a temporal cross-correlation, (.DELTA.I.sub.m (R, t).DELTA.I.sub.m *(R, t)) , between each subaperture at locations R on a projected pupil of the receiver, and a reference subaperture at locations R' on the antenna from the intensity difference signals, and wherein the temporal cross-correlation is a function of the lead/lag time associated with a wavefront slope difference between cross-correlated subapertures, as defined by the equation,
• <.DELTA.I(R, t=0).DELTA.I(R',t)>.tbd.G(R, R', t-T)
• where the lead/lag time, T, is given by
• T=.kappa..DELTA.S(R, R')
• and where .kappa. is a constant that is a function of predetermined parameters of the adaptive system, S((R, R') is the difference between wavefront slopes at locations R' and R in a measurement plane, and G(R, R', t), is a function of pupil geometry, scene spatial frequency power spectral density, and a wavefront sensor filter function;
• matched filtering the cross-correlated signals;
• comparing the output of all of the matched filters and selecting the value of lead/lag time corresponding to the matched filter with maximum peak output to determine the wavefront slope difference;
• and
• reconstructing the wavefront slope differences to produce an error estimate that is adapted to correct for the system wavefront errors.

A cross-coherence, extended scene, wavefront sensing method for use with an adaptive system that corrects adaptive elements of a receiver of the system and measures and separates scene effects from system wavefront errors produced by the system, said wavefront sensing method comprising the steps of:

• processing measured intensity distributions derived from signals received by the receiver to produce a spatially filtered transmitted intensity and a spatially filtered reflected intensity;
• differencing the measured intensity distributions to form intensity difference signals;
• performing a temporal Fourier transform on the differenced signals;
• generating a cross-coherence signal, between each subaperture location and a reference subaperture location from the Fourier transformed signals;
• generating optimal estimates (minimum error estimates) using the real and imaginary pans of the cross coherence signal;
• computing an arctangent on the cross-coherence signal;
• optimally estimating pairwise slope differences and weighting signals derived from the arctangent computation;
• and
• reconstructing the wavefront slope differences to produce an error estimate that is adapted to correct for the system wavefront errors.

A cross-coherence, extended scene, wavefront sensing method for use with an adaptive system that corrects individual elements of an receiver of the system and measures and separates scene effects from system wavefront errors produced by the system, said wavefront sensing method comprising the steps of:

• processing measured intensity distributions derived from the receiver to produce a transmitted intensity, I.sub.m+ (R, t), and a reflected intensity, I.sub.m- (R, t);
• differencing the measured intensity distributions to form an intensity difference signal .DELTA.I.sub.m (R, t);
• performing a temporal Fourier transform on the differenced signals to produce .DELTA.I(R, t);
• generating a cross-coherence signal, .DELTA.I(R, f).DELTA.I*(R', f), between each subaperture at location R', and a reference subaperture at location R, from the Fourier transformed signals;
• generating minimum error estimates using the real and imaginary parts of the cross coherence signal;
• computing an arctangent on the cross-coherence signal to produce ##EQU2## optimally estimating pairwise slope differences and weighting the signals derived from the arctangent computation in accordance with the equation
• .DELTA.S.sub.EST (R,R')=A.DELTA.(R, R', f);
• and
• reconstructing the wavefront slope differences to produce an error estimate that is adapted to correct for the system wavefront errors.

Apparatus for use with an adaptive system for determining correction signals required to correct for system wavefront errors from observations of extended scenes with a receiver and a detector array, said apparatus comprising:

• means for processing measured intensity distributions derived from signals received by the receiver to produce a spatially filtered transmitted intensity and a spatially filtered reflected intensity;
• means for differencing the measured intensity distributions to form intensity difference signals;
• means for performing a temporal Fourier transform on the differenced signals;
• means for generating a cross-coherence signal, between each subaperture location and a reference subaperture location from the Fourier transformed signals;
• means for generating optimal estimates (minimum error estimates) using the real and imaginary parts of the cross coherence signal;
• means for computing an arctangent on the cross-coherence signal;
• means for optimally estimating all pairwise slope differences and weighting the signals derived from the arctangent computation;
• means for removing pi ambiguities;
• and
• means for reconstructing the wavefront slope differences to produce an error estimate that is adapted to correct for the system wavefront errors.

Apparatus for use with an adaptive system that corrects individual elements of an antenna of the system and measures and separates scene effects from system wavefront errors produced by the system, said apparatus comprising:

• means for processing measured intensity distributions derived from signals received by the receiver to produce a spatially filtered transmitted intensity and a spatially filtered reflected intensity;
• means for differencing the measured intensity distributions to form intensity difference signals;
• means for performing a temporal Fourier transform on the differenced signals;
• means for generating a cross-coherence signal, between each subaperture location and a reference subaperture location from the Fourier transformed signals;
• means for computing an arctangent on the cross-coherence signal;
• means for optimally estimating all pairwise slope differences and weighting the signals derived from the arctangent computation;
• means for removing pi ambiguities;
• and
• means for reconstructing the wavefront slope differences to produce an error estimate that is adapted to correct for the system wavefront errors.