Method for removing tilt control in adaptive optics systems

Claim 1

In an adaptive optics system of the type wherein a steering mirror steers an impinging wavefront toward a deformable mirror to impinge on said deformable mirror, said deformable mirror being of the type having its surface deformed selectively by means of a plurality of actuators to compensate for aberrations in said impinging wavefront, and wherein said compensated wavefront from said deformable mirror is sampled by a wavefront sensor array to measure the displacement error of the wavefront, and wherein said measured displacement error is coupled through a controller to control the actuators of the deformable mirror, an improved method of controlling the actuators which utilizes a single multiplication of the measured displacement error by a gain matrix, G', to remove tilt components of the measured displacement errors in controlling the actuators, which comprises: a) adjusting the measured displacement errors to generate signals to control said actuators by multiplying the measured displacement errors by a gain matrix given by G'=(I-X(X.sup.T X).sup.-1 X.sup.T)G(I-A) wherein I=a first matrix, said first matrix is an identity matrix with dimensions of M×M, and M is the number of said actuators, A=a second matrix, said second matrix multiplied by the measured displacement error yielding an average tilt for all elements of said wavefront sensor array, z=GS where z is the displacement error vector in the actuators, S is the measured displacement error vector of the wavefront sensor array, and G is an initial gain matrix; X=is a configuration matrix given by Xc=z where c is the coefficient vector of the planar fit to read z; and X T is the transpose of X.

Claim 3

A method of controlling a deformable mirror, comprising the steps of: steering an aberrated light beam towards said deformable mirror with a steering mirror, said steering mirror imparting a system tilt component to said aberrated light beam, wherein said deformable mirror has a deformable reflective surface controlled by a plurality, M, of actuators, measuring a displacement vector for a wavefront associated with said aberrated light beam using a wavefront sensor array; multiplying said displacement vector with a first gain matrix G' to generate a modified displacement vector, wherein G' is defined as (I-X(X T X) -1 X T )G(I-A), wherein I is a first matrix, said first matrix is an identity matrix of dimensions M×M, wherein X is a configuration matrix, wherein G is an initial gain matrix, wherein A is a second matrix, said second matrix multiplied by measured displacement vector yielding an average tilt for all elements of said wavefront sensor array, and X T is a transpose of X; converting said modified displacement vector to a corresponding electrical signal; and applying said corresponding electrical signal to said plurality of actuators.

Claim 4

A method of controlling a deformable mirror, comprising the steps of: steering an aberrated light beam towards said deformable mirror with a steering mirror, said steering mirror imparting a system tilt component to said aberrated light beam, wherein said deformable mirror has a deformable reflective surface controlled by a plurality, M, of actuators, measuring a displacement vector for a wavefront associated with said aberrated light beam using a wavefront sensor array; multiplying said displacement vector with a first gain matrix G' to generate a modified displacement vector, wherein G' is defined as (I-X(X T X) -1 X T )G(I-A), wherein I is a first matrix, said first matrix is an identity matrix of dimensions M×M, wherein X is a configuration matrix, wherein G is an initial gain matrix, wherein A is a second matrix, said second matrix multiplied by measured displacement vector yielding an average tilt for all elements of said wavefront sensor array, and X T is a transpose of X; converting said modified displacement vector to a corresponding electrical signal; and applying said corresponding electrical signal to said plurality of actuators.