Study On The Performance And Reconstruction Algorithm Of Wavefront Curvature Sensor

The wavefront curvature sensor obtains the wavefront by sensing the differencesbetween the intensities on two planes with different propagation distances, and it is usedsuccessfully in adaptive optics of astronomy, optical test and ophthalmic optics. In theprocess of designing and implementing curvature sensor, a proper propagation distanceshould be chosen to improve the accuracy and spatial resolution, and the reconstructionalgorithms should be applicable to measure wavefront on pupils with different shapes.In this dissertation, the relevant studies with the methods of frequency analysis andeigenfunctions of Laplacian are carried out.With the small aberration approximation, the effect of propagation distance to theperformance of wavefront curvature sensor is analyzed by frequency analysis method.For a short propagation distance, the differences between the intensities caused bywavefront distortion are weak, so the accuracy is affected seriously by the noise inintensity measurement. For a long propagation distance, the differences of theintensities caused by high-frequency aberrations and wavefront curvature do not satisfythe linear relationship and this nonlinear effect increases the measurement error. Aswavefront distortion is composed of various frequencies, the propagation distanceshould be large for low-frequency aberrations, which are greatly affected by themeasurement noise, and small for high-frequency aberrations, which are greatly limitedby the nonlinear effect. The bounded interval of propagation distance is given byconsidering both the nonlinear effect and the noise in intensity measurement.For wavefront curvature sensor, a reconstruction algorithm based oneigenfunctions of Laplacian is proposed. This method is applicable on pupils withdifferent shapes, and does not need iteration or auxiliary functions. The analyticexpressions of the eigenfunctions on circle, rectangular, annular and annular sectorpupils are given. Wavefront reconstructions by the eigenfunction method on thecorresponding pupils are simulated. The aberration plane on circle, rectangular andannular pupils are measured by curvature sensor with grating, and reconstructed byeigenfunctions method. The simulation and experiment results indicate that theeigenfunction method provides an accurate wavefront reconstruction.According to the orthogonality of the gradients of the Laplacian’s eigenfunctions,the eigenfunction method is expanded to wavefront slope sensor. It is proved that thegradients of the eigenfunctions of Laplacian with homogeneous Neumann boundarycondition are orthogonal to each other. A set of basis functions which are orthogonalthemselves and the gradients of which are also orthogonal are found. A reconstructionalgorithm based on eigenfunctions of Laplacian is proposed for wavefront slope sensor.Wavefront reconstruction from the wavefront slope is simulated, and accurate reconstruction results are obtained. Modal cross coupling between basis functions inmodal wavefront reconstruction is discussed. Wavefront reconstruction by usingZernike polynomials and eigenfunctions of Laplacian are compared. The results showthat modal cross coupling error between eigenfunctions of Laplacian is much smallerthan that between Zernike polynomials.The correction algorithm of curvature adaptive optics system is investigated. Thesignal-divided correction algorithm used in astronomy is simulated. The results indicatethat the corrections of the Zernike aberrations with zero curvature are more accuratethan the ones with non-zero curvature. For curvature sensor with phase grating, acorrection algorithm using the whole spatial distribution of curvature signals isproposed. Compared to the signal-divided algorithm, the whole signal algorithm gets asimilar performance while the demand of calibration is reduced as it is not necessary forthe curvature distribution to be divided for sensing and the whole signal algorithm isapplied to the deformable mirror with different actuator distributions.