THE KNIFE EDGE TEST AS A WAVEFRONT SENSOR (IMAGE PROCESSING).

Abstract

An algorithm to reduce data from the knife edge test is given. The method is an extension of the theory of single sideband holography to second order effects. Application to phase microscopy is especially useful because a troublesome second order term vanishes when the knife edge does not attenuate the unscattered radiation probing the specimen. The algorithm was tested by simulation of an active optics system that sensed and corrected small (less than quarter wavelength) wavefront errors. Convergence to a null was quadratic until limited by detector-injected noise in signal. The best form of the algorithm used only a Fourier transform of the smoothed detector record, a filtering of the transform, an inverse transform, and an arctangent solving for the phase of the input wavefront deformation. Iterations were helpful only for a Wiener filtering of the data record that weighted down Fourier amplitudes smaller than the mean noise level before analysis. The simplicity and sensitivity of this wavefront sensor makes it a candidate for active optic control of small-angle light scattering in space. In real time optical processing a two dimensional signal can be applied as a voltage to a deformable mirror and be received as an intensity modulation at an output plane. Combination of these features may permit a real time null test. Application to electron microscopy should allow the finding of defocus, astigmatism, and spherical aberrations for single micrographs at 0.2 nm resolution, provided a combination of specimen and support membrane is used that permits some a priori knowledge. For some thin specimens (up to nearly 100 atom layers thick) the left-right symmetry of diffraction should allow reconstruction of the wave-front deformations caused by the specimen with double the bandpass used in each image.