The Hilbert Transform Fringe Analysis Method And Its Application To The Measurement Of Aspheric

Smart interferometric techniques and analyzing methods for measurement of high quality optical surfaces have been developed, which relate to optics, mechanics, electronics, computer, and some other fields. In the modern optical measurement field, the method of studying deformation is analyzing and calculating a series of static or real time dynamic interference fringes in the end.There stre two sorts of digital processing technique for automatic fringe patterns analysis mostly. One is fringe center method based on fringe luminance analysis. The other is phase measurement on time or space. One of the earliest algorithms for fringe center method was fringe tracking, which mimicked the human approach of following fringe centers. Phase measurement can overcome the problems associated with fringe tracking, and is only limited by the spatial resolution of the camera and power of the computer to handle the volume of data.Among; of phase-measurement algorithms, there mainly are using a digital Fourier transform, phase shift and max-min scanning technique. With Fourier transform, the phase values may be obtained without ambiguity from a single image, but the fringe analyzing procedures are tedious and time consuming. The algorithms of phase shift needs a translating mirror provided phase shifts. The number of frames most frequently used by researchers has been 3, 4 or 5.This paper focuses on the study of the Hilbert transform for analyzing and processing interferogram, and it's applying in the measurement of aspheric surface. The phase information of aspheric surface is evaluated by Hilbert transform only from one interferogram. By integrating the derivative of the analyzed data, we obtain the wavefront aberration of the optical surface over an aperture containing a certain element array. Then the precision iteration to estimate the phase can be developed from the principle of least-squares estimation. In addition, the phase-extraction algorithm, error correction and some applications to the measurement of the surface shape are discussed.The interferometer is radial shearing interference, which based on two parallel zone plate method. The modulated interference fringes are detected by a CCD camera and analyzed by a personal computer.