The development of a predictive autofocus algorithm using a general image formation model

This work outlines the development of a general imaging model for use in autofocus, astigmatism correction, and resolution analysis. The model is based on the modulation transfer function of the imaging system in the presence of aberrations, in particular defocus. The extension of the model to include astigmatism is also included. The signals used are related to the ratios of the Fourier transforms of images captured under di erent operating conditions. Methods are developed for working with these signals in a consistent manner. The model described is then applied to the problem of autofocus. A general autofocus algorithm is presented and results given which re ect the predictive properties of this model. The imaging system used for the generation of results was a scanning electron microscope, although the conclusions should be valid across a far wider range of instruments. It is however the speci c requirements of the SEM that make the generalisation presented here particularly useful.

[1]  H. Netten,et al.  Autofocusing in microscopy based on the OTF and sampling , 1994 .

[2]  Shree K. Nayar,et al.  Shape from Focus , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Murali Subbarao,et al.  Continuous focusing of moving objects using DFD1F , 1994, Electronic Imaging.

[4]  Peter Lawrence,et al.  An Investigation of Methods for Determining Depth from Focus , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Shang-Hong Lai,et al.  A Generalized Depth Estimation Algorithm with a Single Image , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Tae-Sun Choi,et al.  Focusing techniques , 1992, Other Conferences.

[7]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[8]  Robert A. King,et al.  The use of self-entropy as a focus measure in digital holography , 1989, Pattern Recognit. Lett..

[9]  Murali Subbarao.  Parallel Depth Recovery By Changing Camera Parameters , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[10]  G. Rempfer,et al.  A closer look at the effect of lens aberrations and object size on the intensity distribution and resolution in electron optics , 1988 .

[11]  Alex Pentland,et al.  A New Sense for Depth of Field , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  T. Suganuma.  A novel method for automatic measurement and correction of astigmatism in the SEM , 1987 .

[13]  G. Lawes,et al.  Scanning Electron Microscopy and X-Ray Microanalysis , 1987 .

[14]  K. C. Smith.  Astigmatism correction and determination of resolving power in the SEM , 1985 .

[15]  H. Weaver.  Applications of Discrete and Continuous Fourier Analysis , 1983 .

[16]  Emanuel Fischer,et al.  Intermediate Real Analysis , 1982 .

[17]  W. Krakow.  Raster methods for displaying defocus and astigmatism of scanning electron microscope images , 1981 .

[18]  N. Baba,et al.  A method of correcting the distorted spot shape of a deflected electron probe by means of dynamic focusing and stigmator , 1980 .

[19]  David M. Holburn,et al.  An automatic focusing and stigmating system for the SEM , 1979 .

[20]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[21]  W. R. Buckland.  A Guide to Probability Theory and Application , 1974 .

[22]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[23]  E. H. Linfoot.  Information Theory and Optical Images , 1955 .

[24]  H. H. Hopkins.  The frequency response of a defocused optical system , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[25]  G. D. Francia.  Resolving Power and Information , 1955 .

[26]  E. H. Linfoot,et al.  On the assessment of optical images , 1955, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[27]  P. Sturrock.  The Aberrations of Magnetic Electron Lenses due to Asymmetries , 1951 .