OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 10, Iss. 10 — Oct. 1, 1971
  • pp: 2269–2273

Optical Correlation Analysis of Two-Phase Micrographs

F. T. S. Yu and R. J. Bieringer  »View Author Affiliations

Applied Optics, Vol. 10, Issue 10, pp. 2269-2273 (1971)

View Full Text Article

Enhanced HTML    Acrobat PDF (818 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The application of coherent optical techniques to the study of correlations in the detailed structure of electron (or light) micrographs was considered for the case when the structure appears to be random. A statistical autocorrelation analysis was made for a random array of transparent disks on an opaque background, relating the radii of the central and first autocorrelation maxima to the radius and mean separation, respectively, of the disks. Experimental determinations of the two-dimensional autocorrelation function were made both for arrays of disks and ellipses. In each case, the shape of the central maximum was similar to the shape of the objects (when all had the same shape and orientation). In addition, the shape of the first autocorrelation maximum was dependent only upon the distribution of centroids of the objects in the array and exhibited the proper asymmetry when the mean separation of centroids differed for the two dimensions. In this latter case, a rectangular first autocorrelation maximum was observed, implying separability of the two-dimensional autocorrelation function and providing a technique for direct quantitative determinations of the mean separations.

© 1971 Optical Society of America

Original Manuscript: April 21, 1971
Published: October 1, 1971

F. T. S. Yu and R. J. Bieringer, "Optical Correlation Analysis of Two-Phase Micrographs," Appl. Opt. 10, 2269-2273 (1971)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960). [CrossRef]
  2. R. Hosemann, S. N. Bagehi, Direct Analysis of Diffraction by Matter (North-Holland, Amsterdam, 1962), Chap 16
  3. R. E. Beissner, R. L. Bond, W. W. Bradshaw, J. Opt. Soc. Am. 60, 1551 (1970).
  4. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), p. 115.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited