The circle polynomials of Zernike and their application in optics
The Zernike polynomials are orthogonal functions defined on the unit circle, which have been used primarily in the diffraction theory of optical aberrations. A summary of their principal properties is given. It is shown that the polynomials, which are closely related to the general spherical harmonics, are especially useful in numerical calculations. In particular, by using the polynomials as a basis to represent the commonly encountered functions of optical theory, it is often possible to avoid numerical quadrature and computations are reduced to the simple manipulation of expansion coefficients.
PACS Codes02 42.30
Unable to display preview. Download preview PDF.
- 2.S.N.Bezdid'ko: Sov. J. Opt. Technol.41, 425 (1974)Google Scholar
- 3.B.R.A.Nijboer: Thesis, University of Groningen (1942). This has been reprinted (in part) in Physica10, 679 (1943) and Physica13, 605 (1947)Google Scholar
- 4.F.Zernike, H.C.Brinkman: Vehr. K. Akad. Wet. Amsterdam38, 161 (1935)Google Scholar
- 6.E.C.Kintner: Ph. D. Thesis, University of Edinburgh (1976)Google Scholar
- 7.E.C.Kintner: Optica Acta23, 499 (1976)Google Scholar
- 9.E.C.Kintner, R.Sillitto: Optica Acta23, 607 (1976)Google Scholar
- 10.E.C.Kintner: Optica Acta23, 679 (1976)Google Scholar
- 13.M.Hammermesh:Group Theory (Addison-Wesley, Reading, Mass. 1964)Google Scholar
- 14.A.R.Edwards:Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton 1960)Google Scholar
- 16.L.C.Biedenham, H.Van Dam:Quantum Theory of Angular Momentum (Academic Press, New York 1965)Google Scholar
- 17.M.Rotenberg, R.Bivens, N.Metropolis, J.K.Wooten, Jr.:The 3-j and 6-j Symbols (MIT. Press, Cambridge 1959)Google Scholar