Abstract

For an optical system with a large amount of aberration, a merit function ∫ ∫A M (s,ψ) g(s) sd sdψ is proposed, where M(s,ψ) is a relative modulation function introduced by Hopkins, g(s) is a weighting function, and A denotes a circular region in the spatial frequency domain (s,ψ). It is shown that the above quantity can be expressed as a quadratic form of the aberration coefficients by using an appropriate approximation. As a numerical example, we set g(s) = 1 and calculate the coefficients of the quadratic terms of the wave-front aberrations.

© 1971 Optical Society of America

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