Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula.

In a recent paper [J. Opt. Soc. Am. A 19, 1937 (2002)] a recursive analytical formula was derived to calculate a set of new Zernike polynomial expansion coefficients from an original set when the size of the aperture is reduced. In the current paper I describe a more intuitive derivation of a simpler, nonrecursive formula, which is used to calculate the instantaneous refractive power.