Biomedical subjects

Guang-ming Dai

Publications and source records attributed to Guang-ming Dai.

3 recordsLinked to original sources

PubMed2006

Orthonormal polynomials for hexagonal pupils.

The problem of determining the orthonormal polynomials for hexagonal pupils by the Gram-Schmidt orthogonalization of Zernike circle polynomials is revisited, and closed-form expressions for the hexagonal polynomials are given. We show how the orthonormal coefficients are related to the corresponding Zernike coefficients for a hexagonal pupil and emphasize that it is the former that should be used for any quantitative wavefront analysis for such a pupil.

Journal Article↗

PubMed2006

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.

Algorithms↗

PubMed2006

Wavefront expansion basis functions and their relationships.

Wavefront expansion basis functions are important in representing ocular aberrations and phase perturbations due to atmospheric turbulence. A general discussion is presented for the conversions of the coefficients between any two sets of basis functions. Several popular sets of basis functions, namely, Zernike polynomials, Fourier series, and Taylor monomials, are discussed and the conversion matrices between any two of these basis functions are derived. Some analytical and numerical examples are given to demonstrate conversion of coefficients of different basis function sets.

Journal Article↗