Biomedical subjects

Virendra N Mahajan

Publications and source records attributed to Virendra N Mahajan.

5 recordsLinked to original sources

PubMed2007

Nonrecursive determination of orthonormal polynomials with matrix formulation.

A general theoretical approach has been developed for the determination of orthonormal polynomials over any integrable domain, such as a hexagon. This approach is better than the classical Gram-Schmidt orthogonalization process because it is nonrecursvie and can be performed rapidly with matrix transformations. The determination of the orthonormal hexagonal polynomials is demonstrated as an example of the matrix approach.

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PubMed2007

Zernike annular polynomials and atmospheric turbulence.

Imaging through atmospheric turbulence by systems with annular pupils is discussed using the Zernike annular polynomials. Fourier transforms of these polynomials are derived analytically to facilitate the calculation of variance and covariance of the aberration coefficients. Zernike annular shape functions are derived and used to calculate the Strehl ratio and the residual phase structure and mutual coherence functions when a certain number of modes are corrected using, say, a deformable mirror. Special cases of long- and short-exposure images are also considered. The results for systems with a circular pupil are obtained as a special case of the annular pupil.

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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.

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PubMed2005

Axial irradiance of a focused beam.

The principal maximum of axial irradiance of a focused beam with a low Fresnel number does not lie at its focal point; instead it lies at a point that is closer to the focusing pupil. It has been shown by the numerical example of a weakly truncated Gaussian beam that its value increases and its location moves closer to the pupil when spherical aberration is introduced into the beam. Such an increase has been referred to as "beyond the conventional diffraction limit." Similarly, an increase in the value and a shift in the location of the principal maximum of axial irradiance of a uniform beam toward the pupil by the introduction of some spherical aberration has been characterized as an unexpected result. We explain why and how such a result comes about and that it neither invalidates any diffraction limit nor is it unexpected. We illustrate this for uniform as well as Gaussian beams of various truncation ratios. Both focused and collimated beams aberrated by spherical aberration or astigmatism are considered.

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PubMed2005

Strehl ratio of a Gaussian beam.

We discuss the Strehl ratio of systems with a Gaussian pupil and determine the range of validity of its approximate expression based on the aberration variance. The results given are equally applicable to propagation of Gaussian beams. The uniform and weakly truncated pupils are considered as limiting cases of a Gaussian pupil. We show that the approximate expression for Strehl ratio in terms of the aberration variance yields a good estimate of the true value for a strongly truncated pupil but a much smaller value for a weakly truncated pupil.

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