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Dr. Virendra "Vini" N. Mahajan

Dr. Virendra "Vini" N. Mahajan

Distinguished Engineer
The Aerospace Corporation (retired)

26622 Deepbrook Dr

Rancho Palos Verdes CA 90275
United States

tel: 310 544 3290
E-mail: virmahajan12@gmail.com

Area of Expertise

Optical imaging and aberrations


Dr. Virendra N. Mahajan is a graduate of the College of Optical Sciences, University of Arizona, where he is an adjunct professor. He was a Distinguished Engineer at The Aerospace Corporation in El Segundo, California until his retirement in May 2014. He has taught short courses on optical aberrations at the annual meetings of the Optical Society of America and SPIE. He has published numerous papers on diffraction, aberrations, adaptive optics, and acousto-optics. He is a fellow of the Optical Society of America, SPIE and the Optical Society of India. He was a Topical Editor of Optics Letters in the area of Optical Imaging Diffraction from 2002 to 2005. He is the author of Aberration Theory Made Simple (1991), editor of Effects of Aberrations in Optical Imaging (1993), author of Optical Imaging and Aberrations, Part I: Ray Geometrical Optics (1998), and Part II: Wave Diffraction Optics (2001), all published by SPIE.

Lecture Title(s)

Zernike Polynomials and Aberration Balancing
For small aberrations, the Strehl ratio of an imaging system depends on the aberration variance. Its aberration function is expanded in terms of Zernike polynomials, which are orthogonal over a circular aperture. Their advantage lies in the fact that they can be identified with classical aberrations balanced to yield minimum variance, and thus maximum Strehl ratio. We discuss classical aberrations, balanced aberrations, and Zernike polynomials for systems with circular apertures. How these polynomials change for an annular or a Gaussian pupil is also be discussed.

Gaussian Apodization and Beam Propagation
The point-spread and optical transfer functions of a system with a Gaussian pupil are discussed and compared with those for a uniformly illuminated pupil. The results are equally applicable to the propagation of Gaussian beams, such as in laser transmitters. The results are extended to the case of weakly truncated Gaussian pupils, i.e., Gaussian beams that are very narrow compared to the pupil diameter. The analytical results are illustrated by numerical examples.

Beam Focusing and Depth of Focus
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. Its value and location depends on two competing factors: inverse square-law dependence on the distance and the defocus aberration. The value increases and its location moves closer to the pupil when spherical aberration or astigmatism is introduced into the beam. We explain why and how such a result comes about. We illustrate this for uniform as well as Gaussian beams. Focused as well as collimated beams are considered.

Imaging Through Atmospheric Turbulence
In ground-based astronomy, the wavefront of light from a star is distorted as it propagates through atmospheric turbulence, thus degrading the quality of an image. We discuss atmospheric coherence length, MTF reduction factor, the short- and long-exposure images, limiting resolution regardless of how large the telescope aperture is, aberration variance and Zernike aberration coefficients, and the use of adaptive optics to improve image quality.

"Effect of Random Motion on Image Quality"
There is always some image motion during an exposure interval. Source of image motion may, for example, be vibration of optical elements and servo dither in a pointing system. In the case of beam transmitting systems, the beam itself may have some motion associated with it. We discuss the time-averaged PSF, Strehl ratio, encircled power, and OTF for an imaging system undergoing Gaussian random motion. A simple approximate model based on a Gaussian approximation of its motion-free PSF is also developed, and numerical results provided by it are compared with the exact results.

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