# Seminarios

Orthogonal Polynomials in Wavefront Analyis Lunes 20 de Abril 16:00 a 17:00 |
Beam Focusing and Depth of Focus Martes 21 de Abril 11:30 a 13:00 hrs |

**Dr. Virendra N. Mahajan**

The Aerospace Corporation, El Segundo, California

College of Optical Sciences, University of Arizon

**Orthogonal Polynomials in Wavefront Analysis**

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.

**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.

**Biography**

Dr. Virendra N. Mahajan is a graduate of the College of Optical Sciences, University of Arizona, where he is an adjunct professor. He is a Distinguished Engineer at The Aerospace Corporation in El Segundo, California. 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.