Princeton The Beat-Down Phenomenon in Adaptive Optics Amir Give’on Department of Mechanical and Aerospace Engineering, Princeton University Adviser: N.J. Kasdin Jan 2004

Princeton Ever wondered why phase conjugation does not work? Amir Give’on Department of Mechanical and Aerospace Engineering, Princeton University Adviser: N.J. Kasdin Jan 2004

Princeton Princeton TPF project (space-based ) Contrast ratio needed: Aberrations do not change over time The main source of aberrations is the optical components in the system Very long integration time

Princeton Problem: Given an estimate of the wavefront and a realistic DM model, what should be the DM’s shape that will create the most optimal contrast in the image plane?

Princeton Ideal System

Princeton Aberrated System I

Princeton Aberrated System II beat-down

Princeton Aberrated System III Measured aberration: Corrected image:

Princeton Suppose we measure the phase aberration up to some maximum spatial frequency: We may also decompose,

Princeton The components are given by the inner product: And with a bit of manipulations…

Princeton

10 min later… where,

Princeton Optimal Correction The corrected image is given by, The exponential term could be written as,

Princeton While the cost function minimized in conventional phase conjugation is: The cost function we are going to minimize now will be:

Princeton Phase aberration

Princeton Point Spread Function

Princeton Conventional phase conjugation

Princeton Point Spread Function (corrected)

Princeton Components (conventional)

Princeton Components (optimal)

Princeton Point Spread Function (corrected)

Princeton Answer: The shape that will minimize the mean square sum of the components in the series for the exponential term.

Princeton Ideal DM