1. TPF @ 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

2. TPF @ 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

3. TPF @ Princeton Princeton TPF project (space-based ) Contrast ratio needed: 10 10 Aberrations do not change over time The main source of aberrations is the optical components in the system Very long integration time

4. TPF @ 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?

5. TPF @ Princeton Ideal System

6. TPF @ Princeton Aberrated System I

7. TPF @ Princeton Aberrated System II beat-down

8. TPF @ Princeton Aberrated System III Measured aberration: Corrected image:

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

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

11. TPF @ Princeton

12. 10 min later… where,

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

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

15. TPF @ Princeton Phase aberration

16. TPF @ Princeton Point Spread Function

17. TPF @ Princeton Conventional phase conjugation

18. TPF @ Princeton Point Spread Function (corrected)

19. TPF @ Princeton Components (conventional)

20. TPF @ Princeton Components (optimal)

21. TPF @ Princeton Point Spread Function (corrected)

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

23. TPF @ Princeton Ideal DM