The University of Montana
Mathematics Awareness Week Colloquium

Powerful telescopes on the surface of the earth are capable of imaging very faint objects. However, the clarity of these images is no better than that which can be obtained from an amateur's telescope with a 6 inch mirror---hence, the Hubble Space Telescope. This blurring of astronomical images is due to distortions of the wave fronts of light caused by atmospheric temperature variations. One way to correct these distortions is to physically "undistort" the wave fronts with deformable mirrors. This is called Adaptive Optics (AO). Recently, an alternative, software-based approach called Phase Diversity (PD) has been developed. In this talk, I will present an overview of AO and PD, touching on a variety of topics from Physics, Mathematics, and Computer Science. These topics include:

• Stochastic Processes (used to model atmospheric turbulence caused by wind).
• Control Theory (used in the control of deformable mirrors in AO).
• Mathematical Modeling (used to quantify the relationship between the noisy, blurred, recorded image and the "true" image).
• Inverse Problems (used to estimate the true image from the recorded images in PD).
• Computational Mathematics (used to formulate algorithms to efficiently solve the PD estimation problem).
• Computer Science (used to implement these algorithms on parallel computers).

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