Solutions to linear problems in aberrated optical systems
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Abstract
Linear problems are possibly the kindest problems in physics and mathematics. Given sufficient information, the linear equations describing such problems are intrinsically solvable. The solution can be written as a vector having undergone a linear transformation in a vector space; extracting the solution is simply a matter of inverting the transformation. In an ideal optical system, the problem of extracting the object under investigation would be well defined, and the solution trivial to implement. However, real optical systems are all aberrated in some way, and these aberrations obfuscate the information, scrambling it and rendering it inextricable. The process of detangling the object from the aberrated system is no longer a trivial problem or even a uniquely solvable one, and represents one of the great challenges in optics today. This thesis provides a review of the theory behind optical microscopy in the presence of absent information, an architecture for the modern physical and computational methods used to solve the linear inversion problem, and three distinct application spaces of relevance. I hope you find it useful.
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Attribution 4.0 International