In this dissertation fully general conditions are presented to correct linear and quadratic field dependent aberrations that do not use any symmetry. They accurately predict the change in imaging aberrations in the presence of lower order field dependent aberrations. The definitions of the image, object, and coordinate system are completely arbitrary. These conditions are derived using a differential operator on the scalar wavefront function. The relationships are verified using ray trace simulations of a number of systems with varying degrees of complexity. The math is shown to be extendable to provide full expansion of the scalar aberration function about field. These conditions are used to guide the design of imaging systems starting with only paraxial surface patches, then growing freeform surfaces that maintain the analytic conditions satisfied for each point in the pupil. Two methods are proposed for the design of axisymmetric and plane symmetric optical imaging systems. Design examples are presented as a proof of the concept.
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