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  1. Driven by the development of freeform imaging systems, we have combined several concepts and techniques from the literature to analytically generate unobscured freeform starting point designs that are corrected through the third-order image degrading aberrations. The surfaces used in these starting point designs are described as a base off-axis conic that images stigmatically for the central field point, also known as a Cartesian reflector, with an aspheric departure “cap” (quartic with the aperture) added to the base off-axis conic to correct for the third-order image degrading aberrations. Once the aspheric caps are added to the surfaces, the system is then optimized using higher order freeform terms while leaving second-order terms frozen to preserve the focal length of the system during optimization. This technique is used to survey the three-mirror freeform imager solution space. Several systems that are the result of this technique are shown, with different numbers of internal images, internal pupil conjugates and folding geometries. 
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