Analytical solution of an afocal two freeform mirror design problem

Abstract

Abstract:We investigate a new afocal two freeform mirror design problem in first order optics. The resulting first-order partial differential equations for the freeform two mirror system have an analytic solution with the sole condition that the x-y and x'-y' axes are parallel. Two selected solutions are presented. One of them is semiaplanatic (fulfilling the aplanatic condition only for the x-coordinates), while the other is, to our knowledge, the first example of an aplanatic two-mirror system without rotational symmetry. A 11(12), 3292-3307 (1994).

An exploration of the freeform two-mirror off-axis solution space

“…This was mitigated by unconstraining aplanetism on three distinct pupil, field and image plane axis combinations [9]. This observation was made earlier in literature in a different formalism and the authors have introduced the concept of semi-aplanetic to describe such systems [11].…”

“…This allows integrating numerically the high order partial derivatives to construct a 3D representation of the surfaces. It has been shown in literature that a closed-form solution of the surfaces could be found in the afocal case [11] or axial-symmetric case [12,13].…”

Starting point designs for freeform four-mirror systems

“…The freeform "grown" surfaces have more degrees of freedom for aberration compared to conic surfaces but are the most complicated to implement and are currently limited to two mirrors (a four-mirror system can be generated by putting two "grown" surface systems back-to-back). 4,5 The two symmetry types shown in Table 1 are rotational and plane. For obscured starting points, rotational symmetry may be considered.…”