Analytical solution of an afocal two freeform mirror design problem

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.