The periskop is a symmetrical version of the landscape lens, meaning the prescription layout is roughly a mirror image around the stop. The landscape lens is a single meniscus in front of or behind the stop. Symmetry reduces the odd aberrations (coma, distortion, lateral color).
Spherical aberration is minimized by the lens shape.
Distance from the stop to the lens is chosen to compensate for field curvature. Typically the distance is set to flatten sagittal field curvature since it is less pleasing to the eye than longitudinal.
The ideal lens shape and distance from the stop can be calculated from the corresponding aberration formulae.
Alternatively, it takes only an hour or so to bang out an optical design in Zemax: 15 minutes to get the Periskop solution and 45 minutes of tinkering with better corrected variations before undoing and saving the Periskop solution.
Note as a landscape lens derivative, the design family is more appropriate for wider fields of view i.e. landscapes rather than portraits.
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