the curvature of a mirror causes spherical aberration.
the curvature of a mirror causes spherical aberration.
what effect does the curvature of a mirror?
spherical aberration
paul's idea was to start with a mersenne beam compressor, which looks like a cassegrain made from two (confocal) paraboloids, with both the input and output beams collimated. the compressed input beam is then directed to a spherical tertiary mirror, which results in traditional spherical aberration. paul's key insight is that the secondary can then be converted back to a spherical mirror. one way to look at this is to imagine the tertiary mirror, which suffers from spherical aberration, is replaced by a schmidt telescope, with a correcting plate at its centre of curvature. if the radii of the secondary and tertiary are of the same magnitude, but opposite sign, and if the centre of curvature of the tertiary is placed directly at the vertex of the secondary mirror, then the schmidt plate would lie on top of the paraboloid secondary mirror. therefore, the schmidt plate required to make the tertiary mirror a schmidt telescope is eliminated by the paraboloid figuring on the convex secondary of the mersenne system, as each corrects the same magnitude of spherical aberration, but the opposite sign. also, as the system of mersenne + schmidt is the sum of two anastigmats: the mersenne system is an anastigmat, and so is the schmidt system, the resultant system is also an anastigmat, as third-order aberrations are purely additive. in addition the secondary is now easier to fabricate. this design is also called a mersenne-schmidt, since it uses a mersenne configuration as the corrector for a schmidt telescope.
three-mirror anastigmat
for a spherically curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. the focal length is positive for a concave mirror, and negative for a convex mirror. in the sign convention used in optical design, a concave mirror has negative radius of curvature, so









































where "r" is the radius of curvature of the mirror's surface.









































see radius of curvature (optics) for more information on the sign convention for radius of curvature used here.









































section::::in photography.
focal length