Fresnel phasing of segmented mirror telescopes

Shack-Hartmann (S-H) phasing of segmented telescopes is based upon a physical optics generalization of the geometrical optics Shack-Hartmann test, in which each S-H lenslet straddles an intersegment edge. For the extremely large segmented telescopes currently in the design stages, one is led naturally to very large pupil demagnifications for the S-H phasing cameras. This in turn implies rather small Fresnel numbers F for the lenslets; the nominal design for the Thirty Meter Telescope calls for F=0.6. For such small Fresnel numbers, it may be possible to eliminate the lenslets entirely, replacing them with a simple mask containing a sparse array of clear subapertures and thereby also eliminating a number of manufacturing problems and experimental complications associated with lenslets. We present laboratory results that demonstrate the validity of this approach.