  Here a synchronous phase-demodulation method for high spatial frequency
(HSF), concentric-rings Placido fringe pattern is proposed. The earliest use of
this concentric-rings pattern was to gauge non-spherical irregularities of the
human cornea by Portuguese ophthalmologist Antonio Placido in 1880. Most modern
corneal topographers use Placido patterns to test human cornea irregularities;
a field of application of this paper. Another field of application of HSF
conic-carrier fringe patterns is to test wavefronts using what may be called
the Placido-Hartmann screen test. These screens would be formed by periodic
concentric ring apertures. A Placido-Hartmann test would be sensitive to the
radial slope of the wavefront under measurement. Finally as in the
Hartmann-Shack test, one may use a radial lenslet array of toroidal-shaped
lenses to test the radial slope of a wavefront at the focal plane. The main
advantage of estimating the radial slope of a wavefront using a HSF Placido
pattern is that a single radial slope image is sufficient to integrate the full
wavefront shape.
