Synchronous phase-demodulation of high spatial frequency,   concentric-rings, Placido fringe patterns
  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. 
Manuel Servin
physics.optics physics.ins-det physics.med-ph