Space-Time Optics In Shape And Surface Metrology

Basic considerations of similarity between the spatial and temporal frequencies in image formation have been developed along applications for which two classes of examples are given. a) Absolute measurements of optical paths by interferometry in white light ; applications to the determination of surface pping A channelled spectrum (1), observable at the output of a spectroscope set in cascade with a two-beam interferometer illuminated in white light, displays the local path-differences introduced along one arm of the interferometer, the other one being considered as conveying the reference. A relationship holds between the chromatic distribution scaled in temporal frequency and optical delays that are functiortsof time This suggests techniques of longftudinal measurements. Indeed one deals with Fourier transforms both in space and time, allowing to show some equivalence of the channelled spectrum with a Fourier hologram - the reconstruction of longitudinal information being performed at a transverse diffraction plane. This is illustrated in rugosimetry and in the assessient of calibrating tests. b) Statistical properties of random surfaces by spectrat analysis of scattered "Light. By analogy with conventional speckle methods, we have proposed the concept of temporal speckle as the spectrum of the incident radiation spreads over a broad band. It can be stated that no statistical model is needed for surface rugosity and evaluation of the r.m.s. for Gaussian rugosities are presented as illustration. The following text is very close to that of the original lecture and we did not feel the need for any proper introduction to it. A rough idea of the work, which has been given in the abstract, will be further recalled through the fundamentals in the first paragraph below.