Optika '80 szimpózium - Előadások [antikvár]

I-l OPTICS AND THE FOURIER TRANSFORM A. MARECHAL Institut d'Optique B.P, 43 - 91406 ORSAY Cedex France The Fourier Transform has already played an important role in the development of optics in the past and seems to be a very powerful tool in various domains of modern optics. We intend to recall some aspects of its impact in classical optics (either incoherent or coherent) and to give some examples of its present role in the field of temporal optics, specially in the ^study of short pulses, in the methods for pulse shaping etc The viewpoint of applied optics will be adopted, preferably to pure theoretical developments. The Fourier transform is a powerful mathematical tool that can be very efficient when it expresses physical mechanisms : in that case it offers the possibility of efficient analog realizations of mathematical operations. In other cases it offers alternate formulation of physical processes and has led to fundamental concepts like the optical transfer functions. A/ THE FOURIER TRANSFORM IN CLASSICAL OPTICS We will evoque two cases where coherence problems do not appear, and then shift to coherent optics. 1 - Formation of images in incoherent illumination The fundamental mechanism an be represented by a convolution between the object and the diffraction pattern, or more generally the image of an isolated point. When expressed in the Fourier space this mechanism leads to the notion of optical transfer function, as it has been shown by P.M. Duffieux . Optics and electronics have found there a common language. 2 - Fourier transform spectroscopy The Fourier relation between spectrum and interferogram had already been pointed out by Michelson and it was remarkably developped by Jacquinot, Felgett, P.and J. Connesjand others, primarily for high resolution. Interferometric techniques can also be very helpful for moderate resolutions. It was shown recently that the detection of pollutants like S02, No2 etc in the atmosphere (gases having a quasi periodic spectrum) can be performed by a very simple birefringent interferometer adjusted to a characteristic optical path difference related to the periodicity in the spectrum. In tliat case the Fourier transform has led to a useful optical detector. - 9 -