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H. P. Baltes We begin the introductory chapter with a general definition of the inverse optical problem. Next, we discuss the role of prior knowledge and the questions of uniqueness and stability. We then review the various specific inverse problems in optics as well as the contents of Chapters 2 to 6. Finally, we summarize the notation in co herence theory. 1. 1 Direct and Inverse Problems in Optical Physics The "direct" or "normal" problem in optical physics is to :Jredict the emission or propagation of radiation on the basis of a known constitution of sources or scat terers. The "inverse" or "indirect" problem is to deduce features of sources or scatterers from the detection of radiation. An intuitive solution of the optical inverse problem is commonplace: we infer the size, shape, surface texture, and ma terial of objects from their scattering and absorption of light as detected by our eyes. Intuition has to give way to mathematical reconstruction as soon as we wish to analyze optical data beyond their visual appearance. Examples are the extrapola tion and deblurring of optical images, the reconstruction from intuitively inacces sible data such as defocused images and interferograms, or the search for information that is "lost" in the detection process such as the phase. Following CHADAN and SABATIER [1. 1], a general definition of inverse optical problems can be attempted as follows. We describe the sources and scatterers by the set (1.
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When, in the spring of 1979, H.P. Baltes presented me with the precursor of this vo 1 ume, the book on "Inverse Source Problems in Opti cs", I expressed my gratitude in a short note, 11hich in translation, reads: "Dear Dr. Ba ltes, the mere titl e of your unexpected gift evokes memori es of a period, which, in the terminology of your own contribution, would be described as the Stone Age of the Inverse Problem. Those were pleasant times. Walter Kohn and I lived in a cave by ourselves, drew pictures on the walls, and nobody seemed to care. Now, however, Inversion has become an Industry, which I contemplate with as much bewilderment as a surviving Tasmanian aborigine gazing at a modern oil refinery with its towers, its fl ares, and the confus i ng maze of its tubes." The present volume makes me feel even more aboriginal - impossible for me to fathom its content. What I can point out, however, is one of the forgotten origins of the Inverse Scattering Problem of Quantum Mechanics: Werner Heisenberg's "S-Matrix Theory" of 1943. This grandiose scheme had the purpose of eliminating the notion of the Hamiltonian in favour of the scattering operator. If Successful, it would have done away once and for all with any kind of inverse problem.