PROPAGATION OF LIGHT IN FREE SPACE A. Correspondence Between the Spatial Harmonic and the Plane Wave B. Transfer Function of Free Space C. Impulse-Response Function of Free Space OPTICAL FOURIER TRANSFORM A. Fourier Transform in the Far Field B. Fourier Transform Using a Lens DIFFRACTION OF LIGHT A. Fraunhofer Diffraction *B. Fresnel Diffraction IMAGE FORMATION A. Ray-Optics Description of Image Formation B. Spatial Filtering C. Single-Lens Imaging System HOLOGRAPHY | Fundamentals of Photonics Bahaa E. A. Saleh Malvin Carl Teich Copyright 1991 John Wiley Sons Inc. ISBNs 0-471-83965-5 Hardback 0-471-2-1374-8 Electronic CHAPTER FOURIER OPTICS PROPAGATION OF LIGHT IN FREE SPACE A. Correspondence Between the Spatial Harmonic Function and the Plane Wave B. Transfer Function of Free Space C. Impulse-Response Function of Free Space OPTICAL FOURIER TRANSFORM A. Fourier Transform in the Far Field B. Fourier Transform Using a Lens DIFFRACTION OF LIGHT A. Fraunhofer Diffraction B. Fresnel Diffraction IMAGE FORMATION A. Ray-Optics Description of Image Formation B. Spatial Filtering C. Single-Lens Imaging System HOLOGRAPHY Josef von Frauenhofer 1787-1826 developed diffraction gratings and contributed to the understanding of light diffraction. His epitaph reads Approximavit sidera he brought the stars nearer. Jean-Baptiste Joseph Fourier 1768-1830 recognized that periodic functions can be considered as sums of sinusoids. Harmonic analysis is the basis of Fourier optics. Dennis Gabor 1900-1979 made the first hologram in 1947. He received the Nobel Prize in 1971. 108 Fourier optics provides a description of the propagation of light waves based on harmonic analysis the Fourier transform and linear systems. The methods of harmonic analysis have proven to be useful in describing signals and systems in many disciplines. Harmonic analysis is based on the expansion of an arbitrary function of time fit as a superposition a sum or an integral of harmonic functions of time of different frequencies see Appendix A Sec. . The harmonic function Fiv cxpij2vi t which has frequency v and complex amplitude F p is the building block of the theory. Several of these functions each with its own value of Fiv are added to construct the function fit as illustrated in Fig. . The complex amplitude Fiv as a function of frequency is called the Fourier transform of fit . This approach is useful for the description of linear systems see Appendix
