Файл: Ersoy O.K. Diffraction, Fourier optics, and imaging (Wiley, 2006)(ISBN 0471238163)(427s) PEo .pdf

15.8A Simple Algorithm for Construction of 3-D Point

16.2.4Information Capacity, Resolution, Bandwidth, and

16.2.6Distortions Due to Change of Wavelength and/or Hologram Size Between Construction and

16.3The Method of POCS for the Design of Binary

16.5Optimal Decimation-in-Frequency Iterative Interlacing

16.6.1Computer Experiments with the Lohmann-ODIFIIT

17.Computerized Imaging Techniques I:

18.Computerized Imaging II: Image

18.6Reconstruction of a Signal From its

Chapter 5 discusses the Fresnel and Fraunhofer approximations that allow diffraction to be expressed in terms of the Fourier transform. As a special application area for these approximations, diffraction gratings with many uses are described.

Diffraction is usually discussed in terms of forward wave propagation. Inverse diffraction covered in Chapter 6 is the opposite, involving inverse wave propagation. It is important in certain types of imaging as well as in iterative methods of optimization used in the design of optical elements. In this chapter, the emphasis is on the inversion of the Fresnel, Fraunhofer, and angular spectrum representations.

The methods discussed so far are typically valid for wave propagation near the z- axis, the direction of propagation. In other words, they are accurate for wave propagation directions at small angles with the z-axis. The Fresnel and Fraunhofer approximations are also not valid at very close distances to the diffraction plane. These problems are reduced to a large extent with a new method discussed in Chapter 7. It is called the near and far field approximation (NFFA) method. It involves two major topics: the first one is the inclusion of terms higher than second order in the Taylor series expansion; the second one is the derivation of equations to determine the semi-irregular sampling point positions at the output plane so that the FFT can still be used for the computation of wave propagation. Thus, the NFFA method is fast and valid for wide-angle, near and far field wave propagation applications.

When the diffracting apertures are much larger than the wavelength, geometrical optics discussed in Chapter 8 can be used. Lens design is often done by using geometric optics. In this chapter, the rays and how they propagate are described with equations for both thin and thick lenses. The relationship to waves is also addressed.

Imaging with lenses is the most classical type of imaging. Chapters 9 and 10 are reserved to this topic in homogeneous media, characterizing such imaging as a linear system. Chapter 9 discusses imaging with coherent light in terms of the 2-D Fourier transform. Two important applications, phase contrast microscopy and scanning confocal microscopy, are described to illustrate how the theory is used in practice.

Chapter 10 is the continuation of Chapter 9 to the case of quasimonochromatic waves. Coherent imaging and incoherent imaging are explained. The theoretical basis involving the Hilbert transform and the analytic signal is covered in detail. Optical aberrations and their evaluation with Zernike polynomials are also described.

The emphasis to this point is on the theory. The implementation issues are introduced in Chapter 11. There are many methods of implementation. Two major ones are illustrated in this chapter, namely, photographic films and plates and electron-beam lithography for diffractive optics.

In Chapters 9 and 10, the medium of propagation is assumed to be homogeneous (constant index of refraction). Chapter 12 discusses wave propagation in inhomogeneous media. Then, wave propagation becomes more difficult to compute numerically. The Helmholtz equation and the paraxial wave equation are generalized to inhomogeneous media. The beam propagation method (BPM) is introduced as a powerful numerical method for computing wave propagation in

inhomogenous media. The theory is illustrated with the application of a directional coupler that allows light energy to be transferred from one waveguide to another.

Holography as the most significant 3-D imaging technique is the topic of Chapter

13.The most basic types of holographic methods including analysis of holographic imaging, magnification, and aberrations are described in this chapter.

In succeeding chapters, diffractive optical elements (DOEs), new modes of imaging, and diffraction in the subwavelength scale are considered, with extensive emphasis on numerical methods of computation. These topics are also related to signal/image processing and iterative optimization techniques discussed in Chapter

14.These techniques are also significant for the topics of previous chapters, especially when optical images are further processed digitally.

The next two chapters are devoted to diffractive optics, which is creation of holograms, more commonly called DOEs, in a digital computer, followed by a recording system to create the DOE physically. Generation of a DOE under implementational constraints involves coding of amplitude and phase of an incoming wave, a topic borrowed from communication engineering. There are many such methods. Chapter 15 starts with Lohmann’s method, which is the first such method historically. This is followed by two methods, which are useful in a variety of waves such as 3-D image generation, and a method called one-image-only holography, which is capable of generating only the desired image while suppressing the harmonic images due to sampling and nonlinear coding of amplitude and phase. The final section of the chapter is on the binary Fresnel zone plate, which is a DOE acting as a flat lens.

Chapter 16 is a continuation of Chapter 15, and covers new methods of coding DOEs and their further refinements. The method of projections onto convex sets (POCS) discussed in Chapter 14 is used in several ways for this purpose. The methods discussed are virtual holography, which makes implementation easier, iterative interlacing technique (IIT), which makes use of POCS for optimizing a number of subholograms, the ODIFIIT, which is a further refinement of IIT by making use of the decimation-in-frequency property of the FFT, and the hybrid Lohmann–ODIFIIT method, resulting in considerably higher accuracy.

Chapters 17 and 18 are on computerized imaging techniques. The first such technique is synthetic aperture radar (SAR) covered in Chapter 17. In a number of ways, a raw SAR image is similar to the image of a DOE. Only further processing, perhaps more appropriately called decoding, results in a reconstructed image of a terrain of the earth. The images generated are very useful in remote sensing of the earth. The principles involved are optical and diffractive, such as the use of the Fresnel approximation.

In the second part of computerized imaging, computed tomography (CT) is covered in Chapter 18. The theoretical basis for CT is the Radon transform, a cousin of the Fourier transform. The projection slice theorem shows how the 1-D Fourier transforms of projections are used to generate slices of the image spectrum in the 2- D Fourier transform plane. CT is highly numerical, as evidenced by a number of algorithms for image reconstruction in the rest of the chapter.