Optics

Optical Systems and Processes - download pdf or read online

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By Joseph Shamir

ISBN-10: 0819432261

ISBN-13: 9780819432261

A concise, finished reference textual content protecting electro-optical structures, optical method layout, optical physics, holography, Fourier optics, and optical metrology. Emphasizes actual perception geared toward engineering functions. compatible as a sophisticated undergraduate or graduate point textual content; difficulties and ideas are included.

Contents

- Preface
- Introduction
- evaluate of electromagnetic wave propagation
- Linear structures theory
- Wavefront transformations
- easy optical systems
- Non-ideal optical systems
- Statistical elements of light
- Interference and interferometers
- Polarization
- Spatial mild modulation
- Holography
- complicated operator algebra
- Optical details processing
- A: precis of operator relations
- B: Bibliography
- C: difficulties and solutions
- D: Index

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Extra info for Optical Systems and Processes

Sample text

22 LINEAR SYSTEMS THEORY can be defined as δ(x) = lim a rect(ax). (3–8) a→∞ For our present purpose it will be more convenient to derive the δ function from the Gaussian function. In one dimension, the Gaussian function is defined as exp(−a 2 πx 2 ) and then the δ function is derived as the limit [Fig. 3–1(b)], δ(x) = lim a e−a 2π x2 a→∞ . (3–9) It is easy to show that if we integrate this equation, the integral of the right-hand side of the expression is always 1 regardless of the value of a. Therefore, we may define this value also at the limit.

If we disregard nonlinear effects, light propagation may be considered a linear process which can be treated using the advanced procedures of linear systems theory. Traditional linear systems theory was developed for the treatment of temporal signals that are modified by some electronic instrument. In optics we shall be mainly interested in two-dimensional spatial signals. This chapter contains a review of linear systems theory adapted to two-dimensional signals. Assuming that the reader is familiar with the basic concepts of linear systems and Fourier analysis, we shall not dwell on mathematical rigor and many of the results will be stated without proof.

4–7) for the PSF, the convolution of Eq. (4–3) can be written in the form uout(x, y, d) = 1 ejkd Q ∗ uin (x, y, 0), jλd d (4–9) where the convolution is evaluated in two dimensions over the xy plane. Writing explicitly the convolution operation and resubstituting the quadratic phase factor we obtain uout(x, y, d) = ejkd jλd ∞ −∞ k ej 2d [(x−x ) 2 +(y−y )2 ] uin (x , y , 0) dx dy . (4–10) This integral, usually derived in different ways, is generally known as the Fresnel– Kirchhoff diffraction integral [4, 10, 14, 29].

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Optical Systems and Processes by Joseph Shamir


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