# Optical Image Formation and Processing

## 1st Edition

**Authors:**M Francon

**eBook ISBN:**9780323159593

**Imprint:**Academic Press

**Published Date:**28th July 1979

**Page Count:**234

## Description

Optical Image Formation and Processing describes modern physical optics, particularly concerning interference, diffraction, and a simplified theory of partial coherence. The book also discusses polarization, with emphasis on interference phenomena on polarized light. An image is formed in terms of the filtering of spatial frequencies, filtering that is due to transfer function. The text explains holography—a reconstruction of the image of an object beginning from the diffraction patterns produced by the object. A computer can also create artificial variations from the photographic plate which records the hologram, and can synthesize the hologram. The book cites an example of the synthesis of a hologram by a computer using the principle of binary holograms. The text also reviews some experiments dealing with the properties of lasers associated with temporal coherence and power. The book explains that lasers can carry large amounts of information due to their very high frequencies in the order of 300, 000 gigahertz, and recommends the use of optical fibers as the transmission medium instead of using open air. This book can prove useful for technicians, students, and professor connected with optical physics.

## Table of Contents

Preface

Notation

Chapter 1 Luminous Vibrations

1.1 Monochromatic Light Waves. Temporal Coherence

1.2 The Point Source. Spatial Coherence

1.3 The Vibration Emitted by a Point Source as Received in a Plane Situated at a Distance D from the Source

1.4 The Vibration Emitted by a Point Source as Received in the Focal Plane of a Lens

1.5 Important Comments on the Use of the Preceding Formulas

Chapter 2 Interference

2.1 Principle of Interference. Coherent Vibrations

2.2 Experimental Conditions Needed to Ensure That Interference Phenomena Will Be Observable

2.3 Nature of the Coherent Sources Used to Give Rise to Interference Phenomena

2.4 Location of Two-Beam Interference Fringes

2.5 Interference Phenomena Produced by Two Coherent Point Sources. Young's Interference Fringes

2.6 Interference Phenomena Produced by an Infinite Number of Coherent, Equidistant, Point Sources (Grating)

2.7 Remark on the Structure of the Fringes

2.8 White Light Interference Phenomena

2.9 Stationary Waves

Chapter 3 Diffraction

3.1 The Existence of Diffraction Phenomena

3.2 Principle of Huygens and Fresnel

3.3 Simplified Expression for the Amplitude at an Arbitrary Point in the Plane of Observation. Diffraction at Infinity

3.4 Diffraction Pattern at Infinity Due to a Rectangular Aperture

3.5 Diffraction at Infinity by a Thin Slit

3.6 Diffraction at Infinity by a Circular Aperture

3.7 Translation in Its Own Plane of the Aperture Τ Which Delimits the Wavefront

3.8 Diffraction at Infinity by Two Identical Slits

3.9 Diffraction at Infinity by a Large Number of Identical Apertures Similarly Orientated and Irregularly Distributed

3.10 Complementary Screens, Babinet's Theorem

3.11 Elementary Properties of the Correspondence Between the Aperture and the Diffraction Pattern

3.12 Diffraction at a Finite Distance or Fresnel Diffraction

3.13 Fresnel Zone Plate

Chapter 4 Diffraction Gratings

4.1 Grating Composed of an Infinity of Parallel Slits

4.2 Grating Composed of a Finite Number of Slits

4.3 Blazed Grating

4.4 Construction of Gratings. Ghosts

4.5 Sinusoidal Phase Grating

4.6 Two-Dimensional Gratings

4.7 Diffraction by a Crystal

Chapter 5 Partial Coherence

5.1 Quasi-Monochromatic Vibrations

5.2 Relation Between the Length of a Wavetrain (Coherence Length) and the Line Width of the Radiation Emitted

5.3 Remark

5.4 Receiver Illuminated by a Thermal Source

5.5 Spatial Coherence in the Young Experiment

5.6 Degree of Coherence of Two Points T1, and T2 Illuminated by the Extended Source

5.7 Contrast of the Interference Fringes in Young's Experiment

5.8 Michelson's Method for Measuring the Apparent Diameter of a Star

5.9 Measurement of the Apparent Diameter of a Star by the Method of Stationary Waves

Chapter 6 Interference Phenomena in Polarized Light

6.1 Luminous Vibration in an Isotropic Dielectric Medium. Natural Light

6.2 Polarized Light

6.3 Young's Experiment in Polarized Light

6.4 Anisotropic Dielectric Medium. Uniaxial Medium

6.5 Refracted Rays in a Uniaxial Medium. The Plane of Incidence Is Parallel to the Direction of the Optic Axis

6.6 Polarizers

6.7 Path Difference Caused by Traversing a Birefringent Plate Parallel to the Axis

6.8 Interference Phenomena Produced by a Birefringent Plate

6.9 Applications

Chapter 7 Formation of Images. Filtering of Spatial Frequencies by an Optical Instrument

7.1 Spatially Incoherent and Spatially Coherent Objects

7.2 Image of an Extended Object in Spatially Incoherent Illumination

7.3 Image of an Extended Object in Spatially Coherent Illumination

7.4 Transfer Function of an Optical Instrument. Incoherent Object

7.5 Transfer Function in Coherent Illumination

7.6 Phase Contrast and Strioscopy

Chapter 8 Holography

8.1 Introduction

8.2 Amplitude Transmitted by a Photographic Plate After Development

8.3 The Gabor Hologram. Case Where the Object Is a Simple Luminous Point

8.4 Reconstruction of the Image of a Luminous Point

8.5 Remark

8.6 Utilization of a Coherent Background Inclined at an Angle. The Hologram of Leith and Upatnieks

8.7 Case of a General Object

8.8 Fourier Holograms

8.9 Phase Holograms

8.10 Reflection Holograms and Holograms in Color

8.11 Computer-Generated Holograms

8.12 Binary Holograms of the Fourier Type

8.13 Holograms at Several Levels. Kinoforms

Chapter 9 Interferometry

9.1 Michelson Interferometer

9.2 Observation of the Fringes of Equal Thickness

9.3 Fringes of Equal Inclination

9.4 Visability of the Fringes of Equal Thickness

9.5 Temporal Coherence

9.6 White-Light Fringes

9.7 Fringes Produced by Transparent Plates

9.8 Diminution or Augmentation of the Reflecting Power by Means of Thin Transparent Films

9.9 Multiple-Beam Interferometers: Fabry-Perot Interferometer

9.10 Interference Filters

9.11 Interference Spectroscopy

9.12 Holographic Interferometry

9.13 Speckle Interferometry

9.14 Measurement of Deformations or Displacements of Diffusing Objects by Speckle Interferometry

9.15 Applications of Interference Methods

Chapter 10 Elements of the Optical Processing of Information

10.1 Introduction

10.2 Filtering in Coherent Illumination

10.3 Form Recognition by Means of Autocorrelation

10.4 Autocorrelation Function in a Simple Case

10.5 Detection of Differences Between Two Similar Forms

10.6 Information Storage by Means of Holography

10.7 Attenuation of Noise by Superimposition of Images

10.8 Processing of Images by Computer

Chapter 11 The Optics of Lasers

11.1 Beats Produced by Optical Frequencies

11.2 Interference Phenomena Produced by Two Lasers

11.3 Nonlinear Optics

11.4 Intensity of the Electric Field When It Leaves the Crystal

11.5 Method for Increasing the Intensity of the Harmonic. Index Matching

11.6 Second Harmonic and Crystal Symmetry

11.7 Basic Concepts of Optical Communication Using Fibers

11.8 Waveguides and Optical Components

11.9 Coupling Devices in Integrated Optics

11.10 Sources and Detectors in Integrated Optics

Appendix A Review of Some Elementary Concepts Regarding the Fourier Transformation

A.1 Definition

A.2 Translation

A.3 Dilatation

A.4 Case of Two Variables

A.5 Some Common Fourier Transforms

A.6 Useful Relations

A.7 Convolution

A.8 Transform of a Convolution

A.9 Cross Correlation

A.10 Autocorrelation

A.11 Dirac Distribution

A.12 Convolution of a Function F(ζ) with a Delta Function

A.13 Calculation of a Convolution and of a Correlation in Two Dimensions

A.14 Poisson Distribution of Dirac Comb

A.15 Periodic Function

Appendix Β The Fresnel-Kirchhoff Formula and the Phenomena of Diffraction

B.1 The Helmholtz Equation

B.2 Green's Theorem

B.3 The Helmholz-Kirchhoff Integral

B.4 Diffraction by an Aperture Pierced in a Plane Screen. The Kirchhoff Limiting Conditions

B.5 Fresnel-Kirchhoff Formula

Brief Bibliography

Index

## Details

- No. of pages:
- 234

- Language:
- English

- Copyright:
- © Academic Press 1979

- Published:
- 28th July 1979

- Imprint:
- Academic Press

- eBook ISBN:
- 9780323159593