光学原理 第7版PDF|Epub|txt|kindle电子书版本网盘下载

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Ⅰ Basic properties of the electromagnetic field1

1.1 The electromagnetic field1

1.1.1 Maxwell's equations1

1.1.2 Material equations2

1.1.3 Boundary conditions at a surface of discontinuity4

1.1.4 The energy law of the electromagnetic field7

1.2 The wave equation and the velocity of light11

1.3 Scalar waves14

1.3.1 Plane waves15

1.3.2 Spherical waves16

1.3.3 Harmonic waves.The phase velocity16

1.3.4 Wave packets.The group velocity19

1.4 Vector waves24

1.4.1 The general electromagnetic plane wave24

1.4.2 The harmonic electromagnetic plane wave25

（a）Elliptic polarization25

（b）Linear and circular polarization29

（c）Characterization of the state of polarization by Stokes parameters31

1.4.3 Harmonic vector waves of arbitrary form33

1.5 Reflection and refraction of a plane wave38

1.5.1 The laws of reflection and refraction38

1.5.2 Fresnel formulae40

1.5.3 The reflectivity and transmissivity;polarization on reflection and refraction43

1.5.4 Total reflection49

1.6 Wave propagation in a stratified medium.Theory of dielectric films54

1.6.1 The basic difierential equations55

1.6.2 The characteristic matrix of a stratified medium58

（a）A homogeneous dielectric film61

（b）A stratified medium as a pile of thin homogeneous films62

1.6.3 The reflection and transmission coefficients63

1.6.4 A homogeneous dielectric film64

1.6.5 Periodicallv stratified media70

Ⅱ Electromagnetic potentials and polarization75

2.1 The electrodynamic potentials in the vacuum76

2.1.1 The vector and scalar potentials76

2.1.2 Retarded potentials78

2.2 Polarization and magnetization80

2.2.1 The potentials in terms of polarization and magnetization80

2.2.2 Hertz vectors84

2.2.3 The field of a linear electric dipole85

2.3 The Lorentz-Lorenz formula and elementary dispersion theory89

2.3.1 The dielectric and magnetic susceptibilities89

2.3.2 The efiective field90

2.3.3 The mean polarizability:the Lorentz-Lorenz formula92

2.3.4 Elementary theory of dispersion95

2.4 Propagation of electromagnetic waves treated by integral equations103

2.4.1 The basic integral equation104

2.4.2 The Ewald-Oseen extinction theorem and a rigorous derivation of the Lorentz-Lorenz formula105

2.4.3 Refraction and reflection of a plane wave.treated with the help of the Ewald-Oseen extinction theorem110

Ⅲ Foundations of geometrical optics116

3.1 Approximation for very short wavelengths116

3.1.1 Derivation of the eikonal equation117

3.1.2 The light rays and the intensity law of geometrical optics120

3.1.3 Propagation of the amplitude vectors125

3.1.4 Generalizations and the limits of validity of geometrical optics127

3.2 General properties of rays129

3.2.1 The differential equation of light rays129

3.2.2 The laws of refraction and reflection132

3.2.3 Ray congruences and their focal properties134

3.3 Other basic theorems of geometrical optics135

3.3.1 Lagrange's integral invariant135

3.3.2 The principle of Fermat136

3.3.3 The theorem of Malus and Dupin and some related theorems139

Ⅳ Geometrical theory of optical imaging142

4.1 The characteristic functions of Hamilton142

4.1.1 The point characteristic142

4.1.2 The mixed characteristic144

4.1.3 The angle characteristic146

4.1.4 Approximate form of the angle characteristic of a refracting surface of revolution147

4.1.5 Approximate form of the angle characteristic of a reflecting surface of revolution151

4.2 Perfect imaging152

4.2.1 General theorems153

4.2.2 Maxwell's'fish-eye'157

4.2.3 Stigmatic imaging of surfaces159

4.3 Projective transformation（collineation）with axial symmetry160

4.3.1 General formulae161

4.3.2 The telescopic case164

4.3.3 Classification of projective transformations165

4.3.4 Combination of projective transformations166

4.4 Gaussian optics167

4.4.1 Refracting surface of revolution167

4.4.2 Reflecting surface of revolution170

4.4.3 The thick lens171

4.4.4 The thin lens174

4.4.5 The general centred system175

4.5 Stigmatic imaging with wide-angle pencils178

4.5.1 The sine condition179

4.5.2 The Herschel condition180

4.6 Astigmatic pencils of rays181

4.6.1 Focal properties of a thin pencil181

4.6.2 Refraction ofa thin pencil182

4.7 Chromatic aberration.Dispersion by a prism186

4.7.1 Chromatic aberration186

4.7.2 Dispersion by a prism190

4.8 Radiometry and apertures193

4.8.1 Basic concepts of radiometry194

4.8.2 Stops and pupils199

4.8.3 Brightness and illumination of images201

4.9 Ray tracing204

4.9.1 Oblique meridional rays204

4.9.2 Paraxial rays207

4.9.3 Skew rays208

4.10 Design of aspheric surfaces211

4.10.1 Attainment of axial stigmatism211

4.10.2 Attainmcnt of aplanatism214

4.11 Image-reconstruction from projections（computerized tomography）217

4.11.1 Introduction217

4.11.2 Beam propagation in an absorbing medium218

4.11.3 Ray integrals and projections219

4.11.4 The N-dimensional Radon transform221

4.11.5 Reconstruction of cross-sections and the Projection-slice theorem of computerized tomography223

Ⅴ Geometrical theory of aberrations228

5.1 Wave and ray aberrations;the aberration function229

5.2 The perturbation eikonal of Schwarzschild233

5.3 The primary（Seidel）aberrations236

（a）Spherical aberration（B≠0）238

（b）Coma（F≠0）238

（c）Astigmatism（C≠0）and curvature of field（D≠0）240

（d） Distortion（E≠0）243

5.4 Addition theorem for the primary aberrations244

5.5 The primary aberration coefficients of a general centred lens system246

5.5.1 The Seidel formulae in terms of two paraxial rays246

5.5.2 The Seidel formulae in terms of one paraxial ray251

5.5.3 Petzval's theorem253

5.6 Example:The primary aberrations of a thin lens254

5.7 The chromatic aberration of a general centred lens system257

Ⅵ Image-forming instruments261

6.1 The eye261

6.2 The camera263

6.3 The refracting telescope267

6.4 The reflecting telescope274

6.5 Instruments of illumination279

6.6 The microscope281

Ⅶ Elements of the theory of interferenee and interferometers286

7.1 Introduction286

7.2 Interference of two monochromatic waves287

7.3 Two-beam interference:division of wave-front290

7.3.1 Young's experiment290

7.3.2 Fresnel's mirrors and similar arrangements292

7.3.3 Fringes with quasi-monochromatic and white light295

7.3.4 Use of slit sources;visibility of fringes296

7.3.5 Application to the measurement of optical path difference:the Rayleigh interferometer299

7.3.6 Application to the measurement of angular dimensions of sources:the Michelson stellar interferometer302

7.4 Standing waves308

7.5 Two-beam interference:division of amplitude313

7.5.1 Fringes with a plane-parallel plate313

7.5.2 Fringes with thin films;the Fizeau interferometer318

7.5.3 Localization of fringes325

7.5.4 The Michelson interferometer334

7.5.5 The Twyman-Green and related interferometers336

7.5.6 Fringes with two identical plates:the Jamin interferometer and interference microscopes341

7.5.7 The Mach-Zehnder interferometer;the Bates wave-front shearing inter-ferometer348

7.5.8 The coherence length;the application of two-beam interference to the study of the fine structure of spectral lines352

7.6 Multiple-beam interference359

7.6.1 Multiple-beam fringes with a plane-parallel plate360

7.6.2 The Fabry-Perot interferometer366

7.6.3 The application of the Fabry-Perot interferometer to the study of the fine structure of spectral lines370

7.6.4 The application of the Fabry-Perot interferometer to the comparison of wavelengths377

7.6.5 The Lummer-Gehrcke interferometer380

7.6.6 Interference filters386

7.6.7 Multiple-beam fringes with thin films391

7.6.8 Multiple-beam fringes with two plane-parallel plates401

（a）Fringes with monochromatic and quasi-monochromatic light401

（b）Fringes of superposition405

7.7 The comparison of wavelengths with the standard metre409

Ⅷ Elements of the theory of diffraction412

8.1 Introduction412

8.2 The Huygens-Fresnel principle413

8.3 Kirchhoff's diffraction theory417

8.3.1 The integral theorem of Kirchhoff417

8.3.2 Kirchhoff's diffraction theory421

8.3.3 Fraunhofer and Fresnel diffraction425

8.4 Transition to a scalar theory430

8.4.1 The image field due to a monochromatic oscillator431

8.4.2 The totalimage field434

8.5 Fraunhofer diffraction at apertures of various forms436

8.5.1 The rectangular aperture and the slit436

8.5.2 The circular aperture439

8.5.3 Other forms of aperture443

8.6 Fraunhofer diffraction in optical instruments446

8.6.1 Diffraction gratings446

（a）The principle of the diffraction grating446

（b）Types of grating453

（c）Grating spectrographs458

8.6.2 Resolving power of image-forming systems461

8.6.3 Image formation in the microscope465

（a）Incoherent illumination465

（b）Coherent illumination-Abbe's theory467

（c）Coherent illumination-Zemike's phase contrast method of observation472

8.7 Fresnel diffraction at a straight edge476

8.7.1 The diffraction integral476

8.7.2 Fresnel's integrals478

8.7.3 Fresnel diffraction at a straight edge481

8.8 The three-dimensional light distribution near focus484

8.8.1 Evaluation of the diffraction integral in terms of Lommel functions484

8.8.2 The distribution of intensity489

（a）Intensity in the geometrical focal plane490

（b）Intensity along the axis491

（c）Intensity along the boundary of the geometrical shadow491

8.8.3 The integrated intensity492

8.8.4 The phase behaviour494

8.9 The boundary diffraction wave499

8.10 Gabor's method of imaging by reconstructed wave-fronts（holography）504

8.10.1 Producing the positive hologram504

8.10.2 The reconstruction506

8.11 The Rayleigh-Sommerfeld diffraction integrals512

8.11.1 The Rayleigh diffraction integrals512

8.11.2 The Rayleigh-Sommerfeld diffraction integrals514

Ⅸ The diffraction theory of aberrations517

9.1 The diffraction integral in the presence of aberrations518

9.1.1 The diffraction integral518

9.1.2.The displacement theorem.Change of reference sphere520

9.1.3.A relation between the intensity and the average deformation of wave-fronts522

9.2 Expansion of the aberration function523

9.2.1 The circle polynomials of Zemike523

9.2.2 Expansion of the aberration function525

9.3 Tolerance conditions for primary aberrations527

9.4 The diffraction pattem associated with a single aberration532

9.4.1 Primary spherical aberration536

9.4.2 Primary coma538

9.4.3 Primary astigmatism539

9.5 Imaging of extended objects543

9.5.1 Coherent illumination543

9.5.2 Incoherent illumination547

Ⅹ Interference and diffraction with partially coherent light554

10.1 Introduction554

10.2 A complex representation of real polychromatic fields557

10.3 The correlation functions of light beams562

10.3.1 Interference of two partially coherent beams.The mutual coherence function and the complex degree of coherence562

10.3.2 Spectral representation of mutual coherence566

10.4 Interference and diffraction with quasi-monochromatic light569

10.4.1 Interference with quasi-monochromatic light.The mutual intensity569

10.4.2 Calculation of mutual intensity and degree of coherence for light from an extended incoherent quasi-monochromatic source572

（a）The van Cittert-Zernike theorem572

（b）Hopkins'formula577

10.4.3 An example578

10.4.4 Propagation of mutual intensity580

10.5 Interference with broad-band light and the spectral degree of coherence.Correlation-induced spectral changes585

10.6 Some applications590

10.6.1 The degree of coherence in the image of an extended incoherent quasi-monochromatic source590

10.6.2 The influence of the condenser on resolution in a microscope595

（a） Critical illumination595

（b）K？hler's illumination598

10.6.3 Imaging with partially coherent quasi-monochromatic illumination599

（a）Transmission of mutual intensity through an optical system599

（b）Images of transilluminated objects602

10.7 Some theorems relating to mutual coherence606

10.7.1 Calculation of mutual coherence for light from an incoherent source606

10.7.2 Propagation of mutual coherence609

10.8 Rigorous theory of partial coherence610

10.8.1 Wave equations for mutual coherence610

10.8.2 Rigorous formulation of the propagation law for mutual coherence612

10.8.3 The coherence time and the effective spectral width615

10.9 Polarization properties of quasi-monochromatic light619

10.9.1 The coherency matrix of a quasi-monochromatic plane wave619

（a）Completely unpolarized light（natural light）624

（b）Complete polarized light624

10.9.2 Some equivalent representations.The degree of polarization of a light wave626

10.9.3 The Stokes parameters of a quasi-monochromatic plane wave630

Ⅺ Rigorous difiraction theory633

11.1 Introduction633

11.2 Boundary conditions and surface currents635

11.3 Diffraction by a plane screen:electromagnetic form of Babinet's principle636

11.4 Two-dimensioual diffiaction by a plane screen638

11.4.1 The scalar nature of two-dimensional electromagnetic fields638

11.4.2 An angular spectrum of plane waves639

11.4.3 Formulation in terms of dual integral equations642

11.5 Two-dimensional diffraction of a plane wave by a half-plane643

11.5.1 Solution of the dual integral equations for E-polarization643

11.5.2 Expression of the solution in terms of Fresnel integrals645

11.5.3 The uature of the solution648

11.5.4 The solution for H-polarization652

11.5.5 Some numerical calculations653

11.5.6 Comparison with approximate theory and with experimental results656

11.6 Three-dimensional diffraction of a plane wave by a half-plane657

11.7 Diffraction of a field due to a localized source by a half-plane659

11.7.1 A line-current parallel to the diffracting edge659

11.7.2 A dipole664

11.8 Other problems667

11.8.1 Two parallel half-planes667

11.8.2 An infinite stack of parallel,staggered half-planes669

11.8.3 A striP670

11.8.4 Further problems671

11.9 Uniqueness of solution672

Ⅻ Difiraction of light by ultrasonie waves674

12.1 Qualitative description of the phenomenon and summary of theories based on Maxwell's difierential equations674

12.1.1 Qualitative description of the phenomenon674

12.1.2 Summary of theories based on Maxwell's equations677

12.2 Diffraction of light by ultrasonic waves as treated by the integral equation method680

12.2.1 Integral equation for E-polarization682

12.2.2 The trial solution of the integral equation682

12.2.3 Expressions for the amplitudes of the light waves in the diffracted and reflected spectra686

12.2.4 Solution of the equations by a method of successive approximations686

12.2.5 Expressions for the intensities of the first and second order lines for some special cases689

12.2.6 Some qualitative results691

12.2.7 The Raman-Nath approximation693

ⅩⅢ Scattering from inhomogeneous media695

13.1 Elements of the scalar theory of scattering695

13.1.1 Derivation of the basic integral equation695

13.1.2 The first-order Born approximation699

13.1.3 Scattering from periodic potentials703

13.1.4 Multiple scattering708

13.2 Principles of diffraction tomography for reconstruction of the scattering potential710

13.2.1 Angular spectrum representation of the scattered field711

13.2.2 The basic theorem of diffraction tomography713

13.3 The optical cross-section theorem716

13.4 A reciprocity relation724

13.5 The Rytov series726

13.6 Scattering of electromagnetic waves729

13.6.1 The integro-differential equations of electromagnetic scattering theory729

13.6.2 The far field730

13.6.3 The optical cross-section theorem for scattering o felectromagnetic waves732

ⅩⅣ Optics of metals735

14.1 Wave propagation in a conductor735

14.2 Refraction and reflection at a metal surface739

14.3 Elementary electron theory of the optical constants of metals749

14.4 Wave propagation in a stratified conducting medium.Theory of metallic films752

14.4.1 An absorbing film on a transparent substrate752

14.4.2 A transparent film on an absorbing substrate758

14.5 Diffraction by a conducting sphere;theory of Mie759

14.5.1 Mathematical solution of the problem760

（a）Representation of the field in terms of Debye's potentials760

（b）Series expansions for the field components765

（c）Summary of formulae relating to the associated Legendre func-tions and to the cylindrical functions772

14.5.2 Some consequences of Mie's formulae774

（a）The partial waves774

（b） Limiting cases775

（c）Intensity and polarization of the scattered light780

14.5.3 Total scattering and extinction784

（a） Some general considerations784

（b）Computational results785

ⅩⅤ Opries of crystals790

15.1 The dielectric tensor of an anisotropic medium790

15.2 The structure of a monochromatic plane wave in an anisotropic medium792

15.2.1 The phase velocity and the ray velocity792

15.2.2 Fresnel's formulae for the propagation of light in crystals795

15.2.3 Geometrical constructions for determining the velocities of propagation and the directions of vibration799

（a）The ellipsoid of wave normals799

（b）The ray ellipsoid802

（c）The normal surface and the ray surface803

15.3 Optical properties of uniaxial and biaxial crystals805

15.3.1 The optical classification of crystals805

15.3.2 Light propagation in uniaxial crystals806

15.3.3 Light propagation in biaxial crystals808

15.3.4 Refraction in crystals811

（a）Double refraction811

（b）Conical refraction813

15.4 Measurements in crystal optics818

15.4.1 The Nicol prism818

15.4.2 Compensators820

（a）The quarter-wave plate820

（b）Babinet's compensator821

（c）Soleil's compensator823

（d）Berek's compensator823

15.4.3 Interference with crystal plates823

15.4.4 Interference figures from uniaxial crystal plates829

15.4.5 Interference figures from biaxial crystal plates831

15.4.6 Location of optic axes and determination of the principal refractive indices of a crystalline medium833

15.5 Stress birefringence and form birefringence834

15.5.1 Stress birefringence834

15.5.2 Form birefringence837

15.6 Absorbing crystals840

15.6.1 Light propagation in an absorbing anisotropic medium840

15.6.2 Interference figures from absorbing crystal plates846

（a）Uniaxial crystals847

（b）Biaxial crystals848

15.6.3 Dichroic polarizers849

Appendices853

Ⅰ The Calculus of variations853

1 Euler's equations as necessary conditions for an extremurn853

2 Hilbert's independence integral and the Hamilton-Jacobi equation855

3 The field of extremals856

4 Determination of all extremals from the solution of the Hamilton-Jacobi equation858

5 Hamilton's canonical equations860

6 The special case when the independent variable does not appear explicitly in the integrand861

7 Discontinuities862

8 Weierstrass'and Legendre's conditions（sufficiency conditions for an extremum）864

9 Minimum of the variational integral when one end point is constrained to a surface866

10 Jacobi's criterion for a minimum867

11 Example Ⅰ:Optics868

12 Example Ⅱ:Mechanics of material points870

Ⅱ Light optics,electron optics and wave mechanics873

1 The Hamiltoniananalogy in elementary form873

2 The Hamiltonian analogy in variational form876

3 Wave mechanics of free electrons879

4 The application of optical principles to electron optics881

Ⅲ Asymptotic approximations to integrals883

1 The method of steepest descent883

2 The method of stationary phase888

3 Double integrals890

Ⅳ The Dirac delta function892

Ⅴ A mathematical lemma used in the rigorous derivation of the Lorentz-Lorenz formula（2.4.2）898

Ⅵ Propagation of discontinuities in an electromagnetic field （3.1.1）901

1 Relations connecting discontinuous changes in field vectors901

2 The field on a moving discontinuity surface903

Ⅶ The circle polynomials of Zernike（9.2.1）905

1 Some general considerations905

2 Explicit expressions for the radial polynomials R±m m907

Ⅷ Proof of the inequality｜μ12(v)｜≤1 for the spectral degree of coherence（10.5）911

Ⅸ Proof of a reciprocity inequality（10.8.3）912

Ⅹ Evaluation of two integrals（12.2.2）914

Ⅺ Energy conservation in scalar wavefields（13.3）918

Ⅻ Proof of Jones'lemma（13.3）921

Author index925

Subject index936