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E-raamat: Digital Holography [Wiley Online]

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  • Formaat: 350 pages
  • Sari: ISTE
  • Ilmumisaeg: 23-Feb-2012
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1118562569
  • ISBN-13: 9781118562567
Teised raamatud teemal:
  • Wiley Online
  • Hind: 174,45 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Digital HolographySuurem pilt
  • Formaat: 350 pages
  • Sari: ISTE
  • Ilmumisaeg: 23-Feb-2012
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1118562569
  • ISBN-13: 9781118562567
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118562567

This book presents a substantial description of the principles and applications of digital holography.
The first part of the book deals with mathematical basics and the linear filtering theory necessary to approach the topic. The next part describes the fundamentals of diffraction theory and exhaustively details the numerical computation of diffracted fields using FFT algorithms. A thorough presentation of the principles of holography and digital holography, including digital color holography, is proposed in the third part.
A special section is devoted to the algorithms and methods for the numerical reconstruction of holograms. There is also a chapter devoted to digital holographic interferometry with applications in holographic microscopy, quantitative phase contrast imaging, multidimensional deformation investigations, surface shape measurements, fluid mechanics, refractive index investigations, synthetic aperture imaging and information encrypting.
Keys so as to understand the differences between digital holography and speckle interferometry and examples of software for hologram reconstructions are also treated in brief.

Contents

1. Mathematical Prerequisites.
2. The Scalar Theory of Diffraction.
3. Calculating Diffraction by Fast Fourier Transform.
4. Fundamentals of Holography.
5. Digital Off-Axis Fresnel Holography.
6. Reconstructing Wavefronts Propagated through an Optical System.
7. Digital Holographic Interferometry and Its Applications.
Appendix. Examples of Digital Hologram Reconstruction Programs

Introduction xv
Chapter 1 Mathematical Prerequisites 1(26)
1.1 Frequently used special functions
1(9)
1.1.1 The "rectangle" function
2(1)
1.1.2 The "sine" function
3(1)
1.1.3 The "sign" function
4(1)
1.1.4 The "triangle" function
5(1)
1.1.5 The "disk" function
5(1)
1.1.6 The Dirac δ function
6(3)
1.1.6.1 Definition
6(2)
1.1.6.2 Fundamental properties
8(1)
1.1.7 The "comb" function
9(1)
1.2 Two-dimensional Fourier transform
10(7)
1.2.1 Definition and existence conditions
10(1)
1.2.2 Theorems related to the Fourier transform
11(4)
1.2.2.1 Linearity
13(1)
1.2.2.2 Similarity
13(1)
1.2.2.3 Translation
13(1)
1.2.2.4 Parseval's theorem
13(1)
1.2.2.5 The convolution theorem
14(1)
1.2.2.6 The autocorrelation theorem
14(1)
1.2.2.7 The duality theorem
14(1)
1.2.3 Fourier transforms in polar coordinates
15(2)
1.3 Linear systems
17(4)
1.3.1 Definition
17(1)
1.3.2 Impulse response and superposition integrals
18(1)
1.3.3 Definition of a two-dimensional linear shift-invariant system
19(1)
1.3.4 Transfer functions
20(1)
1.4 The sampling theorem
21(6)
1.4.1 Sampling a continuous function
21(2)
1.4.2 Reconstruction of the original function
23(2)
1.4.3 Space-bandwidth product
25(2)
Chapter 2 The Scalar Theory of Diffraction 27(50)
2.1 Representation of an optical wave by a complex function
28(5)
2.1.1 Representation of a monochromatic wave
28(1)
2.1.2 Complex amplitude of the optical field in space
29(2)
2.1.2.1 Plane waves
29(1)
2.1.2.2 Spherical waves
30(1)
2.1.3 Complex amplitudes of plane and spherical waves in a front plane
31(2)
2.1.3.1 Complex amplitude of a plane wave in a front plane
31(1)
2.1.3.2 Complex amplitude of a spherical wave in a front plane
32(1)
2.2 Scalar theory of diffraction
33(12)
2.2.1 Wave equation
33(1)
2.2.2 Harmonic plane wave solutions to the wave equation
34(1)
2.2.3 Angular spectrum
35(4)
2.2.4 Kirchhoff and Rayleigh-Sommerfeld formulae
39(2)
2.2.5 Fresnel approximation and Fresnel diffraction integral
41(2)
2.2.6 The Fraunhofer approximation
43(2)
2.3 Examples of Fraunhofer diffraction patterns
45(6)
2.3.1 Fraunhofer diffraction pattern from a rectangular aperture
45(1)
2.3.2 Fraunhofer diffraction pattern from a circular aperture
46(3)
2.3.3 Fraunhofer diffraction pattern from a sinusoidal-amplitude grating
49(2)
2.4 Some examples and uses of Fresnel diffraction
51(6)
2.4.1 Fresnel diffraction from a sinusoidal-amplitude grating
51(3)
2.4.2 Fresnel diffraction from a rectangular aperture
54(3)
2.5 Collins' formula
57(17)
2.5.1 Description of an optical system by an ABCD transfer matrix
58(4)
2.5.2 ABCD law and paraxial systems equivalent to a lens
62(4)
2.5.2.1 ABCD law of a spherical wave propagating across an optical system
62(2)
2.5.2.2 System equivalent to a lens
64(1)
2.5.2.3 Properties of the transfer matrix
65(1)
2.5.3 Proof of Collins' formula
66(6)
2.5.3.1 Transmission from a thin lens
67(1)
2.5.3.2 Expression of the ideal image
68(2)
2.5.3.3 Proof of Collins' formula
70(2)
2.5.4 Comparison between Collins' formula and the Fresnel integral
72(2)
2.6 Conclusion
74(3)
Chapter 3 Calculating Diffraction by Fast Fourier Transform 77(38)
3.1 Relation between the discrete and analytical Fourier transforms
78(5)
3.1.1 Sampling and periodic expansion of a continuous two-dimensional function
78(1)
3.1.2 The relation between the discrete and continuous Fourier transforms
79(4)
3.2 Calculating the Fresnel diffraction integral by FFT
83(9)
3.2.1 Calculating diffraction by the S-FFT method
84(2)
3.2.2 Numerical calculation and experimental demonstration
86(2)
3.2.3 The D-FFT method
88(1)
3.2.4 Practical sampling conditions due to the energy conservation principle
89(1)
3.2.5 Experimental demonstration of the D-FFT method
90(2)
3.3 Calculation of the classical diffraction formulae using FFT
92(9)
3.3.1 Kirchhoff and Rayleigh-Sommerfeld formulae in convolution form
92(2)
3.3.2 Unitary representation of the classical diffraction formulae
94(1)
3.3.3 Study of the sampling conditions of the classical formulae
95(2)
3.3.4 Example of calculations of the classical diffraction formulae
97(3)
3.3.5 Calculation of diffraction by convolution: summary
100(1)
3.4 Numerical calculation of Collins' formula
101(12)
3.4.1 Collin's direct and inverse formulae
101(2)
3.4.2 Calculating Collins' formula by S-FFT
103(2)
3.4.3 Calculating the inverse Collins' formula by S-FFT
105(1)
3.4.4 Calculating Collins' formula by D-FFT
106(2)
3.4.5 Calculating the inverse Collins' formula by D-FFT
108(1)
3.4.6 Numerical calculation and experimental demonstration
109(7)
3.4.6.1 Demonstration of the S-FFT and S-IFFT methods
110(1)
3.4.6.2 Demonstration of the D-FFT method
111(2)
3.5 Conclusion
113(2)
Chapter 4 Fundamentals of Holography 115(50)
4.1 Basics of holography
116(11)
4.1.1 Leith-Upatnieks holograms
118(5)
4.1.1.1 Illumination in the propagation direction of the original reference wave
120(1)
4.1.1.2 Illumination with a wave propagating along the z-axis
121(2)
4.1.2 Condition for the separation of the twin images and the zero order
123(4)
4.1.2.1 Case where the reference wave is planar
123(2)
4.1.2.2 The case where the reference wave is no longer planar
125(2)
4.2 Partially coherent light and its use in holography
127(14)
4.2.1 Analytic signal describing a non-monochromatic wave
127(4)
4.2.1.1 Analytic signal describing a monochromatic wave
127(1)
4.2.1.2 Analytic signal describing a non-monochromatic wave
128(1)
4.2.1.3 Analytic signal and spectrum of a laser wave
129(2)
4.2.2 Recording a hologram with non-monochromatic light
131(3)
4.2.3 Total coherence approximation conditions
134(5)
4.2.3.1 Identical wave train model
134(1)
4.2.3.2 Temporal coherence of a source emitting identical wave trains
135(4)
4.2.4 Recording a Fresnel hologram
139(2)
4.3 Study of the Fresnel hologram of point source
141(8)
4.3.1 Reconstructing the hologram of a point source
142(4)
4.3.1.1 Hologram illuminated by a spherical wave with the same wavelength
142(3)
4.3.1.2 Hologram illuminated by a spherical wave with a different wavelength
145(1)
4.3.1.3 Case where the reference and reconstruction waves are plane waves
145(1)
4.3.2 Magnifications
146(1)
4.3.2.1 Transverse magnification of the reconstructed image
146(1)
4.3.2.2 Longitudinal magnification
147(1)
4.3.3 Resolution of the reconstructed image
147(2)
4.3.3.1 Influence of the size of the illuminating source
147(1)
4.3.3.2 Influence of the spectral width of the light source
148(1)
4.4 Different types of hologram
149(14)
4.4.1 The Fraunhofer hologram
149(1)
4.4.2 The Fourier hologram
150(5)
4.4.2.1 Component Cu1 (xi, yi)
153(1)
4.4.2.2 Component Cu2 (xi, yi)
153(1)
4.4.2.3 Component Cu3 (xi, yi)
154(1)
4.4.2.4 Component Cu4 (xi, yi)
154(1)
4.4.3 The lensless Fourier hologram
155(3)
4.4.4 The image hologram
158(2)
4.4.5 The phase hologram
160(3)
4.5 Conclusion
163(2)
Chapter 5 Digital Off-Axis Fresnel Holography 165(72)
5.1 Digital off-axis holography and wavefront reconstruction by S-FFT
166(17)
5.1.1 Characteristics of the diffraction from a digital hologram impacted by a spherical wave
166(6)
5.1.1.1 Virtual object
168(1)
5.1.1.2 Conjugate object
169(1)
5.1.1.3 Zero order
170(2)
5.1.2 Optimization of the experimental parameters
172(1)
5.1.3 Experimental reconstruction by S-FFT
173(3)
5.1.4 Quality of the reconstructed image
176(7)
5.2 Elimination of parasitic orders with the S-FFT method
183(8)
5.2.1 Diffraction efficiency of a digital hologram
184(1)
5.2.2 Methods of direct elimination
185(4)
5.2.2.1 Method directly eliminating the object and reference waves
185(3)
5.2.2.2 Method with an arbitrary phase shift of the reference wave
188(1)
5.2.3 Method of extracting the complex amplitude of the object wave
189(2)
5.3 Wavefront reconstruction with an adjustable magnification
191(11)
5.3.1 Convolution with adjustable magnification
192(3)
5.3.2 Experiment with adjustable magnification
195(2)
5.3.3 Elimination of the perturbation due to the zero order
197(4)
5.3.3.1 Spectral distribution and determination of the center of the object wave
197(3)
5.3.3.2 Spectral position of the object wave
200(1)
5.3.4 Method eliminating the perturbation due to the zero order
201(1)
5.4 Filtering in the image and reconstruction planes by the FIMG4FFT method
202(5)
5.4.1 Adjustable magnification reconstruction by the FIMG4FFT method
203(4)
5.4.1.1 Filtering the image plane
203(2)
5.4.1.2 Experimental results
205(1)
5.4.1.3 Local reconstruction by the FIMG4FFT method
205(2)
5.5 DBFT method and the use of filtering in the image plane
207(5)
5.5.1 DBFT method
207(1)
5.5.2 Sampling of the DBFT algorithm
208(2)
5.5.3 Improvement of the DBFT method
210(1)
5.5.4 Experimental demonstration of the DDBFT method
211(1)
5.6 Digital color holography
212(12)
5.6.1 Recording a digital color hologram
213(2)
5.6.2 Standardization of the physical scale of reconstructed monochromatic images
215(1)
5.6.3 Fresnel transform with wavelength-dependant zero-padding
216(2)
5.6.4 Experimental study of the different methods of reconstructing color images
218(6)
5.6.4.1 Two-color image calculated by the zero-padding method
220(1)
5.6.4.2 Reconstruction by the FIMG4FFT and the DDBFT with adjustable magnification
221(1)
5.6.4.3 Three-color digital holography
222(2)
5.7 Digital phase hologram
224(5)
5.7.1 Formation of a digital phase hologram and reconstruction by S-FFT
225(2)
5.7.2 Experimental demonstration
227(2)
5.8 Depth of focus of the reconstructed image
229(6)
5.8.1 Theoretical analysis
229(2)
5.8.2 Comparison with a digital holographic simulation
231(2)
5.8.3 Experiments
233(2)
5.9 Conclusion
235(2)
Chapter 6 Reconstructing Wavefronts Propagated through an Optical System 237(34)
6.1 Theoretical basis
238(8)
6.1.1 Case of a convergent lens
239(1)
6.1.2 Impulse response of the process
240(6)
6.1.2.1 Matrix description of the digital holographic system
240(1)
6.1.2.2 Impulse response from the digital holographic system
241(2)
6.1.2.3 Experimental reconstruction with an afocal system
243(3)
6.2 Digital holography with a zoom
246(5)
6.2.1 Principle of the zoom
247(1)
6.2.2 Study of the zoom
248(1)
6.2.3 Design of the zoom
249(2)
6.2.4 Experimental validation
251(1)
6.3 Reconstructing an image by Collins' formula
251(8)
6.3.1 Reconstruction algorithm
251(3)
6.3.1.1 Experimental setup
251(1)
6.3.1.2 Reconstruction by calculating the inverse Collins formula
252(2)
6.3.2 Adjustable-magnification reconstruction after propagation across an optical system
254(5)
6.3.2.1 Reconstruction with an adjustable magnification in the detector space
255(2)
6.3.2.2 Experimental demonstration for the reconstruction of color images
257(2)
6.4 Using the classical diffraction formulae to reconstruct the wavefront after propagation across an optical system
259(10)
6.4.1 Use of the rigorous diffraction formulae
259(6)
6.4.1.1 Simulation of the overall process
260(4)
6.4.1.2 Experimental results
264(1)
6.4.2 Reconstruction of the object wave in the object and image spaces
265(8)
6.4.2.1 Parameters
265(1)
6.4.2.2 Reconstruction in the image space
266(1)
6.4.2.3 Reconstruction in the object space
267(1)
6.4.2.4 Experimental results
268(1)
6.5 Conclusion
269(2)
Chapter 7 Digital Holographic Interferometry and Its Applications 271(48)
7.1 Basics of holographic interferometry
273(9)
7.1.1 Reconstructing the phase of the object field
273(1)
7.1.2 Optical phase variations and the sensitivity vector
274(1)
7.1.3 Phase difference method
275(1)
7.1.4 Spatial filtering of the phase
276(1)
7.1.5 Phase unwrapping
277(2)
7.1.6 Out-of-plane sensitivity
279(1)
7.1.7 In-plane sensitivity
280(1)
7.1.8 3D sensitivity
280(2)
7.1.9 Sensitivity variation across the field of view
282(1)
7.2 Digital holographic microscopy
282(6)
7.2.1 Principles and advantages
282(1)
7.2.2 Architectures
283(2)
7.2.3 Reconstruction of the object field
285(2)
7.2.4 Phase contrast
287(1)
7.3 Two-wavelength profilometry
288(3)
7.3.1 Principle
288(1)
7.3.2 Two-wavelength profilometry with spatio-chromatic multiplexing
289(2)
7.4 Digital holographic photomechanics
291(12)
7.4.1 Introduction
291(1)
7.4.2 Twin-sensitivity measurement with monochromatic multiplexing
292(5)
7.4.2.1 Principle
292(1)
7.4.2.2 Application: polymer concrete in a three-point bending test
293(1)
7.4.2.3 Experimental results
294(2)
7.4.2.4 Comparison with finite element modeling
296(1)
7.4.3 Twin-sensitivity measurement with spatio-chromatic multiplexing
297(2)
7.4.3.1 Principle
297(1)
7.4.3.2 Application to crack detection in electrical components
297(2)
7.4.4 3D measurement by three-color digital holography
299(4)
7.4.4.1 Principle
299(2)
7.4.4.2 Illustration
301(1)
7.4.4.3 Application to the study of the mechanical behavior of composite materials
302(1)
7.5 Time-averaged digital holography
303(6)
7.5.1 Principle
303(1)
7.5.2 Applications
304(5)
7.5.2.1 Modal analysis
304(1)
7.5.2.2 Analog/digital comparison
305(2)
7.5.2.3 Time-averaged phase
307(2)
7.6 Tracking high-amplitude vibrations
309(5)
7.6.1 Introduction
309(1)
7.6.2 Principle
310(4)
7.7 Three-color digital holographic interferometry for fluid mechanics
314(4)
7.7.1 Principle
314(3)
7.7.2 Application to turbulent flows
317(1)
7.8 Conclusion
318(1)
Appendix. Examples of Digital Hologram Reconstruction Programs 319(20)
A1.1 Diffraction calculation using the S-FFT algorithm
319(4)
A1.1.1 Code for the program: LIM1.m
319(2)
A1.1.2 Examples of diffraction calculations using LIM 1.m
321(2)
A1.2 Diffraction calculation by D-FFT
323(3)
A1.2.1 Code for the program: LIM2.m
323(2)
A1.2.2 Examples of diffraction calculations using LIM2.m
325(1)
A1.3 Simulation of a digital hologram
326(4)
A1.3.1 Code for the program: LIM3.m
326(3)
A1.3.2 Example of the calculation of a hologram with LIM3.m
329(1)
A1.4 Reconstruction of a hologram by S-FFT
330(3)
A1.4.1 Code for the program: LIM4.m
330(2)
A1.4.2 Example of reconstruction with LIM4.m
332(1)
A1.5 Adjustable-magnification reconstruction by D-FFT
333(6)
A1.5.1 Code for the program: L1M5.m
333(3)
A1.5.2 Example of adjustable-magnification reconstruction with LIM5.rn
336(3)
Bibliography 339(16)
Index 355
Pascal Picart has been Associate Professor at Université du Maine-Ecole Nationale Supérieure d'Ingénieurs du Mans (ENSIM, Le Mans, France) since 2005. His research interests include speckle metrology, optoacoustic spectroscopy, and optical biosensors. The current emphasis of his research program is on the development of new techniques in digital holography, holographic image processing, phase imaging and applications in the field of acoustics, structural mechanics and fluid mechanics. He is author/co-author of more than 140 scientific articles, 51 of which were peer-reviewed papers published in international journals.

Jun-chang Li became Director of the Laboratory of Laser Applications at Kunming University of Sciences and Technologies (Kunming, China) in 1987. He has managed several projects funded by the National Science Agency of China and he is author/co-author of three books and more than 50 peer reviewed papers published in international journals. The current emphasis of his research program is on the development of computation methods for diffraction, wave front reconstruction and digital holographic image processing.
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