Book contents
- Frontmatter
- Contents
- Preface to the second English edition
- Preface to the first edition
- Introduction
- 1 Abbe's sine condition
- 2 Fourier optics
- 3 Effect of polarization on diffraction in systems of high numerical aperture
- 4 Gaussian beam optics
- 5 Coherent and incoherent imaging
- 6 First-order temporal coherence in classical optics
- 7 The van Cittert–Zernike theorem
- 8 Partial polarization, Stokes parameters, and the Poincaré sphere
- 9 Second-order coherence and the Hanbury Brown–Twiss experiment
- 10 What in the world are surface plasmons?
- 11 Surface plasmon polaritons on metallic surfaces
- 12 The Faraday effect
- 13 The magneto-optical Kerr effect
- 14 The Sagnac interferometer
- 15 Fabry–Pérot etalons in polarized light
- 16 The Ewald–Oseen extinction theorem
- 17 Reciprocity in classical linear optics
- 18 Optical pulse compression
- 19 The uncertainty principle in classical optics
- 20 Omni-directional dielectric mirrors
- 21 Linear optical vortices
- 22 Geometric-optical rays, Poynting's vector, and the field momenta
- 23 Doppler shift, stellar aberration, and convection of light by moving media
- 24 Diffraction gratings
- 25 Diffractive optical elements
- 26 The Talbot effect
- 27 Some quirks of total internal reflection
- 28 Evanescent coupling
- 29 Internal and external conical refraction
- 30 Transmission of light through small elliptical apertures
- 31 The method of Fox and Li
- 32 The beam propagation method
- 33 Launching light into a fiber
- 34 The optics of semiconductor diode lasers
- 35 Michelson's stellar interferometer
- 36 Bracewell's interferometric telescope
- 37 Scanning optical microscopy
- 38 Zernike's method of phase contrast
- 39 Polarization microscopy
- 40 Nomarski's differential interference contrast microscope
- 41 The van Leeuwenhoek microscope
- 42 Projection photolithography
- 43 Interaction of light with subwavelength structures
- 44 The Ronchi test
- 45 The Shack–Hartmann wavefront sensor
- 46 Ellipsometry
- 47 Holography and holographic interferometry
- 48 Self-focusing in nonlinear optical media
- 49 Spatial optical solitons
- 50 Laser heating of multilayer stacks
- Index
- References
26 - The Talbot effect
Published online by Cambridge University Press: 31 January 2011
- Frontmatter
- Contents
- Preface to the second English edition
- Preface to the first edition
- Introduction
- 1 Abbe's sine condition
- 2 Fourier optics
- 3 Effect of polarization on diffraction in systems of high numerical aperture
- 4 Gaussian beam optics
- 5 Coherent and incoherent imaging
- 6 First-order temporal coherence in classical optics
- 7 The van Cittert–Zernike theorem
- 8 Partial polarization, Stokes parameters, and the Poincaré sphere
- 9 Second-order coherence and the Hanbury Brown–Twiss experiment
- 10 What in the world are surface plasmons?
- 11 Surface plasmon polaritons on metallic surfaces
- 12 The Faraday effect
- 13 The magneto-optical Kerr effect
- 14 The Sagnac interferometer
- 15 Fabry–Pérot etalons in polarized light
- 16 The Ewald–Oseen extinction theorem
- 17 Reciprocity in classical linear optics
- 18 Optical pulse compression
- 19 The uncertainty principle in classical optics
- 20 Omni-directional dielectric mirrors
- 21 Linear optical vortices
- 22 Geometric-optical rays, Poynting's vector, and the field momenta
- 23 Doppler shift, stellar aberration, and convection of light by moving media
- 24 Diffraction gratings
- 25 Diffractive optical elements
- 26 The Talbot effect
- 27 Some quirks of total internal reflection
- 28 Evanescent coupling
- 29 Internal and external conical refraction
- 30 Transmission of light through small elliptical apertures
- 31 The method of Fox and Li
- 32 The beam propagation method
- 33 Launching light into a fiber
- 34 The optics of semiconductor diode lasers
- 35 Michelson's stellar interferometer
- 36 Bracewell's interferometric telescope
- 37 Scanning optical microscopy
- 38 Zernike's method of phase contrast
- 39 Polarization microscopy
- 40 Nomarski's differential interference contrast microscope
- 41 The van Leeuwenhoek microscope
- 42 Projection photolithography
- 43 Interaction of light with subwavelength structures
- 44 The Ronchi test
- 45 The Shack–Hartmann wavefront sensor
- 46 Ellipsometry
- 47 Holography and holographic interferometry
- 48 Self-focusing in nonlinear optical media
- 49 Spatial optical solitons
- 50 Laser heating of multilayer stacks
- Index
- References
Summary
The Talbot effect, also referred to as self-imaging or lensless imaging, was originally discovered in the 1830s by H. F. Talbot. Over the years, investigators have come to understand different aspects of this phenomenon, and a theory of the Talbot effect based on classical diffraction theory has emerged which is capable of explaining the various observations. For a detailed description of the Talbot effect and related phenomena, as well as a historical perspective on the subject, the reader may consult references 3 and 4 and further references cited therein. Since many of the standard optics textbooks do not even mention the Talbot effect, it is worthwhile to bring to the reader's attention the essential features of this phenomenon.
Lensless imaging of a periodic pattern
The Talbot effect is observed when, under appropriate conditions, a beam of light is reflected from (or transmitted through) a periodic pattern. The pattern may have one-dimensional periodicity (as in traditional gratings), or it may exhibit periodicity in two dimensions (e.g., a surface relief structure or a photographic plate imprinted with identical features on a regular lattice).
In what follows we shall present the diffraction patterns obtained from a periodic array of cross-shaped apertures in an otherwise opaque screen. Because the diffraction pattern of a single aperture differs markedly from that of a periodic array of such apertures, we begin by examining the behavior of an individual aperture under coherent illumination.
- Type
- Chapter
- Information
- Classical Optics and its Applications , pp. 367 - 378Publisher: Cambridge University PressPrint publication year: 2009
References
- 1
- Cited by