Fundamentals of Diffraction and Image Formation
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Fundamentals of Diffraction and Image Formation
Lesson
Scalar theory of diffraction
Huygens-Fresnel principle
II-1
Image II-1 – Diffracting aperture
II-2A
II-2B
The angular spectrum of plane waves
II-3
II-4
II-5
II-6
Helmholtz equation
II-7
II-8
II-9
Propagation of the angular spectrum
Image II-2- Propagation of the angular spectrum along z.
II-10
II-11
The propagation phenomenon considered as a linear spatial filter
II-12
Effects of a diffracting aperture on the angular spectrum of a perturbation
Image II-3 -Diffracting aperture located at the plane xOy
Fraunhofer diffraction
Approximations to the Huygens-Fresnel principle
III-1
Fresnel approximations
III-2
Fraunhofer approximations
III-3
Lens properties in relation with the Fourier transform
The thin lens considered as a phase transformer
Image IV-1 Thin lens : front view and side view.
IV-1
IV-2
Image IV-2- Diverse types of converging lenses
Image IV-3- Diverse types of diverging lenses
Image formation under monochromatic illumination
Image IV-9- Image formation under monochromatic illumination
IV-8
Image IV-10- Determining the point-spread function of an imaging system
IV-9
General study of the image formation systems
General scheme
Image V-1- General schematic view of an image formation system
Image V-2 – Imaging system as seen by Abbe
Case of a coherent illumination
V-1
Case study
Fraunhofer diffraction of a sinusoidal amplitude grating
Image CS1 - (a) Transmittance function of a sinusoidal amplitude grating ; (b) image of this grating limited by a square aperture.
Image CS2 - (a) The 3 sinc functions appear in the diffracting field amplitude; (b) enlargement of figure (a) to compare f0 with 2/L.
Image CS3 - (a) Image showing the Fraunhofer diffraction figure of the grating; (b) Evolution of the intensity normalized in y0 = 0 when m = 1.
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