Fourier optics

Fourier optics analyzes light propagation and image formation by decomposing optical fields into spatial frequencies. It uses Fourier transforms to describe diffraction, lenses, and imaging systems.

Spatial frequency: A measure of how rapidly a pattern varies across space, usually expressed in cycles per unit distance. Fourier optics describes optical fields as distributions of these spatial variations.
Huygens–Fresnel principle: A wave principle that treats each point on a wavefront as a source of secondary wavelets. It supplies a wave-based account of the propagation that Fourier optics reformulates mathematically.
Fourier-plane filtering: An optical processing method that modifies selected spatial frequencies in a system's Fourier plane. A lens maps spatial frequencies to positions where masks can selectively alter them.
Geometrical optics: An approximation that describes light as rays and neglects wave diffraction. It predicts ray paths, while Fourier optics captures interference and diffraction.
Fourier transform: A mathematical transform that decomposes a function into its frequency components. It converts an optical field between position and spatial-frequency representations.
Scalar diffraction theory: A theory that models light diffraction with a scalar wave equation, neglecting vector polarization effects. Many Fourier-optics propagation formulas follow from this approximation.
4f optical system: A two-lens arrangement that places an input plane and output plane in conjugate positions around a Fourier plane. It provides a standard arrangement for Fourier transformation and spatial filtering.
Rayleigh criterion: A conventional threshold for resolving two point sources based on the overlap of their diffraction patterns. It gives a practical resolution rule alongside Fourier optics' frequency-cutoff account.
Angular spectrum method: A wave-propagation method that represents a field as plane waves with different propagation directions. It calculates free-space propagation by evolving each spatial-frequency component separately.
Helmholtz equation: A partial differential equation governing monochromatic wave fields in a uniform medium. Its solutions provide the wave fields that spatial-frequency methods propagate.

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