FourierOptik

Fourieroptik, or Fourier optics, is the branch of optics that analyzes and designs optical systems using Fourier transforms. In many setups, a thin lens acts as a Fourier transformer: the complex optical field in the object plane is related to its angular spectrum in the back focal plane, and vice versa. This perspective makes diffraction, imaging, and filtering problems tractable in the frequency domain.

A central idea is the representation of an optical field by spatial frequencies. For coherent illumination, the field distribution at the focal plane is proportional to the Fourier transform of the field in the object plane. In incoherent imaging, intensity is governed by the point spread function of the system, and the image is the convolution of the object with this function, or equivalently the product of their spectra, described by the optical transfer function.

Diffraction is naturally described in Fourier terms: the far-field pattern of an aperture is the Fourier transform of the aperture function (Fraunhofer regime), and near-field effects (Fresnel regime) are treated with extensions of the same principle. The optical transfer function, including the modulation transfer function, characterizes how spatial frequencies are transmitted, attenuated, or shifted, affecting resolution and contrast.

Applications span lens characterization, spatial filtering, and imaging system design. Fourieroptics underpins holography, phase retrieval, and digital holography, as well as adaptive optics and advanced microscopy. It provides tools for deconvolution, image reconstruction, and computational imaging, where optical and digital processing work together to manipulate or recover information from optical fields.