Point spread function

A point spread function (PSF) is the image formed by an optical or imaging system from an ideal point source. It describes how the system distributes light or signal around the source’s image.

Impulse response: A system’s output when its input is an idealized impulse. A PSF is the spatial impulse response of a linear, shift-invariant imaging system.
Deconvolution: A computational method for estimating an underlying signal from data blurred by a known or estimated response. Image restoration uses a PSF model to undo blur, though noise and model errors limit recovery.
Point source: An idealized source whose spatial extent is negligible compared with the system’s resolution. The PSF is defined by the image that such a source produces.
Line spread function: The image formed by an ideal infinitely narrow line, often obtained by integrating a two-dimensional PSF along one axis. Unlike a PSF, it measures response to a line rather than a point.
Convolution: A mathematical operation that combines two functions by integrating products of shifted versions. Convolving an ideal scene with the PSF predicts the blurred image under linear, shift-invariant conditions.
Fluorescence microscopy: Microscopy that forms images by detecting fluorescence emitted by excited molecules. Its measured PSF determines how fluorescent structures appear and how sharply they can be resolved.
Diffraction: The spreading and interference of waves as they pass through openings or around obstacles. Even a perfect finite-aperture optical system produces a diffraction-broadened PSF.
Edge spread function: The image intensity profile across an ideal sharp edge. It is measured from an extended edge, not directly from a point source.
Optical transfer function: The Fourier transform of an optical system’s point spread function, describing its response to spatial frequencies. It expresses the same image-forming response in spatial-frequency terms.
Confocal microscopy: A fluorescence imaging method that rejects out-of-focus light using a pinhole conjugate to the focal plane. Its effective PSF reflects both illumination and detection paths.

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