point spread function: one construct, many systems

In optics, the point spread function is the image a system forms of a single point source: because diffraction and aberrations spread that point into a small blur, the PSF is the impulse response of the imaging system, and the image of any scene is the scene convolved with it. Born and Wolf's Principles of optics derives the diffraction-limited form of this blur for an aberration-free aperture. The referent is the characteristic spread an optical system imposes on a point, which sets its resolution, and it is the same function that astronomers fit to stars and microscopists measure in three dimensions.[1]

Unit

The intensity distribution of the image of an ideal point source

Recovery means

Not applicable

Measured by

Characterised by its width (such as the full width at half maximum) and shape, or in the frequency domain by the optical transfer function

In astronomy the same function describes how a point-like star, blurred by the telescope and the atmosphere, lands on the detector, and measuring brightness in crowded fields means fitting that shared profile to every overlapping star. Stetson's 1987 DAOPHOT: A computer program for crowded-field stellar photometry built PSF-fitting photometry into a standard tool, modelling one empirical point spread function and scaling it to each source. It is the identical construct as the optician's impulse response, here realised for astronomical images and used to pull apart and measure overlapping points of light.[2]

Unit

The modelled image profile of an unresolved star on the detector

Recovery means

Not applicable

Measured by

Built empirically from isolated bright stars, then fit to crowded sources to recover positions and magnitudes

In fluorescence microscopy the point spread function is the three-dimensional blur a sub-resolution fluorescent emitter produces, elongated along the optical axis, and knowing it is what lets deconvolution and localization methods sharpen or super-resolve an image. Maalouf, Colicchio, and Dieterlen's 2011 Fluorescence microscopy three-dimensional depth variant point spread function interpolation using Zernike moments models how this blur changes with depth so it can be corrected. It is the same impulse-response construct as in optics and astronomy, extended into the third dimension of a microscope's focal volume.[3]

Unit

The three-dimensional intensity distribution of the image of a point emitter

Recovery means

Not applicable

Measured by

Measured from sub-resolution fluorescent beads or modelled analytically, then used for deconvolution and localization