Point spread function: Difference between revisions

Revision as of 14:00, 25 June 2024

Revision as of 14:04, 25 June 2024

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[[Image:SquarePost.svg|Square Post Function|right|thumb|220px]]

We imagine the object plane as being decomposed into square areas such as this, with each having its own associated square post function. If the height, ''h'', of the post is maintained at 1/w², then as the side dimension ''w'' tends to zero, the height, ''h'', tends to infinity in such a way that the volume (integral) remains constant at 1. This gives the 2D impulse the siftingshifting property (which is implied in the equation above), which says that when the 2D impulse function, δ(''x'' − ''u'',''y'' − ''v''), is integrated against any other continuous function, {{nowrap|''f''(''u'',''v'')}}, it "sifts out" the value of ''f'' at the ___location of the impulse, i.e., at the point {{nowrap|(''x'',''y'')}}.

The concept of a perfect point source object is central to the idea of PSF. However, there is no such thing in nature as a perfect mathematical point source radiator; the concept is completely non-physical and is rather a mathematical construct used to model and understand optical imaging systems. The utility of the point source concept comes from the fact that a point source in the 2D object plane can only radiate a perfect uniform-amplitude, spherical wave — a wave having perfectly spherical, outward travelling phase fronts with uniform intensity everywhere on the spheres (see [[Huygens–Fresnel principle]]). Such a source of uniform spherical waves is shown in the figure below. We also note that a perfect point source radiator will not only radiate a uniform spectrum of propagating plane waves, but a uniform spectrum of exponentially decaying ([[Evanescent wave|evanescent]]) waves as well, and it is these which are responsible for resolution finer than one wavelength (see [[Fourier optics]]). This follows from the following [[Fourier transform]] expression for a 2D impulse function,