Point spread function: Difference between revisions

Revision as of 14:49, 14 October 2020

Revision as of 10:49, 4 November 2020

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i.e., as a sum over weighted impulse functions, although this is also really just stating the shifting property of 2D delta functions (discussed further below). Rewriting the object transmittance function in the form above allows us to calculate the image plane field as the superposition of the images of each of the individual impulse functions, i.e., as a superposition over weighted point spread functions in the image plane using the ''same'' weighting function as in the object plane, i.e., <math>O(x_o,y_o)</math>. Mathematically, the image is expressed as:

:<math>I(x_ox_i,y_oy_i) = \int\!\!\int O(u,v) ~ \mathrm{PSF}(x_i/M-u , y_i/M-v) \, du\, dv</math>

in which <math display="inline">\mbox{PSF}(x_i/M-u,y_i/M-v)</math> is the image of the impulse function δ(''x_o'' &nbsp;&minus;&nbsp; ''u'', ''y_o'' &nbsp;&minus;&nbsp; ''v'').