I Can't Get No Less Diffraction ...

Started Mar 18, 2013 | Discussions thread
wfektar Contributing Member • Posts: 700
Re: Addendum: I Can't Get No Airy Action ...

Detail Man wrote:

The sinc function is just the FT of a tophat.

I cannot speak for Frans, but it does not appear (to me) that he would dispute your statement.

Hope not, it's just math.

Don't muddy the waters with incoherent vs coherent.

My own looking into the relevance of differentiating between mono-chromatic, coherent light sources and other light sources yields statements similar to this one:

Objects in the optical microscope that are either self-luminous or illuminated by a large-angle cone of light form Airy patterns at the intermediate image plane that are incoherent and do not interfere with each other. This allows the determination of the minimum separation distance between adjacent Airy patterns by examination of the total intensity distribution (the sum of intensities) when these patterns are closely spaced or overlapping. In the case of Airy patterns produced by coherent illumination, the minimum separation distance must be ascertained by adding the pattern amplitudes rather than their intensities.


"pattern amplitudes" just means field amplitudes. Interference takes place at field level, but we can still only observe at energy/intensity/irradiance level ("in quadrature", in geek-speak).

The problem with coherent illumination is that the spatial scale of interference may be comparable or large relative to what you're trying to image. The most easily recognizable manifestation is "laser speckle", which does not actually exist except as an interference pattern on the detector. The magnitude of the speckle ("coarseness") is actually a measure of the relative length scale of coherence length to surface roughness.

... and thus it is the "intensity" (the square of the electromagnetic field strength in units of Volts/Meter, itself in units of Joules/Meter^2) seems to be what is used in these types of analyses.

We can't measure the field at optical frequencies -- it cycle averages to zero. We can measure the energy, which goes as the modulus square of the field, so that's where the square comes from.

I guess that it may be that interference which occurs when the light source is coherent monochromatic (the results of which can be seen in the resulting patterns) are not discernable when the light source is wideband (containing multiple wavelengths without direct phase relationships) ?

They're not. There are phase relationships but they average to zero -- you get a measurable signal because you're squaring the modulus. For the purposes of the OP, don't muddy things up by throwing coherent illumination into it.

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