I have read "Coherence and sampling requirements for diffractive imaging" from Spence et al. where the maximum size of the sample is defined in function of the spatial coherence of the source. Is there also a mathematical relation for spatial coherence and resolution? Thanks
I think yes.
For Abbe lateral Resolution
Lx,y = lambda/(2 NA), 1)
where NA is the numerical aperture.
According to the Fresnel approximation, the resolving power dm of an optical system is given by
dm = 1.22 lambda/(2. NA). 2)
Compare 1 and 2 you can obtain what you need.
Best regards
Mostafa
Mabel, Yes, it is. Spatial coherence length is measured as the square root of coherence area, which is volume under the squared modulus of the mutual intensity. Propagation of the mutual intensity is mathematically described by 2D Fourier transformation of the intensity distribution across the source. (van Cittert and Zernike's theorem) This relationship can be linked to the realtionship between the field across aperture coherently illuminated and the field observed in the Fraunhofer diffration pattern of the aperture. Please see Joseph Goodman's "Statistical Optics, p-210." Shigeo
If your sample is larger than the coherence length, the input field at the edges of your sample has no definite phase relation, and when you scatter, the corresponding interference terms vanish after averaging over e.g. some time on the detector.
The net effect is similar as if you made pictures of two different samples, and added up the intensities. You can no longer express the intensities as the absolute square of some scattered field, which is a silent assumption in the simpler reconstruction algorithms.
There are ways/algorithms around that (H. Quiney, K. Nugent would be names to search for), but they are more complicated, less guaranteed to converge etc. The usual issue.
So to sum up, the coherence length has no direct influence on your resolution. If it smaller than the sample size, things only get more complicated (which may in turn reduce the resolution indirectly due to convergence problems etc.).
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