Resolution and FWHM in Two-dimensional Diffraction

The resolution of a two-dimensional detector is governed to a dominant extent by the PSF. This can be very well observed by the behaviour of the FWHM distribution of reflections over an image plate. The PSF of a standard image plate is roughly 300 pm. The projection A/ of the diffracted beam width d on the image plate in the case of a fully parallel beam is given by  

Adding the FWHM resulting from the point spread contribution would lead to  

As Equation (3) still holds Equation (4) would become  

The detector resolution can be estimated as a convolution of the footprint with the PSF. Placing this in Equation (6) would lead to the following formula, again for an idealized non-tilted detector  

As both the footprint and the PSF can be described by a Gaussian function the FWHM of their convolution is given by  

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