Spatial resolution and exit slits

What sort of exit slit should you use? I like to characterize the proper pinhole diameter in terms of the phase space product: $p=d_{\rm pinhole}(d_{\rm zp}/z)$, where $d_{\rm pinhole}$ is the pinhole diameter, $d_{\rm zp}$ is the diameter of the zone plate, and $z$ is the distance from the pinhole to the zone plate. As you increase $p$ to get more light, you begin to affect your spatial resolution as shown in Figs. 3.19 and 3.20. This is described a bit more in a paper [7].

Figure 3.19: The modulation transfer function MTF as a function of the phase space product of illumination $p$. This is calculated for incoherent brightfield imaging with a lens having a central stop over half its diameter. The calculation assumed cylindrical symmetry; that is, a pinhole rather than a slit.
\includegraphics[height=3.25in]{mtf_source}

Figure 3.20: The intensity point spread function PSF as a function of the phase space product of illumination $p$. This is calculated for incoherent brightfield imaging with a lens having a central stop over half its diameter. The calculation assumed cylindrical symmetry; that is, a pinhole rather than a slit. For all values of $p$, the PSF has been normalized to unit integrated intensity, whereas in fact the intensity will increase approximately as the square of $p$ (that is, approximately as the square of pinhole diameter).
\includegraphics[height=3.25in]{psf_source}

Holger Fleckenstein 2008-07-08