Study of the diffraction in the microscope: Annular condenser

In this work we study the diffraction in the microscope when an annular condenser is used to illuminate the object. We calculate the point spread function (PSF) for a pinhole in an opaque screen illuminated with an annular condenser, consisting in an 1D array of incoherent point sources. We compare it with the PSF for a self-luminous point object, finding that the central disk of the diffraction pattern is narrower and the first intensity minimum is deeper for illuminated objects. We also analyze the resolution of the system by means of the intensity profile produced by two points objects, finding that two self luminous point objects are better resolved than two illuminated objects at the same distance. This suggests that the correlation introduced in the object diminishes the resolution in the former case.