For partially coherent imaging in the scalar wave approximation, the image irradiance is related bilinearly to the object amplitude transmittance through a multi-dimensional integral. The relationship between the object and its image is difficult to comprehend. For objects that vary in one direction, there are diagrams that that aid in understanding the imaging equation. These diagram apply to the cutoff spatial frequency of the image irradiance, the spatial frequency components of the object that contribute to the image, the angular distribution of the illumination, and more. In some cases, back-of-the-envelope image calculations can be done with the graphical method. This tool is useful in a variety of cases of microscopy, projection, and optical testing.
Douglas S. Goodman,
"Graphical methods to help understand partially coherent imaging", Proc. SPIE 5377, Optical Microlithography XVII, (28 May 2004); doi: 10.1117/12.537191; https://doi.org/10.1117/12.537191