Field curvature with Flatteners and compressors
The question is "what is the shape of the field curvature with and without flatteners and compressors, and how does it change with spacing".
Without any flatteners/compressors the typical field curvature of a refractor is approximately 38% of the focal length, inward curving and with astigmatism (oval stars shape pointing toward the center). Taking the example of our 140EDL refractors, it has a focal length of 1048mm and an inherent field curvature of 399mm. If you tried to take an image of a 2 degree field covering a 38mm circle, you would get the result shown in the picture below. For reference, the Airy Disc shown is about 10 microns diameter at 1048mm focal length.
Off-axis, the oval shape results from the difference in field curvature between the sagittal and tangential rays that come from the various parts of the lens. So the job of the flattener/compressor is to not only flatten the curvature, but also bring the sagittal and tangential rays together without introducing other defects such as coma, spherical and chromatic aberrations.