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Excerpt from Field Guide to Geometrical Optics
Field curvature characterizes the natural tendency of optical systems to have curved image planes. A positive singlet has an inward bending image surface.
A perfect image is formed on a curved surface, and the image blur at the paraxial image plane increases as H2. A compromise flat image plane that reduces the average image blur occurs inside paraxial focus.
The field curvature is a bias curvature for the astigmatic image surfaces.
|Sagittal surface:||ΔW20 = –W220H2|
|Medial surface:||ΔW20 = –W220H2–.5W222H2|
|Tangential surface:||ΔW20 = –W220H2–W222H2|
|Petzval surface:||ΔW20 = –W220H2 + .5W222H2|
While not a good image surface, the Petzval surface represents the fundamental field curvature of the system. It depends only on the construction parameters of the system: surface curvatures and element indices of refraction.
These four image surfaces are equally spaced and occur in the same relative order: T-M-S-P or P-S-M-T. The best image quality occurs at medial focus. An artificially flattened field or medial surface can be obtained by balancing astigmatism and field curvature.