Equivalence theory for cross-format photographic image quality comparisons

Equivalence theory is commonly used by photographers in order to obtain equivalent photographs from cameras based on different sensor formats. A complete mathematical proof of equivalence theory that is valid for compound photographic lenses with any chosen pupil magnification is presented. An expression for a correction to the conventional equivalence formulae is derived, which is proven to be formally required whenever focus is set closer than infinity, although numerically significant only for macro photography. Additionally, this paper argues that equivalence theory should be used in practice to appropriately perform cross-format image quality comparisons and demonstrates how various common metrics should be evaluated.