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------------------------- Pupil Magnification versus Angle of View

--------------------------------------------------------- By Bill Claff

All lenses exhibit pupil magnification, the ratio of exit pupil size divided by entrance pupil size.
However pupil magnification is often omitted in the discussion of photographic lenses, perhaps because it is rarely known.
Never-the-less, pupil magnification correlates with Angle of View and knowing even approximate values can be helpful in discussing optics.

This chart was constructed using the detailed datasheets for over 100 Zeiss lenses:

We observe that pupil magnification increases with Angle of View; retro-focal lenses (wide) can have pupil magnification greater than unity.
Conversely, the tele-centric lenses (telephoto) can have pupil magnification well below unity.

This is largely a consequence of designs that are limited by practical Flange to Focal Distance (FFD) restrictions.

In this chart I isolated two groups: fish-eye designs and Biogon/Hologon designs.

Non-rectlinear (fish-eye) designs clearly behave differently and from our small sample appear to have pupil magnification of approximately 4.
However, due to the fish-eye projection magnification will not be evenly distributed along the image circle.

The Biogon/Hologon designs illustrate how pupil magnification near unity can be maintained for wider lenses if desired.

The data also suggest that most symmetrical lenses, those with pupil magnification of unity, have an Angle of View of about 30 degrees.

Furthermore, it appears that zoom lens designs depart from unity more quickly than prime lens designs.

Pupil magnification figures for some photographic lenses may be found at the Optical Bench Hub which has optical prescriptions for a number of lenses from what appear to be matching or closely related patents.