Pupil Geometry in Photographic Lenses

When a photographer adjusts the aperture ring, the physical iris opens or closes. But the optical system negotiates something more subtle: two virtual images of that iris — the entrance pupil and the exit pupil — that govern every light cone passing through the lens. The entrance pupil determines the f-number, defines the perspective projection center, and sets the no-parallax rotation point for panoramic stitching. The exit pupil determines how light arrives at the sensor, controlling the chief-ray angle that digital sensors are sensitive to.

Understanding the distinction between the aperture stop and the pupils — and between the entrance pupil and the exit pupil — clarifies a surprising number of photographic effects that are otherwise mysterious: why macro photographers lose exposure at close focus, why rangefinder wides show corner color casts on digital bodies, why stopping down fixes some corner shading but not all, and what "telecentric" actually means versus the marketing use of the term.

This series walks through the key concepts, one article at a time.

The Articles

• What Is the Entrance Pupil? — The aperture stop, the entrance pupil, and why the f-number is defined by the image of the iris — not the physical hardware inside the lens.
• The Entrance Pupil as Projection Center — Perspective geometry, the no-parallax point for panoramic stitching, and the "nodal point" myth.
• The Exit Pupil and Your Digital Sensor — Chief-ray angle, microlens arrays, color cast from CRA mismatch, and why rangefinder wides can misbehave on digital bodies.
• Why Corners Go Dark — The three distinct causes of corner light falloff: natural radiometric falloff (the cos⁴ law), optical vignetting, and mechanical vignetting — and why stopping down fixes only one of them.
• Telecentricity Explained — What telecentricity actually means, how it is achieved by placing the stop at a group focal point, what it costs, and why most photographic lenses are not telecentric.
• Mirrorless vs. SLR Lens Design — How removing the SLR mirror constraint expands the optical designer's envelope for wide-angle and fast lenses — and what mount geometry does not guarantee.
• Working f-Number — Why macro photographers lose two stops of light at 1:1 magnification, the bellows factor, pupil magnification corrections, and the close-up diopter exception.

The Full Monograph

For the unified graduate-level treatment — first-order definitions, marginal and chief rays, working f-number derivation, panorama rotation theory, generalized illumination law, cos⁴ derivation, pupil aberration overview, telecentricity mechanisms, mirrorless design inferences, and a comprehensive misconceptions section — see the full monograph:

The Aperture Stop in Practice: Entrance Pupil, Exit Pupil, and Telecentricity

The monograph is the authoritative reference; the articles are standalone summaries suitable for readers who want the core idea for one topic without the full mathematical context.

How to Read This Series

Each article is self-contained. The articles build on each other loosely in order — the entrance-pupil articles establish the conceptual framework that the exit-pupil, corner-illumination, and telecentricity discussions depend on — but any article can be read independently.