How to measure distance of exit pupil to sensor plane

Question

Is there an experimental way to determine the distance of the sensor plane to the exit pupil? (acuracy a few milimeters with distances between 10-70 mm)

Why I want this In my lab I am working with a highly angle sensitive sensor, I need the distance of the exit pupil so that I can calculate chief ray angles for different positions on the sensor.

What I have Tried

Using a thin lens assumption and assuming that a collimated beam of light. The angle at which the angle enters the lens (measured from optical axis) is related to the exit pupil and the position of the light spot on the sensor

exit pupil = (distance of spot from center)/tan(incident angle)

My questions

1. Is my approximation valid to determine the position of the exit pupil

2. If not, what is a simple way to get a good approximation of the distance.

Answer 1

As you know, the entrance and exit pupil is the location of the aperture stop. However as seen from both the front and the rear of the lens, the location of this iris diaphragm is elusive, because you are looking at it though lenses of unknown power. Thus what you are after is the location of the virtual image of the iris.

Try this technique: Set the lens so that it is elevated off the bench, perhaps on a stack of books. Stop the iris down to its smallest diameter. Illuminate the iris with a flashlight beam. Mark the center of the rear and front element lens with wax pencil, make a dot. You might choose to use a scrap of marked cellophane tape, instead.

Procure a magnifying glass, perhaps a 10X loupe (you may need less or more power for this task). Peer through the loupe held to your eye. Focus on the blades of the iris diaphragm, as seen from the rear of the lens. Now back off and focus on the spot you made on the surface of the exit lens. You were forced to move the loupe towards or away from the iris blades to obtain focus. The distance the loupe traveled reveals the location of virtual image of the iris (rear exit pupil). Repeat viewing from the front to discover the location of the entrance pupal.

The above procedure might be more accurate if you substitute a close-focusing SLR. Focus on the blades of the iris, then without changing the camera’s focus, back the camera until the mark of the lens is in-focus. The distance the camera traveled reveals the spacing between the last lens element and the location of the virtual image location of the pupil.
Hope this helps!

Answer 2

It's the rear nodal you are trying to find. You won't have much luck unless you have an optical bench. That being said, detach the lens from the camera and place it on your bench or desk. Point it at a transparent metric ruler, illuminated from the rear. With the lens aperture wide open, place a white paper screen behind the lens. The image of the metric ruler will be projected on this screen. Adjust the distances, ruler-to-lens and screen-to-lens, to achieve magnification 1. A second metric ruler helps; use it to measure the length of the projected ruler image.

When magnification 1 (unity sometimes called 1:1) is achieved, accurately measure the distance between target ruler and screen. The screen placement will be 2X the focal length of the lens.Thus -- divide the distance target ruler-to-screen by 4. This will be the focal length of the lens. Divide distance screen to target ruler by 2, this this will be the location of the rear nodal.

Answer 3

Expanding a bit on @alan-marcus answer, here's how I do it. Requirements:

• a digital camera with live view and good manual focusing aids (I use a Sony A7R2).
• a lens that is reasonably fast, reasonably sharp wide open and focuses close (1:2 is enough - I use a Voigtländer APO Lanthar 2/65, which is ideal for this purpose).
• a focusing rail, ideally with millimeter marks.
• a stable tripod.

To measure the exit pupil position of a lens:

1. The lens to be measured should be set to infinity and the aperture stopped down fully.
2. Put it horizontally on a flat surface (e.g. a table) with the mount toward your camera setup. The mount should be aligned parallel to the film plane.
3. Focus your camera on the mount of the lens.
4. Mark the position on the focusing rail.
5. Using the focusing rail, move the camera until the aperture blades are in focus.
6. Note the distance between the current position and the position from step 4.
7. Add the flange distance to 6. (e.g. 46.5mm for Nikon F-Mount).

Usually, you will have to move the camera setup towards the lens. If you have to move it away (i.e. the exit pupil is behind the mount), subtract the distance, obviously.

This is the way I measured the values on http://www.chr-breitkopf.de/photo/exit_pupil.html.