A simple method to estimate the Entrance Pupil position of any lens

Caveat Emptor: As lasers are involved, you need to be aware of the risk to your camera's sensor. So only use a laser if you are prepared to experiment and potentially damage your camera sensor. 

Addendum: An alternative approach to that presented in the original post below, is to only use the lens and project the image on a surface behind the lens. Using this surface image then allows you to locate the entrance pupil rays.

The following snaps, showing my 24-105mm F4L at 24mm, illustrates only using the lens, where we see the projected image, and recorded rays providing an estimate of the entrance pupil location, relative to the physical edge of the front of the lens, the pencil line, or some other lens reference location, eg the rear of the lens, at the flange surface, which is a known distance from the sensor for a given camera system.

Note in the test below I didn't level the lens, which I could have done by placing the lens on a bean bag; also it’s not critical to place the lens so that it projects an in focus image, which would project a small dot, as long as you can locate the entrance pupil with the laser line. In fact, placing the lens at an out of focus position, as shown below, aids finding the point where the line, or lines if the cross lines are visible as below, are centralised, ie when you are shinning the laser line through the pupil on the optical axis:

To further illustrate the work flow, I used my Canon 100mm F4L IS, with focus set to infinity. Having positioned the lens as above, I used a plastic set square to mark the lens rear flange surface. I then recorded two laser lines, either side of the lens axis at the edge of the field of view, ie to be as far from the axis as possible, simply looking to see when the projected image was central, ie by rotating the laser leveller.

Having marked the two lines, I measured where these crossed, realtive to the lens flange position; which gave me a measurement of 43mm.

Knowing this, I then added the Canon EF flange distance (44mm) to this, giving an entrance pupil location of 87mm from the sensor plane.

As a comparison, the PhotonToPhotos Optic Bench Hub gives an infinity entrance pupil location of 87mm ;-)

As a final comment, because the accuracy of the technique pivots around how accurate you are on aligning the angle of the laser line at the on-axis entrance pupil. If creating two lines, one either side of the lens axis, it is recommended that you keep the laser leveller near 45 degrees to the lens axis on a wide angle lens, and at the edge of the angle of view of a lens with a half angle of view of less than 45 degrees.

Once you have located the entrance pupil, you can use the Poor Man’s Optical Bench tool to reverse engineer your lens.

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The following is the original post that shines the laser onto the sensor, which I don’t recommend, ie use the lens only technique above

In the last post I introduced the Poor Man's Optical Bench, that I wrote to help visualise the principals and pupils of any lens, based on the following readily available inputs:

• The location of the entrance pupil, which is the no parallax point of a lens when taking panos, is also the location from where the hyperfocal distance is measured. However, this is a bit of a simplification, as in reality the pupils (entrance and exit) trace out a locus, which for the off axis rays will not be on the axis. However,, we will ignore this and assume the pupil location is the same for all rays. 
• The optical magnification
• Focal length at non infinity focus. Note the lens focal length can/will change during focusing, especially when using a macro lens
• Pupil magnification, which becomes important when carrying out macro photography

Of the above, the most fiddly to estimate, without access to a proper optical bench, is the position of the entrance pupil.

Assuming you don't have access to a physical optical bench, various techniques have been suggested to estimate the location of the entrance pupil, eg using pins, poles, through to using a laser pointer.

In this post, I'm introducing yet another technique, that I believe is superior to the laser pointer technique: that is use a laser leveler.

In my case I am using a cheap laser leveller that I had.

My logic for using a laser leveler, is that it gives you a clear line to record and you don't need to align it to the optical axis, as you do with the laser pointer, which is a dot, not a line. Also it is usually self levering, well mine is.

The method to as follows:

• Tape a sheet of paper to a flat surface
  
• Layout your camera at the focal length (if a zoom) and focus of interest, eg infinity focus
• Locate the sensor plane symbol on the camera and align the laser leveller to this so the laser line goes through the symbol and is parallel to the end of the sheet of paper. Mark the laser line's position with a couple of pencil marks as this will be your zero
• Move the laser lever in front of the lens and off axis, and rotate it until you see the screen image create its maximum blooming. At this point record the laser line on the paper, ie with a couple of marks
• Repeat the above as many times as you like, moving the laser leveller either side of the lens and creating as many 'rays' as you like. Note beams close to the axis will not likely be as accurately located compared to beams away from the axis, hence the technique is best used with wide angle lenses
• Once you have enough information, simply join up the marks to create the sensor baseline and where the rays converge, which is the estimated location of the entrance pupil on the axis of the lens. 

The more careful you are with establishing each ray, the more chance you will have that the rays will come together in a tight cluster. Also, this technique is more suited to wide angle lenses, as attempting to locate the entrance pupil with rays close to the axis is likely to create positioning errors.

As an example I just quickly analysed my Canon 24-105mm F4 at 24mm, focused at infinity, and estimated the entrance pupil at about 117mm from the camera's sensor mark.

If I look at the PhotoToPhotos Optical Bench Hub, the entrance pupil is located at 119mm, when focused at infinity, that is my simple laser leveller technique is different by some 2.5%.

One caveat that is worth mentioning is that fisheye lenses do not have a single, on axis, entrance pupil location. The laser leveller technique, however, will still allow you to carry out ray tracing to get an appreciation of your fisheye lens entrance pupil characteristics.

So, there you have it, a simple method to estimate the location of the entrance pupil, for those that wish to know the non parallax point of a lens, or as input into my Poor Man's Optical Bench.

As usual I welcome any comments on this post, or any of my posts.