Laser Ray Tracing Validation

In the last post I outlined the basic approach to using a laser line leveller to help identify the cardinal points of an unknown lens. The basic workflow being:

1. Set your lens to the required focus, ie magnification, and, for a zoom, the required focal length;
2. Using extension tubes measure the focal length (F) and note the magnification (m). For example, at infinity m = 0. You can also accept a quoted focal length;
3. Take two in focus images of the aperture, one of the entrance pupil and one of the exit pupil. Calculate the pupil magnification (p);
4. Align a ruler along the axis of the lens, ideally at/near the centre of the lens; 
5. Using a laser leveler (ideally two if you have them), take images of two laser lines that point to the (on axis) entrance pupil and the rear flange surface of the lens;
6. Ingest the images into (say) Photoshop and rotate all the layers so the lens axis is horizontal (convention dictates the exit of the lens is on the right;
7. Using Photoshop guidelines and the line tool, identify the position of the on axis entrance pupil and the flange surface;
8. Using the ruler add in the sensor location, ie for a Canon EOS lens, 44mm from the lens flange surface;
9. Measure the distance from the sensor to the entrance pupil (k) and use the following expression to estimate the lens hiatus or internodal distance (I): k - 2*F + F*(1/p - m);
10. Using the PhotonsToPhotos  Thick Lens Optical Bench, enter F, m, p, I and the aperture (N) of interest into the calculator.

In order to show the workflow, in this post I'll look at my Canon 24-105mm F4 IS USM lens and set it to 24mm infinity focus, to compare it to the lens in the PTP database.

In the above we see the optical axis (red) ray in the top image, together with a ray helping to estimate the location of the (on axis) entrance pupil. In the lower image we see two arbitrary rays helping to locate the lens rear flange surface. The third image is a composite view.

The final step is to add a few Photoshop guides, and using the line tool, trace out the laser rays to identify the on axis entrance pupil, the lens rear flange, and, finally, the sensor, ie, in this case 44mm from the lens rear flange surface:

From the above we can estimate the entrance pupil is 76mm from the lens flange, which leads to the entrance pupil being 76+44 = 120mm from the sensor; giving us k.

From the images taken of the pupils, the pupil magnification is about 4.2. As I set the lens to 24mm focal length for this test, and as I wish to compare with the PTP data base, in this case I chose to use the PTP focal length of 24.93mm. This leads to a calculated internodal of 76.1mm.

Putting all the information into the PTO Thick Lens Optical Bench results in the following:

Which can be favorably compared to the PTP Optical Bench:

 

So, there you have it: in about 15mins you can map out any lens, simply using a DIY laser leveler and a few iPhone images.

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