Characterising an unknown lens through laser ray tracing

In the last few posts I've described how one can characterise any lens, by estimating its cardinal points through laser ray tracing. In this post I'll give a real world example of how and why I do it.

As a photographer who likes using old medium format film lenses and sensor bracketing, to create XPan, negative size equivalent, digital captures, I make use of Mamiya 645 lenses, in my case: 35mm, 45mm, 80mm and 150mm. The PhotonsToPhotos Optical Hub does not hold any information on Mamiya 645 lenses.

My favorite lens is the 45mm 645 Mamiya, which, using various adapters, allows me to capture a flat stitched digital negative as if taken with a camera with a 86x36mm sensor. From which I can crop a digital XPan equivalent 617 format image.

The first step is to put the lens at infinity and measure the focal length using extension tubes, which in this case came out at 45.9mm.

I also estimated the minimum focus distance of the lens from the sensor plane, ie  433mm.

I then took an image of the exit and entrance pupils and estimated a pupil magnification of 1.67.

The final measurement was to estimate the on axis entrance pupil position, relative to the rear flange surface of the lens, using the laser leveler technique:

From the above we can estimate this as 72mm. To this we need to add the Mamiya 645 focal flange distance of 63.3mm. Resulting in the on axis entrance pupil being located some 135mm from the sensor plane.

Knowing this location means we know the no-parallax point of the lens, focused at infinity, relative to the sensor plane.

From all the information I then used the PTP Thick Lens Hub to create the following model of the lens:

We also know that the hyperfocal distance is measured from the entrance pupil, so we can now characterise the depth of field scale on the lens (see here), by using the hyperfocal bracketing relationship:

and using the simple equation:

Where x is the minimum focus distance from the entrance pupil, ie 433 - 135 = 298 mm in this case; H is the hyperfocal distance as measured from the entrance pupil, ie (f*f)/(N*c) + f; and n is the number of focus bracketed images we need to take from the hyperfocal to the minimum focus distance, at a given aperture (N). The above then allows us to estimate the circle of confusion baked into the depth of field scale from: (f*f)/(N*(x*(2*n-1)-f).

In this case, at f/22 I estimated the number of focus brackets (n) at 3.6. Feeding in all the data results in a CoC used for the Mamiya 645 45mm depth of field scale at some 53 microns. This may be compared to using the 'standard' full frame 30 microns CoC at the Mamiya 645 crop factor value of 0.62. ie just over 48 microns.

As for using this information in the field, using the Rule of Ten (see link on the right), the hyperfocal distance at 45mm focal length is some 4.5m at f/10 and at a CoC of 45 microns. Thus at, say, a CoC of 15 microns, the hyperfocal is some 4.5*3, ie say 15m away. If I see there is a point of focus in the scene at, say, 5m away, I know I likely need to insert a focus bracket. But I also know the DoF scale uses a CoC of some 50 microns, which will likely create a focus gap if I use the f/10 DoF marks, thus I'll likely use the f/5.6 marks. As I say, all pragmatic and all calculable in my head.

Bottom line: I hope this post has been useful to others, but, as usual, I wrote it for my own record, but freely share it. 

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