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# Reconciling the Thick Lens Model with P2P Optical Bench

Started 8 months ago | Discussions thread
just go with the thick lens model
1

Garry2306 wrote:

Bill/Bernard

Thanks for posting your experience.

In fact I’ve been thinking about how evolve my split/thick model.

My current thinking is to use the thick lens model at minimum focus distance at the min and max focal length of a zoom, ie measure mag and calculate the inter nodal at the two focal length extremes.

Then do the same at around the hyperfocal, ie measure the mag, ie around NC/f, but here assume a thin lens model, ie zero inter nodal.
Then linearly interpolate between focus extremes, ie at x, and the zoom extremes, scaling the inter nodal distance accordingly.
My logic is that the thin lens is a reasonable model for DoF away from the MFD, but at the MFD a thick lens model is a better model for DoFs.

But I’m still exploring

I you have two extension rings, you can determine the focal length and the internodal distance also for the infinity setting of the lens.

To check things, I did measurements and least squares analysis for a well documented old lens some time ago: AI 200mm f/4 lens f=199.7mm h=88.7mm

my measurement at infinity setting (f and h are independent of distance setting for this old lens with fixed internal lens positions, but there is a built helicoid extension going with the distance setting) with bellows extensions 50mm 100mm 150mm 200mm gave

Method_1 f= 201.6 RMS= 2.3   h= 89.6 RMS 0.9

Method_2 f= 202.8 RMS= 0.5    h= 84.0 RMS= 2.4

Method_1 agrees within 1 sigma with the known data. Method_1 : eliminating h from the equations and finding f as the mean estimate, then finding the mean of h, is more accurate than doing a linear regression analysis through the data points as Bill mentioned. I think the equi-weighted regression analysis implies a less appropriate error estimate for the measured data compared to Method_1 .

Below is a comparison of  P2P data with my measurement using 0 and 27.5 mm extension ring.

I see two main differences compared to the P2P simulation based on patent data. The camera with this lens reports a less fast lens at 1:1.  The measured internodal distance is quite a bit smaller. However it is plausible by guessing from the eyeballed pupil positions seen from front and back.

Bernard Delley's gear list:Bernard Delley's gear list
Olympus TG-6 Nikon D7200 Nikon D500 Nikon D850 Nikon AF-S Nikkor 14-24mm f/2.8G ED +11 more
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