Reconciling the Thick Lens Model with P2P Optical Bench

Started 4 months ago | Discussions thread
Bernard Delley Senior Member • Posts: 1,799
Re: just go with the thick lens model

Garry2306 wrote:

I’m keen to try this approach and wondered if you could share the process steps that you undertook. Reading the various posts here has confused me a bit as to how one uses extension rings to work out the inter nodal etc of a lens at, say, the minimum focus distance and ‘infinity’.

You gave the the correct thick lens equation in your opening post. I am slightly elaborating on it. I somehow prefer to use the symbol h instead of your t for the internodal distance. When you turn the focus ring of the lens, you modify the focal length, so f is a function of the 'distance' setting on the lens: f(s) . Also the internodal distance is a function of this setting in general: h(s)

Rewriting, the (your) thick lens equation:

d_i = (2 + 1/m_i + m_i) * f(s) + h(s)

I have also introduced a subscript _i to index the measurements that you do with the same (!) setting of the lens. So each lens measurement yields a pair (triplet) of values:

d_i a sensor - object distance

m_i magnification, derived from the portion of the ruler visible in the image or in LV.

x_i extension ring thickness used, as additional parameter for Method_1

interestingly, the extension ring thickness does not appear in the equation for d_i. But, for each different extension you get another d_i , m_i pair of values. If you have two such measurements, defining 2 equations, you can solve them in Method_1 by realizing the proportionality of m_i with the total extension (ring + internal) of the lens, ex_tot=x_i+e(s):

x_i + e(s) = (1 + m_i)*f(s)

eliminating the unknown internal focus extension e(s) depending on setting s, you find f(s) from

x_1 - x_2 = ( m_1 - m_2 ) *f(s)

In closeup settings of the lens, there may be no extension ring in measurement 2, then x_2=0.

Once you have f(s) , you find h(s) as you already wrote.

If you have several measurements using different extension, then you can find an average f(s) from the different pairs of measurements that can be formed. And you can determine the RMS deviation of each f(s) evaluation from the mean. I would argue the the RMS uncertainty for the mean of f(s) is smaller by a factor sqrt(n-1) than the RMS for the single evaluation. n is the number of measurements. No RMS single can be determined with just two measurements.

I will not go into details of Method_2, which considers a linear regression for d_i and v_i = (2 + 1/m_i + m_i) .

d_i = v_i *f(s) + h(s)

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