Reconciling the Thick Lens Model with P2P Optical Bench

Started 4 months ago | Discussions thread
Bernard Delley Senior Member • Posts: 1,799
DoF estimates

Garry2306 wrote:

Garry2306 wrote:

Bernard Delley wrote:

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)

Bernard

Many thanks: very clear.

Now to find some time.

Cheers

Garry

Bernard

I’ve been thinking, which isn’t alway good

My use case is to code in my CHDK Lua script a ‘better’ lens model. Currently I assume a fixed lens thickness, ie that at MFD. This is a conservative view that introduces positive focus lap insurance when focus bracketing, ie the DoF will likely be reduced because of the fixed hiatus. Based on assuming hiatus at MFD is greater than that at infinity.

If I work out the internodal distance, hiatus, using the method you described, it will be right using the focal length you calculate from knowing the two extensions and magnification.
However, in CHDK and Magic Lantern Lua, the focal length reported is ‘just’ the infinity focal length, ie it doesn’t vary with focus.

I’m therefore thinking that knowing the focal length and thus hiatus at two actual extremes, eg at MFD and, say, around the hyperfocal, won’t be that useful, if the camera only reports a fixed focal length, ie focal length reporting doesn’t vary with focus.
I would welcome an6 thoughts you may have, or anyone else.
Cheers

Garry

The function f(s) shows a lot of variation. For example the 70-300mm zoom shown in my first post goes down from 300mm to 174mm at MFD. So one would have to parametrize that function f(s) properly, gleaning from information that the camera reports.

As I showed in a thread with illustrations gone now estimating DoF becomes more simple when calculating it from the magnification ratio, rather than from the distance. It turns out that the focal length matters little once you settled for a magnification at the focal plane and thus for a field of view at that plane. The separation of the H H'  planes, ~ the internodal, does not matter at all in this approach. There is a universal transition into the hyperfocal regime when you go top sufficiently short focal lengths.

see text under gallery image for details

However DoF from geometrical optics in paraxial approximation is not the whole story. Diffraction and aberrations of the real lens contribute to overall un-sharpness. In practice I take memorized or quicky calculated settings from the DoF model as guidance and may shoot two or three different apertures, to pick later for best effect.

guidance comes from simple formulas:  magnification m = 1 / r , r reduction factor

max Focal length for hyperfocal : Fh = c * f# *r

where f# is always the effective aperture number

closeup limit DoF to either side : dg0 = Fh * r

blur circle for (highlight) point a infinity referred to sensor: CoCi =  f * m / f#  , this one strongly depends on the focal length.

The DoF considerations show that the precise value of the focal length is  not so important in many practical contexts.

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