Zerene stacking step size table question

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Lou Jost
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Zerene stacking step size table question

Post by Lou Jost »

I am testing a medium format lens combo: the Mamiya 250mm f/4.5 apo lens in the rear, and Mamiya 120mm f/4.0 macro lens reversed in front, so m=2.

If I look at the Zerene step-size table for lens combos stopped down in front, Table 2-A, I get a step size of 80 micrometers for a lens at f/4.

If I look in Table 2-B for lenses stepped down in back, I get a step size of just 9 micrometers.

I wonder which one I should use, with both lenses wide open? They are very different.

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Post by rjlittlefield »

I'll have to review the situation for Table 2-A, but at this moment I think that it's only an approximation for combos focused in the front. Tables 2-B and 2-C are exact (within the limitations of the model, of course).

I would analyze as follows...

The exit pupil of the front lens will be 120/4 = 30 mm diameter.

The entrance pupil of the rear lens will be 250/4.5 = 55.6 mm diameter.

The front lens will be the limiting aperture.

That being the case, there are two ways to go.

One is to convert f/4.0 to NA 0.125, and use Table 2-C or the formula that lies behind it.

On that path, the closest value in the table would be for NA 0.14, DOF = 0.028 mm.

The formula sitting behind the table is DOF = lambda/NA^2, so more accurately the DOF would be 0.00055/0.125^2 = 0.035 .

Alternatively, knowing that Feff_rear = Feff_front * m, conclude that the effective aperture at the sensor is f/8 and look that up in Table 2-B, where the value again shows 0.035 .

Does that make sense? Then more interesting, does it match experiment?

--Rik

Lou Jost
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Post by Lou Jost »

Thanks for showing how to think about this! I'll try some experiments.

Lou Jost
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Post by Lou Jost »

I looked at how exposure changes as the rear aperture is closed (front aperture is wide open throughout). The exposure does not change until the rear aperture is closed down to about halfway between f/11 and f/16. From f/22 onward, one stop of aperture closure = one stop less light reaching the sensor.

So this suggests the front aperture is limiting until just past f/11, so EA of the front lens may be higher than what the theory calculated.

I can probably safely use your step value, as a conservative choice, until f/8, and from there on use your table 2-B.

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Post by rjlittlefield »

Just to check... The analysis method that I used assumes that the rear lens is focused at infinity. Was that the case in your experiment?

--Rik

Lou Jost
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Post by Lou Jost »

Yes, as was the front lens.

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Post by rjlittlefield »

OK, then one simple and interesting check is to just measure the pupil diameters. Are they 30 mm and 55.6 mm? Both measurements should be taken in the infinity space between lenses, so looking from the rear into the reversed front lens, and looking from the front into the rear lens.

--Rik

Lou Jost
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Post by Lou Jost »

I'll take it apart and look later, but when I put an adjustable 46mm iris in between the two lenses to run a second set of tests just now, the exposure did not change as I closed down that iris, until it reached about 28-29mm. My exposure meter only registers in 1/3 stop increments, so this is consistent with an exit pupil of 30mm.

perdu34
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Post by perdu34 »

rjlittlefield wrote: The formula sitting behind the table is DOF = lambda/NA^2, so more accurately the DOF would be 0.00055/0.125^2 = 0.035 .
Hi Rik, A couple of, probably irrelevant questions, about this equation.

Why is lambda in mm and not nm? Is it just to give an output that is also in mm?

Why is lambda green? For violet DOF is 24um and red it's 40um. Am I misunderstanding something about colour correction in lenses?

Lou Jost
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Post by Lou Jost »

Every formula has to have all its variables in consistent units or it will require extra factors in the formula to make them so.

Humans and cameras are most sensitive to green light, so it is normal to use that. If you are using monochromatic light of a different color, that should be lambda.

I ran some stacks with my lens combo at different apertures, and compared stopping down the rear lens versus stopping down an aperture between the lenses. It turns out that using the rear lens' aperture caused chromatic aberrations, which got worse as the lens was stopped down further. Stopping down the lens with an added aperture between the two lenses did not cause aberrations. For this combination, it was definitely superior to stopping down the rear lens. This is in line with Rik's analyses of how to stop down a lens combo.

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Post by rjlittlefield »

perdu34 wrote:Why is lambda in mm and not nm? Is it just to give an output that is also in mm?
Yes. NA is just a number, with no units attached. So the calculation lambda/NA^2 gives a value that has the same units as lambda. If you plug in lambda in nm, you get DOF in nm.
Why is lambda green? For violet DOF is 24um and red it's 40um. Am I misunderstanding something about colour correction in lenses?
No, what you've said is correct -- red has more DOF than violet. Resolution varies the same way -- violet can resolve more detail than red. Both of those less/more relationships are easy to confirm by experiment. The exact values are much harder to determine, for the simple reason that sharpness various smoothly with distance from perfect focus. See http://www.photomacrography.net/forum/v ... hp?t=23751 for a lot more about that. For most stacking operations, you want to be running in a regime where the MTF curve just sags more with larger step size, rather than dropping clear to zero at some lower cutoff frequency. As a result, for Lou's application the differences between say 0.030, 0.035, and 0.040 would be a matter of subtle differences in sharpness at the midpoints between steps, rather than clear and obvious focus banding.

In practice there are a lot more considerations that affect choice of "best" step size. A big one is the tendency of features to "squirm" laterally as focus is changed, due to the "utilized aperture" effects. Sometimes linear features on shiny subjects require a lot finer step size to avoid artifacts from squirming, than they would just to maintain sharpness from diffraction-limited DOF. See for example http://www.photomacrography.net/forum/v ... 187#149187 .

The choice of green for lambda is motivated by human vision, as Lou said.

--Rik

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