Depth of Field Confusion

[Damon]

So I have a Canon MP-E65mm f/2.8 1-5x Macro. OK good.

 

I am trying to rectify something I read recently.

Here goes:

 

DOF on the Canon MP-E 65mm Macro Lens ranges from 2.240mm (1x, f/16) to .048 (5x, f/2.8). At 5x and f/16, the MP-E gives a minute .269mm DOF. This sounds worse than it really is as a grain of rice (says Canon) can fill the viewfinder. Subjects this tiny generally do not need as much DOF as something like a flower. (I beg to differ--but that's a different topic)

 

The Canon MP-E 65mm Macro Lens is advertised as an f/2.8 lens. And it can be set down to f/16. F/2.8 is fast, but many lenses can be stopped down well beyond f/16. Well, truth is, the manual gives a chart of the "Effective" apertures for this lens. To calculate these, use this formula ...

Effective Aperture = (Aperture Setting) + (Aperture Setting x Magnification)

 

So, even selecting f/2.8 at 1x magnification results in an effective f/5.6. Selecting f/16 at 5x results in an effective f/96. Selecting f/5.6 at 3x results in an effective f/22.4. Get it?

http://www.the-digit...ens-Review.aspx

 

No I don't. I see the formula, but if I set f16, am I really getting f96 @5X? Is that why the viewfinder almost goes black without a nuclear power source hitting the subject or is this formula deal marketing bunk?

 

-D

[Alex H]

Formula is real. Nominal apertures are usually based at the lens being focused at infinity. When the lens is focused at closer distance, there is a light loss with every lens.

 

The F/2.8 nominal aperture your MP-E 65mm would have if you could focus it to infinity. But it is already extended to focus to 1x magnification, loosing 2 stops of light.

[Alex H]

I have Minolta AF 3x-1x 1.7-2.8 Macro that has nominal aperture of F1.7 at 1x. In reality, it is probably less that F/4

[nfoto]

Aperture (f-number) is always defined for infinity focus.

 

Your formula represents the ideal case of a hypothetical 'thin lens'. In reality the pupil magnification p (=exit pupil/entrance pupil) needs to be factored into the equation. Most lenses are not symmetric so p differs from unity, often significantly so, thus leading to effective apertures very different from what the simple 'thin-lens' formula predicts.

 

N_eff=N*(1+ m/p) (*)

 

(* sometimes the reciprocal of p is used, so be sure to verify your calculations)

 

For a telephoto design, p

 

Diffraction is influenced by the effective aperture, so keep the temptation of stopping down in check. You will be far better off by using your lens wide or near wide open, and apply focus stacking to achieve the required depth of field.

[OlDoinyo]

I would clarify here: diffraction degradation is a function of absolute aperture size rather than f number as such. f/96 at 5x magnification involves a larger aperture than f/96 at infinity. It might be less confusing to view the problem in terms of effective focal length.

[nfoto]

I don't follow you? Why bring in focal length?

[Damon]

First, I may not always grasp some of these concepts when formulas come into play.

 

Thanks Alex. That Minolta lens sounds like a gem.

 

Bjørn, thanks as well. So do you think @f16 (effectively f96) I would in reality be getting 6 times more depth of field?

Re: For a telephoto design, p<< 1 thus this optical principle costs you even more 'loss of light' (of course virtually no light is actually lost, but the size of the projected image circle increases, which leads to the same thing because area intensity is reduced)

-But if I stop down my projected image circle decreases which should make the area intensity increase. I know I am getting this all backwards because clearly the view gets darker as my f number goes up-

--I have shot@f16 and the result is not as sharp for sure. Software helps but is not perfect. I thought f8 was the sharpest for this lens but I will look around some more and double check. You are dead on saying shoot smaller number and stack.

For a moment I thought if I could shoot at f16 my stack sizes could be reduced significantly.

 

OlDoinyo--Re:It might be less confusing to view the problem in terms of effective focal length.

Less confusing is good, if only I could understand it. :)

 

-D

[nfoto]

No, you are not getting more depth of field, just less light.

[Damon]

Thanks!

 

-D

[OlDoinyo]

For nominal focal length L₀, the effective focal length L would be given by L=L₀(1+m/p). For p near 1 at m=5, a 65mm lens is effectively a 390 mm lens, with the same diaphragm opening. Close focusing will not cause worsening diffraction problems, but it will cause the f number to increase because the focal length is greater.

[nfoto]

We're talking about aperture, not focal length. The focal length might change as a lens focuses closer due to its optical design, but not necessarily so. A unit focusing lens does not change its focal length at all. Its effective aperture, however, does change. All good textbooks on optics have the required equations.

 

Alternatively, we could cast the equation into [conjugate] distances in the image vs subject domain and use

 

1/u+1/v=1/f

 

from which m=v/f-1

 

and continue as before. I usually prefer thinking in terms of conjugate distances as these relate closer to the practical issues to solve when doing high-magnification and close-up photography.

[cmoody]

--I have shot@f16 and the result is not as sharp for sure. Software helps but is not perfect. I thought f8 was the sharpest for this lens but I will look around some more and double check. You are dead on saying shoot smaller number and stack.

For a moment I thought if I could shoot at f16 my stack sizes could be reduced significantly.

 

Because of the effective aperture, diffraction softens the image up ridiculously quickly with the MP-E if you try and stop it down. When I've done stacks with it, I use f5-f5.6 regardless of the magnification I am at, anything more seems to not be worth it. Mind you my stacks are not UV, and are all very much still life:

 

Wood ant specimen

 

Instant coffee

 

Tick...

 

Dead ground beetle specimen

[colinbm]

Nicely stacked photos.

[Damon]

Thanks cmoody for that MP-E info. Nothing beats real experience so I appreciate you sharing that as it is not a common lens.

 

-D

[Jorge Garcia]

I do not know formulas but I hare read than DOF depends on magnification and aperture (and magnificacion depends on focal length and subject distance), is this a simplification?

[enricosavazzi]

Trying to reason things out without using formulas often results in major errors. DOF is a typical example of this. There is simply no substitute for math.

 

Magnification is a function of focal length, distance between subject and lens entry pupil, and distance between lens exit pupil and sensor. If you want to obtain focused images, the two distances and the focal length must also satisfy a given mathematical relationship (except for pinholes, which are approximated as having undefined focal length and infinite DOF). However, focal length cancels out when solving the DOF equation, and this is why we say that DOF does not depend on focal length.

[nfoto]

Focal length cancels out for the simplified version of the DOF equation. In the full equation, focal length is insignificant and not influential unless it is extremely short (a few mm at most).

 

So, you basically are right.