DOF effects of add-on diopters

[LordV]

Below is a copy of a post I just made on POTN forum. The question here is is this correct ?

Brian V.

Following a discussion here http://www.dpreview.com/forums/post/56372729 started by user SteB on odd DOF effects using an add-on diopter. I did some DOF tests with my sigma105 lens at infinity focus with a +25 diopter (MSN202) compared to an MPE-65 lens at the same magnification (around 2.3:1). The target is an angled ruler.

You can see from the image below the sigma 105 +diopter shots have a much shallower DOF than the MPE-65. It appears the use of a diopter to increase magnification does not increase the apparent aperture of the system resulting in the shallower DOF. The DOFs actually approximately matched with the sigma at F22 and the MPE-65 at F7.1
I assume the same effect is seen using reversed lenses on the front of another lens.

Brian V

[rjlittlefield]

Yes, this is correct.

The results can be understood this way. Adding a lens in front does not restrict the aperture, so the Sigma 105 at infinity focus and f/22, plus the closeup lens, is still effective f/22 from the standpoint of the camera. But extending a lens does reduce its effective aperture, according to the well known formula f_effective = f_nominal * (magnification+1) [assuming constant focal length and pupil factor = 1]. So the MP-E 65 at nominal f/7.1 and magnification = 2.3 is roughly effective f/23. At constant magnification, both the exposure time and DOF depend on effective aperture, so those two configurations are almost identical. Diffraction blur likewise depends on effective aperture, so that's the same also.

If you were to draw ray diagrams for these two different lens configurations, you would find that the angles are the same. Same light, same image. The "odd DOF effects" are only because the same aperture is described using two very different numbers.

--Rik

[rjlittlefield]

BTW, there are similar "odd DOF effects" when you compare Nikon and Canon macro systems. The user interface of modern Nikon systems works in effective aperture, so when you set "f/16" on the camera, that means effective f/16, already compensated for magnification. But with Canon systems, the user interface works in nominal aperture, not compensated for magnification. As a result, a Canon system set to "f/16" may actually be effective f/32 at 1:1 magnification. To get the same effective apertures at 1:1, you might have to set the Nikon system at "f/16" but set the Canon on "f/8". (The exact numbers depend on the lenses and magnifications involved.) Again, these are just different ways of talking about the same aperture. DOF and exposure time and diffraction blur all depend on effective aperture in the same way on both systems. When Nikon users marvel at the extraordinary DOF of Canon's MP-E 65, it's because they don't understand that the f-numbers don't mean the same thing they're accustomed to.

--Rik

[LordV]

Thanks for the confirmation Rick. Yes I know about the confusion that arises between canon and Nikon cameras and the way the camera expresses apertures on communicating lenses. It just had not registered about add on diopters or add on reversed lenses. It does explain why I was disappointed in the image sharpness when I first got the MPE-65 lens. I had been shooting with a sigma 105 at F11 with 66mm of extn tubes and a reversed 50mm lens on the front with a set aperture of F11. This was in fact sharper than the MPE-65 at F11 at the same mag (around 4:1). That was when I learnt a bit about diffraction and realised the need to open the aperture on the MPE-65 to get sharp results.
Brian v.