The standard conservative formula for total DOF is this:
total DOF = lambda / (NA*NA)
where lambda is the wavelength and NA is the numerical aperture.
For common values of NA, using green light lambda = 550 nm, this gives the following values:
Code: Select all
NA DOF (microns)
0.10 55.0
0.14 28.1
0.15 24.4
0.20 13.8
0.21 12.5
0.24 9.55
0.25 8.80
0.28 7.02
0.40 3.44
0.42 3.12
0.50 2.20
0.55 1.82
0.60 1.53
0.65 1.30
0.70 1.12
0.75 0.98
What these numbers give is the distance between the top and bottom of the zone where the wavefront error is no more than 1/4 lambda across the entire aperture, for a "perfect" lens that has no aberrations at perfect focus.
It represents the depth of field within which (theoretically) there should be no more than 20% loss of contrast, compared to the image at perfect focus.
In other words, if you think in terms of 80% --> 100% --> 80% as you focus through the subject, it's the distance between the two 80's. Sometimes I call this the "two-sided DOF".
This formula corresponds to the first term in the more complex formula given by Nikon at
http://www.microscopyu.com/articles/for ... depth.html. Nikon's formula gives a bigger number, attempting to account for finite sensor resolution.
It also corresponds to the entire formula lambda / (2*NA*NA) used by Mitutoyo, except that Mitutoyo's formula gives the "one-sided DOF" that corresponds to 100% --> 80%.
-----------------------
I think that there is still some legitimate debate about the validity of those formulas for our applications. It's well known that under some conditions, you can stack with a larger step size and still get a good image. No problem there. The question is whether a
smaller step size is required for some subjects, and if so, why?
As far as I can tell, the theoretical formulas were worked out for perfectly flat smooth subjects. They tell how the appearance of that flat smooth subject will change depending on focus.
But for focus stacking the problem is often a little different from that. Our subjects are not necessarily smooth, not even in small areas. Instead they may be nanoscopically rough, with many small bumps and valleys at about the same size as light waves. It is not clear to me exactly how the appearance of those rough subjects may change depending on focus. It's conceivable to me that a rough subject might change appearance more quickly due to interference between neighboring features, but I am not aware of any investigations that address this issue.
In the tests that I have run, the formulas do seem to give pretty good estimates of DOF. See for example the results and methods at
http://www.photomacrography.net/forum/v ... 997#103997 and especially the follow-up at
http://www.photomacrography.net/forum/v ... 108#104108.
But perhaps things are different with other subjects. It would be nice to see that carefully investigated and documented.
--Rik
