## MP-E 65 DOF Calculation For f/2.8 and f/4.0

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lonepal
Posts: 322
Joined: Sat Jan 28, 2017 12:26 pm
Location: Turkey

### MP-E 65 DOF Calculation For f/2.8 and f/4.0

Hi;

I used http://coinimaging.com/calculator.html? for DOF calculations and just asking to approve my calculations.

For example;

DOF@f/2.8, COC:0.018 for 5X = 0.0242mm
DOF@f/4.0, COC:0.018 for 5X = 0.0346mm

Somebody please approve the calculator is right

Thanks.
Regards.
Omer

rjlittlefield
Posts: 21403
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:
Those numbers match the classic ray optics geometry model: 2*C*F*(m+1)/(m*m) for C = circle of confusion, F = nominal F-number, and m = magnification, assuming focusing by extension using a lens with pupil factor = 1.

That formula ignores diffraction, which seems like a pretty fundamental mistake because we're always working in the regime where diffraction is important. But in this case (and many others) it works out OK because the F-numbers are in the critical band where the Airy disk spot size is about the same as COC. That condition makes the geometry-only formula give numbers that are close to what the fundamentally more accurate wave optics model says.

To be specific, the wave optics numbers for 1/4-lambda wavefront error at 550 nm are 0.0248 for f/2.8, and 0.0507 at f/4. The larger DOF predicted by wave optics for f/4 is because F/4 at 5X gives effective f/24, which has an Airy spot size significantly larger than 0.018 mm so the classic formula is pessimistic. For smaller f-numbers it goes the other way and the wave optics formula becomes pessimistic because it does not account for the limitations of sensor resolution.

The reality is that there is no crisp line between "sharp" and "not sharp". The image just becomes gradually more blurred as you get farther away from perfect focus. If you are focus stacking, this means that larger steps produce gradually worse focus banding. For sufficiently small steps you can't see the banding at all; then it becomes maybe detectable with careful study; then clearly detectable with careful study; then immediately obvious to an expert; and so on, until at some point even a first-time viewer would say there's something wrong.

As a result, the judgement of what is an acceptable step size will vary from one photographer to another. Even with the same photographer it can vary from one combination of subject/lighting/lens/application to another.

Use the calculations for guidance. If in doubt, go smaller. If you need a precise number, determine it by experiment.

--Rik

lonepal
Posts: 322
Joined: Sat Jan 28, 2017 12:26 pm
Location: Turkey
Thanks for the explanations Rik!

Then why we do not create a DOF sheet for database for the most common lenses?
When somebody need the average DOF values, for example for MP-E 65, they can use the sheet as a reference.

That's just an idea.
Regards.
Omer

rjlittlefield