Formula for working out the size of slice

[MacroB]

Hello there,

I have a formula for working out the effective aperature: effective f-number= f-number x magnification + orig. f-number.

This makes me wonder if there is such a simple formula for working out the optimal thickness of a slice when photostacking?

Thanks to everyone for making this such an interesting and inspiring site.

MacroB

[AndrewC]

Depends on your lens - some such as microscope objectives or reversed enlarger lenses are easy and there are lots of threads scattered around the forum and on the web. Lot's of people will offer you spreadsheets to download. I've got an online calculator I use for my own needs http://tirpor.com/macro/macro_DOF.htm.

However, I think the best advice is use a formula as a starting point but then do it empirically. Shoot a stack with very small slices and then gradually drop more and more out while stacking it until you see banding start to appear. You very quickly find that for a certain lens / magnification you have a slice depth that suits you.

In this forum search for "DOF AND formula"

[seta666]

If working with microscope objectives this calculator works fine
http://www.microscopyu.com/tutorials/ja ... index.html
Regards

[MacroB]

Hello AndrewC & Seta666,

Many thanks for pointing me in the right direction.

I should have known that it was not quite so simple - have managed reasonably well with the trial and error approach, but will have a look at those website and see if there is anything for the MP-E65 lens.

MacroB

[Charles Krebs]

MacroB,

If you can work with Excel format spreadsheets have a look at:
www.krebsmicro.com/DOF3.xls

(There's also something in this specific to the 65mm MPE).

But as Andrew said, verify any "calculated" values with some actual testing.

[ChrisLilley]

I have a formula for working out the effective aperature: effective f-number= f-number x magnification + orig. f-number.

Yes, assuming the lens is symmetric. Or equivalently,

effective f-number= f-number x (magnification + 1)

This makes me wonder if there is such a simple formula for working out the optimal thickness of a slice when photostacking?

There is, but the equation has a term called the "circle of confusion" and there is no standard value for it. Large values mean that a range of focus is considered 'good enough' or 'in focus'. What is good enough depends on how large the image will be displayed and how picky you are being. There is also a lower limit, because for digital cameras you can't resolve anything smaller than a single photosite.

Personally, for images to be displayed at full camera resolution, a value of three times the sensor pixel pitch is fine enough.

Then, once you have a value for CoC, its

slice = 1.4 x f-number x CoC x (magnification + 1)/(magnification x magnification)

You will notice some similar terms to the equation for effective f number, so

slice = 1.4 x effective f-number x CoC / (magnification x magnification)


The units are the same as the ones you used for the CoC (micrometres, typically).

This assumes that the lens is symmetrical and that the depth of field is symmetrical, and that the slice size is 70% of the symmetric depth of field.

In practice, the symptoms of setting your slice too big is that you get banding of in-focus and out-of-focus areas in the stack. The symptoms of setting your slice too thin is that you take more shots than are needed, you computer spends longer calculating a result than is needed and (depending on the stacking algorithm) that the noise level increases.

[ChrisLilley]

Oh, and I mentioned an assumption of a symmetric lens (a lens with pupil factor = 1). Basically, if you hold a lens up to the light, look through the front, look through the back, and the size of the aperture looks the same both ways, its symmetric.

If its not symmetric, the formula for effective aperture needs to include the pupil factor. Or, equivalently, the formula for effective aperture always includes the pupil factor, but multiplying by 1 is the same as not taking it into account so its omitted for simplicity.

For more details see the FAQ entry What is "pupil ratio" and why would I care?.