Relationship Between Magnification vs Depth of Field

Have questions about the equipment used for macro- or micro- photography? Post those questions in this forum.

Moderators: rjlittlefield, ChrisR, Chris S., Pau

mjkzz
Posts: 1683
Joined: Wed Jul 01, 2015 3:38 pm
Location: California/Shenzhen
Contact:

Re: Relationship Between Magnification vs Depth of Field

Post by mjkzz »

JKT wrote:
Sun Jan 01, 2023 3:49 am
mjkzz wrote:
Sat Dec 31, 2022 4:39 pm
The nice thing about the formulas you're complaining about is that they're quite general. They work for the microscope, and they work equally well for other macro/micro/closeup systems.The nice thing about the formulas you're complaining about is that they're quite general. They work for the microscope, and they work equally well for other macro/micro/closeup systems.
No, it does not work for a lens focusing to infinity and that is why we are still discussing. Fundamentally, it is the "mathematical anomaly", dividing by zero (when focused to infinity), that attracted my attention.

Nikon's equation so far works well for me and it works for all.
If you read carefullly, he never claimed it to work near infinity. That was covered many messages ago. What you don't seem to accept is that Nikon version doesn't work either - the error is just less obvious.
Well, pardon me, I meant for the wave optics part. I think his 2nd equation is "derived" from the first, unless that is not the case, ie, Rik meant the 2nd equation is independent of the 1st.

mjkzz
Posts: 1683
Joined: Wed Jul 01, 2015 3:38 pm
Location: California/Shenzhen
Contact:

Re: Relationship Between Magnification vs Depth of Field

Post by mjkzz »

rjlittlefield wrote:
Sat Dec 31, 2022 7:14 pm
mjkzz wrote:
Sat Dec 31, 2022 4:16 pm
I quote you: "and θ is the maximal half-angle of the cone of light that can enter or exit the lens"
Actually you're quoting Wikipedia. But since I have been one of the editors of that page, I will apologize for never having fixed that bit of confusing wording. I can assure you that none of us who contributed to that page ever intended the interpretation that you're using.

Instead, the key part is the sentence that comes next: "In general, this is the angle of the real marginal ray in the system." In other words, it's the maximum angle of the light that actually gets through the system.

And as noted elsewhere in the same article, "The NA is generally measured with respect to a particular object or image point and will vary as that point is moved."

I have now tweaked the wording in the Wikipedia article to make it consistent with the first figure caption, which was already more clear.

But I'm sure we could discuss wordsmithing all day, and I would never convince you.

So, let me try a different approach.

You may be familiar with WinLens 3D. It is a commercial optical design package with a restricted version that can be downloaded for free.

Following are screen capture images showing WinLens 3D's analysis of a particularly simple optical system: a 100 mm thin lens with radius 20 mm, extended by various amounts so as to give magnifications 0.2, 1.0, and 5X.

Part of that analysis is to calculate the object- and image-side numerical apertures, as well as the image-side effective F-number.

I have added red boxes around those elements of the Aperture panel.


m0dot2.png

m1dot0.png

m5dot0.png


Please note that WinLens 3D says the NA's change depending on system configuration, and that in all cases Object NA, Image NA, and Effective F/Nos vary in the way that I have described earlier.

I wonder, what do you think about this?

--Rik
Rik, Sorry for late reply, two new years and too much feast :-)

I do not have that app at all, but the bottom line is, the wave optics effect should be independent of magnification, once it is built (or set for iris) it is like its inherent property. It is really determined by what is happening around the iris governed by aperture, which implicitly includes focal length.

The DoF due to wave optics is really an idea that if a point is considered as in focus, then, extending it a bit determined by wave optics SHOULD also be considered in focus, hence my "dumb-bell" diagram, the wave optics effect extends the range determined by geometrics.

Anyways, good discussion, thanks for all the inputs.

Post Reply Previous topicNext topic