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[OM] DoF and Focal Length [was] OM macro / closeups vs medium format /

Subject: [OM] DoF and Focal Length [was] OM macro / closeups vs medium format / TLR
From: "John A. Lind" <jlind@xxxxxxxxxxxx>
Date: Mon, 07 Jan 2002 00:13:16 +0000
At 13:45 1/3/02, Frieder Faig wrote:

Good site. Must have been lot of work. I like it.
To be very accurate. Ouer opinions are not opposed to each other. You`ve chosen 1:10 magnification to demonstrate that dof remains practicaly the same. This is true, but only with high magnification like you used.

I´vs found a ugly hyperbola curve for dof depending on focal length.
I´ve some graphics too. have a lock at:

http://studweb.studserv.uni-stuttgart.de/studweb/users/mas/mas12462/Optik/dof_considerations.html

oh, oh, the urls are getting longer and longer...

Frieder Faig

I was able to replicate your graphs by starting at the very beginning with the classical "thin lens" formulae [see note] and doing all the derivations (algebra and geometry) for DoF at constant magnification.

I need to put together the graphics, but here are some observations based on what I've built:

1. You're exactly right that I didn't use enough magnification range to find the hyperbolic shaped curve (not certain yet whether it is a quadratic [conic section]). I haven't looked at it enough and am doubtful I'll try to rearrange it to see. [Already performed enough geometry and algebra getting this far.]

2. For practical application, if the subject distance remains greater than the depth of the DoF, then changing focal lengths and moving closer or farther does not change the DoF significantly (indeed, it's insignificant).

3. The "knee" of the hperbolic shaped curves is approximately at the point subject distance (critical focus distance) equals the DoF. As subject distance decreases *below* the DoF depth, increasing or decreasing focal length makes greater changes in the DoF (indeed it can be quite dramatic).

4. The formula for "hyperfocal distance" based on focal length, aperture and maximum acceptable circle of confusion is actually:
  H = [f^2/(N*c)] + f
    H = hyperfocal distance
    f = focal length
    N = aperture f-stop number
    c = maximum acceptable circle of confusion
Many sources omit the trailing "f" and use only [f^2/(N*c)] which is an approximation (albeit very close; 40-55 millimeters at 10 meters isn't far off).

NOTE:
Some might question the use of "thin lens" formulae for this. In this application, a compound "thick lens" can be modeled as a "thin lens" provided the definition of "critical focus distance" is the front lens node, not the film plane as is commonly used in lens markings. In addition, the image distance is from the rear lens node to the film plane. The gap between the two is the "thick compound lens." Unfortunately Olympus doesn't publish the locations of the front and rear lens nodes and it requires an optical bench to find their locations. Even so, the "gap" between the front and rear nodes doesn't affect the equations, if the proviso of the "critical focus distance" definition is kept in mind.

Hoping I pounded all this in on the keyboard correctly.  Getting late . . .

-- John


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