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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