change of focal length as function of aperture

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Guest

Posted: Wed Jan 09, 2008 8:49 am

What is the formula to recalculate focal length of lens as function of
aperture ?
What is the proper scientific explanation?

I need to know focal length at small aperture, but it is difficult to
measure.
I measure focal length with precision of 0.1% - 0.2% with large
aperture.
Then reduce aperture 2 times.
Then measure focal length and get different result !
Repeatedly (20+ lenses tested) focal length with smaller aperture is
longer by 0.2% ... 0.4%.
Are you _sure_ that such effect does not exist, thus my method of
measurement is wrong?

The line includes only object, symmetric biconvex lens and camera.
refraction index n~1.5,
aperture ~3mm is <1% of object-image distance,
focal length=1micron
Line is asymmetric: |object-lens| / |image-lens| = 3, thus symmetric
lenses are not not the "best form" lenses. But I probably observed
this effect on nearly symmetric line.

Thanks
Krzysztof

Helpful person

Posted: Wed Jan 09, 2008 2:14 pm

Joined: 22 Jun 2004 Posts: 692

On Jan 9, 1:49 pm, ksyr...@gmail.com wrote:

Quote:

Focal length does not vary with aperture. The most likely problem is
with your measurement method.

Spurious answers can be obtained due to spherical aberration. This
will shift the apparent focus as the aperture is changed. However,
focal length is defined by the focal position at the limit as the
aperture is redced to zero.

Richard J Kinch

Posted: Wed Jan 09, 2008 7:29 pm

Guest

Quote:

Then measure focal length and get different result !

The error of your measurement technique, not the focal length, changes with
aperture.

Helmut Wabnig

Posted: Thu Jan 10, 2008 5:44 am

Guest

On Wed, 9 Jan 2008 10:49:44 -0800 (PST), ksyrycz@gmail.com wrote:

Quote:

http://commons.wikimedia.org/wiki/Image:Lens_chromatic_aberration.png

There are at least 5 different definitions of "best focus"
Which one are you using?

w.

DonJan

Posted: Thu Jan 10, 2008 10:01 am

Guest

On Jan 9, 1:49 pm, ksyr...@gmail.com wrote:

Quote:

Measure your EFL as a function of aperture, perform a regression: A +
BY^2 + CY^4 . A is the EFL. You want a lot more data points than
terms in the regression. If the data is monotonic, this method works
well. If you have inflections then you need to see if the results make
sense.

ImageAnalyst

Posted: Sun Jan 13, 2008 8:15 am

Guest

On Jan 9, 1:49 pm, ksyr...@gmail.com wrote:

Quote:

however change depth of focus and depth of field so, like the others
said, you probably are measuring the distance between the lens and the
image with some variation because the depth of focus is now longer
and it has a greater distance where it appears to be in focus - it's
harder to find the place where it's at best focus.

Also I find it hard to believe that the focal length is 1 micron -
that's only 1/100th the width of a human hair's diameter away from the
back principal plane - seems very unlikely. It'd be essentially on
the back surface of the lens!
Regards,
ImageAnalyst

Richard J Kinch

Posted: Mon Jan 14, 2008 12:09 am

Guest

ImageAnalyst writes:

Quote:

Also I find it hard to believe that the focal length is 1 micron

And get a patent if it's true. Think of what we could do with f/numbers
that small.

Posted: Mon Jan 14, 2008 1:15 pm

Guest

Sorry for mistype. Wavelength is 1 micron, focal length is about
100mm.
a=3mm, L=200mm, lamda=0.001mm
Thus Fresnel number F=a^2/(L*lambda)=45

Change of depth of field with aperture is obvious.

My experimental "definition" of focal length f is 1/f=1/x+1/y,
where y is distance between lens and plane of best sharpness.

I preferred not to suggest answer in first post.
If aperture or Fresnel number goes to zero then diffraction could
change distance between lens and plane of best sharpness. Just imagine
small aperture. If camera is far from lens you see nothing except
diffraction. But if object is in infinity and camera is close then
camera shows image of object.

This effect is small. On my line F=45, change of aperture is 50% and
change of focal length Detla_f=10^-3.

I remember a page (can't find it now) about Fresnel micro-lenses of
very small F and large dependence of their focal length from aperture.
And F/Delta_f was of the same order of magnitude as on I get.
OK, I don't use Fresnel lens. Still it is not obvious and I can't
calculate such ?second? order effect.

Dave Martindale

Posted: Wed Jan 16, 2008 9:17 am

Guest

ImageAnalyst <imageanalyst@mailinator.com> writes:

Quote:

As far as I know, aperture doesn't change focal length. It does
however change depth of focus and depth of field so, like the others
said, you probably are measuring the distance between the lens and the
image with some variation because the depth of focus is now longer
and it has a greater distance where it appears to be in focus - it's
harder to find the place where it's at best focus.

Changing aperture *does* change aberrations. If the lens has spherical
aberration, rays that pass near the edge of the aperture converge to a
point which is different from the convergence point for paraxial rays.
When the lens is wide open, the plane of best focus is determined by
minimizing the size of a blur spot created by all of these rays, and it
will be somewhere betweeen the best-focus plane for paraxial rays only
and the best-focus plane for edge rays only. As you stop down the lens,
the rays that suffer most from spherical aberration are removed, the
blur spot gets smaller, *and the plane of best focus moves towards the
paraxial-ray focus plane*.

So this may be what the original poster is observing.

Dave

ImageAnalyst

Posted: Mon Jan 21, 2008 6:13 am

Guest

On Jan 16, 2:17 pm, da...@cs.ubc.ca (Dave Martindale) wrote:

Quote:

ImageAnalyst <imageanal...@mailinator.com> writes:
As far as I know, aperture doesn't change focal length. It does
however change depth of focus and depth of field so, like the others
said, you probably are measuring the distance between the lens and the
image with some variation because the depth of focus is now longer
and it has a greater distance where it appears to be in focus - it's
harder to find the place where it's at best focus.

Changing aperture *does* change aberrations. If the lens has spherical
aberration, rays that pass near the edge of the aperture converge to a
point which is different from the convergence point for paraxial rays.
When the lens is wide open, the plane of best focus is determined by
minimizing the size of a blur spot created by all of these rays, and it
will be somewhere betweeen the best-focus plane for paraxial rays only
and the best-focus plane for edge rays only. As you stop down the lens,
the rays that suffer most from spherical aberration are removed, the
blur spot gets smaller, *and the plane of best focus moves towards the
paraxial-ray focus plane*.

So this may be what the original poster is observing.

Dave

=======================================Dave:
You are correct. Those are good points to make. He also said that
the aperture was only 3 mm -- that's fairly small. Maybe it's some
kind of cell phone camera or optical drive optics. He said that he
sees a diffraction pattern so maybe he has such a small aperture that
he's diffraction limited and can't use normal optical equations (like
the thin lens approximation, etc.). If diffraction is a problem then
you fall under more complicated equations and maybe the plane of
"best" focus *does* change with aperture - I don't know. Even
defining "best" in that realm may be a judgement call - there may be
several "bests" depending on how you define them.
Regards,
ImageAnalyst

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