At 3:52 AM +0100 1/18/05, Listar wrote:
>From: "Jeff Keller" <jrk_om@xxxxxxxxxxx>
>Subject: [OM] Re: f-stops (Was: Solstice web-site news)
>Date: Mon, 17 Jan 2005 10:23:37 -0800
>
>
>I've seen the NA figure for microscope lenses but have never dug into where
>it came from.
I think it came from Abbe's mathematical analysis of microscope
optics and resolution, done in the late 1800s. The NA determines the
resolution of a microscope. Higher NA is better.
I mentioned NA only to buttress my point that only the included angle
of the light cone matters.
>You also switched from sin to tan to calculate the f-stop [which makes sense
>to me ;^) ].
The sine is used to compute the NA given the angle, while the tangent
is used to compute the angle given some linear dimensions of the
light cone. It's easy to see if one draws a little picture.
>The light striking the film plane has to act similar to a
>simple lens (?) whether it is a retro-focus or telephoto
Yes; the light doesn't know any better.
>... but what was it
>that Olympus said about the advantages of retro-focus for digital cameras
I don't recall, but I would guess that the stated advantage of the
retrofocus is that the cone angle is small, and so the CCD chip's
maximum acceptance angle won't be exceeded. If the cone angle is too
large, some light is lost in the CCD, never reaching the
light-sensitive part of the CCD. This is a particular problem in the
corners of the frame.
>Clearly I'm confused about the cone of light on the back side of the lens
>... probably the difference between off axis angle and angle due to edge of
>aperture? I guess I need to look at the 4/3 explanation again.
It's all simple geometry. I would draw a lens system showing the
edge rays for an on-axis object and image, and then the off-axis
situation. The 4/3 system will show the same effects as any other
lens system.
>Any short explanations for NA using sin and/or not using f-stop for
>microscope lenses?
Microscope lenses are diffraction-limited, and are almost always used
at full aperture (max NA), unlike camera lenses. The larger the NA
the greater the resolution.
Joe
>Thanks,
>-jeff
>
>----- Original Message -----
>From: "Joe Gwinn" <joegwinn@xxxxxxxxxxx>
>Subject: [OM] Re: f-stops (Was: Solstice web-site news)
>
>
>>
>> The NA is n sin(a), where "n" is the refractive index of the
>> image-space medium and "a" is the half-angle of the converging code
>> of light. For a photographic lens, the medium is air and so
>> n=1.0000.
> >
>>
>> The half-angle "a" can be computed from the f-stop:
>> Tan(a)=(diameter/2)/(focal length). For our purposes, the NA isn't
>> needed.
>>
>> So, measure the diameter of the converging cone of light just after
>> the last lens, and also the distance from the plane in which that
>> diameter was measured to the image plane (where that cone ends in a
>> point), and compute the f-stop from that: fstop= distance/diameter.
>> It isn't necessary to actually compute the half-angle.
>>
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