E1 focal length multiplier?

Started Jun 26, 2003 | Discussions thread
Joseph S Wisniewski Forum Pro • Posts: 34,390
A bit about lens designs...

Larry Lueck wrote:

Maybe I just spend too much time reading digicam newsgroups, but
I'm just speechless with how little is STILL understood about the Oly
lens! (And why isn't Joe the lens guy in here debunking the

Because you're not the only one who's been been spending too much time reading digicam newsgroups.

The Oly E-1 lenses use a set of lenses at the camera end of the
lens to
focus/direct the light parallel to the CCD. There've been images of
this all over the place. Like here:
http://www.olympus-pro.com/eu/en/product/lenses.html (That's what
I found first, but
I've seen similar images for a long time!)

That image doesn't help the understanding of this issue, unfortunatly. It only shows "chief rays". Picture, instead, "bundles" of rays. Each point on of the subject is the source of a bundle. The bundle only includes the rays that actually make it through the aperture, and for the sake of this discussion we'll assume the aperture is perfectly round. The ray that goes exactly through the center of teh aperture is the "chief ray". The rays that just make it past the edge of the aperture are the "marginal rays". The marginal rays define the shape of the "bundle". For a lens with a round aperture, the bundle takes the shape of a cone, with its apex (point) on a point on the subject, and it's base on the "entrence pupil", the "image" of the aperture as seen from the front of the lens. The chief ray runs right through the center of the bundle.

The bundle then continues to the film or imager, as another cone. The base of this cone is the "exit pupil" of the lens, the image of the aperture as seen from the rear of the lens. The apex, of course, is a point on the imager.

So, for the best match for a digital sensor, you want the lens to be telecentric, which means that all the chief rays arrive perpendicular to the sensor (lust like the Oly picture). The marginal rays are still cones, centered around the chief rays.

Since you need all the light to avoid vignetting, from chief ray to marginal rays and all the rays in between), the rear element of the lens must be large enough to accomodate the base of the complete bundle of rays that is striking a point at the edge of the imager.

The math for figuring out how big the rear elememt and mount opening) have to be is very simple, just a little trig. Since the angle of a ray bundle is determined by the f stop indepently of the focal length (very convenient) you can work the whole thing via similar triangles.

Take a 50mm f2.0 (any old 50mm f2.0). The "real" aperture is a 25mm circle, 50mm from the focal plane. If you add telecentric optics, the exit pupil becomes larger, and moves farther from the focal plane, so the end effect is that the angles of the cones around the chief rays remain the same, although the chief rays become more perpendicular to the sensor.

At a point 43mm from the sensor (the lens mount location) the ray bundle will be 21.5mm in diameter, or 10.75mm in radius. So with a sensor 21.8mm in diameter (10.9mm radius) you need a lens mount that accomodates the sum of the radiuses, which ends up with a 43.3mm diameter.

So, with the mount Kodak and Oly have defined, you can accomodate any telecentric lens up to f2.0.

You can accomodate a non telecentric lens to f1.0, but the angles wouldn't be compatible with the sensor and the vignetting would be horrible.

Now, if we reduced the registration (flange to imager) distance a bit, say to 28mm (this allows room for a full coverage 17mm tall mirror to swing past the rear element of a lens that protrudes 8mm ipast the mounting flange into the film chamber, we see that we can increase the maximum aperture significantly. Keeping the mount diameter at 43mm (approximatly twice the sensor diameter) we increase f stop from 21.5/43 (1/2.0) to 21.5/28 (1/1.28).

So a smaller registration dustance would allow telecentric lenses at f1.4, and near telecentric at f1.2. Although I'm not sure the sensor itself would accept enough light at f1.2 angles to give an f1.2 lens any appreciable advantage over f1.4.

The size of the mount has nothing to do with the light path,

It does. I think we just addressed that sufficiently.

neither does the increased distance between the CCD and the lens
(I forget what this is called.)

Back focus.

It does affect the size of the rear element (which basically defines the size of the mount).

Another misconception: Canon and Nikon CCD/CMOS are only
getting light rays which passed thru the center of the objective
lens. Absolutely false.

Very true.

And we'll leave the discussion about aperture diameters, airy disc diameters, resolution and diffraction for another day.

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