Re: Technical wide-angle question

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----- Original Message -----
From: "Soren Svensson" <soren.svensson@ericsson.com>

> My question is, how short can the focal length be for a certain negative
> size?

That depends on the amount of vignetting or fall-off you are willing to
accept.

> Correct me if I'm wrong but the light fall-off is due to two different
> things.
>
> 1) The distance from the ph to the neg increases as you get farther from
> the center, and therefore you get less light intensity.

Distance increases by a factor of the inverse of the Cosine of the angle
(with respect to a normal line from ph to film plane)

> 2) The round ph turns more and more into en ellipse (as viewed from the
> neg) as you get farther from the center, and therefore the effective
f-stop
> increases.

The apparent area of the initial round pinhole decreases by a factor of
Cosine of the angle

And there is ONE MORE THING affecting the fall-off: the "ellipsis" of light
we talked about, hits the film plane obliquely, therefore covering an area
that is bigger than the original by a factor of the inverse of Cosine of the
angle.

All the above combines to give us the well known COSINE^4 law every single
lens is affected by, including glass lenses. The Cos^4 law means that the
light intensity at a point off-axis is equal to the the intensity at the
center multiplied by the Cos^4 of the angle formed by Point_of_axis -
Pinhole - Center_of_film_plane.

> At some distance out from the center we should reach a value that isn't
> useful > anymore (difference between exposure at the center and that
> point).

That acceptable stops of fall-off with respect to the center is up to you to
decide. Guy mentioned 2.5 times the focal length is the acceptable image
circle. A 8x10 format camera could then have a FL of 130mm max, assuming
2.5 factor. I have done image using 90mm FL on a 8x10 and the light
fall-off is small for "pinhole standards" (IMO), so I'd assume you could go
wider than 2.5 times the focal length.

> I assume that the thickness of the material that constitutes the ph
> matters, but I don't know to what degree.

The thicker the material the "faster" the fall-off, you could apply plain
geometric analisys and find how exactly a given thickness would affect the
fall-off.

> So my question is, what's the equation for the combined light fall-off (my
> geometry is a little rusty :-)? And what would a reasonable cut-off value
> be (assume b&w photo paper as negative and I intend to scan it on a
> regular consumer grade scanner (Epson 1640))?

As I said, I have done 90mm on a 8x10 and I see "acceptable" fall-off. At
the very corners, the light intensity was just 5.5% of that at the center
(based on Cos^4 law).

Back in Feb/2000 I wrote an answer for a related question, you can read it
here:
http://www.pinhole.com/discussion/2000/msg00497.html

That formula can be translated to

F = DIAMETER / (2 * Tangent[arc_COSINE(1 / (2^(S/4)))]

Where the DIAMETER is equal to the diagonal of your image format.

So for 8x10 and assuming we are accepting 6 stops fall-off at the corners,
we would get a Focal length of 61.4mm and an angle of view of 138.6
degrees. A lens with the same angle of view for 35mm format would have to
be 8.17mm!!.

> If I could find out the equation, then I could make a software
> center-filter to get even more useful info from the scan!

Well, I will be waiting for that software center filter.

Guillermo
Received on Mon May 7 21:04:56 2001