At 4:13 AM +0000 12/29/01, olympus-digest wrote:
>Date: Fri, 28 Dec 2001 18:52:43 -0700
>From: will biesele <bill@xxxxxxxxxxx>
>Subject: Re: [OM] XA and photoshop ...
>
>Scott Gomez wrote:
> >The problem would be getting it to match up well. I've got to think this
> >can't be so hard, but it's beyond my Photoshop skills. It's sort of like the
> >inverse of a vignette... Seems like someone should have done it by now, but
> >I'm not finding anything in a Google search, either.
>
>Shot a grey card or northern sky; scan that. Bring into PhotoShop and
>turn it into a negative and do the add layers operation. I'm not all
>that familiar with PhotoShop; but I've read this technique in the
>AstroPhoto mailing lists. It is common with astrophotos.
This sounds about right, but does one _add_ the inverted gray-card photo, or
does one do a pixel-by-pixel _multiply_? By physics, I would expect that one
would need to multiply, or the contrast would fall off at the edges, even if
the addition corrected the average brightness.
Even perfect lenses suffer from cosine^4 falloff; imperfect lenses will be
worse than cosine^4, in addition suffering from vignetting. Said another way,
vignetting and cosine^4 falloff are independent of one another, and a given
lens will always suffer from cosine^4 falloff, and may in addition suffer from
vignetting.
The term "cosine to the fourth power" (cosine^4) is shorthand for
[cosine(theta)]^4, where theta is the angle of the line from the center of the
lens (the rear nodal point, to be precise) to the film plane (in "image
space"), with respect to the optical axis.
Note that theta is not necessarily the angle from lens center to the object out
in the world (in "object space"). A fisheye is the best example: The angle to
an object in the world far exceeds the angle to the image of that object.
The XA came with two possible lenses, both of 35mm focal length, the cheaper
being f/3.5, the more expensive being f/2.8. Looking through the f/2.8 lens
from the film side, I don't see any vignetting, which is plausible given how
short the lens in physically. I don't have a f/3.5 to look at, but I would
expect the same lack of vignetting, for the same reason.
A 35mm frame is 24 by 36 mm, so the corners are 21.6 mm from the center (where
the optical axis penetrates the film plane). With a focal length of 35mm, the
image-space angle is therefore arctan(21.6/35)= arctan(0.6181)= 31.7 degrees,
and cosine(31.7)^4= 0.524, or 0.93 stops falloff; call it one stop.
This is a property of even perfect 35mm focal length lenses used to fill a 35mm
film frame. This is the best one can do; imperfect lenses will be worse.
When making a panoramic collage, I use a long lens and take lots of photos, so
I can stitch the photos together without too much disruption at the splices.
Joe Gwinn
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