A well-known property of lenses is that their illumination level
at the focal plane diminishes as one moves away from the optical
axis. I won't go into the reasons why -- do a search on something
called the Cosine-to-the-Fourth Law and you'll find plenty to read.
Suffice it say geometry for a simple lens conspires in four ways,
each time introducing a cosine factor, so the illumination level
falls off away from the optical axis as Cos^{4}Θ.

For a "normal" lens the focal length (F) is approximately
equal to the sensor diagonal, which is twice the maximum radius,
r_{max}. Therefore the maximum angle, to one of the
corners, is Θ_{max} = Arc-Tangent( r_{max} / F)
= Arc-Tangent(½) = 26.565°. Thus, Cos(Θ_{max})
= 0.894 and Cos^{4}(Θ_{max}) = 0.64. This is
a little less than 2/3rds of a stop. But this is a maximum. For most
of the outer portions of the frame the factor is closer to ½
stop, and for lots of subject matter this is insignificant or so
small it's never noticed.

With negative materials the effect is to some degree canceled out
when an enlargement is made. The enlarging lens has a similar
falloff as the taking lens did, so if the negative is a little
bit thinner towards its edges and corners this is evened out by
a comparable dimunition in the other direction by the enlarging
lens. With slide material the two factors both operate in the
*same* direction and the effect is doubled. With digital
scanning there's no enlarging lens, so the effect now has to
be taken into account with negatives (no longer being mostly
compensated for) and factored in only once with slides.

The lens's field of view is 2 × Θ_{max}, or
almost a radian for a "normal" focal length. With a view camera
the ability to make adjustments, both side/side and up/down
translations as well as lens tilt, requires a lens with a larger
field of illumination than this, maybe something like 70° or
75° for this focal length. Lens specs often include a diameter
of illumination, a linear rather than an angular measure. For 4x5,
the film diagonal is about 150mm, or r_{max} = 75mm. But
an inch of lateral movement is ~25mm's, so in practice an
r_{max} of ~100mm is needed, which is a diameter of 200mm.
This corresponds to Θ_{max} = Arc-Tangent( 2/3 )),
which is above 67° for the angular diameter. This corresponds
to a Cos^{4}Θ factor at r_{max} of a little
more than ½x, meaning 1.06 stops. With the camera back in
portrait or vertical orientation it's possible to make use of this
"feature" to darken clear blue skies progressively by putting the
top of the frame near the edge of the field of illumination through
the use of the camera's shift and tilt adjustments.

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