Light fall-off with wide angle lenses - attn optics gurus! : LUSENET : Large format photography : One Thread

Although I understand theoretical (simple) optics, I need some info on practical optics.

I understand that wide angle formula's, like biogon derived optics, use pupillary expansion to achieve better off axis illumination. My question is can this technique beat the 1-cos^4 law, and if so, there must be some expense in distortion.

I have an old Rodenstock catalog, dated 4/89, that shows the illumination of a 75mm f/4.5 Grandagon-N. This graph shows illumination at f/11 and f/16 exceeding the 1-cos^4 law at off axis positions for about the outer 2/3 of the image circle.

A current Rodenstock data sheet on Grandagons shows illumination for the same lens as becoming asymptotic to the 1-cos^4 law, but not exceeding it across the image circle.

The only apparent difference between the graphs is that the latter is at 1:30 where the former is at 1:infinity magnification.

I don't think Rodenstock have change the lens, and certainly they wouldn't change it to reduce off-axis illumination.

So is the first graph simply in error, and lenses can't beat the 1-cos^4 law, even with this optical "trick"?

-- Glenn C. Kroeger (, October 15, 2000


The Biogon is a very low distortion lens. The 38mm Biogon for the Hasselblad has under 0.5% distortion which shows that the pupillary expansion formula need not carry a distortion penalty. In contrast, the Distagon's 40mm lens has three times the distortion of the Biogon. The Biogon's distortion is about the same as for the Schneider Super Angulon 65mm for LF. I do not know what formula this lens uses. As for the remainder of your questions, sorry can't help you but I am glad you asked.

-- Julio Fernandez (, October 15, 2000.

Yes, it's possible to beat the cos^4 'law'. That only holds true if the projection angle of the lens is the same as the angle of view.
If the lens is a retrofocus design, then the cone of light projected from the back of the lens has a smaller angle than the field-of-view cone.
Most retrofocus lenses have a distortion penalty, as barrel distortion, but this can be very slight.
I have a 90mm Grandagon-N f/6.8, and this has only a slightly longer back focus than its marked focal length.
Of course, the cos^4 law doesn't take any account of the extra glass that the light has to pass through when entering and exiting the periphery of the lens. This probably explains why the trace across the image circle is uneven, and can vary depending on the measuring circumstances.

Basically, I'd say that if you assumed a straightforward cos^4 falloff at normal working apertures, then for all practical purposes you'd be well within tolerable limits of exposure.

-- Pete Andrews (, October 16, 2000.

Moderation questions? read the FAQ