Originally posted by RioRico I was going to object, noting that my 10-17 and 16/2.8 and 21/3.8 lenses produce image circles rather greater than their FL's, else they couldn't fill HF frames let alone FF. Then [lightbulb goes off inside head!] I realized: retrofocus groups! The RF elements spread the image to project it onto the required frame. And EL's don't have RF groups, so the IC:FL relationship holds for such simpler lenses.

Out of curiosity, where do you derive that relationship? I've just scanned a pile of optics PDFs and the term "image circle" is hard to find. My rough gargling for IMAGE.CIRCLE FOCAL.LENGTH hasn't turned up anything. Can you point me to a reference?

Look for "natural vignetting", like at

Vignetting or

Testing Camera Lenses - Vignetting - Bob Atkins Photography *I can't recall ever having seen "Natural Vignetting" and "Image Circle"explicitly related!* **nb**..Here's one!

http://books.google.com/books?id=cuzYl4hx-B8C&pg=PA134&lpg=PA134&dq=natural+...circle&f=false
It is geometric optics.

1) Light intensity falls with the inverse square of distance from a source, and the inverse distance from the aperture to the sensor changes as cos_squared(angle from optic axis).

2) If you look at an aperture from an angle , the apparent area of the aperture falls as cos(angle from normal =angle from optic axis)

3) If light strikes a sensor plane at an angle, the intensity is reduced by cos(angle from from normal = angle from optic axis)

Putting these factors together yields the "Natural Vignetting" equation:

Relative_Intensity = Cos_fourth_power(angle from optic axis)

The angle from the optic axis can be expressed in terms of image circle diameter and distance from the aperture as:

Angle_from_optic _axis = arctan(Image_circle_diameter/2focal_distance)

I think Natural vignetting is basically why the registration distance for most all cameras is similar to the image plane diagonal (image plane diagonal=image circle diameter). (

**nb** RioRico points out that this is incorrect - SLR's registration distance is large to allow for mirror motion.)

I think a good way to understand RetroFocus groups is that they serve to move the aperture away from the image plane specifically to avoid natural vignetting. It contributes to the cost of wide angle lenses.

Dave

PS I think this simple, physical phenomenon explains a lot about why optics systems are the way they are in both natural and technological worlds.

here's some numbers for illustration:

at image_diameter=focal_distance, angle from optic axis = arctan(1/2)=26.56 degrees.

at 26.56 degrees, relative brightness=cos^4(26.56)=0.64

*ie, about 2/3*
at image_diameter=3/4 focal distance, angle from optic axs = arctan(3/8)=20.56 degrees.

at 20.56 degrees, relative brightness=cos^4(20.56)=0.77

*ie, about 3/4*