Vignetting and Light Falloff

What is it?

Vignetting: Physical obstruction causing rapid less light to fall on the film only at the outside.
Light Falloff: Lens optics causing gradual less light to fall on the film as it approaches the edge.

Two things add to light falloff.

Light entering the camera from off-axis sees a foreshortened aperture, so less light is collected.
In rectilinear lens, the solid-angle-to-area magnification increases, spreading the light from the center.

The test

I wanted to see how F-Stop and the zoom of the lens effected light falloff. I did the following test below.
Using my Nikon CoolPix 995 digital camera
I took a piece of velum and placed it in front of the lens.
Evenly light the velum by bouncing light off the ceiling onto it.
Took two pictures, one rotated 90° from the other.
Averaged the two pictures.
Made a duplicate layer, flipped horizontal, averaged and merged with original.
Made a duplicate layer, flipped vertical, averaged and merged with original.
cropped a rectangle from the center to the corner. 100 pixels wide by 1222 pixels long. (smaller re-sampled version below)
Resized image to 1 pixel by 1222.
Made an image of the Histogram.

To read the values for the image I ran a gaussian blur to average out the values. The image with the light falloff correction did not have any blurring.

Note: I also took some images with my FC-e8 fisheye adapter but I do not think I evenly light the velum. It is much harder to get the velum to cover the entire lens and have it evenly light. I will try again, maybe with some sort of lamp shade.

Gradient	Histogram	Lens Specs	Difference from center to shortest edge. Correction used	Difference from center to corner.	Difference: Center - corner after correction	Std Dev after correction
		8.2mm f2.6	13	43	8	1.58
		8.2mm f4.7	9.5	25	3	0.72
		8.2mm f6.0	9	24	2	1.08
		8.2mm f7.5	8.5	23	2	1.01
		31mm f5.1	7	21	1	0.70
		31mm f6.5	5	15	2	0.74
		31mm f10.3	5	15	2	0.70

The correction has fixed all of the light falloff problems very well. The little bit of standard deviation that is left is expected because of the random feathering used with the correction filter.
To see how well it does here is an example of the image 8.2mm at f4.7

Made levels adjustment to both images, to emphasize the differences	Before correction: Std Dev: 7.17 Center to Corner: 25	After Correction: Std Dev: 0.72 Center to Corner 3

Only the widest angle image, at the widest f-stop, 8.2mm f2.6, shows any vignetting. Here it is after the correction, and also with levels adjustment to emphasize the difference.

PanoTools use to have a problem creating circular rings to the image as it tried to correct radial luminance. But I made some changes to DLL that has fixed that. Those changes have been incorporated into most distributions of the dll.

This is what it would look like with the old dll.

But if you take the good one above and apply a Gaussian blur of radius 2.5 I get this, where you can just start to see the rings. It shows that blurring is a good way to hide the randomness that was added and see the underlying pattern. Using Gaussian blur on blue sky will show more banning. It is still much better than the old.

Film camera. 28-90 mm lens @ 28mm with UV filter on front. Film scanned
	Adjusting levels elaborate the light falloff
	PanoTools \| Correct \| Radial Luminance R, G, & B = 35 Trying to eliminate the vignetting has caused the center to go too dark.
	PanoTools \| Correct \| Radial Luminance R, G, & B = 12 The Light Falloff eliminated but the vignetting remains.

Conclusion:

PanoTools | Correct | Radial Luminance does a good job at removing light falloff (with rectilinear at least), but does not help with vignetting.
One of the best ways to eliminate vignetting is to stop down the lens, and don't use filters.

References, Links, and Notes:

From the PanoTools archives Helmut Dersch discusses Radial Luminance.
See photo.net Q18 for more information on vignetting and Light Falloff.
John Houghton explains his methods CORRECTION OF VIGNETTING IN DIGITAL CAMERA IMAGES by creating mask instead.
PanoTools developed by Helmut Dersch.
PTGui developed by Joost Nieuwenhuijse.