Introduction
to MTF
This is the fundamental problem with simple resolution
testing: It does not correlate very well with
our perception of image quality. Modulation Transfer
Function (MTF) was developed precisely because
of this issue. MTF is a plot of contrast versus
spatial frequency, as shown in the upper left
corners of photos 1B and 2B. The MTF plots clearly
show the difference between the two photos 1.
Let's look at the plots in detail:
The horizontal axis is based on printing the photo
on 4 x 6 inch paper. Photo 1 reproduces spatial
frequencies up to about 2 lines+spaces per mm
very well. However, content above 3 lines+spaces
per mm is not resolved at all. Photo 2 does a
poor job of reproducing low frequencies, but retains
about 20 percent contrast all the way up to 10
lines per mm. That's why the small targets in
the resolution chart are visible 2.
So which photo is "better?"
If you are building a camera to take snapshots,
then photo 1 will be more pleasing to your customers.
If you are building a spy satellite, then photo
2 actually contains far more information, and
would be a better choice.
SQF and Human Vision
SQF, or "Subjective Quality Factor"
was developed by Ed Grainger at Eastman Kodak
in the 1970's to predict which photos users would
find most pleasing 3,4,5.
In somewhat simplified terms, SQF is just the
average MTF in a photo from 0.5 to 2 cycles per
mm. When both photos are printed at 4 x 6 inches,
photo 1A has an SQF score of 94 out of 100, while
photo 1B scores only 21.
How Were the Images Made?
The scene was photographed by a high quality digital
camera with 11mp resolution. The digital image
was processed to produce the MTF curves in the
two photos. The processing was done with Reindeer
Graphic's Image Processing Toolkit.
Footnotes
1. Strictly speaking, it doesn't
make sense to talk about the MTF of an image.
If the image is low contrast, we don't know if
this is due to a poor camera, or whether the scene
simply happened to be low contrast. However, if
the scene contains a known reference target, then
we can calculate the MTF of the camera that created
the image. The photos in this article conveniently
contain a resolution target. The MTF curves were
measured from the images with PixelScope OpticStudio™
software.
2. Two lines per mm is not very
high resolution. To put things in perspective,
if you have 20-20 vision you can just barely resolve
one line+space per arc-minute. If you hold a photo
13.5 inches from your eye, one arc-second is10
lines+spaces per mm. (or 250 lines+spaces per
inch)
3. "An optical merit function
(SQF) which correlates with subjective image judgments",
E.M.Grainger and K.N.Cupery, Photographic Science
and Engineering, Vol 16, #3, pp221-230 (1972).
4. "Lens performance assessment
by image quality criteria", K. Biedermann
and Y. Feng, Image Quality: An Overview, Proc.
SPIE Vol. 549, pp36-43 (1985)
5. "Measuring
Images: Differences, Quality, and Appearance"
Garrett M. Johnson, 1999 (PhD Thesis at RIT) |
