CS 39J > Schedule & Notes > Session 11 Detailed Notes |
http://inst.eecs.berkeley.edu/~cs39j/session11.html
11 April 2002
Special thanks to Dr. Below for ensuring the accuracy of these notes.
Dr. John Below is here to complete his lecture from session 7.
When you use pixels in digital photography, you also use the photoelectric effect. The electrons just come from a different place: they come from semiconductor devices that act when light shines on them. But today we will concentrate on silver photography..
<H&D Curve (simulated)> This is the H&D Curve, named after
Herter & Driffield; it is also referred to as the characteristic curve.
Anything that is made out of silver that goes through a photographic process
has an H&D characteristic curve. This curve is "simulated"
but has most of the features of an actual H&D curve. |
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Optics began with telescopes looking at stars. The average star is so far away that it is just a point source of light. It has zero dimension, basically. But if we photograph stars with a real lens, we get a little blurry circle. That blurry circle is called the blur; all photographs map be thought of as blur circles.
<sets up a "point source" with a projector> Pretend that the
projector is a camera lens, and the projected circle of light (on the board)
is a star. Suppose you rotated the camera off-axis. <now looks like a skewed
ellipse> (1) Any photographic image made by a lens is going to be sharper
at the center than at the edges. (2) How much light strikes per unit of area?
The light now spreads over a bigger area, so that bigger area will be dimmer.
The inverse square law is part of the cause of this. The bigger the angle, the
bigger the edges. A correction filter for a wide-angle lens corrects such skewing
problems. It is gray in the middle, and lighter near the edge.
These are carefully-drawn parallel lines: sets of three black lines with gaps of the same width in between them.
If the lens and film were perfectly sharp, then every pattern would be perfectly
reproduced. But, in fact, they are not going to be anywhere near as good. Remember
our point sources of light — or blurs?
The resolving power (R.P.) of the lens is expressed as the number of
line pairs per millimeter on the film. With your photograph of these diagrams,
you can count these lines, but as they become closer and closer together, they
will "merge".
Gidon's question: What about new gigabit films that have 900 lines/mm?
Answer: I know very little about them. "Schumann plates"
provide 1000 or 2000 lines/mm; you can contact-print the finest sensitivities
of the lines that you can only see under a microscope! The downside is that
they are very slow. Most films get faster as they get developed longer. This
is generally a good part of the "secret" of the super-fast films.
The resolving power is the inverse of blur. (Abbreviating resolving power as
R, then R = 1/B ). 100 lines per mm, for example, would give a blur of
0.01 mm. It is hard to treat blurs mathematically since their edges are soft;
as a result, many of the numbers used are approximations.
How do you get high-resolution lenses? Modern optical glass and computer design
make (slightly) sharper lenses.
Smaller focal length lenses tend to be slightly sharper than longer focal lenses
but by no means proportionately.
Slower lenses: An f/1.2 or f/1.4 lens won't generally be as sharp
as some other (often less expensive) lens that is slower.
Generally speaking, lenses are sharper in the center than in the edges,and if
you stop a lens down, it produces sharper images.
Price: With modern lenses, a higher price does not buy much extra sharpness
but does buy better construction in the diaphragm and the mount.
The overall sharpness of an image: knowing the resolving power of all these elements determines the output quality of the printed image. See the equations above. Some say the equations in the bottom box (outlined in purple) are "more accurate", but produce optimistic results. Using the equations in the upper box would be more realistic, in Below's experience. In ordinary practice, the experimental error is greater than the differences between the equations.
Some typical ranges for the resolving power:
RL |
200 lines/mm 35 mm camera lens |
RF |
200 lines/mm Panatomic-X film |
RP |
60-80 lines/mm photographic paper (virtually all, B&W and color) |
When you enlarge a picture, the blur also grows by the same magnification factor as the overall image.
Even if an optical system were perfect in every way, the images produced would not be perfectly sharp. This is due to a problem called "diffraction" which is a consequence of the wave nature of light.
It is hard to visualize, but imagine a body of water into which a stone is dropped. Waves radiate out in circles from the center of the disturbance. Now suppose one introduces a foreign solid barrier in the path. When they strike the barrier, the waves are broken up and scattered in all directions, spoiling the smooth regular wave pattern.
Light acts in an analogous way when passing through a lens. The edge of the iris diaphragm constitutes the barrier marring the evenness of the waves, and hence reducing the R of the image. Lord Rayleigh derived a relationship:
where is the wavelength of the light used and d is the diameter of the aperture. An average R for white light is given by:
Note that R is dependent on nothing but the f/#; the larger the f/#, the poorer the resolution. This works against stopping down to improve the image. The practical effect is shown below.
Stopping down makes the diffraction worse and decreases the sharpness,
so the actual result (using the chain rule) causes ... |
How do you choose an f/stop so maximize the sharpness of the image? There
is a problem: if we don't stop down enough, then we will have a focus
problem. If we stop down too much then we will have a diffraction problem.
If your camera makes it possible, measure the "depth of focus"
(not "field") halfway between the images of the
nearest object and halfway to the farthest object you want sharp.
A. set the focus halfway.
B. stop down "far enough."
For best overall sharpness, use the following table:
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*This data was obtained by Stephen Peterson & Paul K. Hansma, Photo Techniques, Mar/Apr '96 pp. 51-57
A Note by Kawaldeep Grewal
John Below informed us that the resolving power of a modern lens is sufficient for all practical matters. However, there is a further interesting aspect of blur induced by lenses, called bokeh. This is an aspect of photography that affects the overall look of certain images. For this aspect, the more expensive German optics (zeiss, leica, schneider) excel over Nikkor and Cannon.
Bokeh is the adjective used to describe the quality of out-of-focus elements in photographs. Bokeh is strictly dependent on the optics of a lens, arising from spherical aberrations in the optical elements. No standard metrics have been proposed to measure bokeh, although most people seem to agree as to what constitutes "good" bokeh.
Good bokeh is characterized by soft transitions between out-of-focus elements, and bad bokeh results in artifacts which tend to provide unwanted texture to background elements.
For a more detailed explanation, see Bokeh Explained by Ken Rockwell. For a computer graphics based visualization, see Dan Wexler's implementation of bokeh in his renderer.
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