CS 39J > Schedule & Notes > Session 11 Detailed Notes

CS 39J: Session 11

http://inst.eecs.berkeley.edu/~cs39j/session11.html
11 April 2002
Special thanks to Dr. Below for ensuring the accuracy of these notes.


Introduction

Dr. John Below is here to complete his lecture from session 7.


H & D Curve

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.

The H&D Curve graphs density (D) vs. the amount of exposure. The "blackness" (A) is the ratio of the amount of light hitting to the amount light passing through the film.

The blacker the film, the less light gets through and the more the light is absorbed. 

Exposure is the intensity of the light hitting the film times the time the shutter was open. We usually ignore the units, and only pay attention to the difference between the numbers on this axis. Note that a difference of 0.3 on the logE axis represents a factor of 2 in exposure.

Both scales are logarithmic.  Recall that logarithms are a way of compressing numbers. Briefly, you can write "1000, 100, 10, or 1". Putting these on the same scale would be difficult. (A better way of thinking about these is through exponents, which may be more familiar to you.)

First, consider the bottom left of the H&D curve.  This is the "base + fog".  This is wheredensity which results in the absence of any exposure to light, and arises mainly from the development of some unexposed grains.

Now, consider the next region of the H&D curve.  The graph gradually collects density (moving from left to right). The toe region in the lower left does not have rapid response to light.

The straight line region is when the film blackens in a general way and steepens proportionately (or almost so) to exposure.

Exposure beyond that is in the shoulder region, where the graph bends over in response to further exposure. In extreme cases, the most intensely illuminated parts of negative may actually show reversal from a negative to a positive. Thus, it is possible to have a photograph with a black sun. Ansel Adams, for example, has a famous picture called "The Black Sun", a picture of the sun and an oak tree in the Sierras. This effect is called solarization.


The steeper the curve, the more contrasty the film is.  The speed of the film can be measured by measuring how much exposure is necessary to exceed base + fog by some arbitrary amount, usually [delta]D=0.10. The best separations are made when photographs are kept on the straight line, but this may require less contrasty development.

What about forming a characteristic curves for pixels instead of silver?  There would still be logarithm of exposure (along the bottom horizontal axis), but on the left there would be the electrical output of the semiconductors (on the left vertical axis) and we would obtain a purely straight line. The equivalent to base+fog is "dark current" and "hum." (Anna asked a question about this. The devices still have a "fog" effect because environmental heat still causes the devices to give off a few electrons.) One of the advantages of digital photography, therefore, is that it does a better job in handling shadows and highlights; with very little work, we can simultaneoulsy achieve more detail in shadows and highlights.

Solarization: An effect of overexposure. That part of the negative that gets overexposed becomes like a "positive." 

For color film, the principles are the same, but the curves are complicated by the color response.

[ Diagram of H&D Curve, simulated ]

N LogN
1000 3
100 2
10 1
1 0

 


Blur

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.


Resolving Power & Sharpness

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.


Complex Systems: The Chain Rule(s)

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
150 lines/mm — view camera lens (4x5 or larger)

RF

200 lines/mm — Panatomic-X film
125 lines/mm — HP5+ 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.


Wave Effect and its consequences

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 [lambda] 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.

 

[ Graph: Intrinsic Sharpness of a Near-"Ideal" Lens ]

Stopping down makes the diffraction worse and decreases the sharpness, so the actual result (using the chain rule) causes ...

Generally speaking, if you have a modern lens, you can maximize the image quality by stopping down 1 or 2 stops. With a 35mm camera, you can use f/4 or f/5.6.

Notice that the focal length was not mentioned in this discussion. This is because the effect is independent of focal length.

 


Finding Best F-stop for Compromisable Depth

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:

Focussing in Practice*
Focus Spread (mm) Optimum Aperture (F/stop)
.17 8
.33 11
.66 16
1.3 22
2.7 32
5.5 45
11 64

*This data was obtained by Stephen Peterson & Paul K. Hansma, Photo Techniques, Mar/Apr '96 pp. 51-57

 

 


Bokeh

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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