The
chemical response of the film is determined by two parameters: the amount of
light that strikes the film and the sensitivity of the chemicals to that
exposure. The intensity depends on three parameters:
(1) the diameter of the lens, which determines how
much light enters the camera,
(2) the focal length of the lens, which determines
the size of the image that is produced by the object and therefore how the
energy captured by the lens is distributed over the film plane,
(3) the amount of time the shutter is open
The
amount of light that is captured by the lens depends directly on the area of
the lens opening, which varies as the square of the diameter. Likewise
the energy striking a given area of the film varies inversely as the square
of the focal length, since the focal length affects both the length and the
width of the image, and it is the product of these two quantities that
determines the area. Increasing the focal length increases the length and width
of the image linearly, and increases the area (and therefore decreases the
intensity on the film) by the same quadratic factor. The shutter time enters
linearly – doubling the exposure time doubles the intensity of the light
striking the film plan.
Since
the diameter of the lens and its focal length have the same dependence on the
amount of light striking the film, and since the ratio of these two quantities
(f/D) is the f/number, it is possible to combine these two effects into the statement
that the amount of light striking the film varies as the square of the
f/number, with increasing f/numbers implying corresponding decreases in the
amount of light.
There
are 3 methods for specifying the “speed” of a film – that is, the relationship
between the amount of light that strikes the film and the density of the
chemical reaction (the “exposure”) that results. All of these speed
specifications are relative, in that they specify the sensitivity of a
particular film compared to the sensitivity of some standard. These 3 methods
are the ASA (American National Standards Institute) scale, the DIN (Deutsche
Industrie Norm) scale and the ISO (International Standards Organization) scale.
All of these scales are based on the following figure, which shows the chemical
response of the film as a function of the intensity of the light that strikes
it.
Note
that the scale on the x-axis is logarithmic rather than linear. Each division
on the x-axis therefore represents a certain multiplicative increment rather
than an additive increment as would be true for a linear scale. The most common
multiplicative increment is an increase (or decrease) in the intensity by a
multiplicative factor of 2, and this same multiplicative factor is used in
calculating exposures as discussed below.
Using
this curve for any film, the testing laboratories can assign a relative speed
number to it. The ASA index is linear: a film rated as ASA 50 is twice as
sensitive as one rated as ASA 25, and requires half the light for the same
chemical exposure. The DIN scale is explicitly logarithmic. An increase of 3 in
the DIN rating corresponds to a factor of 2 increase in sensitivity. Thus DIN
21 is twice as sensitive as DIN 18. The ISO index is also logarithmic, but is
computed using a slightly different method than is used by the DIN system. The
results are basically the same as for the ASA method. The correspondence is
that ASA 100 is equivalent to DIN 21, which is equivalent to ISO 100/21
degrees. Using these definitions, ASA 200 would be DIN 24, ASA 400 would be DIN
27, etc. Most film is characterized using both the ASA and DIN values.
Although
the details vary from one type of film to another, there are three general
characteristics that all films share:
(1)
a relatively flat region at very low light intensities. Nothing much happens in
this region over a significant range of intensities. This region is responsible
for what is often called “reciprocity failure,” which means that beyond some
point, decreasing the intensity of light that strikes the film results in
almost no change in the exposure of the chemicals. In other words, a wide range
of exposure times produces about the same (underexposed) image.
(2)
the central region, which is roughly a straight line on the logarithmic
display. Equal changes in intensity produce roughly equal changes in the
density of the film exposure.
(3)
a relatively flat region at very high light intensities. The film is saturated
at these intensities and further increases in intensity cannot produce
additional exposure. The picture will be “over-exposed” with too little
contrast, because even the darkest area of the image produced almost the same
chemical reaction as the brightest area.
Most
photography is done in region (2), although the other regions are used for
special effects. For example, region (1) is often used for long exposures at
night. A film that is intended for photographing printed text is designed to
have a very narrow region (2), so that the response of the film is either in
region (1) or in region (3). That is, it is either fully exposed or not exposed
at all – consistent with the nature of the material, which is black and white
with no intermediate shades of gray.
Digital
cameras have the same sort of response curve, but it is usually not published.
The advertising for digital cameras tends to concentrate on the number of
pixels in the image instead. Although this is an important parameter since it
sets the resolution of the camera, the sensitivity of the digital recording
medium, expressed in units comparable to an ASA number would be very useful in
determining what level of light would be required to take a picture. Many of
the earlier digital cameras had sensitivities comparable to film rated at ASA
100 – not very sensitive by film standards.
Since
the exposure in region (2) varies smoothly with intensity, it is possible to
trade-off the various parameters that affect the intensity while preserving
more or less the same exposure. For example, decreasing the speed of the
shutter by a factor of 2 can be compensated for by decreasing the f/number by
1.4 (the square root of 2) thereby increasing the amount of light that strikes
the film by the same factor of 2. Thus there are pairs of f/numbers and shutter
speeds that give essentially the same exposures. The choice among these
equivalent settings is driven by other considerations. For example, using a
larger f/number will increase the depth of field but require a longer exposure
time, whereas using a faster shutter
speed will capture a static image of an object that is moving rapidly but will
require a smaller f/number to capture adequate light during this shorter exposure
time.
Although
any number of values could be chosen, it is common to use values both for the
shutter speed and for the f/number that change by a factor of 2 starting at f/1
and a shutter speed of 1 sec. Thus the common choices are:
f/number
values: 0.7, 1, 1.4, 2, 2.8, 4, 5.6, 8,
11, 16, 22, …
shutter
speeds: 1, 1/2, 1/4, 1/8, 1/15, 1/30,
1/60, 1/125, 1/250, 1/500 …
In
both series, the values are rounded to convenient fractions.
Within
the linear region of the exposure curve, 1/60 at f/8 results in the same
exposure on the film as 1/30 at f/11, etc. That is, an increase of a factor of
2 in the time the shutter is open (from 1/60 to 1/30) is compensated by
decreasing the size of the lens opening by the square root of 2 from f/8 to
f/11. Furthermore, changing the ASA rating of the film by a factor of 2 would
require a corresponding compensation either by a change in shutter speed of a
factor of 2 or a change in f/number by a factor of 1.4.
Since
there is usually more than one acceptable combination of f/number and exposure time,
automatic cameras usually have several choices: an “aperture priority” mode in which
the user can choose the f/number and the camera then chooses the correct
exposure time and a “shutter priority” mode in which the user chooses the
exposure time and the camera chooses the f/number to match it. The camera tries
to keep both parameters in the middle of their respective ranges by default.
When
a camera is used with an electronic flash, then most of the light usually comes
from the flash, and the duration of the flash (which is usually very short) sets
the effective exposure time. The shutter speed is pretty much irrelevant in
this situation, provided that the motion of the shutter and the firing of the
flash are synchronized. See the previous topic for a discussion about this.
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