The characteristic curve

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The appropriate means for assessing the contrast behavior of the visual system and photographic image carriers is the characteristic curve. In the specifically photographic field, it is also called the
density curve or, after the founders of modern sensitometry, the Hurter-Driffield curve (HD curve). Ferdinand Hurter and Vero Charles Driffield were the first to study the behavior of light-sensitive materials in the 1870s.

The characteristic curve gives the amount of light on the x-axis in logarithmic steps with a base of 10, but the resulting density (which are logarithmic values in themselves; see below) on the y-axis is linear. Thus, the light increases tenfold from one numerical value to another, or decreases by a factor of 10, allowing for a clear representation of a wide range of brightness, without compressing the smaller spectrum of stimulus responses/density values to a level too difficult to differentiate.

Figure 6 shows a typical characteristic curve. On the horizontal x-axis we find the input quantity. In photography, we typically use the logarithm of the exposure time in lux seconds (illuminance in lux times exposure time in seconds) as the input quantity of light. We obtain the direct values by exponentiating 10 with these numbers. The number 0 means 10, because 10⁰ (=10*0) is 10. The number 1 stands for 100 (10¹ = 100), 2 stands for 1000 (10² = 1000), and so on. For the negative exponents, which can also occur, the following results: 10^-1 = 1, 10^-2 = 0.1, 10^-3 = 0.01. A step of 0.3 to the right means a doubling of the amount of light, because 10^0.3 = 2. In perception experiments, the logarithm of the intensity is along the x-axis.

The numbers on the vertical y-axis represent the output quantity corresponding to the input value. In photography, this is the density of the image carrier. The density is a measure of the opacity of the film. It is greater when less light passes through. To determine it, one sends light through the negative and measures the amount of light before the light passes through the negative and the amount of light that has passed through the negative. Opacity is the ratio of the amount of light that enters to the amount that has already passed through. If a negative lets through 1/100th of the light, the amount of light irradiated is 100 times the amount of light transmitted, and the opacity is 100. Density is the logarithm of opacity by ten. The density value 1 means that the film transmits 1/100 of the amount of light because the opacity is 100 and the logarithm of 100 is 2 (10¹ = 100). The value 3 indicates a relatively dark negative, as it only allows the ten-thousandth part of the irradiated light to pass through (10³ = 10,000). In relation to the visual system, the y-axis displays the receptor response as a relative stimulus response.

Point A represents the base density, which is created by the developer producing a small amount of silver even in unexposed areas of the film. There the film is then very slightly blackened and does not let all the light through.

Nothing happens if the exposure keeps increasing until it reaches the threshold value at point B. Only now is the exposure strong enough for the first exposure nuclei to form in the silver halide grains. We also use the value of point B to determine the film speed. The further to the left it is on the scale, the more sensitive the material. The film now reacts better and better, albeit disproportionately, to the further increase in exposure. We also refer to the resulting sag as underexposure. Only between points C and Edoes the curve describe an approximate straight line and does a constant increase in exposure translate into a proportional increase in density. That is why we call this section the linear region. Only in this part are the brightness differences of the subject optimally converted into density differences (tonal values). Therefore, we refer to the section C-E as the area of correct exposure. Behind point E, the density curve flattens out again and enters the overexposure area, where the highlights of a shot normally lie. Point F marks the maximum density, after which a further increase in exposure no longer blackens the film. We also refer to the area between E and F as the shoulder.

Both in the shoulder and in the sag, different subject brightnesses are reproduced less differently than in reality. Motif areas in the shoulder and sag that are twice as bright appear less than twice as bright on the developed (positive) image. Since the image of a color film is composed of dyes, not silver, each of which can react differently to an exposure, there isn’t a single density curve in the color area, but rather three distinct color density curves.

The luminance L describes the light emitted by a surface. Here, the surface itself has the ability to both illuminate and reflect light. The luminance is defined as the ratio of the luminous intensity and the area projected onto the plane perpendicular to the direction of radiation and is specified in candela per square meter (cd/m²).

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