Tone value

The term tonal value refers to the different levels between light and dark of a color or black and white image, be it in a digital data set, on a transparent carrier (film) or on a reflective image, photographic or printed. For a picture element (point) it describes a color or gray value within a specified color or gray level spectrum, specified in 0 - 100%. 100% means maximum darkness or color coverage (full tone) of the imaging medium. Accordingly, 0% stands for complete transparency of the film or blank paper for halftone prints. The tonal value is determined from measurements of the optical density or the degree of reflection (previously: remission) and calculated from these measured values using the Murray-Davies formula . It is marked with the symbol after the Standard Offset process . ${\ displaystyle A}$

Tonal value on copy film

Right halftone image, left strongly enlarged grid

The tone value is a description for the gray value in halftone originals. All tone values between highlights (light areas of the image) and shadows (dark areas of the image) correspond to different degrees of blackening. The tone value is a relative measure that knows values between full transparency of a film material used (0%) and full blackening under the selected working conditions (100%). In this context, the optical density, a perceptual measure of the intensity of blackening, is also important. In the case of a positive film, the apparent proportion of the area covered is given in percent. In the case of a negative film, on the other hand, the percentage that is missing from 100% tone value is indicated.

Tonal value in digital image technology

Photo and its brightness value distribution in the GIMP program

The tonal range of an RGB color channel of digital image files comprises a range which is predetermined by the bit depth. With 8 bits there are 2 ⁸ = 256 discrete values for each color. The lowest value corresponds to color not available , the highest color maximum available . The final color results from the combination of the three color channels in the additive color mixture . So RGB = (0,0,0) corresponds to black and RGB = (255,255,255) corresponds to white .

For some areas of application, a gradation of 256 color values is no longer sufficient. Digital scanners offer a tonal range of 16 bits (corresponding to 2 ¹⁶ = 65536 gradations) and more per color channel. High-quality DSLR cameras from 2009 have a theoretical tonal range of 14 bits; the range is actually even smaller. He will u. a. limited by the processes in the AD converter . A higher tonal range can also be useful for HDR images. While JPEG images are usually limited to 8 bits per color channel, 16-bit data can e.g. B. be saved in TIFF file format.

Tonal correction

Tonal value correction by changing the brightness, contrast and / or gamma value

A Levels in this context is a mathematical function modified f (x), the brightness distribution of individual color channels or of the overall image, for example:

A linear function (“straight line”) f (x) = x leaves the tonal values unchanged.

A correction function, which has a slight S-shape compared to the straight line, increases the image contrast . If you mirror the curve at the diagonal f (x) = x, the contrast is weakened to the same extent.

A linear correction function (“straight line”) f (x) = 1 - x “inverts” the brightness values towards a negative image .

A simple power function f (x) = x (so-called gamma correction ) changes light and dark values non-linearly. ${\ displaystyle ^ {\ gamma}}$

Finally, the tonal value correction can also be carried out discontinuously using a table ( lookup table ).

Tonal corrections.
Above: Original image
Middle: Tone value spread
Below: Tone value compensation

Incorrectly exposed images do not use the available gray value range. The darkest areas of the image are gray, not black, or the lightest areas are not white.

A variation in dot gain (engl. Histogram normalization ) shifts the darkest point on the black point and the lightest to the white point. The values in between are interpolated linearly.

A Tonwertausgleich (Engl. Histogram equalization ) also transformed the extreme values in black and white. The values in between are converted in such a way that the tonal values are evenly distributed over the gray values. The sum function over the gray values increases linearly.

Tonal value in printing technology

The tone value is a measure of how muted a color area appears to a normal observer. There is the idea that a colored surface consists of a portion of fully covered color (full tone) and color-free areas and the eye cannot resolve these different portions. In the effect on the eye (and on optical measuring devices) there is also a physical phenomenon, the catching of light. Both together form the tone value. It is an optical and not a geometric measure. This is why it was previously also called "optically effective area coverage" . It is calculated using the Murray-Davies formula and can be measured with the aid of densitometers . In some measuring devices it is still incorrectly referred to as "area coverage". ${\ displaystyle A}$ ${\ displaystyle F _ {\ text {D}}}$

Diagram of tonal value, area coverage and optical densities in print

Strictly speaking, the tone value always applies to one color, black, cyan, magenta or yellow. An unprinted area has a tone value of 0%, a full tone area 100%. If the tonal values of all colors of an image area are added up, the total tonal value is obtained. The total tonal value is also known as the total inking . So it may be that a printing area with z. B. 300% total inking is characterized. In printer language , a 25% tone value is called a quarter tone. Accordingly, a 50% tone value is called a semitone or half tone and a 75% tone value is called a three-quarter tone. In photographic technology, on the other hand, all non-screened, homogeneously colored color fields are referred to as halftones . That is why a halftone is called a halftone simulation.

The dot gain is also a term from printing technology. It describes the effect that halftone dots on the printed sheet are, due to the process, larger than on the print template, i.e. the print image is darker. Like the tonal value, the dot gain is specified in percent. A grid area, which is laid out with an area coverage of 80%, creates a coverage of z. B. 85%. In addition, there is the light trap, for example also with a contribution of 5%. In this case, the dot gain would be 10%.

Measure and calculate tonal values

In a movie

In the case of black and white films, the optical densities are measured with a see-through densitometer . The device is calibrated at a transparent and a flat blackened area and then the raster or image areas that you want to assess are measured.

On one print

Densitometer for determining the optical density of reflective originals

Spectral densitometer for the individual measurement of densitometric and colorimetric quantities.

A spectrophotometer is used to measure the reflection factors of an unprinted area of the printing material (blank), a fully printed area (full tone) and the intended measuring points (grid) in an image or print. ${\ displaystyle R _ {\ text {B}}}$ ${\ displaystyle R _ {\ text {V}}}$ ${\ displaystyle R _ {\ text {R}}}$

{\ displaystyle R _ {\ text {R}} = {\ frac {I _ {\ text {R}}} {I _ {\ text {0}}}}}

with as luminous flux over the grid surface and with as luminous flux over white standard and

{\ displaystyle I _ {\ text {R}}}

{\ displaystyle I _ {\ text {0}}}

{\ displaystyle R _ {\ text {V}} = {\ frac {I _ {\ text {V}}} {I _ {\ text {0}}}}}

with as luminous flux over the full tone.

{\ displaystyle I _ {\ text {V}}}

From this one can calculate the degree of reflection for the grid area and for the full tone. We relate the reflectance to the blank paper and only compare the measurements using the grid and full tone: ${\ displaystyle \ beta _ {\ text {R}}}$ ${\ displaystyle \ beta _ {\ text {V}}}$

{\ displaystyle \ beta _ {\ text {R}} = {\ frac {R _ {\ text {R}}} {R _ {\ text {B}}}} = {\ frac {I _ {\ text {R} }} {I _ {\ text {B}}}}}

and .

{\ displaystyle \ beta _ {\ text {V}} = {\ frac {R _ {\ text {V}}} {R _ {\ text {B}}}} = {\ frac {I _ {\ text {V} }} {I _ {\ text {B}}}}}

The optical density is a perceptual, logarithmic measure:

{\ displaystyle D _ {\ text {R}} = - \ log \ beta _ {\ text {R}} = \ log {\ frac {1} {\ beta _ {\ text {R}}}}}

and: with

{\ displaystyle D _ {\ text {V}} = - \ log \ beta _ {\ text {V}} = \ log {\ frac {1} {\ beta _ {\ text {V}}}}}

${\ displaystyle D _ {\ text {R}}}$ = optical density in the grid = optical density in full tone. ${\ displaystyle D _ {\ text {V}}}$

The [Murray-Davies formula] is used to calculate the tonal value from these values, expressed in%: ${\ displaystyle A}$

{\ displaystyle A = {\ frac {1-10 ^ {- D _ {\ text {R}}}} {1-10 ^ {- D {\ text {V}}}}} \ cdot 100 \, \% }

You can also measure the optical densities with a densitometer or modern spectral densitometer and insert them directly into the Murray-Davies formula. Modern measuring devices already output all the required measured values, including the tone value.

Web links

Tone values, histogram and tone value curve

literature

Helmut Kipphan (Hrsg.): Handbuch der Printmedien. Technologies and production processes. Springer, Berlin et al. 2000, ISBN 3-540-66941-8 .