Luther condition

In color photography as well as in color measurement technology, the Luther condition is a technical requirement for suitable analysis components with which human color perception is to be simulated in the best possible way. This requirement is named after the German colloid and photo chemist Robert Thomas Dietrich Luther , who first formulated it in 1927 in his scientific paper From the field of color stimulus metrics .

Formulation of the Luther condition

Tristimulus curves: Luther demanded that - taking into account the sensitivity of the color film material - the transmittance of the color filter layers simulate the spectral sensitivity curves of the three types of cones X (red), Y (green) and Z (blue).

Robert Luther was one of the most important students of the Nobel Prize winner in chemistry, Wilhelm Ostwald . Luther's actual research and teaching area was photography , but like his doctoral supervisor Ostwald, he also dealt with color theory . This makes it understandable that Luther made important advances in the field of color photography and color measurement technology.

On the one hand, he developed a process that was later used to standardize the spectral sensitivity of photographic materials . On the other hand, he wanted to make the light-sensitive information carrier silver bromide known from black and white photography usable for color photography by destroying a dye with the help of a coupled reaction through the silver, so that in a second development step a dye image is created instead of the conventionally developed silver image (silver color bleaching process) .

The immediate aim of his research was to create thin layers whose spectral filter effect should enable the exposure and development of color films. He was thus one of the pioneers of color-correct three-layer color film , as it has been produced since the 1930s.

For this purpose, he needed suitable color filters that can simulate human color perception, taking into account the spectral sensitivity of the photographic materials . Based on trichromatism - the color vision with the red, green and blue sensitive cones on the retina of the eye - he was looking for three light analysis filters whose spectral transmittance was such that they did justice to the sensitivity of the photoreceptors on the retina, but at the same time also took into account the spectral sensitivity of the photographic material. Based on the spectral sensitivities of the film materials used at the time ( 1927 ), he described the transmission curves of the filters in his work From the field of color stimulus metrics, which are suitable for trichromatic color analysis or measurement.

The spectral transmittance of the analysis filters, i.e. their light attenuation factor as a function of the wavelength , is described by the curves ${\displaystyle \tau (\lambda )\!\,}$ ${\displaystyle \tau \!\,}$ ${\displaystyle \lambda \!\,}$

${\displaystyle \tau (\lambda )_{X}\!\,=k_{X}\cdot {\frac {{\bar {x}}(\lambda )}{s(\lambda )}}}$for the red-orange filter analysis ,

${\displaystyle \tau (\lambda )_{Y}\!\,=k_{Y}\cdot {\frac {{\bar {y}}(\lambda )}{s(\lambda )}}}$for the green filter analysis and

${\displaystyle \tau (\lambda )_{Z}\!\,=k_{Z}\cdot {\frac {{\bar {z}}(\lambda )}{s(\lambda )}}}$for blue-violet filter analysis

With

• the yardstick constants for the overall attenuation effect of the filters, i.e. coefficients between 0 and 1; ${\displaystyle k_{X},k_{Y},k_{Z}\!\,}$
• the three spectral retinal cone sensitivity curves (named in 1931 and standardized as CIE - norm spectral value curves ); ${\displaystyle {\bar {x}}(\lambda ),{\bar {y}}(\lambda ),{\bar {z}}(\lambda )}$
• the spectral sensitivity curve of a suitable light receiver (silver bromide layer in the color film, sensor in the three-range device). ${\displaystyle s(\lambda )\!\,}$

These formulas can be interpreted in words as follows: Not only the color filters, but also the light receiver are analysis components. They always work together, so they always have to be coordinated.

As a consequence, Luther also made a general requirement for the technical simulation of color vision.

Today's meaning of the Luther condition

Application in color measurement technology

In addition to color photography, the Luther condition formulated in 1927 became particularly important for color measurement. Because the basics of color measurement technology are already anchored in it. The Luther condition was first taken into account in the three-range measuring devices ( colorimeter ), the color measuring devices with the simplest structure. Colorimeters have three filters whose spectral transmittance in connection with the spectral sensitivity of the sensors corresponds exactly to the standard spectral value curves ( tristimulus curves ). Today these devices are only used for measurements on monitors or colored liquids. In incident light measuring devices, the spectral distribution of the measuring light source (with approximately a standard illuminant) is also included in the calculation of the measured values. For monitor measurements, the D50 standard illuminant has always been simulated mathematically as a reference.

Approx. this method has experienced a renaissance since 2000 with the use of video cameras as colorimeters. The CCD or CMOS sensors of the camera are not behind filters with the usual spectral transmittance for red, green and blue channels. Rather, the three filters have the spectral characteristics of the tristimulus curves. In this way the video camera becomes a fast and fairly reliable detector for the slightest color difference. The main application is the expansion of inspection systems on printing machines with a function for the automatic minimization of color fluctuations.

Modern color measuring devices , i.e. spectrophotometers and spectral densitometers , also meet the Luther requirement. Although they have a polychromator instead of the three-range filter set , which splits the light into all spectral colors, the light source – polychromator – sensors (pre-switching / blocking filter) sensors are still able to simulate human color vision. This is possible by calculating the corresponding color index from the measured spectral reflectance .

Deliberate violation of the Luther condition

But useful applications can also be created by deliberately bypassing the Luther requirement. In this way, true-to-life color reproduction should be achieved in multi-spectral photography. This is why this color camera application does not use three trichromatic analysis filters in front of the camera sensor, but at least seven on an upstream filter wheel. As the spectral transmittance of these filters overlap as much as possible, a higher information density can be achieved through individual measurements under the respective filter channels and their subsequent computational "interconnection", comparable to the information density in a spectral densitometer . The primary goal is to generate a larger original data color space than would be possible with a conventional RGB camera. On the synthesis side, i.e. in offset printing , more than the usual four printing inks should of course be used - for example from the Hexachrome system - in order to achieve a significantly larger color space in printing.

Luther-Nyberg color body

Out of his demand for trichromatic filters, Luther also developed the idea of ​​a color space for body colors ( i.e. substances containing color pigments ) in the aforementioned article From the field of color stimulus metrics , which he called color space . But unlike in Ostwald's color body, Ostwald's double cone (1918), Luther did not create an arbitrarily circular but a color space model based on eight selected optimal colors . The color stimulus -Messwertkurven X, Y, Z of color samples that the optimal colors closest came convicted Luther in more manageable color space coordinates. For this purpose, he created the so-called color moments M₁ and M₂ as color space axes - quasi torques that are at right angles to each other and attack the lightness axis A (gray axis) of the color body. The color moments are based on a centering of the color stimulus curves (marked as X ', Y', Z ') in order to be able to consider their brightness independently of the spectral composition of the white light ( type of light ); all X, Y and Z coordinates related to the light type then assume the value 100.

${\displaystyle M_{1}\!\,=Y'-X'}$

${\displaystyle M_{2}\!\,=Y'-Z'}$

While M₁ and M₂ for the color type are, so the shade with a certain degree of saturation, the vertical passing through the intersection of M₁ and M₂ Raumachsenkoordinate indicates the lightness value A. In this way, a layer can be defined in the color space model for each brightness level A = 0 ... 100 of the selected optimal colors, the contour of which corresponds to the maximum saturated color tones. The saturation (chroma) of a specific hue (hue) can be determined from the color moments M₁ and M₂ as the Euclidean distance of the color locus (referred to by Luther as chromatic moment M ) from the color space axis A (where M₁ = M₂ = 0 and from the formula fall out) calculate:

${\displaystyle M\!\,={\sqrt {M_{1}^{2}+M_{2}^{2}}}}$

A year later, the Swedish physicist ND Nyberg described in his work to build up the colors of the body in space all the sensations of light an identical color space construction, which is why since then in the literature from Luther Nyberg'schen color body or Luther-Nyberg-color body is spoken.

literature

• Luther, Robert: From the field of color stimulus metrics. Journal for technical physics 8 (1927), pages 540-558
• Nyberg, ND: On the structure of the color body in the space of all light sensations. Zeitschrift für Physik 52 (1928), pages 406-410
• Richter, Manfred : Introduction to colorimetry. Walter de Gruyter - Göschen Collection, Volume 2608, Berlin and New York 1976. ISBN 3-11-004751-9

Individual evidence

1. ^ TU Ilmenau , Faculty of Computer Science and Automation, Department of Graphic Data Processing: Optical Multi-Range Measurement System (Opticolor) ( Memento from June 22, 2009 in the Internet Archive ), section “Principle of the multi-range measurement system”, accessed on February 4, 2010
2. ↑ IDD: Colorimeters. Practical color measurement and color science in paper technology . TU Darmstadt , pp. 17–21 , archived from the original on 2014 ; Retrieved February 5, 2010 . 
3. ↑ Advanced Vision Technology Ltd: SpectraLink Online Press / Job color verification and management ( Memento December 29, 2009 in the Internet Archive ), accessed February 14, 2010
4. ↑ [1] : RWTH Aachen University : Research Area Multispectral Technology (Multispectral Color Image Recording) , accessed on February 4, 2010
5. ↑ echo productions: ( Memento of August 24, 2010 in the Internet Archive ) R. Luther, ND Nyberg , accessed on February 4, 2010
6. ↑ Archived copy ( Memento of the original from August 13, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. : TU Dresden : Dresdner UniversitätsJournal 20 (2009) No. 3, see photo in the article “Decisive basics of modern color measurement”, page 8, accessed on February 5, 2010