BILD UND TON • Journal of Movie- and Photo-Techniques • Number 2-4/1973, 26. Volume pp. 45-48, 59, 69-73, 107-110, 120

Reaction-kinetic processes
of the emergence of the latent image
and the photographic blackening

Ewald Gerth

The article is a rearranged and for better comprehensibility reworked excerpt of the postdoctoral thesis of the author, which concerns especially the reaction-kinetic process of the step-like build-up of development centers in the lattice of silver halide crystals in a photographic emulsion during the exposure to light.
Dissertation (B), TU Dresden 1972, Habilitation 1991 --- Book 2013: ISBN 978-3-8316-4299-1

The solution is given by a matrix transformation of the center components, consisting of conglomerated silver atoms and arranged as a vector, which is transformed in a multidimensional “reaction space” by a resolving matrix during a transition process from an initial composition to the end composition. The resolving matrix is represented as an expansion of a matrix exponential function, yielding immediately the algorithm for the numerical calculation in a computer program.

The analytical representation as a system of differential equations, the solution of which provides a sequence of linear vector transformations by means of matrices, leads to a new theory of the photographic elementary process. The vector of the initial distribution of the centers of different reaction order arranged in a reaction chain is redistributed by multiplication with a reaction matrix – the so-called “exposure matrix”, which contains all exposure parameters.

The formulation of the process of the step by step growing centers by means of matrices gives new explanations of many phenomena observed empirically at photographic materials. There are above all the photographic effects like those established by Schwarzschild and Weinland. The Schwarzschild-effect is explained regarding the setting of an equilibrium of forward and backward reactions between the first two steps in the reaction chain by recharging the centers with free electrons. The Weinland-effect shows the non-commutativity as the blackening result of two exchanged consecutive exposures with equal light quantity E  t (E intensity, t time) but different values of E and t, which is explained by means of the non-commutative multiplication of different exposure matrices. Besides the Weinland-effect, non-commutative double-exposure effects are also those of Clayden, Villard, Herschel, and Becquerel. All these photographic effects are in good accord with the theory of the matrix-based formulation of the photographic process.
The photographic effects are demonstrated experimentally and theoretically relating to the postdoctoral thesis of the author.

The final result of the intracrystalline build-up process of development centers is the emergence of the latent image formulated analytically as the exposure matrix B(E,t) or in the reduced form as the Schwarzschild-product E  tp. This is given by the occupation quantity of the silver bromide microcrystals in the photographic emulsion with silver particles, which in the photographic developing process convert the whole crystals to black metallic silver.
The therefrom emerging photographic blackening density D(E,t) is a function of the reaction-kinetic result B(E,t) resp. relating to the exposure magnitudes with the independent variables intensity E and time t.

Comment of the author:
The present article was published in 1973 in the professional movie-technical journal BILD UND TON. The journal was distributed only in the restricted zone of the GDR, so that it is nearly impossible to get any exemplar even from a library. Therefore, in order to make the article available for the interested reader, the author decided to install the full text in the INTERNET.

Article available in German by the web-address:

P 41. Gerth E.:
Reaktionskinetische Prozesse
der Entstehung des latenten Bildes
und der photographischen Schwaerzung
Bild und Ton 26 (1973) 45-48, 59, 69-73, 107-110, 120
Reaction-kinetic processes
of the emergence of the latent image
and the photographic blackening


The numbers of the references are related to the Register of Published Articles of E. Gerth.

P 8. Gerth E.:
Grundriss der heutigen Theorie des photographischen Prozesses
Bild und Ton 16 (1963) 268-271, 296-301, 333-335, Heft 9-11
General outline of modern theory
of the photographic process

P 16. Gerth E.:
Analytische Darstellung der Schwärzungskurve
unter Berücksichtigung des Schwarzschild-Effektes

Z. wiss. Phot. 59 (1965) 1-19
Analytic representation of the photographic characteristic blackening curve
accounting for the Schwarzschild-effect
P 22. Gerth E.:
Zur theoretischen Deutung des Schwarzschildschen Schwaerzungsgesetzes -
mit einer Wuerdigung des Begruenders der Wissenschaftlichen Photographie:
Karl Schwarzschild 1873-1916

Wiss. Z. PH Potsdam 10 (1966) 339-410

On the theoretical interpretation
of Schwarzschild's law of blackening -
with a recognition of the founder of Scientific Photography:
Karl Schwarzschild (1873 - 1916)

P 36. Gerth E.:
Analytische Darstellung der Schwaerzungsfunktion
mit Hilfe von Matrixfunktionen

Annalen der Physik 27 (7) (1971) 126-128
Analytic representation of the photographic
characteristic blackening curve by matrix functions

Abstract HTML-Version
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P 43. Gerth E.:
Zur analytischen Darstellung der Schwaerzungskurve II.
Die Belichtungsmatrix
J. Signal. AM l (1973) 259-268
On the analytic representation of the photographic characteristic curve II.
The exposure matrix

Karl Schwarzschild 1873-1916

Last update: 2019, November 11th