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

Abstract

Thearticleis 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 amatrix transformationof 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 asystem 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 bySchwarzschildandWeinland. TheSchwarzschild-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. TheWeinland-effect shows the non-commutativity as the blackening result of two exchanged consecutive exposures with equal light quantityE • t(Eintensity,ttime) but different values ofEandt, which is explained by means of the non-commutative multiplication of different exposure matrices. Besides theWeinland-effect, non-commutative double-exposure effects are also those ofClayden,Villard,Herschel, andBecquerel. 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 theformulated analytically as thelatent imageexposure matrixB(E,t) or in the reduced form as theSchwarzschild-productE • t. 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.^{p}

The therefrom emergingphotographic blackening density(DE,t) is afunctionof the reaction-kinetic resultB(E,t) resp.relating to the exposure magnitudes with the independent variablesE^{.}t^{p}intensityandEtime.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:www.ewald-gerth.de/41.pdf

P 41. Gerth E.:

Reaktionskinetische ProzesseBild und Ton 26 (1973) 45-48, 59, 69-73, 107-110, 120

der Entstehung des latenten Bildes

und der photographischen Schwaerzung

Abstract:Reaction-kinetic processes

of the emergence of the latent image

and the photographic blackening

References

The numbers of the references are related to the

Register of Published Articlesof 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

Abstract: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

Abstract:Analytic representation of the photographic characteristic blackening curveP 22. Gerth E.:

accounting for the Schwarzschild-effect

Zur theoretischen Deutung des Schwarzschildschen Schwaerzungsgesetzes -

mit einer Wuerdigung des Begruenders derWissenschaftlichen Photographie:

Karl Schwarzschild 1873-1916

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

Abstract: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

Abstract:Analytic representation of the photographic

characteristic blackening curve by matrix functions

Abstract HTML-Version

Quoted by: SAO/NASA ADS Physics Abstract Service

P 43. Gerth E.:

Zur analytischen Darstellung der Schwaerzungskurve II.J. Signal. AM l (1973) 259-268

Die Belichtungsmatrix

Abstract:On the analytic representation of the photographic characteristic curve II.

The exposure matrix

Karl Schwarzschild 1873-1916

Last update: 2019, November 11^{th}