Photographic Double-Exposure Effects -

according to the theory

Ewald Gerth

Extended Abstract

The characteristics of consecutive photographicdouble exposureswith different magnitudes of light intensity and time duration is thenon-commutativityof the finally after development resulting blackening. On the theoretical foundation of a step-like build-up process of development centers with forward and backward reactions, asystem of differential equationsis set up, the solution of which provides a sequence of linear vector transformations by means of matrices. 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 analytical formulation of this process of step by step growing centers using matrix algebra gives new explanations of many phenomena observed empirically at photographic materials. There are above all the photographic effects like those established bySchwarzschildandWeinland. -Exempli gratia:

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 typical for double-exposuresnon-commutativityas 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.

Typical non-commutative double-exposure effects are:

the Weinland-effect,the Clayden-effect,

the Villard-effect,

the Herschel-effect,

the Becquerel-effect

Photographic effects with an interim treatment are added:

the Schwarzschild-effect,

the Sabattier-effect,

the Albert-effect,

the solarization-effect

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.

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 curve

accounting for the Schwarzschild-effectP 22. Gerth E.:

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 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

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: 2020, January 22^{nd}