Photographic Double-Exposure Effects -
according to the theory

Ewald Gerth

Extended Abstract

The characteristics of consecutive photographic double exposures with different magnitudes of light intensity and time duration is the non-commutativity of 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, a system of differential equations is 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 by Schwarzschild and Weinland. - 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-exposures 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.

    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.


    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 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

    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: 2020, January 22nd