Reciprocity Law Failure Research Articles

Estimation of the Critical τ Period in Latent-Image Formation by Intermittent Exposures*

Low-intensity reciprocity-law failure in photographic exposure represents an inefficiency arising from the regression of the latent image in its early stages of growth. Evidence has been given to show that the stable sublatent image requires for its formation the action of two or more quanta in a small critical time period, τ. A new method for evaluating this critical time period by intermittent exposures is described.Experiments carried out on four commercial emulsions showed approximately equal τ periods of the order of 3 seconds. Studies were also made on three experimental emulsions to determine the effect of certain types of chemical sensitization on the critical τ period. These experiments were carried out for both the surface and the internal latent image by means of varied development procedures. The critical τ period varied between 3 and 10 seconds for the surface image and remained essentially constant at about 4 seconds for the internal image. Results indicate that chemical sensitization increases the critical τ period of the surface latent image and slightly decreases the critical τ period of the internal image.

Practical Aspects of Reciprocity-Law Failure

The occasional failure of sensitometric data to provide a reliable indication of the practical performance of photographic materials is usually attributable to the failure of the reciprocity law. The effect of reciprocity-law failure on the characteristic D-log E curves of various films is shown graphically. The influence of developing time and of the temperature of the film on the effectiveness of exposure at various intensity levels is discussed. Certain generalizations are made about the failure of the reciprocity law which may be helpful in reconciling differences between laboratory measurements and the results obtained in motion picture practice.

Ancora su talune determinazioni sensitometriche in spettrografia

Plate calibration with a group of homologous lines gives more accurate results than the use of a step sector. Using two different source units and two spectrographs the effect of these on plate calibration curves for several different types of plate has been explored, the measurements made for this purpose are also statistically evaluated to give estimates of the variability due to the plate emulsion, to the spectral source, and to microphotometry. The importance of reciprocity law failure and the use of algebraic transformations to extend the linear portions of calibration curves are also discussed with adequate data.

A Note on Intermediate Intensity Reciprocity-Law Failure at and Near the Optimum in Photographic Exposure

A Note on Intermediate Intensity Reciprocity-Law Failure at and Near the Optimum in Photographic Exposure

Phenomenological Theory of Intermediate Intensity Reciprocity-Law Failure at and near the Optimum in Photographic Exposure

Phenomenological Theory of Intermediate Intensity Reciprocity-Law Failure at and near the Optimum in Photographic Exposure

Errata*: Low Intensity Reciprocity-Law Failure in Photographic Exposure: Energy Depth of Electron Traps in Latent-Image Formation; Number of Quanta Required to Form the Stable Sublatent Image

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text J. H. Webb, "Errata*: Low Intensity Reciprocity-Law Failure in Photographic Exposure: Energy Depth of Electron Traps in Latent-Image Formation; Number of Quanta Required to Form the Stable Sublatent Image," J. Opt. Soc. Am. 40, 883_6-883 (1950) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

The practical roentgenographic importance of reciprocity law failure.

The practical roentgenographic importance of reciprocity law failure.

The Practical Roentgenographs Importance of Reciprocity Law Failure

The Practical Roentgenographs Importance of Reciprocity Law Failure

On the Photographic Reciprocity Law Failure and Related Effects. II. The Low Intensity Sequence Effect

A quantitative theory of all details of the low intensity sequence effect is given on the basis of the following assumptions. A monatomic Ag speck is unstable against thermal agitation, a diatomic speck is stable, but for development a speck of more than two atoms is required. The theory is based on that for low intensity failure as developed in paper I.

Low Intensity Reciprocity-Law Failure in Photographic Exposure: Energy Depth of Electron Traps in Latent-Image Formation; Number of Quanta Required to Form the Stable Sublatent Image*†

A method is outlined whereby the energy depth, ∊, of the traps for the initially trapped electrons in latent-image formation can be determined from measurements of reciprocity-law failure at two different temperatures, T1 and T2. The analysis leads to the equation for determining ∊, logt2t1=0.434∊k(1T1-1T2),where t1 and t2 are the exposure times of two low intensity exposures of equal density and equal efficiency made at the two temperatures, and k is the Boltzmann constant.Experimental reciprocity-law failure curves for different temperatures are given for a series of emulsions, including results obtained with surface, internal, and total development. The average value of ∊ found from several commercial emulsions using total development is 0.77 ev, and for one experimental emulsion using internal development, 0.65 ev.A theoretical study of low intensity reciprocity-law failure is carried out by probability equations derived by L. Silberstein. These equations are used to calculate the fractions of grains that acquire a just-stable sublatent-image speck under the conditions that its establishment requires the absorption of 1, 2, or 3 quanta within a critical time, τ. It is found from this analysis that the reciprocity-failure curves approach the limiting slopes of 0, 1, or 2 at low intensities for the respective cases of singlet, doublet, or triplet hits in time, τ. This gives a sharp criterion for distinguishing between these cases, and comparison of experimental and theoretical curves indicates that the absorption of 2 effective quanta within a time, τ, is required to form the stable subimage speck.Experimental reciprocity-failure curves at different temperatures indicate that the curves at different temperatures have the same shape but are shifted in the direction of lower intensity with lowered temperature. An explanation of this phenomenon is obtained from the theoretical treatment of the reciprocity-failure curves in terms of the critical time, τ.Finally, the reciprocity-failure characteristic of the developable latent-image is derived from the curve for the stable subimage by assuming that the subimage is formed by 2 quanta within a time, τ, and then brought to developable size by the addition of 6 more quanta. This procedure yields a reciprocity curve that is in good agreement with experimental measurements carried out here and that is also of the generally correct shape to represent the reciprocity-failure characteristic at low intensities.

On the Photographic Reciprocity Law Failure and Related Effects. I. The Low Intensity Failure

(1) The order principle (o.p.) states: ``The grains of an emulsion become developable in the course of an exposure in a given sequence independent of the exposure and development variables.'' This hypothesis appears to have a wide range of applicability. It forms an ideally simple link for correlating experimental isodense exposures and theoretical single grain response predictions. Moreover, in many cases where the o.p. is not strictly applicable, corrections can be derived (Section 12) which again make quantitative comparison of theory and experimental data possible. (2) Extending ideas of Gurney, Mott, and Webb, a quantitative theory of the low intensity reciprocity law failure (l.i.f.) is developed, by analyzing the statistics of light absorption and the survival function of the electrons. Confrontation of various theoretical possibilities with experimental data selects the following basic assumptions: (a) A monoatomic Ag speck of sub-latent image is unstable against thermal agitation, but a diatomic speck is stable for most practical purposes; finally a triatomic speck is completely stable. (b) The energy required to set free an electron from a monoatomic speck (electron trap depth) is not the same for all traps. There must be a quasi-continuous distribution of depths (e.g. as given by formula (10)). With these assumptions the theory describes satisfactorily the principal features in the shape of experimental l.i.f. curves. It is found that the l.i.f. slope varies systematically with grain size and the theory checks qualitatively with this result. The experimental temperature dependence of l.i.f. curves agrees satisfactorily with the theory.

Fundamentals of Photographic Theory

THIS book is a condensed version of "The Theory of the Photographic Process", by Dr. C. E. K. Mees, and it should prove a valuable text-book for those possessing the requisite knowledge of physics and chemistry and the necessary photographic experience to apply this knowledge . The chapter on the photographic emulsion is somewhat meagre, but succeeding chapters on the formation of the latent image and on reciprocity-law failure and other exposure effects are good. As one would expect, the chapters on development (mechanism of development, composition and reactions of developers, and general kinetics of development) reflect the fact that Dr. T. H. James has for many years made valuable contributions to this subject. After a discussion of fixing and washing, the authors devote three excellent chapters to a study of sensitometry, and a further chapter to the theory of tone reproduction. New material published since the date of Dr. Mees's work is included, and the discussion in chapter 11 on the new speed constants adapted by the American Standards Association is of particular interest. Finally, the authors deal with the structure of the developed image and with sensitizing and desensitizing. The book is very free from errors for a first edition ; the only one worth noting is that the formulae on p. 103 are not quite correct. The index is adequate, and the printing, lay-out and paper are first-class.

The Photographic Reciprocity-Law Failure for Radiations of Different Wave-Length*

The reciprocity-law failure of a number of dye-sensitized emulsions has been studied for radiations of different wave-length. The curves showing the exposure, It, to give a certain density, d, as a function of the exposure time, t, are found to be essentially, but not always exactly, parallel if curves referring to the same density are compared. This is in agreement with previous experience. For the case of complete parallelism, a relation is derived between the slope, G, of the intensity scale H and D curves obtained with radiations of different wave-length, λ1 and λ2, and exposure times, t1 and t2: 1/G(λ1,t1)-1/G(λ2,t1)=1/G(λ1,t2)-1/G(λ2,t2).This means that, for a given emulsion, the shapes of spectral-sensitivity curves (log exposure required to obtain a certain density as a function of wave-length) for different exposure times are identical, providing all the exposures within one spectral-sensitivity curve are of the same duration. The above equation is compared with the experimental results and found to hold within rather narrow limits.The bearing of the experimental results on tone reproduction and on the distribution of the latent image within the silver bromide grains is discussed.

Reciprocity Law Failure in X-Ray Films

The reciprocity law constitutes one of the fundamental rules of photography and of radiography. It states that the quality of a series of photographic or radiographic films will be uniformly constant if the exposure times with which the films are made vary reciprocally with the intensities of the exposing radiation. Thus, the law implies that when other things are equal a roentgenogram exposed for 1.0 second and with a tube-current of 100 milliamperes will be identical to one exposed for 10 seconds and with a tube-current of 10 milliamperes.2 The reciprocity law is based on the assumption that the density or blackening of a photographic film is dependent merely on the exposure or quantity of radiant energy which the film absorbs and is independent of the rate at which the energy is applied (i.e., is independent of the intensity of the exposing radiation).

The Photographic Reciprocity-Law Failure and the Ionic Conductivity of the Silver Halides*

A method is given for determining from reciprocity-law failure measurements at different temperatures the value of the energy exponent ∊ in the equation for ionic conductivity of silver bromide (1)Ni=Ae−∊/kT ions/sec.According to present theory, the reciprocity-law failure at high intensities is due to the sluggishness of the secondary process of latent-image formation consisting of migration of Ag+ ions to the specks. The free electrons produced in the grains by exposure can move practically instantaneously and independently of temperature. However, if the Ag+ ions cannot move up to the specks at a sufficient rate to keep them discharged, an inefficiency is introduced. This inefficiency may be said to depend upon the number of free electrons produced in the grain per second, Ne, compared with the number of free Ag+ ions, Ni, available for ionic conduction. The number of free electrons produced can be controlled by the light intensity, I, whereas the number of conducting Ag+ ions can be controlled by temperature in accordance with Eq. (1). By choosing points on the reciprocity curves made at different temperatures such that the change of efficiency arising from a change of intensity I1 to I2 is equal to the change of efficiency arising from a change of temperature T1 to T2, the relation is shown to hold (2)logI2/I1=0.434∊k(1T1−1T2).Substitution of experimental values in this equation for I1, I2, and T1, T2 gives a value of ∊ = 0.69. Direct measurement of the ionic conductivity at different temperatures on a single crystal of AgBr gives the value of ∊ = 0.66. The close agreement between the ∊ values obtained by photographic means and by direct measurement affords quantitative evidence that the high intensity reciprocity-law failure is due to the ionic conductivity effect alone.

An Intensity-Scale Monochromatic Sensitometer*

A working model of a monochromatic sensitometer covering the wave-length region from 3500 to 11,000A has been built. Monochromatic radiation used for exposure is obtained from a double monochromator employing transmission replica gratings as the dispersing elements. The intensity of this radiation is measured with a thermopile. Intensity-scale exposures upon the photographic material result from the use of a specially designed intermittent intensity-scale sector wheel. The same time of exposure is employed at all wave-lengths, and therefore the spectral sensitivity curve derived from the intensity-scale characteristic curves is independent of any reciprocity law failure which the emulsion may exhibit.

A Theoretical Treatment of the Two-Quanta Hypothesis as Applied to the Photographic Reciprocity Law Failure*

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text Ludwik Silberstein, "A Theoretical Treatment of the Two-Quanta Hypothesis as Applied to the Photographic Reciprocity Law Failure*," J. Opt. Soc. Am. 29, 432-447 (1939) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

The Photographic Reciprocity Law at Low Temperature*

The results of measurements of reciprocity law failure at 20°C and at −186°C are given for two different high speed panchromatic emulsions, one low speed unsensitized emulsion, and one high speed orthochromatic emulsion. These measurements, covering the range in exposure time from 116 second to 17 minutes 4 seconds, show that in each case the reciprocity law failure, at both high and low intensity, is normal at 20°C, but has disappeared entirely at −186°C. These results are in complete agreement with those recently published by Berg and Mendelssohn.

Latent Image Theory and its Experimental Application to Motion Picture Sound-film Emulsion<!--<xref ref-type="other" rid="fn1-10.5594_J12939">*</xref>-->

In a previous paper the writer attempted to show that the latent photographic image is formed in two distinct and separate steps. In the present paper this theory is compared with recent physical research. The writer concludes that each of the photographic steps consists of the attraction of one electropositive silver ion to a sensitizing speck on the grain surface which has previously captured an electron. — The reciprocity law failure at high intensities is explained by the minimum time required for the attraction of a silver ion. The reciprocity law failure at low intensities, is explained by assuming that a sensitizing speck which has attracted only one silver, ion is unstable and that the number of grains activated by a single capture decreases exponentially with time. — From these physical theories the whiter deduces mathematical relations governing the photographic characteristics. H&U curves and reciprocity failure curves computed front these relations are in good qualitative agreement with experimental curves. — The assumption of an unstable intermediate state of insufficiently exposed grains implies certain effects of delayed fogging (and delayed development which are verified by experiments.

An Experimental Study of Latent-Image Formation by Means of Interrupted and Herschel Exposures at Low TemperatureMeasurements of Reciprocity Law Failure at Low Temperature*

The present paper contains results of experiments carried out to test the theory of latent-image formation recently proposed by Gurney and Mott. In their theory, these authors have introduced the concept of electrolytic transport of Ag+ ions to account for the nucleation of latent image Ag about the sensitivity specks preexistent on the surface of the grains. The Ag+ ions are supposed to diffuse to the specks under the attraction of electrons trapped there during the exposure to light. The first experiment consisted of a series of intermittent exposures made at liquid air temperature with warm-up periods between flashes. The results indicate that something vital to the photographic process takes place during the warm-up period between exposures. The second experiment consisted of a series of Herschel exposures made under the following temperature conditions: (a) White-light exposure 20°C, Herschel exposure 20°C; (b) white-light exposure 20°C, Herschel exposure −186°C; (c) white-light exposure −186°C, Herschel exposure 20°C; (d) white-light and Herschel exposures both at −186°C; (e) case (d) repeated with warm-up period between the exposures. The results obtained are radically different under the different conditions. Finally, results are presented on reciprocity measurements at temperatures 20°C, −78°C, and −186°C. These results show that the low-intensity reciprocity law failure has disappeared at −78°C and that the high intensity failure has practically disappeared at −186°C. All of the foregoing results are shown to have ready interpretation on the Gurney-Mott picture of latent-image formation.