PHOTOGRAPHIC SENSITOMETRY 



181 



some practical photographic material. The region of reversal is not included in these 

 curves, as it is of no practical importance. 



The various individual curves of the family of Fig. 18 have been plotted for varying 

 times of development. The lowest curve is for a development time of 2 min., and the 

 highest curve represents development time of 15 min. 



The finite density for very low values of exposure represents density due to 

 development and other types of fog. It is at once apparent, as might be expected, 

 that the fog density increases with the time of development. Although fog occurs in 

 all practical cases (it may be relatively low for certain types of emulsions), fog does 

 not contribute anything useful to the image but merely provides a deposit of silver 

 uniformly over the surface. For this reason the curves often published by manu- 

 facturers are "corrected for fog" by subtracting the amount of fog density — assumed 

 constant for all values of exposure — ^from the measured density at any specified 



3.0 



2.0 



1.0 



12 3 4 5 



20 



25 



10 15 



Developing Time I'n Minutes 



Fig. 19. — Time-gamma curves for typical photographic materials for two different values 



of development constant k. 



exposure value. The effect of this fog correction is to shift all the curves somewhat 

 lower on the density scale. For such fog-corrected characteristics the density indi- 

 cated by the ordinates is, not the absolute value of density of the photographic mate- 

 rial, but rather the density due to exposure in excess of the fog density. If the fog 

 density is very small, as in the case of process or lantern-slide naaterials, the corrected 

 and uncorrected family of curves may not differ appreciably. The difference between 

 curves which are or are not corrected for fog will be much greater, however, in the case 

 of many panchromatic materials which have inherently greater fog. 



Time-gamma Curves.- — It will be seen from Fig. 18 that the increase in gamma is 

 not a linear function of the development time. Instead y increases fairly rapidly with 

 time for low values of development time, but as the development time increases, 

 the increment in per unit of time decreases. Ultimately, the characteristic 

 curves approach a definite value of gamma when the time of development is 

 infinitely long. The value of the maximum gradient, or Gmax, for infinitely long 

 development time is known as "gamma infinity" and is represented by the 

 symbol 7„. If we plot y against the time of development Td, the manner in which y 

 increases with developing time will become more evident. The y-Td curve of Fig. 19 

 shows this relationship, from which it is evident that, as Td is prolonged, y approaches 

 a limiting value which is designated t=o and commonly spoken of as gamma 



