PHOTOGRAPHIC SENSITOMETRY 205 



the exposure range of the positive is obtained from the opacity range of the negative. 

 the print will give accurate monochrome rendition of the original image. The condi- 

 tion that 7p = 1 is a sufficient condition for the production of a print having proper 

 tone rendition, but it is unnecessarily rigid. 



The opacity range of the positive material Op is 



«• = <iy 



(60) 



Similarly, the exposure range of the positive is a function of the opacity range of the 

 negative, as shown by the relation 



(t)-(ir 



Consequently, by substituting k{En/in)yn for Ep/ip in the equation for Op, the opacity 

 range of the positive may be expressed as 



Op = ^(1^)^" = Kki^^Y""' (62) 



Now the exposure range of the negative material En/in is in turn proportional to the 

 brightness range of the original image or subject so that, if this brightness range is 

 expressed by B^JBi, we have 



(1) = ^(1;) '■^^ 



and finally 



Op = KkM[^^ = (^) (64) 



This equation shows that the opacity range of the positive or print is proportional 

 to the brightness range of the original image raised to some power which is the product 

 of the gammas of the positive and negative materials. So long as the product of the 

 gammas is unity, i.e., ynjp = 1, the absolute values of the individual gammas is of 

 little consequence. Therefore, if we have a negative in which the gamma is different 

 from unity, we may still obtain accurate tone rendition by so selecting the printing 

 medium that its gamma is such that the product will be unity. For example, if the 

 negative is "flat" so that 7„ = K, then proper tone in the print may be obtained by 

 using a ' ' contrasty grade " of paper such that jp = 2. The product of the gammas will 

 be ypjn = M X 2 = 1 and we shall have established the condition of proper tone 

 rendition. 



Graphical Representation of Tone Rendition. — Up to the present time, it has been 

 assumed that the straight-line regions of the D-logio E curves of both negative and 

 positive materials were the only portions used. This assumption does not conform to 

 practice, and in extending the representation of tone rendering in monochrome, it is 

 desirable to use graphical methods to show the effect of the various characteristics. 

 Mathematical methods, which are both simple and accurate, can no longer be used 

 when curvature of the characteristics enters into consideration. 



A method of representing the entire and essential concepts in the proper tone 

 rendition of the complete photographic process has been developed by Jones, ' and that 

 method is reproduced here. The method consists of using the second of four quad- 

 rants to represent the brightness and brightness range of the original subject (the 

 resultant H and D characteristics of the negative exposed to the subject), the third 



1 Jones, L. A., J. Optical Soc. Am., 5, 232 (1921); J. Franklin Inst., 190, 39 (1920). 



