204 HANDBOOK OF PHOTOGRAPHY 



as faithfully as possible, the images of the negative, except that they will, of course, be 

 reversed in tone. This diagram has been so prepared that by its use and by an analy- 

 sis of the print the photographer may determine errors which may have been made, 

 either in the exposure of the print or in selecting the type of paper for a given negative. 



Tone Rendition. — In most applications of photography, the ultimate goal is a 

 positive print, either a transparency or paper print, in which the brightnesses of the 

 elementary areas of the original subject are to be reproduced in the positive print. 

 For correct rendition of tones in monochrome photography, the brightness of these 

 elementary areas in the final print must equal the brightness of the corresponding 

 elementary areas of the original subject or image. The final print is the result of two 

 reversal processes (the negative and the print), both of which have already been 

 discussed in some detail. 



Let B represent the brightness of the original subject, and Bp the brightness of the 

 resultant print, the brightness varying with each elementary area from point to point. 

 Then if for all elementary areas Bp is exactly equal to B, the monochrome rendition of 

 the original subject in the print will equal the brightness of the original subject as 

 evaluated by the human eye, and perfect rendition of tone results. Because of the 

 limitations of photographic materials, this ideal condition is never completely realized, 

 although it may be approached more or less closely. 



The exposure range of the negative En is proportional to B, and the relationship 

 between density and exposure ranges is then 



En 

 Dn = JnO-Ogio En — logio in) = 7n logio ^:- (55) 



In 



where in is the inertia, or the exposure corresponding to the intersection of the straight- 

 line portion of the Z)-logio E curve, extended to the zero density axis. But the density 

 range is also given in terms of the opacity range 0„, and the transmission range Tn is 

 given in terms of the relation 



Dn = logio On = lOgia (^) (56) 



so that 



D„ = logio On = logio (jt) = Jn logic -^ (57) 



By taking the antilogarithms of both sides of the equation, we obtain 



«» - (r.) = m- <-> 



If now, the negative is developed so that 7 = 1, then the opacity range of the negative 

 will be directly proportional to its exposure range. 



In the printing process, the exposure range of the positive material Ep is inverselj^ 

 proportional to the opacity range of the negative On. The opacity range of the posi- 

 tive printing material is given by 



where the symbols have the same meaning as given above but refer to the positive 

 printing material rather than to the negative, as indicated by the subscript p. If 

 the positive material is printed in such a manner that 7p = 1, either through proper 

 development or by selection of the proper grade of paper, then the silver deposit on the 

 print will have an opacity range which is proportional to its exposure range. Since 



