PHOTOGRAPHIC SENSITOMETRY 



197 



photographed on the negative. If we designate by J? 2 the brightness of the brightest 

 part of the original image and by Bi the brightness of the darkest elementary area of 

 the original image and if we designate the opacities of the corresponding elementary 

 areas by O2 and Oi and the transmission by Ti and Ti, respectively, then we require 

 that the condition of proper photographic reproduction be such that 



B2 



AO2 = ~ 



and 



B^ = AOi = 



Ti 



(46) 



(47) 



where A is a proportionality constant. The brightness range of the original subject is 

 AB = B% — Bi, and the opacity range of the corresponding subject as photographed as 

 AO = AO1 — A0\. Therefore, the relation between the brightness range of the 

 original image and the image as photographs is such that 



AB = A{a0) 



(48) 



These relations show that for accurate rendition of tone values in monochrome, the 

 brightness and the brightness range of the original image must be rendered on the 

 negative as proportional opacities and opacity 

 ranges, respectively. 



If we plot a curve of the brightness and opac- 

 ity of the original and photographed images on 

 rectangular coordinates, as in Fig. 27, we obtain 

 a straight line for the region of correct exposure. 

 But the brightness of the original image deter- 

 mines the exposure which is given to the photo- 

 graphic material so that we might, if we chose, 

 plot Fig. 27 with exposure as the abscissas rather 

 than the brightness. We would then have a Yiq. 27. — Opacity of negative 



graph showing a straight-line relationship between material as a function of the bright- 

 the exposure of the original image and the opacity ^ess of the subject being photo- 

 j. , , , , 1 J ■ graphed. The curve greatly re- 



of the photographed image. ^^^^^^^ ^^^ ^^pi^^^ Z)-logio ^ 



Let us go one step farther and, mstead of characteristic, 

 plotting the exposure and the opacity, plot the 



logarithms of these values on cross-section paper. The resultant graph would then 

 have as its ordinates logio 0, which by definition is the density, and would have 

 as its abscissas logio E. We find that this new plot is, consequently, merely the 

 straight-line portion of the H and D characteristic, and we may immediately draw the 

 conclusion that for properly rendering tone values the exposure and density relations 

 must be such that the entire image is photographed on the straight-line portion of the 

 H and D curve. 



If the exposure is so chosen that all the brightness range of the original subject 

 does not fall upon the straight-line portion of the curve, some distortion of tone 

 values will occur. If too small an exposure is given, the less bright portions of the 

 original image may be compressed in the density range required for accurate reproduc- 

 tion. This condition will be apparent to the photographer by the fact that the detail 

 is lacking in the shadows of the original subject (the less dense portions of the nega- 

 tive). On the other hand, if too great an exposure is given, the brightest portions of 

 the original subject may not be represented on the negative by their true proportional 

 differences in density. In this case, the practical photographer makes vise of sensi- 



