PHOTOGRAPHIC SENSITOMETRY 179 



The latitude of a photographic material is closely related to the maximum contrast 

 which may be recorded on that material without distortion of tone rendering. For 

 proper tone rendering the maximum contrast Cmax of a photographic material may be 

 specified as the difference in densities between the extreme ends of the straight-line 

 portion of the H and D curve. If D2 is the maximum density corresponding to the 

 point D on the straight portion and Di is the minimum density on the straight portion 

 of the curve, the maximum contrast for correct tone rendition is 



Cmax = Dz - Dl (18) 



But D2 = A + -y logio Eo, and Di = A -\- y logio Ei. Consequently, the maximum 



contrast may be expressed in terms of the exposure range, and latitude may be 



expressed as 



Ei 

 Cmax = 7 logiu E2 — y logio El = y logio ^ , (19) 



= yL (20) 



where L is expressed in logio E units. In these equations, 7 is the slope of the straight- 

 line portion of the D-logio E characteristic. Attention should be directed to the fact 

 that the L and y for a given photographic material depend upon the characteristics of 

 material as well as its development. For a given photographic material y depends on 

 development. The symbols Cmax, L, and y refer only to the straight-line portion or 

 linear region of the D-logio E curve; the extension and the application of these symbols 

 to the curved portions of the characteristic is unwarranted. 



Gradient and Gamma. — The gradient or slope of the H and D characteristic is 

 another important factor in specifying the characteristics of photosensitive materials. 

 The gradient of the D-logio E characteristic is defined as the derivative 



G= -^y-, j^ = tan a (21) 



ddogio E) ^ ■' 



where, as usual, dD represents a differential increment of density, d(logio E) represents 

 a differential increment of logio E, and a represents the angle between the character- 

 istic curve and the abscissa. In general the gradient is not constant. At the extreme 

 left of the curve, the gradient may begin with a finite value, in the region of under- 

 exposure, but builds up to a maximum value in the region of correct exposure repre- 

 sented by the straight line. Beyond the point D the slope (gradient) continually 

 decreases in the region of overexposure until at the point E, representing the maximum 

 density to which the material may be processed, the gradient is zero. Beyond point 

 E the gradient is negative in the region of reversal. 



For the straight-line portion of the curve the gradient of any single characteristic 

 curve is constant and is usually defined in terms of the angle a which the line CD 

 makes with the abscissa. The slope of this straight line is designated as 



/-I n dD 



ir = trrff = -jTj =T- = tan a = y = constant (22) 



d(logio E) 



Since the region between D and C is constant, we may replace the differentials by 

 finite differences and write 



^ ~ A logio E' ^^^^ 



Thus, if D2 and Di are the density differences corresponding to exposures of E2 and 

 El (in meter-candle-seconds), then so long as these two points Di-logio Ei and Da-logio 



