260 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 5 



where I is the intensity of the incident light, and / that of the trans- 

 mitted light. It is sometimes desirable to obtain an output signal 

 that is proportional to the logarithm of the incident light flux, for 

 instance, if the optical density D is to be displayed on a linear scale. 

 A method to operate a photomultiplier with a logarithmic charac- 

 teristic has been described by Sweet 1 and is illustrated in Fig. (5-1)26. 



-vUrWUrK4ArUrWUrW-L/T 



Ra 0. 



M\\- Es i£ 



Fig. (5-1)26. Circuit for the operation of a photo- 

 multiplier with a logarithmic characteristic [from 

 M. H. Sweet, J. Opt. Soc. Am., 37, 432 (1947); by 

 permission]. 



First, the direct light from the source L (without absorber) is per- 

 mitted to fall upon the photomultiplier; the illumination intensity 

 at the cathode is I and the observed current at the photomultiplier 

 output is i Q . Second, an absorber A is brought between the source L 

 and the photomultiplier ; the light intensity at the cathode is reduced 

 to the level I and causes a lower output current i. The supply voltage 

 to the photomultiplier is then raised by the amount AE until the 

 former value of the output current i is reached again. The sensitivity 

 of the tube, i.e., the current for a given illumination, is nearly an 

 exponential function of the supply voltage, as shown in Fig. (5-1)15; 

 therefore, the variation of the supply voltage AE at constant output 

 current is nearly inversely proportional to the logarithm of the illu- 

 mination intensity, and a meter measuring the applied voltage can 

 be calibrated directly in terms of the optical density D of the ab- 

 sorber. Measurements of the optical density usually extend over a 

 range of D from to 3, corresponding to a range of illumination 

 intensities from 1 to 1,000. Over this range the characteristic devi- 

 ates from a straight line (correct logarithmic function) by about 10 

 1 M. H. Sweet, J. Opt. Soc. Am., 37, 432 (1947). 



