X-RAY MICROSCOPY 



d(Mm)/^m = |^/l + (P^ 



In (papi) 

 (Low Magnification) 



(.dp2/p2) 



(W 



where (dp2/p2) is the relative error of the 

 higher photometer reading. The low magni- 

 fication error function, presented in brackets 

 in (14) has a minimum value as illustrated in 

 Fig. 13. In order to minimize such error, p2 

 should be set at full photometer scale reading 

 and P2 should lie between about }^ and ^2 of 

 this P2 reading. This requires a corresponding 

 values of yfxm in the range 0.7 to 2.0. It is 

 important to note the rapid increase of the error 

 in nm for lower values of yfxni. 



To measure relatively small values of /xm, 

 it is clearly evident that the exposure time 

 be such as to gain a maximum value for the 

 contrast, 7. As may be deduced from the 

 characteristic curves, D vs log E, as plotted 

 in Fig. 14, this requires exposures for rela- 

 tively high densities, contrary to conven- 

 tional x-ray practice. It is convenient that 

 this high-7 region also produces optimum 



visual contrast — a fact which has been long 

 recognized. And finally since 7 is constant in 

 this high-density region, the relation given 

 in (12) need not apply only for small values 

 of jjLm, as assumed at the outset of this analy- 

 sis. 



For high magnification work, the domi- 

 nant source of photometric error is emulsion 

 granularity. It has been found that for such 

 errors, (dpi/pi) = (^^2/^2) = a constant for 

 a given high magnification measurement 

 (500 to lOOOX). For this case we rewrite (13) 

 as 



d inyn) lixm = \/2 (dp/p) /yfim = \/2/m»i (y/N) (15) 



The value of (dp/p) , as due mainly to photo- 

 graphic noise and designated by the symbol 

 A'', has been measured as the average value 

 of the relative variation in the photometer 

 signal as read from microphotometer tracings 

 at various microradiogram densities using a 

 0.5 by 1.0 micron slit. The results of such 

 measurements are also illustrated in Fig. 14. 

 It should be noted that nm increases more 



PHOTOMETRIC ERROR Ai./* = e(APi/P«) 



Y jJ-TI » 



0.5 1.0 L5 2.0 



8 



.£. 



WHERE Aft/ft - RELATIVE 

 ERROR OF Pt READING 



ASSUMING ■ y/in = LOGe Pt/Pi 



SAMPLE SIGNAL 



BACKGROUND — 



ZERO light- 

 Fig. 13. The prediction of error for a measurement for the case of constant absolute photometric 

 error, dpi ~ dp2 , as typical in low -magnification work. 



688 



