ULTKASOFT X-RAY MICROSCOPY 



larity to that of Lippmann emulsions and 

 lower contrast. Pattee has carried this work 

 (7) much further and has developed an in- 

 strument, called the microfluoroscope (p. 

 563), which permits direct viewing of the 

 image from such a phosphor recording ma- 

 terial, gaining the necessary maximum in- 

 tensity by placing the sample within 0.1 mm 

 or less of a microfocus source. He has re- 

 ported that adequate intensity has been 

 obtained for direct viewing, using a 3 mi- 

 cron aluminum target foil, at 9 kilovolt 

 excitation. At the Stockholm Symposium on 

 X-Ray Microscopy in 1959, Auld and Mc- 

 Neil reported that xerography (8). with 

 liquid developers, will also yield resolution 

 comparable to that of the concentrated 

 Lippmann emulsions. To date none of the 

 non-photographic recording materials has 

 been demonstrated as being superior to the 

 photographic method for ciuantitative meas- 

 urements in ultrasoft microradiographic 

 analysis. 



The following analysis is given in order to 

 establish an optimimi procedure in photo- 

 graphic measurement for microradiography. 

 Let us consider first the determination of the 

 absorption parameter /xm (n the mass ab- 

 sorption coefficient and m the mass-per-unit- 

 area-thickness) for a small object which has 

 caused only a relatively small variation in 

 the density of the microradiogram. The pho- 

 tographic blackening or density will be de- 

 fined as Ds in the region originally under the 

 sample object, and as Db in the immediate 

 surrounding. The corresponding x-ray ex- 

 posures which resulted in these densities will 

 be defined as Es and Eb . The photographic 

 densities are related to the photometer read- 

 ings on the microradiogram, (p2 in the sam- 

 ple region, pi in the immediate surrounding, 

 and po ill the clear emulsion) by the defining 

 equations 



D, = log (P0/P2) and Db = log (po/pi) (S) 



The ratio of the x-ray exposures for the sam- 

 ple and surroundings is equal to the ratio of 



the corresponding intensities (reciprocity law 

 obtaining for these wavelengths) and there- 

 fore given, from {1), as 



EJEi = e-*"" 



(9) 



SO that 



log Eb - log E, = y.m log e = A (log E) (10) 



Since the parameter jum is measured by the 

 value A(log E), it is convenient to present 

 the emulsion characteristics as 



D = /(log E) (11) 



as is conventional for light photography. 

 Then from (8), (10) and (11) and for rela- 

 tively small differences between Eb and Es , 

 we may write 



^D/A(\ogE) = df/d(logE) 



7 = log (p2/pi)/fi»i log e 



giving finally 



y/im = In (P2/P1) 



(W 



where 7 is the slope of the D vs log E charac- 

 teristic, conventionally designating emulsion 

 contrast, and log(p2/pi)/log e has been re- 

 placed by the logarithm to the natm'al base, 



e, viz. In(p2/pi). 



We may now determine the effect of the 

 measurement errors upon the determination 

 of fim. By differentiating (12) we obtain 



d(nm)/ixni = 



^^(dpi/p-i) T (dpi/pi) 



yfitn 



V(dpi/pi)^ + (dp2/p2)^ 

 (jixm) 



(IS) 



in which we have added (T) errors in the 

 usual manner. 



In order to define the conditions required 

 for minimvmi error it is necessary to define 

 the type of photometric error, (dp/p), in- 

 volved in a given measurement. For loiv mag- 

 nification Avork in which emulsion granularity 

 is not the dominant source of error, we may 

 often have dpi ^ dp2 ~ a constant over the 

 entire range of the photometer scale. For this 

 case, (18) may be rewritten as 



687 



