ULTRASOFT X-RAY MICROSCOPY 



sis. References to most of the work accom- 

 plished to date in x-ray microscopy may be 

 found in the several that are listed at the 

 end of this paper (1). 



The wavelengths in the 10 to 50 A region 

 are of particular value for the quantitative 

 analysis of micron-size systems of organic 

 and light element inorganic composition — 

 i.e. for elements up through Ge 32. This 

 follows from the fact (to be established in a 

 later section) that at least 60% absorption 

 is required for precisions in the one to five 

 percent region in the measurement of the 

 parameter nm, where m is the sample mass- 

 per-unit-area "thickness" and m is the mass 

 absorption coefficient as defined by the ex- 

 pression for the ratio of transmitted to inci- 

 dent monochromatic x-radiation 



10 



SAMPLE THICKNESS FOR 

 37% TRANSMISSION 



t = I/Io = e- 



(1) 



It is shown in Fig. 2 that in order to have 

 60 % absorption for either light element in- 

 organic or organic materials with thicknesses 

 of the order of one micron, wavelengths in 

 the 10 to 50 A region should be employed. 

 The discontinuities in these curves are due 

 to the presence of critical K or L absorption 

 edges. Ultrasoft radiations are of very great 

 value for the microanalysis of this highly im- 

 portant problem area of the lighter element 

 samples not only because optimum absorp- 

 tion signal may be gained, but also because 

 either the K or the L absorption edges for 

 the elements of atomic number 6 to 32 lie 

 in this 10 to 50 A x-ray region. These absorp- 

 tion edges form the bases for sensitive, 

 differential absorption analysis. 



In the sections that follow, analysis and 

 experimental results are presented in order 

 to illustrate optimum methods and instru- 

 mentation and application of high resolu- 

 tion, ultrasoft x-ray microscopy for quantita- 

 tive analysis. 



Resolution Limit for X-Ray Microscopy 



As stated above, the first requirement for 

 resolving microscopic detail of fractional 



5 10 50 



A -ANGSTROMS 



Fig. 2. Indicating the necessity for using the 

 ultrasoft wavelength in order to gain the sufficient 

 absorption in micron-size systems for quantitative 

 measurement. 



micron dimensions is sufficient contrast for 

 detection and measurement. This must be 

 met, for samples comprised of elements from 

 the lower half of the periodic table, by the 

 use of the ultrasoft wavelengths (10 to 100 

 A). It is important to note, however, that as 

 the wavelength is increased in order to gain 

 contrast, the diffraction blurring of the image 

 also increases. The resolution limit is reached 

 when this diffraction error becomes com- 

 parable wdth the object dimensions which 

 are required for minmiimi absorption con- 

 trast. 



The characteristics of the diffraction error 

 for an image formed by monochromatic 

 radiation from a point source is illustrated 

 in Fig. 3. The effect of having a finite source 

 size and perhaps polychromatic radiation is 

 simply the superposition and addition of 

 many such intensity patterns so as to blur 

 the edge of the image. The minimum error 

 may be measured by the distance, /, from 



677 



