POINT PROJECTION X-RAY MICROSCOPY 



ELECTRON 



BEAM 



\ 



FRINGES 



i>M(J^X^ 



Fig. 3. Image formation by projecting x-ray microscopj'. Unsharpness in the image plane = Ms. 

 First Fresnel fringe half -width in the image plane = M(bX)i. (From W. C. Nixon, Proc. Roy. Soc. A232: 

 475, 1955.) 



found in the double condenser lens systems 

 of modern electron microscopes where a long 

 working distance is needed from the lens to 

 the specimen stage. In this case the second 

 lens is weak and aberrations occur but the 

 electron intensity (unlike the x-ray intensity) 

 is sufficient for high magnification on the final 

 screen. 



The electron beam when striking the tar- 

 get will be scattered and diffused within the 

 metal foil to give a source of x-rays approxi- 

 mately equal to s where s = 2p and p is the 

 penetration distance of the electrons at the 

 kilovoltage applied to the electron gun. A 

 specimen represented by a straight edge a 

 distance b away will cast an enlarged x-ray 

 image onto the screen or photographic plate 

 at distance a with the magnification M = 

 a/h. The blurring due to the source size is 

 also enlarged by M and so the "resolution" 

 in these terms in the object is similar to the 

 x-ray source size. 



This simple projective magnification 

 means that a thick specimen is magnified by 

 different amounts from front to back but the 

 total specimen image is all in focus. This is 

 easily demonstrated by using a point source 

 of light, say a flashlight bulb and two bat- 

 teries, and a coarse mesh grid. In a darkened 

 room the projected image of the grid will be 



seen to vary in magnification as the grid is 

 tilted but the image will remain sharp within 

 the limits imposed by the size of the point 

 source of light. There is no overlapping of 

 out-of-focus layers of the specimen and 

 stereographic techniques for qualitative 

 viewing and quantitative measurement can 

 be used even at the highest magnification 

 hoped for in the future. 



These x-rays have a wavelength of 1 to 10 

 A, very much shorter than the 4000 A of blue 

 light in an optical microscope. This means 

 that the diffraction limit on resolution is 

 much less serious in x-ray microscopy at the 

 present time but as the resolution improves 

 this effect will join the geometrical limits dis- 

 cussed above. 



The magnitude of the Fresnel diffraction 

 fringes is shown in Fig. 3 and the width of 

 the first fringe at the plate, i.e., in the image, 

 is D = AI(hXy'^ or in terms of the specimen, 

 d = (bxy^. In this case b is the distance 

 shown in the figure and X is the x-ray wave- 

 length. The recognition of such fringes as a 

 resolution limit is determined by the total 

 magnification of the x-ray micrograph. This 

 fringe width, d, in microns is plotted against 

 the plate distance, a, in cm in Fig. 4. Vari- 

 ous constants must be chosen for this equa- 

 tion, such as the optical magnification of the 



649 



