J. W. MENTER 



Fig. 10. Sodium faujasitc crystal viewed along [110] showing two sets of ( 1 1 I) planes intersecting at 70 '. 



with the (402) reflection corresponding to ^ = 5.97 A 

 since a microphotometer trace across the image 

 shows that the intensity distribution follows fairly 

 closely a function of the form cos- 0. This would be 

 expected from interference between two beams, i.e. 

 the zero order and the first order (20T) indicating 

 that although the (402) beam passes through a 50 /( 

 aperture to the image it is making no useful contri- 

 bution to the image of the planes. 



Resolution of image. — The high resolution appar- 

 ent in the image can be explained in terms of simple 

 lens theory: neglecting effects of chromatic aberra- 

 tion and astigmatism, the phase delay imposed on a 

 ray passing through a lens at an angle -x is given by 

 e = J Cja*, where Cj is the spherical aberration con- 

 stant. The diffracted beams from the crystal lattice 

 may be regarded as plane parallel beams approxi- 



mately equal in width to the width of the specimen 

 (neglecting the finite divergence of the incident illu- 

 mination). Thus provided a and Cg are small the 

 distortion of the wave front of the narrow diffracted 

 beam in passing through the lens may be very small 

 (7). A simple calculation shows that the difference 

 in phase between the two ends of a wavefront of 

 width Ir is given by Gr-* Ar /\ where /is the focal 

 length of the lens and /■ the distance of the beam 

 from the axis in the lens plane. Inserting values for 

 the (20T) reflection from platinum phthalocyanine, 

 /• 10-3 cm, Cs 0.28 cm,/ 0.3 cm, Ar 10^ cm, 

 we find that the phase difference across the wavefront 

 Ae = 3 > 10 '^ cm, i.e. ^e< /, since A =4 lO"'" 

 cm. Thus the wavefront remains virtually undistorted 

 in passing through the lens and is able to form an 

 image of the (20T) planes by interference with the 



