24« 



THE DIFFRACTION THEORY OF MICROSCOPY 



puted, the reader should consult a recent publication by Osterberg and 

 Wilkins (1949). Unit spheres are drawn about the axial points Oq and 

 in the object and image space of the objective, respectively, as in 

 Fig. VI 1. 3. The unit sphere about the point Oq is regarded as the inci- 

 dent wave front of reference whose amplitude is taken as the constant 

 unity with unpolarized light. The unit sphere about the point is 

 regarded as the locus of the corresponding spherical wave converging 

 upon 0. This spherical wave of reference is a wave front, and its 



Fig. VII.3. The reference unit spheres. 



normals with optical direction cosines p, q are real rays only when 

 spherical aberration is absent and when the diffraction plate is either 

 uncoated or is coated uniformly. Ai(p, q) is defined as the amplitude 

 variation over the spherical wave. Ai(p, q) depends on the zonal 

 properties of the diffraction plate and on the manner in which the axial 

 rays are converged by the objective. Both Aiiy, q) and the phase 

 variation over the spherical wave can be determined by triangulating 

 rays from Oq into the neighborhood of point 0. In performing this 

 triangulation of the axial bundle of rays, w^e adopt the convention that 

 the supporting plate (if any) which bears the coating material of the 

 diffraction plate is to be considered as one of the elements of the ob- 

 jective and that the supporting plate shall be considered as uncoated. 

 The usual integral over the lateral spherical aberration (Luneberg, 1944, 

 p. 224) determines 2TrWo(p, q), the phase variation over the spherical 

 reference wave. Triangulation of the l)undle of axial rays in accordance 

 with the above convention serves also to determine T{p, q), the am- 

 plitude transmission along the axial rays. Since the spherical reference 



