248 



THE DIFFRACTION THEORY OF MICROSCOPY 



notation of Fig. VII. 4 that 



p = — n sin d cos </> = —np cos 0; 



q = —n sin ?? sin <^ = — /?p sin </>; 



p = sin ?? = 



n 



(3.5) 



Fig. VII.4. Geometrical relations among the optical direction cosines p, q, the 

 polar angle t?, and the azimuthal angle <^. 



In microscopy the refractive index n is ahvays unity in the image space. 

 Henceforth we shall therefore set 



n = \. 



(3.6) 



p is the zonal numerical aperture of the objective with respect to the 

 image space. Furthermore, 



Pm = sin §m (3-7) 



is the maximum numerical aperture of the objective with respect to its 

 image space. p,„ is related to the numerical aperture, N.A., of the objec- 

 tive in accordance with the equation 



\M\ 



= N.A. 



(3.8) 



For optical systems that are symmetrical about their optical axis, it 

 follows at once that 



Tip.q) ^ Tip); 



k{p, q) = kip); 



W^iV,q) ^ WM] 



'/'(?>,. q) = '/'(p)- 



(3.9) 



