282 THE DIFFRACTION THEORY OF MICROSCOPY 



phenomena can take place when both branches of the first spectral order 

 pass through the conjugate area. In general, the passage of the com- 

 plete first order through the conjugate area is to be avoided. 



A comparison of Sections 10.1 and 10.3 with Section 10.2 shows that 

 5 values near ±X/4 are useful for enhancing contrast in the image of 

 pure phase gratings, but that 8 values near or X/ 2 are useful for enhanc- 

 ing contrast in the image of pure absorption gratings. An actual 

 grating may present dift'erences both in absorption and in phase trans- 

 mission. Hence several diffraction plates having different h and 8 values 

 are required for obtaining optimum contrast in the image of different 

 periodic structures. The same conclusion applies to non-periodic 

 object structures but is more difficult to demonstrate theoretically. 



11. THE IMAGE FUNCTION F,(x, y, po, go) FOR A UNIFORM OBJECT 

 PARTICLE IN A LARGE FIELD OF VIEW 



The field of view of a microscope often extends over a very large field of 

 view as measured in wavelengths and often contains an assembly of 

 particles each of which may be regarded as substantially uniform in 

 amplitude and phase transmission. The amplitude and phase trans- 

 mission of the surround will be assumed to be substantially uniform. 

 In considering the assembly of particles, it is sufficient to construct a 

 theorem which applies to a single particle. This theorem is easily 

 generalized to more than one particle. 



Let the object function /(xq, yo, po, go) = .fi = 1 for points .ro, yo of 

 the surround and let f{xo, yo, Po, Qo) = /o for points .ro, ^o which fall 

 within the particle. We suppose that the surround extends over a 

 practically infinite number of wavelengths.' The location, size, and 

 shape of the particle are not restricted. However, the particle should be 

 located near the optical axis and shall be thin. Equation 8.10 now 

 assumes the form 



Fo{.i-, y, Po, Qo) = Fu(x, y, Po, qo) + Fa(x, y, po, Qo) 01.1) 

 in which Fu and Fd are defined as 



Fu{x,y,po,qo)^ f f .^-■'^'-«+''«^«> 



X U{x - Mxo, y - Myo) dxo dyo] (11.2) 



^2wKpox{i+qoyo) 



Fd{x,y,Po,qo)^f\\ 



*' *^area of the particle 



X U{x - Mxo, y - Myo) dxo dyo] (1 1 .3) 



/-/o-/i=/o-l=r'^-l. (11.4) 



Fq{x, y, po, qo) describes the amplitude and phase distribution produced 



