42 



AN ELEMENTARY THEORY OF PHASE MICROSCOPY 



6. REPRESENTATION OF THE UNDEVIATED AND DEVIATED WAVES 



It will be noted from Fig. II. 5 that the light radiated from a point C 

 in the condenser diaphragm passes through the object specimen ob- 

 liquely. With extended sources of light most of the light is necessarily- 

 incident obliquely upon the object plane. This obliquity is usually 

 ignored in the elementary discussions of phase microscopy, but even a 

 simplified explanation should take into account the large phase varia- 



Normal N 



Incident wave front W 



Fig. 11.12. The incidence of an arbitrarily inclined wave front W upon the ob- 

 ject plane XqYo. The polar angle do and the azimuthal angle ao of the normal N 



to the wave front are arbitrary. 



tions introduced bj'^ the inclination of the wave fronts which illuminate 

 the object specimen. The incidence of an inclined wave front upon the 

 object plane XqYq is illustrated in Fig. 11.12. It is sufficient to select 

 a wave front that intersects the object plane along the Xq axis and to 

 consider the simpler orientation of Fig. 11.13. 



The amplitude of the incident wave front will be taken as unity and 

 its phase retardation as zero, so that the number unity represents the 

 amplitude and phase along the incident wave front. Because the wave 

 front is inclined at an angle ^o with respect to Fq, the inclined wave front 

 induces a variable phase distribution along the Yq direction in the object 

 plane. The wave front that intersects a point yo will be a wave front 

 which is parallel to W but which belongs to a slightly earlier portion 

 of the incident wave train. The phase of the wave disturbance at 

 yo = yo is therefore advanced with respect to the wave disturbance 

 present at yo = 0. Since d = yo sin do, the optical path difference 

 d is noyo sin Oq/X wavelengths or 2Tnioyo sin Qq/X radians. Let all 



