FRANQON'S SYSTEM FOR PHASE MICROSCOPY 153 



through also crosses the point 0' as it leaves the hemisphere. There- 

 fore 0' is the image of 0. Since the point is at the center of curvature 

 of a spherical reflecting surface, the image at 0' has a magnification 

 equal to unity, is free from both chromatic and spherical aberration, 

 and is free from coma. Although the object specimen is small, it has 

 some extent and therefore a small amoimt of astigmatism is present in 

 the image of a specimen centered at 0. Frangon has shown that with 

 a microscope objective of a given numerical aperture the proper selection 

 of the radius of curvature of the hemisphere can limit the astigmatism 

 to a tolerable amount. 



From Fig. III. 12 it can also be seen that either the deviated or the 

 undeviated rays which make a very small angle with the optical axis 

 would strike the non-metallized aperture CD of the hemisphere and 

 would, except for the small fraction reflected at the glass-air surface, 

 pass directly through the hemisphere. Such rays would not travel the 

 same length of optical path as do the rays making a greater angle with 

 the optical axis and would not be brought to a focus at 0'. The opaque 

 region KL prevents any deviated or undeviated ray from passing 

 directly through the aperture CD without first being reflected by the 

 hemispherical surface. Therefore, because of the presence of the opaque 

 area KL, the deviated and undeviated rays travel equal lengths of 

 path in Frangon's hemisphere except for the difference deliberately in- 

 troduced by means of the diffraction plate. Since the field of the micro- 

 scope system has some extent about 0, the diameter of the area KL 

 should be at least ec^ual to the diameter of the aperture CD. The 

 maximum angle of inclination 13 which a deviated ray that enters the 

 microscope objective can make with the optical axis of any hemisphere 

 in this arrangement is 60°. The dotted line OT in Fig. III. 12 shows this 

 deviated ray. The largest section of a hemisphere required for this 

 device is delimited by the rays deviated 60° from the optical axis. If 

 the hemispherical section is made of glass with a refractive index of 1.52, 

 the numerical aperture of this intermediate image-forming system can 

 be made as great as 1.52 sin 60°, or approximately 1.32. This is suf- 

 ficient numerical aperture for almost all oil immersion objectives. In 

 Fig. III. 12 the microscope objective is represented as being immersed. 



Figure III. 13 shows two methods of imaging the opening in the con- 

 denser diaphragm on the conjugate area of the diffraction plate. The 

 substage condenser is not shown. A illustrates the design common in 

 phase microscopy in which the condenser diaphragm is at the first focal 

 plane of the substage condenser. Any two rays that intersect at a point 

 in the plane of the condenser diaphragm emerge from the substage con- 

 denser as parallel rays. Such parallel rays which are not deviated by 



