PHENOMENA OF PHASE MICROSCOPES 23 



It follows directly from Lummer's theorem that the image of a particle 

 should show no contrast, irrespective of the optical path difference be- 

 tween the particle and the surround, when the light transmissions of the 

 particle and the surround are alike. If the light transmissions of 

 the particle and the surround are alike, the amplitude distribution over 

 the object plane will be uniform. According to Lummer's theorem, the 

 amplitude distribution over the image plane will then be uniform. 

 Since the eye or photographic plate is sensitive only to the amplitude 

 or to the energy density that is proportional to the square of the ampli- 

 tude, the image plane will appear to be uniformly illuminated even 

 though the phase distribution over the image plane is non-uniform. 

 Consequently, the particle should be invisible when its light transmission 

 does not differ from that of the surround. 



One of the weaknesses or oversimplifications of the simplified theory 

 of microscopy appears in the prediction that the particle should be 

 invisible in the microscope whenever the light transmissions of the parti- 

 cle and the surround are alike no matter what optical path differences 

 exist between the particle and the surround. It is a well-known ex- 

 perimental fact that when the optical path differences between the 

 particle and its surround are greater than 3^ wavelength the particle is 

 visible whether or not the iris in the substage condenser is stopped 

 down. Furthermore, when the optical path difference is less than }/8 

 wavelength the visibility of the particle can be increased by stopping 

 down the iris diaphragm in the substage condenser and by readjusting 

 the state of focus of the image. Depending on the spherical aberration 

 of the objective, the particle may be rendered visible when the optical 

 path difference between the particle and its surround is only 0.04 

 wavelength. With these small optical path differences the visibility 

 or contrast is poor, however, and the image becomes unduly distorted 

 by the necessity of observing an out-of-focus image surrounded by an 

 increased amount of adverse diffraction effects. The visibility of such 

 particles in the ordinary microscope is due largely to the fortunate 

 circumstance arising from the failure of real objectives to fulfill the 

 conditions postulated in Lummer's theorem. When the optical path 

 differences between the particle and the surround become small enough, 

 the degree of visibility of the particle approaches zero, the value pre- 

 dicted by Lummer's theorem if the light transmissions of the particle 

 and of the surround are equal. 



3.2. Phenomena of phase microscopes 



In phase microscopy a diffraction plate is introduced for the purpose 

 of obtaining additional controlled violations of the conditions of Lum- 



