DARKEST CONTRAST WHEN A = 53 



microscope to satisfy the conditions of Lummer's theorem or to an out-of- 

 focus image or to both. Since an out-of-focus image is necessarily dis- 

 torted, we see that the phase microscope is in principle capable of pro- 

 ducing images of better contrast and definition than should be expected 

 from the ordinary microscope even when the optical path difference 

 between the particle and its surround becomes large. 



11. DARKEST CONTRAST WITH PARTICLES DIFFERING FROM THEIR 

 SURROUND ONLY IN ABSORPTION 



Suppose that A = but that g ^ I. In this case Eqs. 9.2-9.4 reduce 

 to the set 



h=\l-g\; (11.1) 



sin 5 = 0; (11.2) 



1 - g 



cos 5 = ] 1 = sgn{l — g). (11-3) 



|1 - 91 



Equations 11.2 and 11.3 are equivalent to the statements 



8 = when g < \; (11.4) 



8 = IT when g > 1. (11.5) 



This means that the particle should appear darkest by choosing h in 

 accordance with Eq. 11.1 and by choosing 5 = or tt according as the 

 particle transmits less or more light than its surround. Since Gp, the 

 energy density over the geometrical image of the particle, is theoretically 

 zero when h and 5 are chosen in accordance with Eqs. 11.1, 11.4, and 

 11.5, it is theoretically possible to In-ing about a great improvement in 

 the contrast in the image of particles that differ from their surround by 

 a slight amount in absorption. As the amplitude transmission of the 

 particle approaches that of the surround, g approaches unity and the 

 required h value approaches zero so that an increasing amount of absorb- 

 ing material has to be added to the conjugate area of the diffraction 

 plate as the particle approaches the surround in amplitude transmission. 

 If the particle is viewed in a polanret microscope (Osterberg, 1947a), 

 a polanret 8 setting of 6 = or tt at optimimi darkest contrast con- 

 stitutes experimental evidence that A is negligibly small and enables 

 the observer to decide whether g <: I. 



In summary, we can expect that, when the particle differs from its 

 surround only by a slight amount in absorption, contrast in the image 

 of the particle can be improved by selecting a diffraction plate from a 

 series of diffraction plates whose conjugate and complementary areas 

 differ in optical path by either zero or 3^ wavelength and whose ampli- 

 tude transmission ratios h are small. 



