30 AN ELEMENTARY THEORY OF PHASE MICROSCOPY 



Schlieren method, the image is not advantageous for the usual purposes 

 of microscopy on account of the ensuing loss of definition in the image. 

 Deterioration in the definition results from the fact that the image is 

 formed by the deviated wave alone when the undeviated wave has been 

 blocked at the conjugate area. At least some of the undeviated wave 

 should be transmitted in order to obtain a reasonably good image. 



As a compromise between the degree of bright contrast and definition, 

 a fairly reliable rule of thumb is to add no more absorbing material to 

 the conjugate area than is required to reduce the amplitude of the 

 undeviated wave to the amplitude of the deviated wave. Optimum 

 useful contrast in the image is therefore obtained when the conjugate 

 and complementary areas of the diffraction plate are coated with absorb- 

 ing materials to equalize the amplitudes of the undeviated and deviated 

 waves and with refracting materials to cause the undeviated and 

 deviated waves to interfere constructively or destructively according as 

 the particle appears in bright or dark contrast. We have seen that, 

 when the particle differs from its surround only in optical path and when 

 the optical path of the particle exceeds that of the surround by a small 

 amount, the particle appears bright or dark according as the optical 

 path of the conjugate or complementary area is increased by 3^ wave- 

 length. Such particles are common in biological research. 



Particles whose optical path is slightly smaller than that of the sur- 

 round are encountered less frequently. With such particles the S wave 

 of Fig. II. 4 lags behind the particle P wave by a small amount A. If 

 the D wave is constructed so that D -{- S = P, the required D wave 

 leads the S wave by almost 3^ wavelength. Since the undeviated wave 

 is now retarded by J^ wavelength with respect to the deviated wave, 

 the two waves can be made to interfere constructively for obtaining a 

 bright particle by increasing the optical path of the complementary area 

 of the diffraction plate by 3^ wavelength with respect to the optical 

 path of the conjugate area, or the two waves can be made to interfere 

 destructively for obtaining a dark particle by increasing the optical 

 path of the conjugate area by 3<C wavelength with respect to the comple- 

 mentary area. Contrast in the image can be expected again to be 

 optimum when enough absorbing material is added to the conjugate 

 area to equalize the amplitudes of the undeviated and deviated waves. 

 Also these conclusions drawn from the simplified theory for particles of 

 lower refractive index than their surround are in qualitative agreement 

 with experiment. 



The above considerations relative to the phase microscopy of particles 

 that differ from their surround only by a small amount in optical path 



