80 INSTRUMENTATION 



the surrounding material. If the optical path through the conjugate 

 area is 3^ wavelength less than the optical path through the comple- 

 mentary area, then the contrast of the image of the above particle will 

 be reversed. 



Let us discuss the phenomena of phase contrast in terms of the 

 properties g and A of the specimen and in terms of the essential physical 

 constants h and 5 of the difTraction plate. The symbols g, A, /i, and B 

 are defined in Chapter II following Eq. 8.8. The general-purpose 

 diffraction plates suggested in the preceding paragraph have the design 

 specifications 0.25 ^ K^ ^ 0.40 and 5 = ±X/4 = ±90°. Such diffrac- 

 tion plates do produce satisfactory contrast in the image of object 

 specimens for which g = I and for which < |a| < X/8 = 45°. The 

 following paragraphs will show that this empirical conclusion is at least 

 consistent with the simple theory presented in Chapter II. 



Figure II.14S refers to a particle for which g = I and for which 

 A = +X/18 and describes the changes that occur in the light intensity 

 in the image of the particle and in the image of its surround as h and 8 

 are varied. No serious deterioration in either dark or bright contrast 

 is predicted as 6 varies between —70° and —110° or between 70° and 

 110°. The variation in the light intensity in the image of the particle 

 is not symmetrical about the points 5 = ±90° since optimum contrast 

 does not occur at |5| = 90°. The h value for the general-purpose 

 diffraction plate lies between li = 0.5 and h = 0.()32. Only the greatest 

 value for /; in Fig. II.14B belongs to this range. Nevertheless, the 

 tolerance on the value of 8 suggested by these curves is at least in 

 qualitative agreement with observations. Figure II.14B has another 

 point of interest. The figure indicates that, if the diffraction plate is 

 fabricated of materials that have indices of refraction which remain 

 constant throughout the visible region and if 5 = ±90° at X = 5401 A, 

 then satisfactory contrast in the image may still be expected if white 

 light rather than a narrow band of wavelengths in the neighborhood 

 X = 5461 A is used to illuminate the object specimen. A variation of 

 ±20° in 8 from 5 = 90° at X = 5500 A is equivalent to the phase varia- 

 tion associated with wavelengths in the range 4500 A to 7000 A. 



Equations II. 10.2 and II. 10.5 describe the conditions for darkest 

 possible contrast when ^ = 1. They state that as the optical path 

 difference between the particle and its surround approaches zero the 

 amplitude transmission of the conjugate area should also approach zero. 

 Further, as the optical path difference between the particle and its 

 surround increases, the necessary optical path difference between the 

 conjugate and complementary areas becomes less than 90° in absolute 

 value. Theorem 5 in Section 13 of Chapter II requires that the step in 



