42 PROGRESS IN MICROSCOPY 



i.e. to increase the condenser N.A. so as to lessen blur as much as 

 possible. The curves in Fig. 1.52 correlate the results set forth in 

 paragraph 7, and show that the image contrast of a small disk in 

 coherent illumination is improved 2 to 1. \f r is the radius of the black 

 disk, then: 



08 A 



''-^r^- - (1.7) 



2/7 smM 



In order to determine the perception of a small detail, i( is this 

 formula which should be used in microscopy since, regardless of con- 

 denser N.A., and under normal observation conditions, phenomena 

 occur as if illumination were coherent. As an instance, with a 1-30 N.A. 

 objective and 2. = 06 jli, r = 002 /<. This theoretical result implies, 

 naturally, a perfect objective. 



Let us now revert to the examples of achromatic, lluoritc and 

 apochromatic objectives mentioned in § 5. The chromatic cITecl of 

 these three types of objectives on the contrast of an imaged small 

 dark disk can be assessed as follows: using the same objectives as 

 previously, it is found that the contrast of a small disk (radius 08 //) 

 is 033 for a perfect objective, 0-31 for the apochromatic objective, 

 0-27 for the fluorite objective and 01 8 for the achromatic objective 

 (focusing wave-length =0-56//). The contrast achieved with an apo- 

 chromatic objective is improved 2 to I (hus making much smaller 

 details resolvable. 



Image of bright small disk on black ground 



When the disk is small in relation to (he dillraction-disk radius, 

 the image is a conventional diffraction disk (Airy's disk), whether 

 illumination is coherent or incoherent. Image perception is then only 

 a matter of luminous flux. 



Image of thin black line on white ground in coherent or partially coherent 

 illumination 



As with a small black disk Fig. 1.51 shows the general aspect of 

 the results. As the line attains the perception limit f its width is 

 derived as follows: 



001 A 



s-~.'. (1.8) 



2ns\nu 



The black-line contrast is improved 235 to I in coherent illumi- 

 nation compared with incoherent illumination. If ns'mu ^ 130 and 



