IINTKKFEKENCE MICROSCOPY 



The quantity Ct is the dry mass per unit area 

 of the specimen. 



The total dry mass of cells or iiucloii (;aii 

 therefore be determined by integrating the 

 dry mass per unit area over the area of the 

 specimen. If the thickness, t, can be measured 

 by one of the methods described earlier, 

 then the concentration, C, can be determined 

 from equation (7). Or if the index ris can be 

 measured as described, equation (5) can be 

 used to determine concentration. 



Precautions and Precision 



The greatest potential source of random 

 and systematic errors is the observer him- 

 self. In the extinction method it is difficult 

 and treacherous to set the object at mini- 

 mimi when the background is changing lumi- 

 nance simultaneously. The tendency often 

 is to set on maximum contrast rather than 

 on extinction. The half -shade or photometer 

 eyepieces help to overcome this difficulty by 

 changing the task to one of matching. In 

 this method the observer should adjust back 

 and forth through the match position sev- 

 eral times in order to avoid errors due to 

 after-image effects. For the most exacting 

 work it is desirable to have an iris or other 

 diaphragm which can be adjusted to limit 

 the field of view to the specimen. 



In the discussion of optical path and thick- 

 ness measurements it was assumed for sim- 

 plicity that the rays all passed through the 

 specimen parallel to the optical axis of the 

 microscope. In interference microscopes of 

 the Leitz, Dyson, Linnik, Mirau, and 

 Baker types a cone of rays is incident on the 

 specimen. Oblique rays generally receive a 

 different retardation than normal rays. 



In transmission microscopes a ray inci- 

 dent at an angle 71 , on a flat plate-like speci- 

 men receives a retardation of 



8 = t(n2 cos 72 — Wi cos 7i) 



relative to the corresponding reference ray 

 (81). Here no and ni are the indices of the 

 sample and of the immersion liquid; 72 and 



7i are the respective angles of the rays meas- 

 ured from the optical axis. Averaging this 

 fiuantity over the whole cone of rays gives 

 approximately 



5„ = K«2 — «l) 



1 + 



4nin2 



where da is the measured, average path dif- 

 ference, (NA)c is the numerical aperture of 

 the condenser system used, which may be 

 different from that of the objective. 



Up to (A^^)c = 0.4 this expression is ac- 

 curate to 0.1 % or less and may be used to 

 correct for oblicjuity errors. The equation 

 suggests two ways to reduce the error. A 

 low condenser NA produces less error, but 

 it also reduces resolution and image lumi- 

 nance. Whenever the sample permits, one 

 should use the highest possible index 7ii of 

 immersion medium, thus reducing obliquity 

 error without sacrificing resolution. 



It is interesting that for objects of index 

 greater than the surround the transmission 

 microscopes give a measured optical path 

 which is slightly too large. Whereas in the 

 reflection interference microscopes it has 

 been found that the readings are slightly too 

 small (32, 33). 



For precision work it is necessary to pay 

 as much attention to the path taken by the 

 reference beam as to that of the object beam, 

 since measurements involve them both. For 

 the Dyson system methods have been given 

 (18) for assuring that the reference area 

 which is mostly outside the field of view, is 

 sufficiently free from inhomogeneous mate- 

 rial. In the shearing systems (AO-Baker, 

 Frangon, Johanssen and Afzelius) the ref- 

 erence beam passes through an area which 

 is within the field of view, and the slide 

 should be rotated if necessary to make sure 

 this area is clear. As seen in the eyepiece of 

 an AO-Baker shearing microscope the sharp 

 image is at B (Fig. 12). An out-of -focus 

 image is seen at A . This means that the ref- 

 erence beam for area A went through the 

 specimen, which is a distance d to the right 



432 



