218 PROGRESS IN MICROSCOPY 



is involved when the thickness of the detail varies continuously as, 

 for instance, in the case of the object depicted in Fig. 8.8. When 

 changing over from the area B to the area A, the path difference 

 variation is continuous and all that is required is to follow up the 

 deformation of a specific fringe (see Chapter VI, § 1). Assuming that 

 the object shown in cross-section (Fig. 8.8) has the shape of a small 

 extended strip perpendicular to the plane of the figure, the appearance 

 is the one shown in Fig. 8.9. There is no uncertainty as to the shift 

 of fringes and the shift d observed in Fig. 8.9 is the actual shift evincing 

 the thickness e of the object derived from the equation (8.4). 



Measuring a thickness with the multi-wave interference microscope 



Changing over to white light, in multi-wave microscopes, is not 

 feasible. Therefore, if the object being measured originates a sub- 

 stantial fringe shift, there are no means to measure the actual value 

 of the path difference in white light. Nevertheless, in some cases, tu3 

 problem is solved by observing the phenomena with two monochro- 

 matic radiations. It follows that such a difficulty is only present when 

 there is a break between the fringes within and around the object. 

 Such is the case in the object shown in Fig. 8.2. Provided it is as- 

 certained that the thickness e of the object is small in relation to A, 

 the observed shift d is the actual shift. Such being the case, the thick- 

 ness e of the object is derived by expressing the shift as a portion K' 

 of one inter-fringe space. 

 Then: 



d' = K'l = 2e (8.5) 



whence the thickness e. 



There is, likewise, no problem in the present instance provided 

 the thickness of the detail varies continuously in relation to the field 

 surrounding it: merely following up the deformation of a specific 

 fringe will serve the purpose. The appearance of the field is very 

 similar to the one shown in Fig. 8.9 but the fringes are very narrow. 



Measurement accuracy 



No mention has yet been made about a prominent factor: the 

 N.A. of the incident light-beam. It is granted that the path difference, 

 following reflection or after passing through the transparent object is 

 clearly determined as 2e and {n—n')e, respectively. These values 

 square with path differences when the incident light-beam consists 



