INSTRUxMExNT CLASSIFICATION AND APPLICATIONS 



of the object which is out of focus or which 

 has suffered very heavy aberrations. 



III. The reference field contains an image 

 of the object which is displaced laterally. 



Each of the above three classes can also 

 be divided into instruments for transparent 

 or for opaque objects. As all these types of 

 instruments possess both advantages and 

 disadvantages, the selection of a type suit- 

 able for a given kind of work is a matter 

 reciuiring some care. 



In instruments of Class I the information 

 given by the interference pattern is quite 

 explicit, i.e., the relationship between in- 

 tensity and optical thickness of the object 

 does not depend on the properties of the 

 object at points other than the one being 

 considered. This may be contrasted with the 

 state of affairs m phase-contrast microscopy 

 where the intensity is related to the mean 

 optical thickness in the neighborhood of the 

 object point. 



This is not necessarily the case in instru- 

 ments of Class II, where an effect similar to 

 that seen in phase-contrast microscopy may 

 arise due to the influence of the image in the 

 reference field. The effect of this image may 

 be removed, however, by suitable design, as 

 described later. 



In instruments of Class III the informa- 

 tion may be explicit if the object is so small 

 that the images in the two fields do not over- 

 lap; otherwi.se the intensity is a fmiction of 

 the difTerence of optical thicknesses at two 

 points at a distance apart equal to the sep- 

 aration of the two images. If this distance is 

 made very small the two images will appear 

 almost as one and the intensity will then 

 very nearly be a function of the gradient of 

 optical thickness in the direction of the dis- 

 placement of the two images. 



The Formation of Contrast 



In order that the image and reference 

 fields should be coherent it is neces.sary to 

 fulfil two requirements. Firstly, both fields 

 must be illuminated by light from the same 

 cross-section of the light beam from the 



.source and which is distributed in exactly 

 the same way in the two fields. Secondly, 

 the two fields mast be aligned so that points 

 in each field which correspond from the 

 point of view of the source are superimposed 

 with an accuracy which, it can be shown (1), 

 is equal to the resolving limit of a perfect 

 objective of aperture equal to that of the 

 illuminating condenser. For good fringe con- 

 trast it is also necessary that the intensities 

 of the two fields be equal. 



Under these conditions, if there is a path 

 difference p between the two fields, which 

 are taken each to be of unit intensity, the 

 intensity given by the combined fields is 

 given by 



7 = 2(1 -1- cos 27rp/X) 



a) 



where X is the wavelength used. If a detail 

 in the topograph}^ of the specimen introduces 

 an additional small path difference dp, the 

 corresponding change, dl, in intensity is 



(4ir/\)dp sin 2irp/\. 



The contrast C is then given by 



C = 



dl 



2irdp wp 



tan — 



X X 



{2) 



It is evident from {2) that the contrast at 

 any point can be brought to the best value 

 by suitable adjustment of p, the "back- 

 ground" path difference. The contrast will 

 be greatest when p/X is an odd multiple of 

 X, but will not in practice become infinite 

 becau.se of parasitic hght in the instrument. 

 In general, however, such values of p will 

 not give the best conditions, for then the 

 intensity will depend on the square of dp, 

 giving reduced weight to details with small 

 values of dp and concealing the sign of the 

 path-difference variation. Furthermore, as 

 these values of p correspond to dark-field 

 conditions, the intensity of the image is 

 greatly reduced. It is generally better to 

 depart somewhat from the.se conditions to 

 obtain a more nearly linear variation of in- 

 tensity^ with path difference and retain a 

 reasonable image brightness. It can be seen 



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