GEOMETRICAL MEASUREMENTS 165 



the axial setting accuracy. It is not feasible to locate the position 

 in depth of the object A with greater accuracy than Af^A^ = 2e. 

 Granting Lord Rayleigh's tolerance (Chapter I, § 6), defective focusing 

 should not entail a variation of the optical path exceeding one quarter- 

 wave. Then, accuracy of axial setting is: 



2e > . \ ,, (5.2) 



477Sin^w/2 



2e = 1 /< for A = 0-6 /< and ns'mu = 0-65 . 



To sum up, provided the microscope be used with a 5 mm diameter 

 exit pupil, accuracy of transverse and axial settings can be educed 

 from the following formulae: 



Transverse setting Axial setting 



1-22/. ^ / 



J > 2e 



lOOwsinw 4nsm^ul2 



N.B. It should be pointed out that measurement accuracy depends on 

 many factors other than setting accuracy, such as stability, clearances, 

 expansion, stresses and so forth. It is but rarely that full use can be 

 made of the setting accuracy provided by high N.A. objectives. 



Role of the observer's eye in axial settings 



Let us consider an axial setting carried out with an instrument 

 lacking a reticle. As focusing changes, the instrument-image changes 

 in depth and the instinctive excursion of the eye keeps it in focus as 

 long as it remains within the limits of sharp vision. 



Fig. 5.2. Accuracy of an axial setting (2f). 



Setting on the image may therefore be correlated to any position 

 of the image within the eye-accommodation amplitude. The result is 

 some uncertainty as to the object's position, called "depth of ac- 

 commodation". 



