SPECIMEN COLLECTOR PHOTOMULTIPLIER 



OBJECTIVE 

 LENS 



BEAM 

 DEFLECTING 

 COILS 



FIRST 

 LENS 



GUN 



"^LIGHT 

 PIPE 



VIDEO 

 AMPLIFIER 

 (GAMMA 



tPNTROLl 



MAGNIFICATION 

 ICONTROLS 



z 



tm 



-JTSTI 



SCANNING 

 GENERATOR 



SCANNING 



VISUAL 



DISPLAY 



TUBE 



RECORDING 

 TUBE 



Fig. 1. Schematic diagram of an electromagnetically focused and deflected scanning microscope. 



diffraction at the objective aperture will 

 each cause a point object to be imaged in 

 disks of confusion, the diameters of which 

 are given by the folio whig expressions. 



Spherical aberration 



Astigmatism da = Zaa 



Diffraction d/ = 1.22 X/a 



The maximum current density, ja , in the 

 Gaussian spot, i.e., in the absence of aber- 

 rations, may be determined from Langmuir's 

 formula (12) which in the form applicable 

 to the electron microscope is 



(1) 



(2) 

 (3) 



eV 

 Ja = J — a^ amp/cm2 



(5) 



where Cs is the coefficient of spherical aber- 

 ration, Za is the axial astigmatism, X is the 

 electron wavelength and a is the semi-angu- 

 lar aperture which the objective subtends at 

 the specimen. 



In order to estimate the combined effect 

 of spherical aberration and diffraction in the 

 conventional transmission microscope, the 

 disks of confusion may be assumed to con- 

 tain a Gaussian distribution of intensity and 

 their diameters may be added in quadrature 

 (U). This procedure will be applied in the 

 present case to estimate the total effective 

 diameter of the electron spot, i.e. 



or 



d2 = do- + dr + da- + rf/2 



C,2 (1.22X)2 



(4) 



where do is the Gaussian spot diameter, 



where e is the electronic charge, V is the ac- 

 celerating voltage, T and j are, respectively, 

 the temperature and emission density of the 

 gun filament and A' is Boltzmann's constant. 

 [Haine and Einstein (13) have verified that 

 the current density predicted by this equa- 

 tion is achieved by the type of gun used in 

 the electron microscope when operated at 

 moderate values of emission density (<2 

 amp/cm'-). For higher values of emission the 

 current density falls below the predicted 

 value because of space charge effects.] 



Langmuir's theory predicts that awaj^ 

 from the center of the spot the current den- 

 sity will fall off according to a Gaussian dis- 

 tribution, hence, the diameter of the spot is 

 often defined as being the width of the 

 Gaussian distribution curve at half-height 

 (13). A definition for the effective diameter 

 which appears to be more satisfactory for 

 cathode-ray tubes and for the scanning mi- 

 croscope is that diameter which includes 

 80 % of the total current (14, 15). 



243 



