SCANNING 



element to the next will be detectable as a 

 change AB m the brightness of the picture 

 only if the basic signal-to-noise ratio exceeds 

 B/AB by a factor of about, 5 [Rose (16)]. 

 AB/B = C is then the threshold contrast. 



It may be shown (9, 17) that during in- 

 teraction of the beam with the specimen, 

 the signal-to-noise ratio may be reduced by 

 roughly a factor of 4. Further, possibly only 

 one-third of the emitted electrons are effec- 

 tively collected, thus 



/ 



n 20 

 3 - C 



or 



n > 



1200 



(10) 



Therefore, to detect a contrast change of 5 % 

 between adjacent picture elements requires 

 a minimum of 4.8 X 10^ electrons per ele- 

 ment . 



If the specimen is scanned in a square 

 raster containing N lines, i.e., A^- elements, 

 in a total time Ts seconds, then each element 

 is covered in a time T^/N^ seconds and the 

 required spot current will be 



i = ne —- amp 



t = 1200 T3::r Camp 



(11) 



C^Ts 



(For a 300-line picture, a threshold contrast 

 of 5% and a scanning time of 5 minutes, 

 i = 2.31 X 10-" amp). Substitution of this 

 expression for i in equation 9 gives for the 

 minimum spot diameter 



dmin = 1.29C,i'^X3'4 1.52 X 10-« 



(" 



m 

 c^, 



f \3/8 



-T + lj (12) 



This basic equation includes all the fac- 

 tors which affect the resolving power of the 

 scanning microscope. In Figure 2, the spot 

 diameter is plotted for three different values 

 of A^ as a function of the recording time for 

 the following typical parameters: Cs = S 



120 180 240 300 



RECORDING TIME (SECONDS) 



Fig. 2. Electron .'jpot diameter, dmin , as a 

 function of recording time, Ta , according to 

 equation 12. 



cm, X = 10-9 cm, (F = 15 kV), c = 57o, 

 T = 2800°K, j = 3.5 amp/cm^ [effective 

 emission density at a filament life of 8-10 

 hours (13, 18)]. It will be seen that a re- 

 solving power close to 100 A is theoretically 

 obtainable if the field is reduced to 150 

 lines. 



Poor focusing will occur at the top and 

 bottom of the picture if the number of lines 

 or elements scanned in the vertical direction 

 of the picture is too great. The more oblique 

 the angle of observation the fewer the num- 

 ber of lines or elements which can be re- 

 solved. At an angle of 45° this will be about 

 300 lines. The number of elements scanned 

 in the horizontal direction may be much 

 greater, although this will entail either longer 

 recording times or lower resolving power 

 according to equation 12. 



The Beam Scanning System. The de- 

 flecting system may be electromagnetic or 

 electrostatic. The latter allows a somewhat 

 simpler physical construction and associated 

 circuitry but, at high beam-voltages, the 

 deflecting potentials may become incon- 

 veniently large, the deflection sensitivity be- 

 ing proportional to the beam-voltage, and 

 raster distortion may be introduced. These 

 disadvantages may be overcome by intro- 



245 



