Experimental compensation of parasitic octopole aberrations in small-bore quadrupole lenses

Using a procedure of experimental ray tracing, measurements of the aberrations of an achromatic quadrupole lens are made, from which 3rd-order coefficients such as 〈xa2b〉 = − 0.6 km and 〈yab2〉 = 5 km may be estimated. Both these coefficients would be zero in a lens with perfect quadrupole symmetry, so that they must arise from parasitic effects. Theory predicts that the first coefficient can be compensated by electric excitation of the eight lens poles, while the second coefficient arises from parasitic octopole fields inclined at an angle of 22.5° to the principal sections of the quadrupoles. Since the quadrupoles contain no pole at this azimuth, we have added an inclined electric octopole corrector upstream of the doublet. It is found that the inclined octopole can be used to set 〈yab2〉 = 0 within the accuracy of the experimental measurements.