An Improved Approach For Calculating Aberration Integrals

A gcncral approach havc bccn outlincd to calculatc thc frst ordcrpropcrtics and thc third Ordcr abcrrations of a chargcd p7articlc passingthrough a l■ lagnetic rleld The featurc of this procedurc is that it may bcconsidcrcd on analytical approach and hencc it is absent from thc sorts ofcrrors usually inhcrcnt with thc numcrical proccdure 「his approach,howcvcr,is bascd as an thc ncw analメiCal mcthod for solving thc wclトknown paraxial ray cquation which is introduccd latcr Accordingly, tllcconvcntional abcrration and distortion coefacients have been fonnulatcd byuslng thヽncw ldca Thcrcancr,an ottCa市c cOmparisonヽmadc bctwccn the formulated expressions and the correspondence analytical forms' Theresults have clearly shown that they are exactiy identical. Thereby, theintroduced approaih may be used to replace any numerical approachdealing with- the passing of a charge particle throughout anyelectro=magnetic imaging fields. Moreover, the presented approach issimpler than the conventionai numerical techniques and has less storagesize and execution time.