Differential algebraic method for arbitrary-order aberration analysis of combined electron beam focusing-deflection systems

Aberration analysis of electron mirrors by a differential algebraic method

“…The DA method computes aberrations, theoretically to arbitrary order, in a single ray trace, using a non-standard analysis technique on an extension of the real space R, which is called n D v . As already noted [8,9], n D v is the collection of DA-quantities, of order n, with v expansion variables. Remarkably, it has many properties similar to R, such as arithmetic operations and their laws, ''zero'' and ''unit'', ordering, ''positive'' and ''negative'', etc.…”

Simulation software for designing electron and ion beam equipment

“…Paraxial rays and aberrations are then computed in terms of x(t), y(t), h(t), and their time derivatives _ xðtÞ, _ yðtÞ, _ hðtÞ. For computing the aberrations, we have used the differential algebra (''DA'') method [15,16]. The coordinates x(t), y(t), h(t) and velocity components _ xðtÞ, _ yðtÞ, _ hðtÞ are represented by DA Quantities, called X(t), Y(t), H(t) and _ X ðtÞ, _ Y ðtÞ, _ H ðtÞ.…”

Dynamic Correction of Higher-Order Deflection Aberrations in the Environmental SEM

“…The coefficients are defined by the optical system and can be calculated by various methods, including aberration integrals [2,3], the differential algebra method [9], or regression analysis [11], which is our method of choice.…”