Aberrations of a multipass matrix system.

A three-objective multipass matrix system has been theoretically analyzed with respect to the aberrations of the third order. An expression has been derived in the three-dimensional coordinate system relating the position of a point in the output slit to that of a point in the input slit, depending on the construction peculiarities of the system given and the parameters of the matrix of intermediate images. Conditions of image focusing upon the input slit and astigmatism compensation have been derived. Relationships to determine the field curvature and distortion have been derived.