Crossed aperture lenses for the correction of chromatic and aperture aberrations

The chromatic and aperture aberrations of crossed five-aperture lenses are analyzed by direct ray tracing. The apertures are rectangular and the voltages are applied in such a way that the first-order properties of the crossed lens are similar to those of a quadrupole doublet. It is shown that in astigmatic modes the chromatic and aperture aberrations of one of the linear images can be simultaneously eliminated or made negative. It is also shown that stigmatic modes exist in which the magnification is different in two perpendicular planes and in which the image blurring caused by the chromatic and aperture aberrations in the direction of smaller magnification is ten times smaller than that given by a round lens of the same focal length and the blurring in the other direction is at least two times smaller. The stigmatic crossed lens also gives a larger working distance than the equivalent round lens. The crossed lens will therefore be preferable for many probe forming systems.