A scanning electron microscope using a quadrupole doublet as the focusing lens is described. The optical properties of an unsymmetrical, ``pseudostigmatic'' (unequal magnifications in perpendicular planes) doublet are summarized, and rotational misalignment of the elements is discussed. Experimental studies were made to determine the dependence of the final image size on lens aberrations and construction defects. A computer was used to fit the experimental data to a generalized spot size equation. Separate experiments were made on both magnetic and electrostatic doublets, and the smallest experimental image size (which appears to be limited by astigmatism) was 150 by 450 Å using either quadrupole system. Experimental results agree with recent computer predictions for these doublets, and further calculations indicate that the use of quadrupoles and octupoles in a scanning microscope may be advantageous.