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The design equations for constrained metal-plate lenses are derived. These lenses prove to have exceptional wide-angle scanning properties. The scanning aberrations are investigated by means of a power series expansion of the phase error. This analysis indicates that the square-law error is a function of lens depth and may be eliminated by the proper choice of lens thickness. It is also indicated that coma is associated with the inner lens contour, and that elliptical or double-correction-point lenses have minimum coma. The mechanism of refocussing is investigated and its first-order effect is given as a power series. The scanning performance of various lens, types is expressed by means of formulas giving the number of beamwidths scanned as a function of the f/D ratio. Experimental data are presented on a lens capable of sweeping a one-degree beam 100 beamwidths. Further data indicate the importance of smooth contours and compact structures in achieving low spurious radiation and large scanning angles.