in the plane to a more general curve in three dimensions for volumetric applications an ideal line tweezer focuses to a line segment with a specified intensity distribution and has the steepest possible intensity gradients in all directions perpendicular to the line this can be achieved in principle by inverting the mathematical relationship between light in the lens 39 focal volume and the electric field in the plane of the doe 300 the result generally involves modulating both the amplitude and phase of the incoming light which is not possible given the doe 300 that modulates only phase or only amplitude the key point in the present invention is that a line tweezer is inherently one dimensional and thus both its amplitude and phase information can be encoded in a two dimensional phase only doe 300 by using one dimension to encode phase information and the transverse dimension to encode amplitude information as an example we form a uniformly bright line tweezer of length l aligned with the u0177 axis in the lens 39 focal plane the field in the trapping plane may be approximated as the inverse fourier transform of this field yields the associated field in the doe plane which is a purely real valued function because u03c8 u03c1 involves only amplitude modulations and has both negative and positive values it might not seem possible to encode it on a phase only doe 300 however u03c8 u03c1 does not depend on u03c1 x and this presents the opportunity on which shape phase modulation is based where.