  We present a method that leverages projected light patterns as a mechanism
for freeform deformations of a thin liquid film via the thermocapillary effect.
We developed a closed-form solution for the inverse problem of the thin-film
evolution equation, allowing to obtain the projection pattern required in order
to achieve a desired topography. We experimentally implement the method using a
computer controlled light projector, which illuminates any desired pattern onto
the bottom of a fluidic chamber patterned with heat absorbing metal pads. The
resulting heat map induces surface tension gradients in the liquid-air
interface, giving rise to thermocapillary flow that deforms the liquid surface.
If a polymer is used for the liquid film, it can then be photocured to yield a
solid device. Based on the inverse problem solutions and using this system, we
demonstrate the fabrication of several diffractive optical elements (DOEs),
including phase masks for extended depth of field imaging, and for 3D
localization microscopy. The entire process, from projection to solidification,
is completed in less than five minutes, and yields a sub-nanometric surface
quality without any post-processing.
