Systems and methods for writing spatially varying holograms

A method of conically recording a hologram comprising:

• defining a plurality of grating planes for a hologram in a recording medium;
• determining a plurality of grating vectors for corresponding ones of the plurality of grating planes;
• rotating the recording medium until an average of the plurality of grating vectors is zero along one axis;
• determining exposure angles for a first writing beam to generate the hologram;
• rotating the first writing beam to align the first writing beam with the recording medium;
• defining a plurality of second vectors for a second writing beam as a sum of the plurality of grating vectors with a plurality of first vectors of the first writing beam;
• subtracting a first linear phase from the first writing beam and a second linear phase from the second writing beam;
• and
• subtracting a first quadratic phase from the first writing beam and a second quadratic phase from the second writing beam.

A method of conically recording a hologram comprising:

• defining a plurality of gratings for a hologram recorded in a volume of a recording medium;
• determining a plurality of grating vectors for corresponding ones of the plurality of gratings;
• rotating the recording medium until an average of the plurality of grating vectors is zero along one axis;
• determining exposure angles for a writing beam based on the recording medium not being rotated;
• subtracting a linear phase from the writing beam by reflecting the writing beam from a mirror that is tilted to compensate for the linear phase;
• and
• subtracting a quadratic phase from the writing beam by passing the writing beam through a toric lens.