Projecting non-diffracting waves with intermediate-plane holography. 
We introduce intermediate-plane holography, which substantially improves the ability of holographic trapping systems to project propagation-invariant modes of light using phase-only diffractive optical elements.  Translating the mode-forming hologram to an intermediate plane in the optical train can reduce the need to encode amplitude variations in the field, and therefore complements well-established techniques for encoding complex-valued transfer functions into phase-only holograms.  Compared to standard holographic trapping implementations, intermediate-plane holograms greatly improve diffraction efficiency and mode purity of propagation-invariant modes, and so increase their useful non-diffracting range.  We demonstrate this technique through experimental realizations of accelerating modes and long-range tractor beams.