Binarization

Figure 4: Inversion symmetry in binarized holograms. (a) A continuous hologram encoding a $4\times 4$ array of tweezers. (b) The binary version generates an array with missing tweezers. (c) A continuous hologram encoding a $4\times 2$ array of tweezers. (d) The binary version of hologram (c) makes a satisfactory $4\times 4$ array of tweezers.

The most straightforward phase modulators offer just two levels of phase delay, and are known as binary holograms. Beyond quantization errors and their attendant loss of efficiency, binarization also imposes inversion symmetry on the output wavefront, $E^f(\vec \rho) = E^f(-\vec \rho)$, and so limits what patterns can be generated. This might not seem a problem for inversion-symmetric patterns, but interference between two sides of the pattern can lead to unsatisfactory results, as shown in Figs. 4(a) and (b). If, however, we anticipate the reflection and calculate a phase mask encoding only half of the array, we achieve much better results, as shown in Figs. 4(c) and (d). In practice, we repeat this calculation about twenty times and choose the binary hologram with the best performance.