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Improved spot array generation using diffuser pixels to represent complex-valued modulations

Controllable surface roughness can be used to program the complex transmittance of individual pixels for the purpose of designing Fourier transform holograms. We are developing a photolithographic process for the fabrication of these custom diffuser pixels. Continuous variation of the recording parameters requires extreme accuracy. Therefore, we initially consider the possibility of designing diffractive optics with a small number of effective complex values: e.g. 0.5 magnitude at -120, 0, and 120 degrees. A recently developed ternary pseudorandom encoding algorithm then can be used to encode any desired fully complex function. Simulated designs of spot array generators are used to show that fidelity improves by increasing the number of roughness cells per pixel. Further improvements result from using more complex values, as is shown for designs with an additional zero-valued transmittance (represented by a completely randomly rough pixel). These results indicate that it is practical to fabricate high-fidelity custom diffractive optic functions with only a few recording states. The major advantage of this technique is that any desired complex-valued modulation pattern can be directly encoded and fabricated on a pixel-by-pixel basis, thereby accelerating the speed of both the design and the fabrication process.