Retrieving the phase of diffraction orders generated with tailored gratings

Abstract

A technique is performed to quantitatively evaluate the intensity and phase of the diffraction orders generated by tailored phase gratings displayed onto a liquid-crystal spatial light modulator (LC-SLM). The SLM displays the grating together with a lens to obtain the Fourier transform. The setup is converted into a polarization common-path interferometer by simply rotating a polarizer. This configuration allows a phase-shifting interferometry algorithm to be applied to retrieve the phase of the diffraction orders. The quadratic phase arising in the system, which must be subtracted, is calibrated using triplicator gratings of varying periods. Various tailored designs with controlled phase shift between diffraction orders are experimentally tested to prove the advantage and simplicity of the technique.

Diffraction gratings with full amplitude, phase, and polarization control: physical realization on liquid-crystal spatial light modulators

“…We have provided an experimental arrangement that is useful to implement these gratings using a phase-only LC-SLM. The system can be very easily (simply by rotating a polarizer) transformed into a polarization common-path interferometer, useful to also verify the relative phase relations among the diffraction orders [16].…”

“…We introduce the procedure for the designing continuous phase gratings that generate diffraction orders with amplitude and phase designed at will. Next, a recent development to transform the SLM into a self-interferometer system is introduced, showing show it allows measuring the phase of each order on-site [16]. Finally, we explain how to generalize the phase diffraction grating designs to PDG designs.…”

“…We have presented different examples of such phase grating designs with different constraints in several previous works [7,11,14,16]. Here, as an illustrative example, Table 1 presents two designs recently presented in [17].…”

“…The system in Fig. 1 is transformed into a common-path polarization interferometer simply by rotating P1 [16,17]. The polarization perpendicular to the SLM LC director axis is unaffected and remains collimated and serves as the reference beam.…”

“…A constant phase can be added to the displayed CGH in order to change the interference condition, thus allowing the application of phase-shifting (PSI) algorithms to retrieve the phase at the FT plane. After proper calibration of a residual quadratic phase in the detector plane [16], the phase of the diffraction orders can be experimentally evaluated. The result is shown in the second row in Figs.…”