## 3 Liquid Crystal on Silicon (LCoS) Calibration Procedure and Phase Modulation Responses  
We have used a parallel-aligned nematic LC device of LCoS-SLM technology from Holoeye (Pluto-BB-HR, HOLOYE Photonics AG, Berlin, Germany) with 1920 \(\times\) 1080 pixels of size \(8\times 8\)\(\upmu\)m\({}^{2}\), fill factor of 87%, and refreshing rate of 60 Hz. This device is a phase-only SLM working on a reflective mode. An achromatic half-wave plate with a nearly flat retardance over the operation range (400-800 nm) from Thorlabs (AHWP05M-600, Thorlabs GmbH, Dachau/Munich, Germany) was used to adjust the polarization plane of the incident beam from a tunable Ar ion linearly polarized laser (35 KAP431, Cvi Melles Griot, Inc., Albuquerque, New Mexico, USA) to obtain a phase-only modulation output. Normal incidence of the impinging collimated beam combined with the use of a beam splitter was chosen to assure an optimal response of the LCoS display in terms of phase modulation depth and negligible depolarization [12]. Characterization of the LCoS device was carried out to assure an optimal implementation of multiorder diffractive lenses. The procedure was done by means of the Michelson interferometer with coherent illumination shown in Figure 2. A broadband hybrid metal dielectric coating cube beamsplitter (03 BSC009, Cvi Melles Griot, Inc., Albuquerque, New Mexico, USA) (BS in Figure 2) that exhibits little polarization sensitivity for the 450-700 nm spectral range was used in the setup to assure that it did not significantly affect the linear polarization state of incident beams. A flat mirror slightly tilted with respect to the SLM plane permitted us to obtain an interferogram pattern of the two beams consisting of a set of vertical fringes. The corresponding interferogram was acquired with a charged coupled device (CCD) camera (pco.1600, PCO AG, Kelheim, Germany) with 1600 \(\times\) 1200 pixel resolution and 14 bit dynamic range (Figure 3a). The SLM screen was divided in two uniform sectors, one half with a constant grey level kept as a reference and the other half with a varying uniform grey level among the 256 grey levels available (Figure 2b). The fringe shift between the two sectors allowed us to calculate the phase variation for each grey level (Figure 3a). The procedure is described with more detail in ref. [13]. Figure 2: (**a**) Michelson interferometer setup for characterization of the LCoS display (BS stands for beam splitter and SF for spatial filter). The tunable linearly polarized Ar ion-laser and the half-wave plate are not shown. (**b**) Scheme of the Michelson interferometer with a detailed view of the spatial light modulator (SLM) input plane. Calibration curves were obtained for different configuration conditions of the SLM display in order to optimize the configuration parameters to achieve a variety of phase modulation ranges. The Holoeye modulator is electrically addressed by means of a standard digital video interface (DVI) connector and works with two bit-plane configurations (5-5 and 18-6), which allow mapping the 256 video grey levels to either 192 or 1216 index levels of the look-up table (LUT), respectively, loaded in the hardware of the device. Even though the number of addressable values for the 5-5 bit-plane profile is lower, this configuration is intended to reduce the flickering effects of the display. For this reason, the 5-5 bit-plane scheme was the chosen configuration for the calibration of the device, except for the case of the maximum 8\(\pi\) phase modulation, which was only achieved by the 18-6 bit-plane profile. Initially, the LUT (also named gamma curve) provided by the SLM manufacturer (\"default gamma\", curve with cross markers in Figure 3b) was used to control the display. Two electronic potentiometers were properly adjusted to obtain a given device response. By modifying the varying grey level among the 256 grey values, the phase modulation response was measured (\"nonlinear ph. mod.\", line with cross markers in Figure 3c).