**4.2.2 Experimental results**

250 Advanced Holography – Metrology and Imaging

degrees are desired to maximize the efficiency of holograms generated with LCDs. However, as shown in Fig. 10, the electrical sequences applied in LCoS display produce time-fluctuations of the phase, which degrade the efficiency of the generated holograms.

In this situation, to maximize the efficiency of digital holograms generated with LCoS displays, a trade-off between phase modulation depth (as large as possible) and amplitude

Next, the suitability of the different electrical sequences to maximize the efficiency of the implemented holograms is experimentally analyzed. Besides, different mapping schemes for

Next, two possible mapping schemes, for the ideal phase-only distribution implementation of holograms, are reviewed. These schemes are represented in Fig. 12, where the truly

Fig. 12. Mapping scheme implementation: In red, the linear mismatching encoding (model

1) and in blue, the saturation mismatching encoding (model 2).

**4.2.1 Linear phase mismatching and saturated mismatching encoding schemes**  To accurately implement digital holograms with LCDs, it is very important to experimentally generate a real phase distribution as close as possible to the designed one. However, as a consequence of diverse non-linearities related to the experimental implementation, the ideal phase distribution is never achieved. To reduce different LCDs degradation sources, some authors have proposed diverse strategies (Davis et al., 1998; Márquez et al., 2001). For instance, if the available dynamic range is less than 360 degrees, the minimum Euclidean distance projection principle (Juday, 2001; Moreno et al., 1995) can be applied. In this way, the modulation diffraction efficiency may be greatly enhanced by selecting an appropriate mapping scheme for the implementation of the phase function onto

Thus, small amplitude of the fluctuations is desired as well.

phase-only distribution implementation are also reviewed.

the restricted phase-only domain (Moreno et al., 1995).

of the time-fluctuations of the phase (as small as possible) has to be found.

In this subsection, we compare the efficiency of a basic continuous digital hologram, the blazed grating (Fujita et al., 1982), generated with our PALCoS display when uploading the different electrical sequences (i.e. sequences #1, #2 and #3). For all the sequences, the implementation is conducted by using the linear phase mismatching scheme. In this way, we have limited the phase range between 0 and 360 degrees and we have applied a look-up-table to produce a linear increment for the average phase values. Besides, the phase modulation provided by sequence #3 is lower than 360 degrees (see Fig. 11), and so, the saturated mismatching encoding is applied for this sequence as well.

In all the cases, the blazed grating is written to the modulator and the corresponding intensity of the zero and of the first diffracted orders is measured as a function of the time by using the diffraction based set-up given in Fig. 5 and by illuminating the PALCoS display with a He-Ne laser (633 nm). The period of the grating is fixed to 16 pixels, being the sufficient number of pixels to neglect the effect of the quantification of the phase levels.

The measurements obtained for the intensity diffracted to the zero (in blue) and to the first (in red) orders are plotted in Fig. 13. In Fig. 13(a) and Fig. 13(b), we have plotted the results obtained when using the sequence #1 and #2 respectively. Next, Fig. 13(c) and Fig. 13(d) show the results obtained when using the sequence #3, the former when applying the linear mismatching and the latter when applying the saturation mismatching encoding.

The largest intensity fluctuations are measured when addressing the sequence #1 (Fig. 13(a)) and the best diffraction efficiency is obtained for the sequence #3 with the saturated encoding (Fig. 13(d)). In this way, the sequence #3, even providing a phase modulation lower than 360 degrees (see Fig.11), is the most stable and efficient addressing sequence.

The results here provided evidences that to maximize the efficiency of digital holograms generated with LCoS displays, it is important to find a trade-off between the phase modulation depth and the amplitude of the time-fluctuations phenomena in LCoS displays. In this framework, a mathematical model suitable to evaluate the LCoS display response in presence of time-fluctuations on the phase becomes helpful (Lizana et al., 2010).

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Fig. 13. Normalized intensity for the zero and first orders obtained when addressing a blazed grating and the addressing sequence: (a) #1, (b) #2, (c) #3 with linear mismatch, and (d) #3 with saturated mismatch.
