## 3 Characterization Method  
When analyzing the data storage system, we find various sources of limitations. The initial one is produced by the aperture of the lenses. For that reason, we have to test the resolution capability of our setup by using a standard 1951 USAF test target. So, the first step for characterizing the optical system is to obtain the resolving power of the complete optical system composed of lenses L4, L5 and L8. To do that, we relay the image from the PA-LCoS plane onto the CCD camera but we place a negative 1951 USAF resolution test chart instead of our PA-LCoS device, and we capture the reflected image with the help of the CCD camera. Reference beam is blocked and no recording material is introduced. In Figure 2, we show the retrieved image of the 1951 USAF resolution test target. From this image, we conclude that our limit is Group 4 element 6 for both horizontal and vertical orientation, which corresponds to a resolution of 28.50 lp/mm or equivalently 35.09 \(\upmu\)m per line pair. This a line width of 17.54 \(\upmu\)m, which, translated into pixels in our PA-LCoS, means that a stripe width of two pixels (8 + 8 \(\upmu\)m) cannot be resolved. Once we calculated our optical system resolution limit, we introduced the PA-LCoS instead of the USAF resolution test target. We evaluated whether there were additional limitations related with the well-known anamorphic effects presented by this kind of microdisplays [10; 11; 22]. To do that, in our optical system, we prepared some test patterns with different resolutions and with two orientations, vertical and horizontal. The images have the aspect presented in Figure 3, where we show the pattern that corresponds with a bit size of 8 \(\times\) 8 pixels in the PA-LCoS. We alternated between black and white stripes of a selected width. The position and width of the stripeswere generated in a random way to avoid periodic diffractive effects. We added fiducial marks for centering and rotation, and to detect the position of the information bits. These marks also enabled evaluating the quality of the image or  
Figure 2: Relayed image when the negative USAF pattern is used instead of PA-LCoS. distortion during the capture. The width of the lines composing the fiducial marks was always 8 pixels, which was our reference to evaluate the resolution used in the data page in the case we do not know it. We configured our setup for binary intensity modulation (BIM) [6]. To do that, we uploaded to the PA-LCoS an electrical configuration that offers a 180\({}^{\circ}\) retardance range, with a good linearity, and permitted obtaining the maximum contrast and less flicker, as we analyzed in [26]. The maximum contrast would be produced when the polarizers in the object beam are crossed with respect to each other and they form a 45\({}^{\circ}\) angle with respect to the alignment direction of the LC director in the PA-LCoS display. In Figure 4, we show the calibration measurements done for the PA-LCoS. These calibration measurements were obtained with the configuration described above, and the 11.5\({}^{\circ}\) incident angle commented in the setup description. As we used BIM, we only used two values of gray level. These values have to offer the maximum contrast. In Figure 4, we selected gray level 14 as black level (lowest intensity) and gray level 248 as white level (highest intensity). To analyze the errors introduced by the optical system, we illuminated the PA-LCoS (see Figure 1) and, through lenses L4, L5 and L8, we produced the image of the data page onto the CCD camera [25]. The image data obtained was then digitally analyzed [6]. We note that positions for lenses L4, L5 and L8 are the same as in the previous characterization step with the USAF resolution test target and there is no reco  
Figure 4: Normalized intensity introduced by the PA-LCoS. Figure 3: Vertical and Horizontal patterns used; (**a**): Vertical stripes pattern; (**b**): Horizontal stripes pattern.