## 3 Experimental Procedure  
Figure 2 shows the experimental setup for volume retardagraphy. A diode laser with a wavelength of 406 nm was uses for recording and reconstruction. A liquid crystal on silicon spatial light modulator (SLM; Hamamatsu X10408-5) was used to give data pages to recording beam. The polarization state of the laser beam after QWP1 is adjusted to linear with an azimuthal angle by rotating a half-wave plate (HWP1) and QWP1. By using QWP1, \(p\)- and \(s\)-polarization components were converted into right- and left-circular polarization components, respectively. In this setup, when the homogeneous image was inputted to the SLM and the pixel value was changed, the azimuthal angle of the linear polarization was changed corresponding to the pixel value because the phase difference between right- and left-circular polarization components were changed. The size of patterns modulated by the SLM  
was reduced by two lenses and the beam was focused by using an objective lens. A polarization-sensitive recording medium made of 9,10-phentanthrenenequinone doped polymethylmethacrylate (PQ-PMMA) was put between two objective lenses. The thickness of the medium was 1 mm. Then, the position of the back of the medium was set to the position of the Fourier plane of the recording pattern. The recording beam was illuminated onto the medium. The power of the recording beam at the recording plane and the irradiation time were set to 8 mW and 33 ms, respectively. In recording, a phase data page as shown in Figure 3 was displayed on the SLM. In the SLM, the phase of _p_-polarization component was modulated corresponding to the phase data page. The phase data page consisted of 15 \(\times\) 14 symbols. A symbol consisted of 2 \(\times\) 2 data pixels. The data pixel consisted of 10 \(\times\) 10 pixels of SLM. The pixel size of SLM is 20 \(\upmu\)m \(\times\) 20 \(\upmu\)m. The phase value was four-valued and the valued of 0, 0.5\(\pi\), 1.0\(\pi\), 1.5\(\pi\) rad was used. In a symbol, the phase value was set as the four values were different each other. Then, a symbol can express 24 cases, that is, the information amount of symbol is more than 4 bits. Therefore, a recording digital data was divided by every 4 bits and converted into phase data pages. In this experiment, 12 phase data pages were recorded in multiple by laterally shifting the position of the medium by using a linear stage (SIGMA KOKI SGSP20-20(X)). The shift amount was set to 100 \(\upmu\)m.  
In reconstruction, a homogeneous pattern was displayed on SLM and a polarizer was put between the SLM and the QWP1. The transmission axis of the polarizer was set as _s_-polarization component is transmitted. Then, the _s_-polarized beam was converted into left circular polarized beam by using QWP1. The recorded phase data pages were reconstructed by illuminating the left circular polarized beam. Then, a reconstructed signal beam with right-circular polarization was generated from the recorded medium. The reconstructed signal beam was imaged on a CCD plane by using an objective lens and telecentric optical system. The right- and left-circular polarization components were converted into 45\({}^{\circ}\) and -45\({}^{\circ}\) linear polarization components by using QWP2. The reconstructed signal beam with 45\({}^{\circ}\) linear polarization and the transmitted illumination beam with -45\({}^{\circ}\) linear polarization were interfered through an analyzer. Therefore, an interference pattern between reconstructed signal beam and transmitted illumination beam was captured using the CCD camera. Then, the phase between the  
Figure 2: Experimental setup for volume retardagraphy. L, OL, M, HWP, QWP, P, A, SLM, VR are lens, objective lens, mirror, half-wave plate, quarter-wave plate, polarizer, analyzer, spatial light modulator, variable retarder, respectively. Focal lengths (mm) are denoted around lenses. The polarizer is used in only reconstruction.