## 5 Optical Experiment  
For experimental testing of MCDDC, the lensless optical encryption scheme with spatially incoherent illumination based on two LCoS spatial light modulators (SLM) was used (see Figure 7). For description of packing/unpacking procedures, see Section 3. Nd-YAG laser with a wavelength of 532 nm was used as a light source. The filtered divergent light beam is formed by a combination of a lens and a pinhole. The pinhole was  
Figure 6: Dependencies of the density of data encoding on BCH error correction level for MCDDC with different number of gray levels (color online). Figure 7: The experimental scheme of MCDDC lensless optical encryption with spatially incoherent illumination. placed in the focus of microscope lens in order to filter possible low-frequency wavefront distortions which can lead to inhomogeneity of input plane illumination. The rotating diffuser destroys spatial coherence of radiation and suppresses speckle-noise due to the formation of a new speckle pattern every time its rotation results in new grain structure been illuminated. Its rotation speed should be high enough so that during frame exposure time, many speckle patterns would be averaged, effectively suppressing speckle noise. In our setup, the diffuser rotation speed was equal to 1200 rpm, its radius--5 cm and typical grain size--10 \(\upmu\)m. The amplitude LCoS SLM HoloEye LC2012 with 1024 \(\times\) 768 pixels (SLM1; pixel size is 36 \(\times\) 36 \(\upmu\)m) was used for the display of MCDDC. The phase LCoS SLM HoloEye GAEA-2 with 4160 \(\times\) 2464 pixels (SLM2; pixel size is 3.74 \(\times\) 3.74 \(\upmu\)m) was used for the display of encoding diffraction optical elements (DOE). The beamsplitter cube reflects light from the SLM2 to the Flare 48 MP camera with a resolution of 7920 \(\times\) 6004 pixels (pixel size is 4.6 \(\times\) 4.6 \(\upmu\)m) which was used for the registration of encrypted images. Polarizers were used for the elimination of depolarization introduced by the diffuser, SLM1 and SLM2. Exposure time was set to 33 ms, and images were registered with a maximum signal close to saturation, but not reaching it. The necessary level of illumination was acquired by regulating the laser power. The DOE's focal lens and distances determine system's optical magnification according to thin-lens formula, as well as the size of encoding DOE's point spread function and, therefore, the size of an encrypted image. In addition, the optical distance between SLM2 and camera must be known in order to construct the decoding filter as described in [49]. The tolerance for this distance when constructing decoding filter, according to our experiments on similar setup in [49], is \(\pm\)0.5%. The optical distance between SLM1 and SLM2 was 34 cm, between SLM2 and the camera--38 cm, and DOE's focal length--19 cm. An image of a single SLM1 pixel occupies a section of 10.1 \(\times\) 10.1 pixels of the camera. One element of encoding DOE PSF occupies a section of 2.6 \(\times\) 3.7 pixels on the camera. MCDDCs with 128 \(\times\) 128 elements and 254 \(\times\) 254 elements with four gray levels and with the input error correction level of 21.7% were used in the experiments (see Figure 8). The size of the fuzzy outline area for containers with 128 \(\times\) 128 elements is 10% of the linear size of the container on each side, and for containers with 254 \(\times\) 254 elements--25% of the linear size of the container on each side. Encryption was carried out with two encryption keys with 128 \(\times\) 128 elements with densities that were characterized by normalized average energy (NAE) 0.0005 and 0.001 and with two gray levels. The encryption keys with different NAE values and corresponding encoding DOEs are shown in Figure 9. The size of the encoding DOEs was 4000 \(\times\) 2464 elements. Figure 8: The test MCDDC images with 128 \(\times\) 128 elements (**a**) and 254 \(\times\) 254 elements (**b**). The number of incorrect pixels in the decrypted image was used as a measure of decryption error.