Metasurface-based key for computational imaging encryption

Abstract

Optical metasurfaces can offer high-quality multichannel displays by modulating different degrees of freedom of light, demonstrating great potential in the next generation of optical encryption and anti-counterfeiting. Different from the direct imaging modality of metasurfaces, single-pixel imaging (SPI) as a typical computational imaging technique obtains the object image from a decryption-like computational process. Here, we propose an optical encryption scheme by introducing metasurface-images (meta-images) into the encoding and decoding processes as the keys of SPI encryption. Different high-quality meta-images generated by a dual-channel Malus metasurface play the role of keys to encode multiple target images and retrieve them following the principle of SPI. Our work eliminates the conventional digital transmission process of keys in SPI encryption, enables the reusability of a single metasurface in different encryption processes, and thereby paves the way toward a high-security optical encryption between direct and indirect imaging methods.

Fig. 1. Decryption of different images with a dual-channel Malus metasurface as the keys.

Three meta-images can be achieved by adjusting the polarization directions of the bulk-optic polarizer and the analyzer (Channel 1: α₁ = 22.5° and α₂ = 67.5°; Channel 2: α₁ = −22.5° and α₂ = 22.5°; Hybrid channel: α₁ = −15° and α₂ = 60°). Serving as meta-keys, three meta-images are used together to obtain different cipher images and further fulfill the decoding process based on the SPI principle. Photo credit: Peixia Zheng, University of Macau.

Fig. 2. Design principle and experimental results of the dual-channel meta-image display.

(A) Unit-cell structure. The designed silver nanobrick has dimensions of length L = 160 nm, width W = 80 nm, height H = 70 nm, and cell size C = 300 nm. (B) Simulated reflectivities (R_l, R_s) and transmissivities (T_l, T_s) under linearly polarized incident light polarized along the long (l) and short axes (s) of the nanobrick, respectively. (C) Calculated transmitted intensity under channels 1 and 2. The black dots indicate the four orientation candidates and their binary intensity code states. (D) Partial SEM photos of the fabricated sample. Scale bar, 500 nm. (E) Illustration of recording two different binary patterns into the same nanobrick arrays shown in (D). (F) Experimentally captured meta-images under four different cases. Channel 1: α₁ = 22.5° and α₂ = 67.5°; Channel 2: α₁ = −22.5° and α₂ = 22.5°; Hybrid channel: α₁ = −15° and α₂ = 60°; Unpolarized: without polarizer and analyzer. Scale bars of 20 μm are shown in all meta-images.

Fig. 3. Encryption process with meta-images as the key.

The blue area shows the transformation from meta-image 3 into a ternary matrix. The pink area indicates the matrix encoding flow with different matrix operations (i.e., Left-shift and Up-shift). The yellow area is the schematic of the SPI encryption and the least significant bit (LSB) steganography. Target image 1 (Baboon) is from the University of Southern California–Signal and Image Processing (USC-SIPI) Image Database. Cover image is from Peixia Zheng, University of Macau.

Fig. 4. Scheme of the decryption processes with meta-images as the key.

The red box shows the retrieval of cipher images from meta-image 1. The blue box shows the retrieval of keys with meta-image 2 containing the matrix operations and together with meta-image 3 providing the transformation matrix. Photo credit: Peixia Zheng, University of Macau.

Fig. 5. Error tolerance study of the decryption processes with correct keys.

The left box shows two recovered images with different error ratios using the compressed sensing TV regularization recovery algorithm. The right box shows recovered images from conventional second-order CF method. The first row shows the recognized images (57 pixels × 57 pixels) from meta-image 3 with different error ratios. Three-valued errors are applied to random pixel in the recognized images, where the white, green, and blue dots represent the error value 2, 1, and 0, respectively. Photo credit: Peixia Zheng, University of Macau.