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Liu YL, Dai ST, Zhu YM et al. Full-dimensional complex coherence properties tomography for multi-cipher information security. Opto-Electron Adv 8, 240278 (2025). doi: 10.29026/oea.2025.240278
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Full-dimensional complex coherence properties tomography for multi-cipher information security
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Abstract
Optical coherence is a fundamental property of light, playing a key role in understanding interference, propagation, and light-matter interactions for both classical and quantum light. Measuring the coherence properties of an optical field is crucial for a wide range of applications. However, despite many proposed measurement schemes, significant challenges still remain. In this work, we present a protocol to measure the full-dimensional coherence properties of a partially coherent beam. The method is based on tomographing the complex coherent modes of the partially coherent field within its coherence time. Once the complex coherent modes are reconstructed, all coherence properties including field correlation and its higher-order correlations (e.g., intensity correlation) can be recovered for beams that are either spatially uniformly or non-uniformly correlated. We perform a proof-of-principle experiment to measure the complex field correlation and intensity correlation of a structured partially coherent beam synthesized by random modes. Additionally, we discuss the application of full-dimensional complex coherence function tomography in coherence-based multi-cipher information security. The robustness of our system in complex environments is also evaluated. -
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References
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Supplementary information for Full-dimensional complex coherence properties tomography for multi-cipher information security 
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Liu YL, Dai ST, Zhu YM et al. Full-dimensional complex coherence properties tomography for multi-cipher information security. Opto-Electron Adv 8, 240278 (2025). doi: 10.29026/oea.2025.240278
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Figure 1.
(a) Random-mode representation for the CGSM beam, in which its CSD function can be decomposed as Eq. (2). The average spectral density I(r) (b), the real (c) and imaginary (d) parts of the DOC µ(rd), as well as the normalized intensity correlation g2(rd), where the reference point set as rf = 0, (e) obtained from the ensemble average over the random modes. (f) The complex field of a random mode. (g) Real and imaginary parts of the DOC extracted from the spatial correlation within the single random mode shown in (f). Cross-lines of the real part (h) and imaginary part (i) of the DOC µ(x1, 0), as well as the intensity correlation g2(x1,0) (j). The solid curves, triangle dots, and circular dots represent the results obtained from theoretical model, by the ensemble average over random modes set, and the spatial correlation within a single mode. (k–o) Schematic diagram for the retrieval of complex field of a random mode using the off-axis holography method. The beam parameters used in the calculation are ω0 = 1.0 mm, δ0 = 0.12 mm, and m = 1. The number of the random modes N used in the simulation is N = 2000.
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Figure 2.
(a) Experimental setup for generating a structured partially coherent beam and measuring its mode set. (b) A series of computational generated holograms (CGHs) loaded on the SLM. (c) Instantaneous intensities of the mixed fields captured by the CCD. (d) Experimentally reconstructed complex fields of the random modes. (e) Average spectral density of the generated CGSM beam by making ensemble average over N = 2000 random modes (circular dots for cross line and density plot at the top left corner) and the corresponding theoretical result (solid curve and density plot at the top right corner). (f) The first column shows the recovered DOC and intensity correlation from the ensemble average over N = 2000 random modes. The second column shows the results obtained by the spatial correlation within a single random mode. The third column are the corresponding results for the cross lines at y1 = 0. The generated CGSM beam with m = 1. (g) The recovered DOC and intensity correlation for the CGSM beam with m = 2.
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Figure 3.
(a) The dependence of the correlation coefficient (the pentagrams for experimental results and the dashed line for simulation results) on ω0/δ0. (b–g) The modulus of the DOCs recovered from numerical simulation for different values of ω0/δ0 that correspond to those of six pentagrams. (h–m) The experimental results of the modulus of the recovered DOCs corresponding to the simulation results in (b–g). (n) The modulus of the DOC calculated from the theoretical model in Eq. (4).
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Figure 4.
(a) Principal diagram of coherence-based multiple cipher optical image encryption and decryption. (b, g and l) are the three original images, English letter "A", Chinese character "GUANG", and the picture panda, respectively. (c–f, h–k, m–p) The decryption results for the "A", Chinese character "GUANG", and the picture panda, with different decryption keys. (q–u) Experimental results of the recovered images with different numbers N of the random modes. The corresponding simulation results for the decryption images are shown in the insets (within the yellow dashed circle).
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Figure 5.
The measured speckles for a random mode when the partially coherent beam source is partially blocked by the obstacle with rectangular (a), triangular (d), and circular ring (g) openings and is disturbed by a dynamic random noise (j). (b, e, h, k) The recovered images with correct keys. (c, f, i, l) The recovered images with incorrect keys. In (a–l), the encoded image is an English letter "A". (m–x) show the corresponding experimental results for the case when the encoded image is a "panda". The insets in the recovered images are the corresponding simulation results.
