Generalized Optics-Free Cross-Correlation Ghost Imaging via Holographic Projection with Grayscale and Binary Amplitude-only Computer-Generated Holograms

Abstract

In certain applications or wavelength regimes, essential optical components for imaging systems are either unavailable or challenging to fabricate. To address this, we propose an optics-free classical ghost imaging (GI) scheme utilizing visible light. By employing grayscale and 0-1 binary amplitude-only computer-generated holograms (CGHs), generated via a modified Gerchberg-Saxton algorithm combined with Otsu's thresholding method, we achieve accurate replication of light intensity distributions with central symmetry in the holographic projection plane. Experimentally, we first optimized system parameters by analyzing the point spread function (PSF) and subsequently demonstrated cross-correlation GI through the precise replication of dynamic speckle patterns. Furthermore, by incorporating sparse target patterns, we significantly enhanced the imaging quality. Given the high-speed modulation capabilities of digital micromirror devices (DMDs) for 0-1 binary amplitude-only CGHs, the proposed scheme represents a significant advancement toward practical implementation, particularly in the X-ray regime where conventional optics are difficult to employ.

Figures (8)

• Figure 1: Data flow diagram of cross-correlation ghost imaging (CC-GI) utilizing perfect conjugate projection. Blue solid arrows represent numerical operations performed in the computer, while red dashed arrows denote free-space diffraction by CGHs in the experimental setup. GS, Gerchberg–Saxton algorithm; CGH, computer-generated hologram; SUM, light intensity summation; CC-GI, cross-correlation ghost imaging.
• Figure 2: (a) Schematic of the experimental setup for cross-correlation ghost imaging with holographic projection. ND, neutral density filter; BE, beam expander; SLM, amplitude-only spatial light modulator; CCD, charge-coupled device camera. The test objects in (b) and (c) are binary and grayscale, respectively.
• Figure 3: Key results of holographic projection using the target pattern shown in Fig. \ref{['01']}. (a1) Grayscale amplitude-only CGH. (a2) Binary (0–1) CGH derived from (a1) via Otsu’s algorithm. (b1) and (b2) Reconstructed patterns corresponding to the CGHs in (a1) and (a2), respectively. The insets on the right of (b1) and (b2) demonstrate accurate replication of light intensity with central symmetry. All four main subgraphs and their insets share a common color bar.
• Figure 4: Experimental results of the normalized second-order correlation function for holographic reconstructed patterns using an all-ones matrix as the effective target pattern. (a) Relationship between $g^{(2)}(0)$ and the CGH diameter $D_{\text{CGH}}$. Here, the effective target pattern consists of $N$ = 100 pixels per dimension. (b) Relationship between $g^{(2)}(0)$ and the number of pixels $N$ per dimension in the effective target pattern. Here, the CGH diameter $D_{\text{CGH}}$ is 2.8 mm. (c) and (d) Second-order bunching curves for holographic reconstructed patterns generated from grayscale and binary amplitude-only CGHs, respectively, with parameters $D_{\text{CGH}}$ = 2.8 mm and $N=100$. The measured values for the auto-correlation ($\text{AC}_{\text{GR}}$, red hollow triangles) and cross-correlation ($\text{CC}_{\text{GR}}$, purple hollow squares) cases using reconstructed patterns from grayscale CGHs are indicated. Similarly, the corresponding values obtained from binary CGH reconstructions are marked by black hollow circles ($\text{AC}_{\text{BI}}$) and green hollow diamonds ($\text{CC}_{\text{BI}}$), respectively.
• Figure 5: Sparse matrix target pattern and holographic reconstructed patterns. (a) Target pattern: an all-zeros matrix with $0.1\%$ of the pixels randomly set to 1 in the upper-left 100×100 region. (b) and (c) Holographic reconstructed patterns generated from grayscale and binary (0–1) amplitude-only CGHs, respectively. All three subplots and the five insets share a common color bar.