Correlation visibility and generalized Siegert relation for random light beams
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910248511471616 |
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| author | Cui, Yi Hou, Wanting Xiong, Jun Ye, Zhiyuan |
| author_facet | Cui, Yi Hou, Wanting Xiong, Jun Ye, Zhiyuan |
| contents | Phase difference is central to classical coherence theory. With the advancement of various light-field modulation techniques, artificially generated pseudo-thermal light sources or random light beams can exhibit exotic wavefront correlation properties. However, such spatial wavefront correlations cannot be fully characterized using the phase difference alone. For instance, for a pair of conjugate pseudo-thermal beams, the spatial wavefronts exhibit a significant anti-correlation, meaning that the sum of their wavefronts tends to be constant. In this work, we propose the concept of degree of wavefront correlation $p^{(1)}$, ranging symmetrically from $-1$ to $+1$, for numerically calculating the wavefront correlation properties among various pseudo-thermal light sources, and the sign (positive or negative) can be used to determine the tendency-whether it leans toward wavefront-difference or wavefront-sum correlation. Numerical results demonstrate that the classical Siegert relation does not apply to pseudo-thermal light sources that exhibit wavefront-sum correlation properties. To address this, we propose a generalization valid for all Gaussian pseudo-thermal light. Experimentally, we introduce the measurable quantities of correlation visibility $\mathcal{V}_g$ and correlation background $μ_g$, which form a two-dimensional classification framework $\{μ_g,\mathcal{V}_g\}$ that enables the experimental characterization of diverse Gaussian pseudo-thermal light using a common-path interferometer and intensity correlation measurement. Furthermore, the correlation visibility $\mathcal{V}_g$ can serve as an observable criterion for a zero-mean, non-circularly symmetric, and jointly Gaussian distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23788 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Correlation visibility and generalized Siegert relation for random light beams Cui, Yi Hou, Wanting Xiong, Jun Ye, Zhiyuan Optics Phase difference is central to classical coherence theory. With the advancement of various light-field modulation techniques, artificially generated pseudo-thermal light sources or random light beams can exhibit exotic wavefront correlation properties. However, such spatial wavefront correlations cannot be fully characterized using the phase difference alone. For instance, for a pair of conjugate pseudo-thermal beams, the spatial wavefronts exhibit a significant anti-correlation, meaning that the sum of their wavefronts tends to be constant. In this work, we propose the concept of degree of wavefront correlation $p^{(1)}$, ranging symmetrically from $-1$ to $+1$, for numerically calculating the wavefront correlation properties among various pseudo-thermal light sources, and the sign (positive or negative) can be used to determine the tendency-whether it leans toward wavefront-difference or wavefront-sum correlation. Numerical results demonstrate that the classical Siegert relation does not apply to pseudo-thermal light sources that exhibit wavefront-sum correlation properties. To address this, we propose a generalization valid for all Gaussian pseudo-thermal light. Experimentally, we introduce the measurable quantities of correlation visibility $\mathcal{V}_g$ and correlation background $μ_g$, which form a two-dimensional classification framework $\{μ_g,\mathcal{V}_g\}$ that enables the experimental characterization of diverse Gaussian pseudo-thermal light using a common-path interferometer and intensity correlation measurement. Furthermore, the correlation visibility $\mathcal{V}_g$ can serve as an observable criterion for a zero-mean, non-circularly symmetric, and jointly Gaussian distribution. |
| title | Correlation visibility and generalized Siegert relation for random light beams |
| topic | Optics |
| url | https://arxiv.org/abs/2605.23788 |