Holographic image sensor using speckle-correlation scattering matrix

Abstract

The holography measures the both amplitude and wavefront of incident light, while photography cannot obtain the wavefront information, which gives volumetric and depth perception. However, in spite of the significant progress in electronic devices, direct holography has not been achieved in optical regime yet, because of the insufficient bandwidth. This issue is a so-called phase problem, which has been one of the classic issues in numerous disciplines.

Though reference-field-assisted interferometric methods proposed by D. Gabor have been popularly used in wide disciplines, introducing a reference field raises several fundamental and practical issues. To remedy the issues, several reference-free holographic methods have been proposed

however, most of them have to sacrifice the generality of the incident field by introducing assumptions, and/or require multiple measurements.

Here, we propose an optical diffuser as a holographic lens exploiting the speckle-correlation scattering matrix. Utilizing the spatially random property of diffused light, I find it is possible to reconstruct complete complex information of incident light field from the single snapshot of the diffused speckle pattern. The physical principles of the proposed method are derived analytically based on the Isserlis’ (or Wick’s) theorem, which is one of the mathematical features of Gaussian random variables. The proposed idea is experimentally demonstrated by simply placing a commercial diffuser in front of camera successfully.

Furthermore, by the quantum interpretation of proposed method, I show that the speckle-correlation scattering matrix represents the full quantum state of incident photons, which is represented by the density matrix. Using the fact, the density matrices of photons are directly measured in the position-polarization basis for both pure and mixed states of photons. We expect that the present method proposes a new avenue in various quantum-related fields such as quantum information theory, quantum computing, and quantum cryptography by employing the randomness upon the quantum state measuring part.