Non-Line-of-Sight (NLoS) imaging aims to recover images of objects hidden from direct view by opaque barriers or scattering media. Existing techniques, broadly categorized as time-of-flight (ToF) based and memory effect (ME) based, have limitations. ToF methods, while offering real-time reconstruction over a large volume, suffer from low resolution (cm-scale). ME-based approaches, although achieving high resolution (<100 µm), are constrained by a highly restricted field of view (<2°). This paper introduces Synthetic Wavelength Holography (SWH) as an advancement in NLoS imaging, addressing these limitations by leveraging spectral correlations in scattered light. SWH utilizes coherent light at two closely spaced wavelengths (λ₁ and λ₂) to preserve phase information at scales exceeding a synthetic wavelength (SWL) Λ, significantly larger than λ₁ and λ₂. The synthetic phase encodes a holographic representation of the hidden object. This principle extends beyond optical applications and is potentially adaptable to other wave phenomena, expanding its applicability.

Numerous attempts have been made to develop NLoS imaging techniques. These methods fall broadly into two categories: those addressing continuous scattering (e.g., fog, tissue) and those addressing discrete scattering (e.g., walls). Time-of-flight (ToF) based methods utilize temporally modulated sources and fast detectors to reconstruct a surface representation of the hidden scene. While recent advances have demonstrated centimeter-scale resolution and near real-time capabilities, these methods often require raster-scanning large areas, limiting their efficiency. Alternatively, memory effect (ME) based techniques exploit spatial correlations in scattered light to attain high resolution. However, their field of view is severely limited by the angular decorrelation of scattered light. The existing disparity in resolution and field of view between ToF and ME methods highlights the need for a technique that combines their respective advantages.

Synthetic Wavelength Holography (SWH) exploits spectral correlations in scattered light at two closely spaced wavelengths (λ₁ and λ₂) to create a hologram of the hidden object at a synthetic wavelength (SWL) Λ = λ₁λ₂/|λ₁ - λ₂|. The method uses a continuous wave (CW) tunable laser source and a lock-in focal plane array (FPA) camera for measurement. The lock-in camera detects the complex-valued synthetic field E(Λ) = E(λ₁)E*(λ₂), where E(λᵢ) is the speckle field at wavelength λᵢ. The synthetic phase ∠E(Λ) encodes information about the hidden object, and backpropagation of E(Λ) at the SWL Λ reconstructs the object's image. Two interferometer designs are employed: a dual-wavelength heterodyne interferometer and a superheterodyne interferometer. The dual-wavelength design minimizes light loss but is sensitive to object motion and environmental fluctuations. The superheterodyne design improves robustness but has lower light throughput. The choice between these depends on specific application requirements. Both approaches can be implemented with one or two tunable lasers, and the superheterodyne design even allows for single-shot acquisition. To minimize radiometric losses, a lensed fiber needle is used for reference beam injection. Experiments were conducted for both reflective NLoS imaging ('looking around corners') and transmissive NLoS imaging ('looking through scatter'). In reflective imaging, a wall serves as a virtual source (VS) and virtual detector (VD), indirectly illuminating and receiving light from the hidden object. In transmissive imaging, the object is placed behind a scattering medium (e.g., ground glass diffuser or milky plastic plate). Image reconstruction involves backpropagating the synthetic hologram at the SWL. For multi-wavelength illumination, synthetic pulse holography can be implemented to enhance longitudinal resolution. Experiments with wavefront sensing through scatter using pre-existing data showed that SWH can recover phase variations in wavefronts from volumetric scattering samples. The Rayleigh Quarter Wavelength Criterion (RQWR) is introduced to describe the limitation in recovering phase information when spectral correlations are lost due to excessive wavefront error.

The SWH method demonstrated several key advantages over existing NLoS imaging techniques: 1. **Small probing area:** SWH uses a small probing area (58 mm × 58 mm), enabling imaging in confined spaces, unlike the larger probing areas (≈1 m²) of many ToF-based methods. 2. **Wide angular field of view:** SWH provides a nearly hemispherical field of view, significantly exceeding the limited FoV of ME-based approaches. 3. **High spatial resolution:** The method achieves sub-millimeter resolution (<1 mm), surpassing the resolution of ToF methods. 4. **High temporal resolution:** Holograms are reconstructed from two shots within milliseconds, compared to the longer acquisition times of many other methods. Single-shot acquisition is also possible with a superheterodyne approach. Experimental results validated these claims. Imaging the letter 'N' (15 mm × 20 mm) around a corner showed improved resolution with decreasing SWL, consistent with classical holography. Imaging through a diffuser and a milky plastic plate demonstrated the ability to reconstruct images even under strong scattering conditions. The smallest achievable SWL was evaluated in these experiments, showing a correlation between the minimum SWL and the level of scatter. Synthetic pulse holography experiments, using multiple SWLs, improved longitudinal resolution by creating a computationally engineered pulse train. Wavefront sensing through scattering media was also demonstrated, proving the versatility of SWH. The Rayleigh Quarter Wavelength Criterion (RQWR) helps define the conditions under which the method can accurately reconstruct the objects. The RQWR places a fundamental limit on the resolution achievable by a wide class of NLoS imagers, including ToF methods.

The findings address the limitations of existing NLoS imaging techniques by demonstrating a method that combines high resolution, a wide field of view, and fast acquisition times. The ability to image through significant scattering, as shown in the experiments with the milky plastic, is particularly significant. The extension to wavefront sensing through scattering media opens new possibilities beyond traditional NLoS imaging. The Rayleigh Quarter Wavelength Criterion (RQWR) provides a theoretical understanding of the limitations of SWH and other NLoS imaging techniques, identifying the conditions under which the recovery of phase information is possible. The success of SWH in diverse scenarios underscores its potential for a wide range of applications, including medical imaging, autonomous navigation, and industrial inspection.

This work presents SWH, a novel NLoS imaging technique that overcomes the limitations of existing methods by combining high resolution, wide field of view, and high temporal resolution. The successful application of SWH to both reflective and transmissive scenarios demonstrates its versatility. Future research directions include exploring the application of SWH to other wave phenomena (e.g., ultrasound, X-rays, radio waves) and further improving the technique's robustness to noise and various scattering conditions. The potential to combine SWH with other imaging modalities offers exciting possibilities for advancements in NLoS imaging.

The primary limitation of SWH is the spectral memory effect, analogous to the angular memory effect in ME-based techniques. When spectral correlations between the two wavelengths are lost due to excessive wavefront error, the reconstructed images suffer from speckle artifacts. Judicious selection of the interrogation wavelengths is crucial to mitigate this limitation. While the superheterodyne interferometer design increases robustness to environmental fluctuations and object motion, it also reduces light throughput, making it challenging for light-starved NLoS scenarios. The use of speckle diversity in the reflective NLoS experiments helped in mitigating the increased speckle artifacts due to decorrelation but increased the measurement time. Further improvements in laser power and detector sensitivity could potentially alleviate some of these limitations.