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The generation of speckle patterns via random matrices, statistical definitions, or apertures may not always result in optimal outcomes. Issues such as correlation fluctuations in low ensemble numbers and diffraction in long-distance propagation can arise. Instead of improving results of specific applications, our solution is catching deep correlations of patterns with the framework, Speckle-Net, which is fundamental and universally applicable to various systems. We demonstrate this in computational ghost imaging (CGI) and structured illumination microscopy (SIM). In CGI with extremely low ensemble number, it customizes correlation width and minimizes correlation fluctuations in illuminating patterns to achieve higher-quality images. It also creates non-Rayleigh nondiffracting speckle patterns only through a phase mask modulation, which overcomes the power loss in the traditional ring-aperture method. Our approach provides new insights into the nontrivial speckle patterns and has great potential for a variety of applications including dynamic SIM, X-ray and photo-acoustic imaging, and disorder physics.

Artificial intelligence has recently been widely used in computational imaging. The deep neural network (DNN) improves the signal-to-noise ratio of the retrieved images, whose quality is otherwise corrupted due to the low sampling ratio or noisy environments. This work proposes a new computational imaging scheme based on the sequence transduction mechanism with the transformer network. The simulation database assists the network in achieving signal translation ability. The experimental single-pixel detector’s signal will be ‘translated’ into a 2D image in an end-to-end manner. High-quality images with no background noise can be retrieved at a sampling ratio as low as 2%. The illumination patterns can be either well-designed speckle patterns for sub-Nyquist imaging or random speckle patterns. Moreover, our method is robust to noise interference. This translation mechanism opens a new direction for DNN-assisted ghost imaging and can be used in various computational imaging scenarios.

Quantum entanglement has emerged as a great resource for spectroscopy and its importance in two-photon spectrum and microscopy has been demonstrated. Current studies focus on the two-photon absorption, whereas the Raman spectroscopy with quantum entanglement still remains elusive, with outstanding issues of temporal and spectral resolutions. Here we study the new capabilities provided by entangled photons in coherent Raman spectroscopy. An ultrafast frequency-resolved Raman spectroscopy with entangled photons is developed for condensed-phase molecules, to probe the electronic and vibrational coherences. Using quantum correlation between the photons, the signal shows the capability of both temporal and spectral resolutions not accessible by either classical pulses or the fields without entanglement. We develop a microscopic theory for this Raman spectroscopy, revealing the electronic coherence dynamics even at timescale of 50fs. This suggests new paradigms of optical signals and spectroscopy, with potential to push detection below standard quantum limit.

Optical imaging through scattering media has long been a challenge. Many approaches have been developed for focusing light or imaging objects through scattering media, but usually, they are either invasive, limited to stationary or slow-moving media, or require high-resolution cameras and complex algorithms to retrieve the images. By utilizing spatial–temporal encoded patterns (STEPs), we introduce a technique for the computation of imaging that overcomes these restrictions. With a single-pixel photodetector, we demonstrate non-invasive imaging through scattering media. This technique is insensitive to the motion of the media. Furthermore, we demonstrate that our image reconstruction algorithm is much more efficient than correlation-based algorithms for single-pixel imaging, which may allow fast imaging for applications with limited computing resources.

We present a novel method, to our knowledge, to synthesize non-trivial speckle patterns that can enable sub-Rayleigh second-order correlation imaging. The speckle patterns acquire a unique anti-correlation in the spatial intensity fluctuation by introducing the blue noise distribution on spatial Fourier power spectrum to the input light fields through amplitude modulation. Illuminating objects with the blue noise speckle patterns can lead to a sub-diffraction limit imaging system with a resolution more than three times higher than first-order imaging, which is comparable to the resolving power of ninth order correlation imaging with thermal light. Our method opens a new route towards non-trivial speckle pattern generation by tailoring amplitudes in spatial Fourier power spectrum of the input light fields and provides a versatile scheme for constructing sub-Rayleigh imaging and microscopy systems without invoking complicated higher-order correlations.