We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging.

The arbitrary Nth-order intensity correlation measurement with thermal light is both theoretically and experimentally investigated. In a double-slit interference scheme with thermal light, we compare the results for higher- and lower-order intensity correlation and demonstrate that the visibility of the interference pattern can be dramatically enhanced while the resolution can also be improved when the order N becomes larger. The experimental results are in agreement with our theoretical analysis.

We propose and experimentally demonstrate a high-efficiency single-pixel imaging (SPI) scheme by integrating time-correlated single-photon counting (TCSPC) with time-division multiplexing to acquire full-color images at an extremely low light level. This SPI scheme uses a digital micromirror device to modulate a sequence of laser pulses with preset delays to achieve three-color structured illumination, then employs a photomultiplier tube into the TCSPC module to achieve photon-counting detection. By exploiting the time-resolved capabilities of TCSPC, we demodulate the spectrum-image-encoded signals, and then reconstruct high-quality full-color images in a single round of measurement. Based on this scheme, strategies such as single-step measurement, high-speed projection, and undersampling can further improve imaging efficiency.

In ghost imaging with thermal light (GITL), the bucket signals are analog signals playing the role of weights in the algorithms of image reconstruction. However, diverse bucket signals seemed to be completely ignored in conditional-averaging GITL, which was recently proposed by two groups [ Appl. Phys. Lett. 100, 131114 (2012); Chin. Phys. Lett. 29, 074216 (2012)]. Even so, positive and negative ghost images were obtained by averaging just partial reference signals. To understand this effect, one needs to determine the statistical relation between random bucket signals and reference signals. Here, we apply probability theory to GITL by regarding thermal light intensities as stochastic variables, and then deduce the joint probability density function between the bucket and reference signals. Positive and negative images are formed in ensemble averaging of the product of the reference signal and two logic quantities of the bucket signals. The visibility and contrast-to-noise ratio of these images in conditional-averaging GITL are analyzed in detail in both theory and experiment. As for applications, we perform an experiment of remote conditional-averaging GITL and verify that the image quality is maintained when the bucket signals are extremely attenuated. Our method can be applied to any ghost imaging scenarios in which the specific statistics of the optical source is given.

We propose an incoherent interferometer which can partly modify the spatial correlation property of thermal light. Applying the interferometer to the two-photon double-slit interference with thermal light, we find that the subwavelength interference patterns appear in the intensity correlation not only between two same polarized photons at different positions but also between two orthogonally polarized photons at the same position. The latter can correspond to the two-photon double-slit interference using a two-photon entangled source. Our experimental result suggests that a thermal light source is capable of accomplishing subwavelength lithography technique to surpass the Rayleigh resolution limit.

This research presents a coherent structured illumination single-pixel imaging scheme to image objects with complex amplitudes. By utilizing a phase-only spatial light modulator for phase modulation, we can efficiently generate the Hadamard basis structured light and the reference light that interfere with each other to form the coherent structured illumination. Using the 4-step phase-shifting, the spectrum of the object is acquired by detecting the zero-frequency component of the object light with a single-pixel photodetector. The desired complex-amplitude image can be further retrieved by applying an inverse Hadamard transform. The proposed scheme is experimentally demonstrated by imaging two etched glass objects, a dragonfly wing, and a resolution test chart. Benefiting from the phase modulation, this scheme has a high efficiency, a high imaging quality, a high spatial resolution, and a simple and stable configuration to obtain both the phase and amplitude information of the target object. The proposed scheme provides a promising complex-amplitude imaging modality with single-pixel detection. Thus it might find broad applications in optical metrology and biomedical science.