Quantum ghost imaging offers many advantages over classical imaging, including the ability to probe an object with one wavelength and record the image with another (non-degenerate ghost imaging), but suffers from slow image reconstruction due to sparsity and probabilistic arrival positions of photons. Here, we propose a two-step deep learning approach to establish an optimal early stopping point based on object recognition, even for sparsely filled images. In step one we enhance the reconstructed image after every measurement by a deep convolutional auto-encoder, followed by step two in which a classifier is used to recognise the image. We test this approach on a non-degenerate ghost imaging setup while varying physical parameters such as the mask type and resolution. We achieved a fivefold decrease in image acquisition time at a recognition confidence of $$75\%$$ 75 % . The significant reduction in experimental running time is an important step towards real-time ghost imaging, as well as object recognition with few photons, e.g., in the detection of light sensitive structures.

Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to analytically propagate any desired field, making the calculation fast and easy. By selecting a basis other than that of planes waves, we overcome the problem of numerical artefacts in the angular spectrum approach and at the same time are able to offer an intuitive understanding for why certain classes of fields propagate as they do. We outline the concept theoretically, compare it to the numerical angular spectrum approach, and confirm its veracity experimentally using a range of instructive examples. We believe that this modal approach to propagating light will be a useful addition to toolbox for propagating optical fields.

Quantum ghost imaging offers many advantages over classical imaging, including low photon fluxes and non-degenerate object and image wavelengths for imaging light sensitive structures, but suffers from slow image reconstruction speeds. Image reconstruction times depend on the resolution of the required image which scale quadratically with the image resolution. Here, we propose a super-resolved imaging approach based on neural networks where we reconstruct a low resolution image, which we denoise and super-resolve to a high resolution image. To test the approach, we implemented both a generative adversarial network as well as a super-resolving autoencoder in conjunction with an experimental quantum ghost imaging setup, demonstrating its efficacy across a range of object and imaging projective mask types. We achieved super-resolving enhancement of $$4\times$$ 4 × the measured resolution with a fidelity close to 90$$\%$$ % at an acquisition time of N$$^2$$ 2 measurements, required for a complete N $$\times$$ × N pixel image solution. This significant resolution enhancement is a step closer to a common ghost imaging goal, to reconstruct images with the highest resolution and the shortest possible acquisition time.

Single-pixel quantum ghost imaging involves the exploitation of non-local photon spatial correlations to image objects with light that has not interacted with them and, using intelligent spatial scanning with projective masks, reduces detection to a single pixel. Despite many applications, extension to complex amplitude objects remains challenging. Here, we reveal that the necessary interference for phase retrieval is naturally embedded in the correlation measurements formed from traditional projective masks in bi-photon quantum ghost imaging. Using this, we develop a simple approach to obtain the full phase and amplitude information of complex objects. We demonstrate straightforward reconstruction without ambiguity using objects exhibiting spatially varying structures from phase steps to gradients as well as complex amplitudes. This technique could be an important step toward imaging the phase of light-sensitive structures in biological matter.

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