Correlation Plenoptic Imaging Research Articles

Analytical form of the refocused images from correlation plenoptic imaging

Correlation plenoptic imaging (CPI) is emerging as a promising approach to light-field imaging (LFI), a technique for concurrently measuring light intensity distribution and propagation direction of light rays from a 3D scene. LFI thus enables single-shot 3D imaging, offering rapid volumetric reconstruction. The optical performance of traditional LFI, however, is limited by a micro-lens array, causing a decline in resolution as 3D capabilities improve. CPI overcomes these limitation by measuring photon number correlations on two photodetectors with spatial resolution, in a lenslet-free design, so that the correlation function can be decoded in post-processing to reconstruct high-resolution images. In this paper, we derive the analytical expression of CPI images reconstructed through refocusing, addressing the previously unknown mathematical relationship between object shape and its final image. We show that refocused images are not limited by numerical aperture-induced blurring, as in conventional imaging. Rather, the image features of CPI can be explained through an analogy with imaging systems illuminated by spatially coherent light.

Assessing the 3D resolution of refocused correlation plenoptic images using a general-purpose image quality estimator

Correlation plenoptic imaging (CPI) is emerging as a promising approach to light-field imaging (LFI), a technique enabling simultaneous measurement of light intensity distribution and propagation direction from a scene. LFI allows single-shot 3D sampling, offering fast 3D reconstruction for a wide range of applications. However, the array of micro-lenses typically used in LFI to obtain 3D information limits image resolution, which rapidly declines with enhanced volumetric reconstruction capabilities. CPI addresses this limitation by decoupling the measurement of the light field on two photodetectors with spatial resolution, eliminating the need for micro-lenses. 3D information is encoded in a four-dimensional correlation function, which is decoded in post-processing to reconstruct images without the resolution loss seen in conventional LFI. This paper evaluates the tomographic performance of CPI, demonstrating that the refocusing reconstruction method provides axial sectioning capabilities comparable to conventional imaging systems. A general-purpose analytical approach based on image fidelity is proposed to quantitatively study axial and lateral resolution. The analysis fully characterizes the volumetric resolution of any CPI architecture, offering a comprehensive evaluation of its imaging performance.

3D Correlation Imaging for Localized Phase Disturbance Mitigation

Correlation plenoptic imaging is a procedure to perform light-field imaging without spatial resolution loss, by measuring the second-order spatiotemporal correlations of light. We investigate the possibility of using correlation plenoptic imaging to mitigate the effect of a phase disturbance in the propagation from the object to the main lens. We assume that this detrimental effect, which can be due to a turbulent medium, is localized at a specific distance from the lens, and is slowly varying in time. The mitigation of turbulence effects has already fostered the development of both light-field imaging and correlation imaging procedures. Here, we aim to merge these aspects, proposing a correlation light-field imaging method to overcome the effects of slowly varying turbulence, without the loss of lateral resolution, typical of traditional plenoptic imaging devices.

Light-field imaging from position-momentum correlations

Correlation plenoptic imaging (CPI) is a light-field imaging technique employing intensity correlation measurements to simultaneously detect the spatial distribution and the propagation direction of light. Compared to standard methods, in which light-field images are directly encoded in intensity, CPI provides a significant enhancement of the volumetric reconstruction performance in terms of both achievable depth of field and 3D resolution. In this article, we present a novel CPI configuration where light-field information is encoded in correlations between position and momentum measurements, namely, points on a given object plane and points of the Fourier plane of the imaging lens. Besides the fundamental interest in retrieving the properties of position-momentum correlation, the proposed scheme overcomes practical limitations of previously proposed setups, providing higher axial homogeneity and robustness with respect to the identification of reference planes.

Compressive sensing-based correlation plenoptic imaging

Correlation Plenoptic Imaging (CPI) is an innovative approach to plenoptic imaging that tackles the inherent trade-off between image resolution and depth of field. By exploiting the intensity correlations that characterize specific states of light, it extracts information of the captured light direction, enabling the reconstruction of images with increased depth of field while preserving resolution. We describe a novel reconstruction algorithm, relying on compressive sensing (CS) techniques based on the discrete cosine transform and on gradients, used in order to reconstruct CPI images with a reduced number of frames. We validate the algorithm using simulated data and demonstrate that CS-based reconstruction techniques can achieve high-quality images with smaller acquisition times, thus facilitating the practical application of CPI.

Deep learning approach for denoising low-SNR correlation plenoptic images

Correlation Plenoptic Imaging (CPI) is a novel volumetric imaging technique that uses two sensors and the spatio-temporal correlations of light to detect both the spatial distribution and the direction of light. This novel approach to plenoptic imaging enables refocusing and 3D imaging with significant enhancement of both resolution and depth of field. However, CPI is generally slower than conventional approaches due to the need to acquire sufficient statistics for measuring correlations with an acceptable signal-to-noise ratio (SNR). We address this issue by implementing a Deep Learning application to improve image quality with undersampled frame statistics. We employ a set of experimental images reconstructed by a standard CPI architecture, at three different sampling ratios, and use it to feed a CNN model pre-trained through the transfer learning paradigm U-Net architecture with VGG-19 net for the encoding part. We find that our model reaches a Structural Similarity (SSIM) index value close to 1 both for the test sample (SSIM = 0.87 pm 0.02) and in 5-fold cross validation (SSIM = 0.92 pm 0.07); the results are also shown to outperform classic denoising methods, in particular for images with lower SNR. The proposed work represents the first application of Artificial Intelligence in the field of CPI and demonstrates its high potential: speeding-up the acquisition by a factor 20 over the fastest CPI so far demonstrated, enabling recording potentially 200 volumetric images per second. The presented results open the way to scanning-free real-time volumetric imaging at video rate, which is expected to achieve a substantial influence in various applications scenarios, from monitoring neuronal activity to machine vision and security.

Periodic patterns for resolution limit characterization of correlation plenoptic imaging

The measurement of the spatio-temporal correlations of light provides an interesting tool to overcome the traditional limitations of standard imaging, such as the strong trade-off between spatial resolution and depth of field. In particular, using correlation plenoptic imaging, one can detect both the spatial distribution and the direction of light in a scene, pushing both resolution and depth of field to the fundamental limit imposed by wave optics. This allows one to perform refocusing of different axial planes and three-dimensional reconstruction without any spatial scanning. In the present work, we investigate the resolution limit in a particular correlation plenoptic imaging scheme, by considering periodic test patterns, which provide, through analytical results, a deeper insight in the resolution properties of this second-order imaging technique, also in comparison with standard imaging.

Correlated-photon imaging at 10 volumetric images per second

The correlation properties of light provide an outstanding tool to overcome the limitations of traditional imaging techniques. A relevant case is represented by correlation plenoptic imaging (CPI), a quantum-inspired volumetric imaging protocol employing spatio-temporally correlated photons from either entangled or chaotic sources to address the main limitations of conventional light-field imaging, namely, the poor spatial resolution and the reduced change of perspective for 3D imaging. However, the application potential of high-resolution imaging modalities relying on photon correlations is limited, in practice, by the need to collect a large number of frames. This creates a gap, unacceptable for many relevant tasks, between the time performance of correlated-light imaging and that of traditional imaging methods. In this article, we address this issue by exploiting the photon number correlations intrinsic in chaotic light, combined with a cutting-edge ultrafast sensor made of a large array of single-photon avalanche diodes (SPADs). This combination of source and sensor is embedded within a novel single-lens CPI scheme enabling to acquire 10 volumetric images per second. Our results place correlated-photon imaging at a competitive edge and prove its potential in practical applications.

Comparative analysis of signal-to-noise ratio in correlation plenoptic imaging architectures

Correlation plenoptic imaging (CPI) is a scanning-free diffraction-limited 3D optical imaging technique exploiting the peculiar properties of correlated light sources. CPI has been further extended to samples of interest to microscopy, such as fluorescent or scattering objects, in a modified architecture named correlation light-field microscopy (CLM). Interestingly, experiments have shown that the noise performances of CLM are significantly improved over the original CPI scheme, leading to better images and faster acquisition. In this work, we provide a theoretical foundation to such advantage by investigating the properties of both the signal-to-noise and the signal-to-background ratios of CLM and the original CPI setup.

Refocusing Algorithm for Correlation Plenoptic Imaging.

Correlation plenoptic imaging (CPI) is a technique capable of acquiring the light field emerging from a scene of interest, namely, the combined information of intensity and propagation direction of light. This is achieved by evaluating correlations between the photon numbers measured by two high-resolution detectors. Volumetric information about the object of interest is decoded, through data analysis, from the measured four-dimensional correlation function. In this paper, we investigate the relevant aspects of the refocusing algorithm, a post-processing method that isolates the image of a selected transverse plane within the 3D scene, once applied to the correlation function. In particular, we aim at bridging the gap between existing literature, which only deals with refocusing algorithms in case of continuous coordinates, and the experimental reality, in which the correlation function is available as a discrete quantity defined on the sensors pixels.

Resolution Limit of Correlation Plenoptic Imaging between Arbitrary Planes

Correlation plenoptic imaging (CPI) is an optical imaging technique based on intensity correlation measurement, which enables detecting, within fundamental physical limits, both the spatial distribution and the direction of light in a scene. This provides the possibility to perform tasks such as three-dimensional reconstruction and refocusing of different planes. Compared with standard plenoptic imaging devices, based on direct intensity measurement, CPI overcomes the problem of the strong trade-off between spatial and directional resolution. Here, we study the resolution limit in a recent development of the technique, called correlation plenoptic imaging between arbitrary planes (CPI-AP). The analysis, based on Gaussian test objects, highlights the main properties of the technique, as compared with standard imaging, and provides an analytical guideline to identify the limits at which an object can be considered resolved.

Classical Ghost Imaging: A Comparative Study of Algorithmic Performances for Image Reconstruction in Prospect of Plenoptic Imaging

Ghost Imaging has been extensively explored for 25 years for a two reasons: the rich physics of second-order photon correlations that enable this imaging scheme and the possibility of implementing new imaging protocols with interesting real-life applications, e.g. imaging in turbulent media, investigation of sensitive samples in low-flux regimes, 3-D plenoptic imaging, and so on. Since the first demonstration of Ghost Imaging, several extended versions of the Traditional Ghost Imaging algorithm have been proposed, such as Correspondence Ghost Imaging, Pseudo-Inverse Ghost Imaging, and normalization techniques that rely on different computational approaches to obtain the image from measured data. So far, a direct comparison of all above-mentioned protocols for the same experimental parameters is still lacking. In this work, we experimentally and numerically implement a number of different methods and systematically compare them in terms of the obtained SNR and computational cost. Furthermore, we investigate their compatibility with Correlation Plenoptic Imaging, a technique strictly connected to Ghost Imaging, that allows refocusing of images, increasing the depth of field (DOF) and making 3D visualization possible. Our results can provide useful guidelines for the choice of a suitable numerical algorithm for in the light of Ghost Imaging applications.

Correlation plenoptic imaging between arbitrary planes

We propose a novel method to perform plenoptic imaging at the diffraction limit by measuring second-order correlations of light between two reference planes, arbitrarily chosen, within the tridimensional scene of interest. We show that for both chaotic light and entangled-photon illumination, the protocol enables to change the focused planes, in post-processing, and to achieve an unprecedented combination of image resolution and depth of field. In particular, the depth of field results larger by a factor 3 with respect to previous correlation plenoptic imaging protocols, and by an order of magnitude with respect to standard imaging, while the resolution is kept at the diffraction limit. The results lead the way towards the development of compact designs for correlation plenoptic imaging devices based on chaotic light, as well as high-SNR plenoptic imaging devices based on entangled photon illumination, thus contributing to make correlation plenoptic imaging effectively competitive with commercial plenoptic devices.

Correlation plenoptic imaging for microscopy applications

Plenoptic microscopy is a promising technique which allows refocusing and depth-of-field enhancement, in post-processing, as well as scanning free 3D imaging. However, in its conventional implementation, spatial resolution is highly sacrificed and cannot reach the diffraction limit set by the numerical aperture of the imaging system. We recently proposed a novel method, named Correlation Plenoptic Imaging (CPI), based on measuring intensity correlation of either chaotic or entangled photon light sources. However, such protocols are not well suited for microscopic purposes: they cannot be employed with scattering or fluorescent samples and are extremely sensitive to diffusive effects. Here we consider and compare novel CPI protocols which overcome these problems and enable to perform plenoptic microscopy at the diffraction limit for generic samples; we present both theory and simulations, discuss the improved robustness with respect to previous protocols against turbulence around the sample, and highlight the physical limits of the proposed technique.

Nonclassical noise features in a correlation plenoptic imaging setup

Sub-shot-noise imaging and correlation plenoptic imaging are two quantum imaging techniques that enable to overcome different problems of classical imaging systems. Combining the two techniques is not trivial, since the former is based on the detection of identical corresponding modes to subtract noise, while the latter requires the detection of different modes to perform directional reconstruction. In this paper, we experimentally show the possibility to obtain a noise-reduction factor smaller than one, a necessary condition to perform sub-shot-noise imaging, in a setup that can be adapted to correlation plenoptic imaging.

Signal-to-noise properties of correlation plenoptic imaging with chaotic light

Correlation Plenoptic Imaging (CPI) is a novel imaging technique, that exploits the correlations between the intensity fluctuations of light to perform the typical tasks of plenoptic imaging (namely, refocusing out-of-focus parts of the scene, extending the depth of field, and performing 3D reconstruction), without entailing a loss of spatial resolution. Here, we consider two different CPI schemes based on chaotic light, both employing ghost imaging: the first one to image the object, the second one to image the focusing element. We characterize their noise properties in terms of the signal-to-noise ratio (SNR) and compare their performances. We find that the SNR can be significantly higher and easier to control in the second CPI scheme, involving standard imaging of the object; under adequate conditions, this scheme enables reducing by one order of magnitude the number of frames for achieving the same SNR.

Correlation Plenoptic Imaging: An Overview

Plenoptic imaging (PI) enables refocusing, depth-of-field (DOF) extension and 3D visualization, thanks to its ability to reconstruct the path of light rays from the lens to the image. However, in state-of-the-art plenoptic devices, these advantages come at the expenses of the image resolution, which is always well above the diffraction limit defined by the lens numerical aperture (NA). To overcome this limitation, we have proposed exploiting the spatio-temporal correlations of light, and to modify the ghost imaging scheme by endowing it with plenoptic properties. This approach, named Correlation Plenoptic Imaging (CPI), enables pushing both resolution and DOF to the fundamental limit imposed by wave-optics. In this paper, we review the methods to perform CPI both with chaotic light and with entangled photon pairs. Both simulations and a proof-of-principle experimental demonstration of CPI will be presented.

Correlation Plenoptic Imaging With Entangled Photons

Plenoptic imaging is a novel optical technique for three-dimensional imaging in a single shot. It is enabled by the simultaneous measurement of both the location and the propagation direction of light in a given scene. In the standard approach, the maximum spatial and angular resolutions are inversely proportional, and so are the resolution and the maximum achievable depth of focus of the 3D image. We have recently proposed a method to overcome such fundamental limits by combining plenoptic imaging with an intriguing correlation remote-imaging technique: ghost imaging. Here, we theoretically demonstrate that correlation plenoptic imaging can be effectively achieved by exploiting the position-momentum entanglement characterizing spontaneous parametric down-conversion (SPDC) photon pairs. As a proof-of-principle demonstration, we shall show that correlation plenoptic imaging with entangled photons may enable the refocusing of an out-of-focus image at the same depth of focus of a standard plenoptic device, but without sacrificing diffraction-limited image resolution.

Correlation Plenoptic Imaging.

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable three-dimensional imaging in a single shot. However, in standard plenoptic imaging systems, the maximum spatial and angular resolutions are fundamentally linked; thereby, the maximum achievable depth of field is inversely proportional to the spatial resolution. We propose to take advantage of the second-order correlation properties of light to overcome this fundamental limitation. In this Letter, we demonstrate that the correlation in both momentum and position of chaotic light leads to the enhanced refocusing power of correlation plenoptic imaging with respect to standard plenoptic imaging.