Vision is the main way for humans to obtain information about the objective world. It is estimated that about 80% of human perception of external information comes from vision, and the visual perception ability of the human eye is mainly based on a well-known physical principle of imaging. Generally speaking, the essence of imaging is to establish a point-to-point mapping between the object plane and the image plane, with the human eye itself being a typical imaging system. However, restricted by the visual performance of the human eye, there are limitations in time, space, sensitivity, spectrum, resolution, and other aspects. Therefore, human beings have invented a variety of imaging systems and methods, such as telescope, microscope, and video camera, to extend and expand the observation capabilities of humans, which makes us see farther, finer, and clearer.

With the development of science and technology, optical imaging technology, as an indispensable part of our daily life, has been widely used in industrial production, medicine, science, national defense, and other fields. Most of the existing optical imaging technologies are based on intensity observation, which acquires the first-order coherence of the light field. The intensity fluctuation of the light source is often considered as a harmful factor affecting the intensity observation, scilicet, the performance of the imaging system. What is more, the imaging results usually depend on the key parameters of the core devices, such as the numerical aperture of the lens, the pixel size, and the pixel number of the detector^[1–3]. In recent years, based on the second-order correlation of specific light fields, a new imaging method named ghost imaging (GI) has been developed^[4–18]. Images of the object/scene can be obtained by calculating the second-order correlation function between the intensity distribution of the illumination field and the intensity of light transmitted/reflected by the object. The illumination field is actively or passively modulated to contain random fluctuations, with the modulation patterns usually taken as reference. Echoes from the object are recorded by a detector with no spatial resolution, referred to as bucket detection. Different from traditional imaging, GI takes the intensity fluctuation of the light source as a gain of information acquisition ability, or as a novel information channel, which is similar to that of communication technology. At the same time, GI is no longer limited to the design of hardware and the performance of core components but focuses also on the use of efficient and flexible software algorithms to reconstruct images, which is expected to break through the technical bottleneck of traditional imaging technology. Many theoretical and experimental studies have proved that GI has the characteristics of high efficiency in information extraction, disturbance resistance, and parallel acquisition of multidimensional information^[19–45].

The first realized information acquisition based on second-order correlation of light fields can be traced back to the HBT experiment demonstrated in 1956, which was a brand-new method to obtain the angular diameter of the star by measuring the second-order auto-correlation function of light fields^[46]. In 1963, Glauber established the theory of quantum coherence of light fields, which promoted the rapid development of quantum optics and laid a theoretical foundation for the invention of GI technology^[47]. In 1994, Klyshko proposed a two-photon correlation scheme which in rapid sequence was experimentally verified by Shih’s group in 1995^[5]. It was the first proof-of-principle demonstration of image acquisition by exploiting the second-order cross-correlation function of the light field, which invoked a research tide on GI. Subsequently, GI with entangled light^[5], pseudo-thermal light^[12,18], and true thermal light sources^{[10,11,48–50]} has been realized, and the physics of GI has been intensively discussed^{[7,8,16,51–56]}. Up to now, full-wave band GI^[57-62] and a counterpart ghost version corresponding to traditional imaging techniques, such as ghost diffraction^[17,18,63], ghost interference^[64–67], ghost pinhole imaging^[68], ghost holography^[69–71], ghost ptychography^[72,73], ghost panorama^[74], ghost phase imaging^[75–77], and ghost coherent imaging^[37,78], have been verified. In the most recent ten years, thanks to the development of compressed sensing and deep-learning technology, a series of GI applications has been carried out quickly by combining those techniques with the physical principle of GI^[6,79]. Significant progress has been made, especially in the fields of remote sensing^{[21,41,80–89]}, three-dimensional (3D) imaging^[90–97], microscopy^{[57,98–107]}, and optical communication^[108–115].

In this paper, we first review the physical principle, technical characteristics, and development process of GI. Then the main considered applications of GI and corresponding benchmark results in recent years are briefly reviewed, with an overview shown in Fig. 1. Finally, the scientific and technical problems that need to be further studied toward practical applications of GI are discussed.

In a typical GI system, two entangled or correlated beams are employed, as shown in Fig. 2. The interested object is located on one path, with the transmitted or reflected light collected by a bucket detector, which contains no spatial resolution; while the intensity distribution of the other beam (called a reference path) is recorded by an array detector (or scanning with a point-like receiver). The beams can propagate freely or through designed optical paths, with hr(x→;x→r) and ho(x→;x→i) being the propagation functions for two beams, respectively. From this configuration, neither detector can provide any image of the object, while the correlation between their results turns out to show the image of the object, due to the intrinsic correlation from the source. The second-order correlation is defined as G(2)(x→,x→′)=⟨Ir(x→)Io(x→′)⟩⟨Ir(x→)⟩⟨Io(x→′)⟩,(1)where ⟨·⟩ represents the ensemble average. When the free-propagation distances of the object path and reference path are equal, we have ho(x→;x→i)=O(x→)hr(x→;x→r),(2)which leads to the fact that the correlation between surface of the array detector and that of the object will be only determined by that of the illumination source. (If the propagation distances are not equal, such correlation can be maintained via secondary imaging with lens, with a possible magnification factor.) Results of the bucket detection read B=∫Io(x→′)dx→′=∫O(x→′)Ir(x→′)dx→′, where O(x→) is the transmission/reflection distribution of object; then $$\begin{gathered} G(2)(x→)=⟨BIr(x→)⟩⟨B⟩⟨Ir(x→)⟩=∫dx→′O(x→′)⟨Ir(x→′)Ir(x→)⟩∫dx→′O(x→′)⟨Ir(x→′)⟩⟨Ir(x→)⟩ \\ =1αO(x→′)⋆g(2)(x→,x→′), \end{gathered}$$(3)with α=∫O(x→′)dx→′ representing the total reflection of the object and ⋆ being the operation of convolution, and g(2)(x→,x→′)=⟨Ir(x→′)Ir(x→)⟩⟨Ir(x→)⟩⟨Ir(x→′)⟩(4)here represents the normalized second-order correlation of the illumination field in the reference path, which serves as the point spread function (PSF) for imaging. Ignoring the diffraction effect, and taking Eq. (2) into account, the above correlation is directly determined by the second-order coherence of the source as g(2)(x→0,x→0′)={δ(x→0−x→0′),entangled1+δ(x→0−x→0′),classical.(5)

Therefore Eq. (3) offers an image of the object. One thing worth noting is that the δ-function correlation of classical sources and entangled sources derived above only holds under certain conditions. Specific analyses are needed in particular experiments. Taking diffraction into account, the δ-function will degrade into a single-peaked function, with the width of the peak being the spatial resolution of imaging. Such resolution will show similarity to that of traditional imaging, with the width determined by the effective aperture of the system. The difference lies in the fact that for ghost imaging the size of the source should be included when considering the effective aperture^[116]. Another thing to be noted is that the above discussion is done under an unlimited number of samplings for the ensemble average in Eq. (3). In practice, the performance of GI can be degraded in resolution or signal-to-noise ratio (SNR) of the outputs due to the limited number of samplings.

In addition, if we replace the bucket detector with a point detector and set the propagation distance of the reference equal to the distance of propagation through the object to the point detector in the object path, the modulus of the Fourier transformation of the object’s transmittance can be obtained by the second-order correlation G(2)(x→o,x→r) of light fields between two paths in Eq. (1), which is called Fourier-transform GI^[12].

To understand the physics of ghost imaging, researchers tried to explain it in different ways. For GI with an entangled source, it is rather clear that the position–momentum entanglement provides the correlation between results of two detectors^[7]. Or, it is a natural result of two-photon interference. This can also be explained by the Klyshko picture, that the twin photons collaborate to complete the optical path that was covered by single photons in a traditional imaging configuration^[5]. As an analog of the entangled version, GI with classical sources initiated intense debates upon its first demonstration. It can also be explained in a quantum version as the result of two-photon interference, as well as in a classical way by correlation of intensity fluctuations. Also, the Klyshko picture was used to illustrate the structure taking the thermal source as a phase conjugator^[16].

The most fundamental differences between GI with an entangled source and a classical source are all caused by the difference between the states of the illumination field used. For an entangled source, a two-photon state appears as almost a pure state. Those possible two-photon propagation cases, which can generate coincidence between two detectors, are coherent, resulting in a complete two-photon interference. By contrast, the state of the classical field is a thermal state, or mixed state. There exist indistinguishable cases, which will also provide two-photon interference when considering the correlation between two detectors, while those distinguishable cases will provide incoherent background in correlation function between two detectors. Due to such a mixture, the two-photon interference results are degraded into classical correlation. Such a background leads to a result that the visibility of GI with a classical source will not be higher than 1/3.

From Eq. (1), it is easy to see that there will be an inevitable background when using classical sources, which results in images of low visibility. To make this better, people also operate with fluctuation correlation as ΔG(x→)=⟨BIr(x→)⟩−⟨B⟩⟨Ir(x→)⟩⟨B⟩⟨Ir(x→)⟩=⟨ΔBΔIr(x→)⟩⟨B⟩⟨Ir(x→)⟩,(6)where ΔI=I−⟨I⟩ represents the fluctuation of the field or signal. From this equation, researchers became more aware of the fact that fluctuations in the echoes actually contain information on the object. The more deviation from the mean value, the more information the signal carries. Therefore, by simply selecting and summing up those illumination patterns corresponding to the echoes of high positive (or negative) fluctuation, without taking the bucket value itself into computation, the image can also be achieved. That is the main idea of corresponding GI^[117,118]. Further, to improve the performance of imaging under conditions of tiny fluctuation due to almost transparent objects, or influences of imperfect distributed illumination, differential GI and normalized GI are discussed^[119–121].

Mathematically, by expressing the image with values of discrete pixels, the procedure of GI can be expressed as a linear equation. Taking the object as an M×1 column vector O, N times of samplings form an N×M matrix A, where each row represents one sampling, with the illumination intensity on the very pixel being the matrix element. Thus, the results of bucket detection turn out to be an N×1 vector as B=AO.(7)

Corresponding to Eq. (3), the image is reconstructed as O^GI=ATB=ATAO,(8)where AT is the transpose of A and ATA shows up as a unit matrix with a uniform background for thermal illumination. With N<M and random matrix A, solving Eq. (7) becomes similar to that of compressive sampling, which therefore boosted studies on reconstruction algorithms based on compressive sampling^{[61,107,122–125]}. Along with compressive sampling, another concept of single-pixel imaging^[79,90,126] also emerged, which performs random sampling on the image plane while also detecting with a detector of no spatial resolution. Due to the similarity between single-pixel imaging and GI, researchers refer to each other, which encourages the ideas and systems of both methods becoming unified. Based on the rapid expansion of machine learning in recent years, deep learning also gets involved as a performance booster by data processing^[127–129].

Revisiting from the perspective of information acquisition, the framework of GI appears as an encoding–decoding procedure, with information on the object encoded by the illumination patterns, transformed into lower dimensional bucket detection results, and then decoded via reconstruction algorithms. Physically, the illumination patterns can be generated with rotating ground glass, spatial light modulators, digital mirror devices, and so on. With actively controlled and computable patterns, the reference arm can be replaced with computing and therefore physically omitted, forming computational GI^[14].

The above discussions from different viewpoints enable researchers to gain deeper understanding about GI as well as various developments in the design of imaging systems and reconstruction algorithms. Toward the improvement of performance under different experimental conditions, strategies and algorithms were developed by evaluating properties of different kinds of patterns^{[44,45,57,130–137]}, sorting or combining the patterns into a certain sequence^{[125,138–141]} or even in an adaptive way^{[123,124,142–149]}, and designing better algorithms^{[14,117,119–122,127,150–152]}.

For traditional imaging, the processes of detection and imaging are inseparable, and the spatial intensity distribution of a light field illuminating the target plane is required to be uniform. However, as shown in Fig. 1, the object light path of a GI system is used for low-dimensional signal detection, while the reference light path is used for spatial resolving, which shows a feature of detection-imaging separation. At the same time, the image acquisition of GI is the result of time-based statistical average measurement. For each measurement, the spatial intensity distribution of the light field is required to have a large fluctuation. However, it is expected to be uniform upon statistical averaging over time. All those differences distinguish GI from traditional imaging with regard to some characteristics, such as imaging resolution and SNR.

Similar to previous imaging methods, imaging resolution and SNR are the most important parameters to evaluate imaging performance. By combining the traditional imaging features with the physical principle of GI, relevant analysis and definitions on imaging resolution and SNR have been carried out, which provided a basis for the design and performance evaluation of GI systems^{[18,119,153–155]}.

Spatial resolution of GI. As we know, the spatial resolution of traditional imaging can be determined by the width of the PSF of the system^[156]. Drawing on this feature, the spatial resolution of GI can also be evaluated by constructing or calculating the corresponding PSF. Many theories and experiments have shown that the spatial resolution of GI mainly depends on the average transverse size of the speckles on the object plane^[18,153]. According to the coherence theory of the light field, the PSF of GI corresponds to the normalized second-order correlation function distribution of light field g(2)(x), and its full width at half-maximum is equivalent to the spatial resolution of GI^[47,153]. It is usually obtained by calculating g(2)(x) of the center pixel as g(2)(x,x=0)=⟨I(x)I(x=0)⟩⟨I(x)⟩⟨I(x=0)⟩,(9)where I(x) is the intensity distribution of the light field on the object plane and ⟨·⟩ denotes the ensemble average.

In addition, according to the matrix representation of GI reconstruction algorithm, the PSF of GI can also be obtained by the feature matrix Mc, namely^[155], Mc=(A−IsA¯)TA,(10)where Is is an N×1 column vector whose elements are all 1 and Mc is an M×M matrix. Moreover, A¯=1N∑s=1NAs represents row averaging of the matrix A, which is a 1×M row vector. If we choose the data in the middle row of the matrix Mc and reshape the data as a two-dimensional image, the PSF of GI can be achieved.

SNR of GI. For traditional imaging, the imaging SNR is equivalent to the detection signal-to-noise ratio (DSNR), which is mainly limited by shot noise, namely, SNRTI=DSNR=10×log10(I)^[154]. Because ghost images result from ensemble statistics based on the measurement of intensity fluctuations, the SNR of an image will be closely related to the number of measurements (N), the minimum gray difference to be distinguished (ΔTmin), and the number of speckles occupied by the object itself on the object plane (ns), appearing as^[119,157]$$\begin{gathered} SNRGI=[ΔOGI(x)]min2ΔOGI2(x) \\ =NΔTmin2ns, \end{gathered}$$(11)where ns=AobjAcoh; Aobj and Acoh are the transmission/reflection area of the object and the coherence area of speckles on the object plane, respectively. From Eq. (11), it is clearly seen that the quality of GI will increase with N and ΔTmin getting larger, and will decrease as the complexity of the scene increases.

Other evaluations of image reconstruction. Similar to common evaluation methods used in traditional imaging or computational imaging, evaluation functions such as mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) with respect to a reference image can be also used to estimate quantitatively the reconstruction fidelity of GI^[122,158]. Taking the visibility of the ghost image into account, the contrast-to-noise ratio (CNR) was developed to estimate the reconstruction quality, based on the fact that the second-order intensity fluctuation inside and outside the area of the object is different^[159]. Currently, it is still a challenge to develop a framework for imaging quality evaluation, universal for different scenarios and independent of the reference image.

As described above, GI has the feature of detection-imaging separation, and the image acquisition is the result of a time-based statistical averaging measurement, which will produce some unique technical advantages. In comparison with traditional imaging, GI shows the following advantages. 1)In the condition of staring detection, high-dimensional imaging can be obtained with the use of a low-dimensional detector. In practical application, when the dimension or bandwidth of the detector is not high enough, we can often achieve higher-dimensional information on the target by means of spatial scanning. For example, a 3D image can be obtained via a lidar with a time-resolved single-pixel detector in the mechanical or electrical scanning mode^[160]. A spectral image can be obtained using an array detector in the push-broom scanning mode^[161]. In order to facilitate signal postprocessing and image fusion, these spatial scanning methods are not only required to be simple and regular, but also the accuracy and reliability of scanning system are required to be relatively high. What is more, it also requires later image correction and registration. However, GI belongs to a staring detection mode using optical spatial random scanning; thus it does not require the process of image correction and registration. In addition, a single measurement for GI contains information on almost all the pixels of the target, so it is easier to obtain the target’s high-dimensional information even if a low-dimensional detector is used^[10,15,16]. For example, GI lidar via coherent detection can obtain the distance, velocity, microvibration, and image information on the target, and can solve the distance–velocity coupling problem of traditional lidar^[37,38]. The spectral image information of the target can be achieved by single-shot GI spectral camera with the use of a common CCD/CMOS^[40]. More than 1012fps (frames per second) four-dimensional imaging can be obtained when a streak camera is adopted^[39]. Infrared and terahertz images can be also achieved with a single-pixel detector^[60,61]. Therefore, lidar, spectral imaging, ultrafast photography, and single-pixel infrared/terahertz imaging based on GI principles promise potential advantages in the field of remote sensing, target recognition, and security inspection.2)Near-field phase imaging ability with an incoherent light source. In comparison with amplitude, the phase of the image usually contains much richer and finer structural information, which is of great significance for microstructure analysis and early medical diagnosis^[162]. In order to obtain the phase information, diffraction imaging is often adopted and a coherent light source is one of the necessary conditions^[163]. For some detection wavebands with important applications, such as X-ray, CT technology that can obtain the amplitude information has been widely used in medical diagnosis because of its strong penetrability and high spatial resolution. However, due to the lack of desktop coherent X-ray sources, X-ray medical phase imaging has always been one of the most difficult problems in the field of the life sciences. Now thanks to the GI technique, the Fourier spectrum of the object can be obtained with incoherent light, even if it is located in the near field of the source^[12,57]. This provides a new approach for X-ray medical phase imaging; thus, a desktop GI-based phase microscopic imager with nanoresolution is expected to be invented.3)High efficiency in information acquisition. Traditional imaging employs a point-to-point sampling mode; therefore it often requires M measurements for an image with M pixels. What is more, in order to save storage space, the obtained images are usually compressed. This means that, in traditional imaging process, compressible images are first sampled. In contrast, a global random measurement mode is adopted by GI, and a single measurement contains information of almost all the pixels from the target^[10,15,16]. Usually, an image with M pixels can be obtained with the measurements N≪M, and the processes of sampling and image compression are simultaneously performed^[122,164]. Therefore, GI can not only save storage space, but also reduce the number of required measurements for image reconstruction or the pixel number of the detector^[79,122]. Moreover, multiplexing encoding can also be performed on different dimensions (such as polarization, spectrum, and temporal domain), which enables the capability of multidimensional information acquisition in parallel^[165–167]. The approach has obvious technical advantages for high-resolution imaging with a large field of view (especially for those detection wavebands where a large-array detector is inaccessible), medical imaging (reducing the radiation dose in medical diagnosis), spectral imaging (enhancing the bandwidth product), and other applications.4)Strong resistance against disturbance. Traditional imaging technology is based on the principle of the first-order correlation of the light field and can only obtain high-quality images when there is no influence from the environment. If the reflected light of the target passes through some harsh environments (such as clouds, fog, haze, smoke, and dust), the point-to-point correspondence between the object plane and the image plane is destroyed, which will lead to dramatic degradation in image quality^[168,169]. However, by exploiting the high-order correlation characteristics of the light field, GI and other related technologies can still reconstruct images against harsh environments, therefore enabling people to see scenes that cannot be seen by traditional imaging technology (for example, heterodyne detection GI lidar working through environment with strong background light^[30,170]; high-resolution GI through scattering media and turbulence^{[20,21,23,24]}; disturbance-free single-pixel imaging via complementary detection^[25]; scattering imaging via memory effect^[26,27]). Therefore, GI technology promises important application prospects in the fields of underwater detection and imaging in foggy weather.5)The above superiorities of GI mainly arise from the ability of parallel encoding and energy collection due to its working mode. On the contrary, drawbacks also arise due to the fact that information about the objects is obtained indirectly via statistical averaging. To achieve images of high quality, GI requires a rather large number of samplings, which slows down the imaging procedure. Since the information is obtained via correlation of fluctuations, the bucket detector is expected to characterize such fluctuations in bucket signals. However, if the object occupies a large number of pixels, the bucket detection will appear as signals of small variance and relatively high mean value. Therefore, a detector of large dynamic range is required. This is why the ghost images usually show up better when taking a CCD camera as the bucket detector, the dynamic range of which is actually expanded using multiple pixels. For experiments using single-photon detectors, which only provide 1-bit signals, estimation over a large sequence of illumination pulses is usually necessary. Therefore, the imaging quality of GI is determined by the ratio between the size of objects and the spatial resolution, the number of samplings, the dynamic range of the bucket detector, etc. In practice, researchers have to find a compromise that considers different factors. Also, new reconstruction algorithms have been developed to relax the requirements on hardware and software.

Comparison between different techniques is usually a main concern, especially when considering practical applications. However, when compared to different techniques, the superiorities or drawbacks appear in different ways, or are even interchanged. People have studied certain cases, but conclusions do not seem to have converged yet.

During the development of GI, researchers were not only interested in the physics, trying to understand how an image is achieved and figure out the outstanding features of GI as discussed above, but were also interested in possible applications of GI. In different fields of application, there are diverse problems to be solved under specific situations.

Toward the permanent goal of imaging, namely, seeing farther, finer and clearer, researchers actually struggle with limited sources and inescapable influences from the environment. The limitation of sources includes the limited energy of illumination, performance of achievable devices, limited sampling time due to motion or other temporal evolution, limited storage space as well as storage for the devices, accessible wavelength, etc. Environmental influence includes factors such as turbulence, scattering, ambient background, and interference between equipment. Based on the principle of GI, and a variety of developed techniques, people will always discover solutions.

In the field of remote sensing, GI lidar contains the possibility of revolutionizing the style and performance of remote detection^[80,92,93]. Traditional lidar provides no spatial resolution within the illumination area. Therefore, only information of one “single-pixel” can be achieved, including the existence, distance, Doppler shift of the target, and so on. To obtain images, beam scanning is necessary. By contrast, GI offers spatial resolution within the illumination area, relaxing the necessity of scanning. However, the information acquisition mode of GI also raises different challenges. Although the image of the target can be achieved, a statistical average is required over a rather large number of samplings. As a result, in earlier realizations, obtaining an image usually takes a long time, while the imaging quality is usually not satisfactory. Therefore, attention must mainly be paid to enhancing imaging speed and quality, except for those on improving working distance and expanding dimensions of information.

To improve the imaging speed of GI, researchers make various effort. By developing pseudo-thermal source of a high refreshing rate, the overall time for a certain number of samplings can be reduced. Furthermore, optical phased array (OPA) techniques were introduced to generate masks at a rate of up to gigahertz^[171,172]. The imaging speed of GI is greatly improved. Our group has also realized OPA-based GI. By optimizing the reconstruction algorithm toward higher efficiency of information extraction, the number of required samplings can be reduced, thus reducing the required time for sampling. Also, the time consumption of data processing can be cut down via algorithm optimization. Further, taking the flexibility of illumination design into account, GI can be carried out in an adaptive way, which is enhanced by relaxing the requirements both on the number of samplings and data processing. To enhance imaging quality, attention is mainly focused on exploring the performance of different designs on illumination patterns, as well as that of reconstruction algorithms. To advance the working distance of sensitivity of GI towards physical and practical limits, imaging with fewer photons is of interest. Investigations on GI from single-photon detection or even undetected signals have been reported. Toward a better understanding of the target, higher-dimensional imaging with GI has been greatly developed with 3D imaging, velocity measurement, Doppler-shift estimation, and so on.

By introducing time-resolved technology to GI lidar, 3D images can be reconstructed by GI lidar^[92]. Combining GI lidar with first-photon imaging technology, 3D imaging can be achievable with 0.01 photons/pixel over 100 km^[87]. With the help of sparsity constraints, superresolution images can be reconstructed by GI lidar^[153]. It not only has the ability of superresolution^{[128,153,173]}, decoupling the mutual restriction between velocity and distance detection^[41,42], but also can obtain microvibration imaging information^{[30,128,170,174]}. Incorporating the physical model of GI into a deep neural network, a far-field superresolution GI with twofold enhancement over the diffraction limit has been achieved^[128]. In addition, as detection distance increases in remote sensing, backscattered signal light becomes weaker, and the influence of ambient light matters more. Additional temporal encoding in the illumination profile is introduced to improve robustness against ambient light and possible cross talk^[28,175]. Further, GI lidar via coherent detection with good anti-background-light performance has been verified at the irradiation SNR lower than −30dB^[30,170]. Moreover, micro-Doppler effect-based vibrating objects were also obtained by GI lidar via coherent detection in 2021^[38]. Then, Liu et al. proposed a coincidence imaging method based on GI to obtain objective different microvibration distributions based on complex target models and time-frequency analysis^[174].

Field tests have also been performed for the progress of practical applications. The first field test of GI GISC was done over a distance of 1.0 km^[80]. Later, another test comparing GI lidar and conventional imaging verifies the advantages of GI lidar under real atmospheric conditions^[82]. From 2016 to 2018, a series of tests on different platforms including balloon-borne, vehicle-borne, and airborne has been reported^[83–85]. In 2020, experiments in tracking and imaging unmanned vehicles were conducted^[87].

In addition, there exist other factors affecting the performance of GI lidar that require intensive study. For instance, turbulence and scattering on the light path, especially that located between the illumination source and the object, will introduce a mismatch between the realized illumination and the recorded patterns on the reference path, causing degradation in imaging quality. Relative motion between the platform and the target also introduces motion blur. Since these concerns are also involved in different fields of research related to imaging under many different scenarios, we choose to discuss them separately in the following subsection.

It is well known that imaging in complex media, such as atmospheric turbulence, atmospheric scattering, underwater and biological tissue scattering, has always been a key problem to overcome in optical imaging applications. GI may provide a new solution to such classic bottleneck problems of traditional imaging methods. Since GI was invented, a series of works has reported that GI can obviously alleviate the disturbance of the medium on the transmission path, especially for the receiving path^{[19,20,22–24,110,176–179]}. Ghost diffraction and GI through atmospheric turbulence^{[19,20,176,177]} and scattering media^[23,24,110] were first discussed. Later, compared with traditional imaging through atmospheric scattering, a model for explaining the intrinsic advantage of GI was built^[22]. Recently, the imaging quality of GI through complex dynamic scattering media has been enhanced via temporal correlation^[178], and bidirectional GI has obtained the object’s image hidden inside strongly scattering media^[180]. Especially in underwater detection, GI with detection distance up to 9.3 attenuation lengths has been demonstrated^[179]. Also, high-resolution imaging and detection for high-speed moving targets is a challenge in remote sensing. By combining spatial coding methods with modern information theory, positioning, tracking, and imaging of moving targets based on GI were invented^{[39,88,89,181–183]}. In 2012, Zhang et al. first demonstrated that the motion blurring can be removed by correcting the intensity distribution recorded by the reference detector in the procedure of image reconstruction^[181]. In order to discover the weak target with fewer measurements, Sun et al. proposed a cross-correlation-based GI to track and image moving objects^[88]. Later, based on mask modulation and single-pixel detection, real-time tracking and imaging of fast-moving objects have also been realized^[182,183]. Recently, when the angular velocity of the moving target is up to 165 mrad/s, simultaneously tracking and imaging have been achieved by a GI system with a four-quadrant detector, and the tracking accuracy can even reach 1/7 of the imaging resolution^[89].

As described above, GI can obtain high-dimensional light-field information with a low-dimensional detector. It can effectively solve the limitations of the performance of traditional detectors and the bandwidth product of information acquisition in practical applications^{[7,184–186]}. For example, as a typical application, high-resolution staring imaging has been extended to the detection wavelength bands where spatially resolving detectors of a large array are inaccessible. Since visible GI with a single-pixel detector was verified by Bromberg^[15], GI in the wavelength band of infrared^{[60,62,100,187]}, terahertz^[61,188,189], microwave^{[155,190,191]}, and X-ray^[12,57–59] has been successively demonstrated. Especially in the field of X-ray microscopy imaging, tabletop X-ray GI and ghost diffraction with ultralow radiation have been realized^[57,59]. Later, an image with a spatial resolution of 10 µm has been achieved with a sampling rate as low as only 18.75% of the Nyquist sampling limit, based on a robust deep-learning algorithm^[129,192]. Recently, even atomic GI^[193,194], electron GI^[26], and neutron GI^[195,196] have been successfully performed, which dramatically promotes the development of particle physics. What is more, similar to traditional imaging approaches, GI schemes for different light-field dimensions, such as temporal GI^[34,36,197], spatial 3D GI^[80,90,92], spectral GI^[40,198,199], polarized GI^[32,167,200], phase GI^[201,202], and panorama GI^[74], have also been proposed. Moreover, by combining spatial modulation with spectral detection/imaging, some techniques such as single-frame wide-field nanoscopy, noninvasive spectral characterization, and ultrafast photography have been developed to improve the imaging SNR, imaging speed, and the capability of high-dimensional information acquisition^{[39,101,203,204]}. For example, by applying a spatial random phase modulator in a wide-field microscope to achieve random measurement of fluorescence signals, a single-frame wide-field nanoscopy based on GI under sparsity constraints has been developed, even reaching the precision of single-molecule localization below 25 nm under an ultrahigh emitter density of 143μm−2^[101]. Also, single-shot hyperspectrally compressed ultrafast photography enables simultaneous recording of the spatial, temporal, and spectral information of objects^[39].

GI uses high-order correlation of light fields to achieve high-dimensional information with low-dimensional detection. The introduction of encoding and decoding of high-dimensional light-field information in GI enables joint use of optics and data-processing and also opens a way of combining optical imaging with modern information sciences to achieve optimal perception under the framework of information theory^[205]. Researchers realized very recently that study from the view of information theory in order to construct a general framework of image acquisition will lead and extend GI into a quite broader and deeper range, both in terms of theory and application. However, the information theory of GI is far from complete. It is necessary to construct an accurate and universal optimal estimation framework for GI with information theory, giving a quantitative description of the performance of the imaging system and evaluating the imaging results without reference. Therefore, limitation and capability of information carrying and acquisition will be clearer, especially under photon-limited conditions. Universal objective methods for optimization of encoding and decoding toward better performance will also be possible. In addition, by introducing the booming quantum method and quantum parameter estimation theory^[206,207], GI is expected to return to quantum imaging and explore new quantum phenomena. Since “Rayleigh’s curse,” induced by the diffraction effect in GI still exists^[208], whether it is possible to break it, especially for continuous scenes, will be of great interest. Moreover, combining the practical advantage of quantum technology, such as quantum machine learning^[209], is also a challenging topic.

In terms of imaging performance optimization, with the rapid developments of new light-field modulation technology (such as metasurfaces^[210–212]), computing power resources, and more excellent photodetection devices, it is challenging to construct a performance optimization universal strategy for GI with different devices, computing powers, and application constraints. With artificial intelligence^{[127–129,213]}, how to design suitable GI also needs further exploration. In addition, in order to further promote the development of GI, it is necessary to quantitatively analyze the advantages and disadvantages of GI technology in various applications and complete several typical application demonstrations, including remote sensing, underwater and astronomical detection, and microscopy. Although there has been some discussion in recent years^{[22,186,214–218]}, GI still needs further analysis, especially considering specific engineering problems. Although GI has been extended to biological imaging, remote sensing, and other applications in recent years, how to use the characteristics of modulation and demodulation in GI to carry out task-driven nonimaging GI detection research is still in the ascendant.

No matter what kinds of practical applications are considered, common challenges lie in the pursuit of extreme performance, including issues related to high-dimensional information fusion and reconstruction, multidimensional encoding and detection, new modulation devices with higher speed and higher dimensions, large field-of-view imaging with high speed and high resolution (more than megapixels), and high-quality image reconstruction in low-detection SNR. In addition, as a way for information acquisition, novel detection methods based on correlation, such as high-accuracy tracking and positioning without imaging, ptychographic microscopy, are also promising.