Abstract

We generalize the theory of ghost scattering with scalar incoherent light sources to the case of stochastic electromagnetic beams under the first-order Born approximation. We derive the expressions for the correlation of intensity fluctuations of the far-zone scattered fields and use them to study the properties of the scatterers. When the incident beam belongs to the class of electromagnetic Gaussian Schell-model beams, we discuss the dependence of ghost scattering results on the parameters such as the coherence lengths, source widths, polarization amplitudes, and degree of coherence. We find under the condition of linear polarized incident beams the scalar ghost scattering results can be retrieved, while the deviation from linear polarization may significantly distort the electromagnetic ghost scattering results.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Light scattering can be used to study a lot of phenomena related to the interaction of light waves with materials, and has been treated in Ref [16] in great detail. Many other aspects of the application of light scattering also have been actively investigated, such as in particle characterization [7], material analysis [8], atmospheric optics [9], nanometer optics [10], condensed matter physics [11], physical chemistry [12], biomedicine [13], and astrophysics [14]. Further development of novel light scattering techniques is important since it can provide new diagnostic methods in different research fields.

Recently, based on the idea of ghost imaging, we have proposed a kind of ghost scattering scheme to study light scattering with either scalar incoherent light fields or biphoton quantum states [15,16]. Ghost imaging is a kind of nonlocal and indirect imaging technique. One can use the spatial correlation properties of fluctuating light fields (either thermal or entangled) to retrieve the information of the object via spatial intensity correlation measurements between two spatially correlated light beams (the reference beam and the test beam) [1728]. Ghost imaging has attracted noteworthy interest and stimulated lots of studies, such as methods to improve imaging quality [2938], and imaging through different circumstance [3949].

In our ghost scattering scheme, we replace the objects in the GI scheme with scatterers and place the detectors far from the scatterers, then we perform nonlocal correlation measurement of the far-zone intensity fluctuations in the test and reference scattering paths. We can obtain the scattering information of the test scatterer in the reference arm with the help of a fixed point like detector in the test arm, just like the case in GI. Since the nature of light fields is vector electromagnetic fields, it is interesting to study the influence of the polarization properties of the incident light fields on the behavior of ghost scattering. In the past decades, the unified theory of coherence and polarization of random electromagnetic fields has been established [50], and the propagation and scattering properties of stochastic electromagnetic beams have been widely investigated [5159]. With the help of the weak scattering theory of stochastic electromagnetic beams [1], the aim of this paper is to generalize the scalar ghost scattering theory with classically incoherent light fields to the case of stochastic electromagnetic beams.

The paper is organized as follows. In section 2, under the first-order Born approximation of stochastic electromagnetic beams scattering, we present the ghost scattering model and derive the expressions for the correlation of intensity fluctuations of the far-zone scattered fields, showing how the scattering information of the test scatterer can be obtained from the measurement in the reference arm. Then in section 3, we provide numerical examples of ghost scattering with the so called stochastic electromagnetic Gaussian Schell-model (EMGS) beams and discuss the influences of polarization properties and other parameters on the ghost scattering results. Finally, conclusions are given in section 4.

2. Model and theory

The electromagnetic ghost scattering model is shown in Fig. 1, which is very similar as the ghost scattering model with scalar incoherent fields [15] except the source is replaced by a stochastic electromagnetic beam. A stochastic electromagnetic beam is split by a beam splitter into two beams which are propagating in two different paths called as test path and reference path. In the test path, an unknown test scatterer with the refractive index distribution $n(\vec {r}_a)$ is illumined and the scattered field is detected by a point-like detector $D_t$ located at the far-zone position $\vec {r}_1$. In the reference path, we place a known object with the refractive index distribution $n(\vec {r}_b)$ as a reference scatterer, and measure the scattered fields from this scatterer via a point-like detector $D_r$ fixed at the far-zone position $\vec {r}_2$. Experimentally, $D_t$ can be scanned over the space, and $D_r$ also can be changed. The scattering intensity signals recorded in $D_t$ and $D_r$ are correlated by a correlator to obtain the correlation of intensity fluctuations (CIF). We will derive the formula of CIF under the weak scattering condition and show that the scattering information of the unknown test scatterer can be retrieved from it.

 

Fig. 1. Geometry of the electromagnetic ghost scattering model. An incident stochastic electromagnetic beam is split into two beams by the beam splitter (BS). An unknown test scatterer is illuminates by one of the beams and the far-zone scattered fields are detected by the test detector $D_t$ located at $\vec {r}_1$. The other beam is scattered by a reference scatterer and considered as a reference beam, with the far-zone scattered fields detected by the reference detector $D_r$ located at $\vec {r}_2$. The scattered signals measured by the test and reference detector $D_t$ and $D_r$ are further processed by the correlator to realize ghost scattering.

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From the vector electromagnetic scattering theory [1], for a quasi-monochromatic vector incident field (centered at wavelength $\lambda$) $\vec {E}^i(\vec {r}_0)=\begin {bmatrix} \vec {E}^i_x & \vec {E}^i_y & \vec {E}^i_z \\ \end {bmatrix}^T$ and the scatterer refractive index distribution $n(\vec {r}_0)$ within the region $V$, under the first-order Born approximation, the far-zone scattered field $\vec {E}^s(\vec {r})$ has the form,

$$\vec{E}^s(\vec{r}) = \frac{e^{jkr}}{r} \int_V d^3 r_0 F(\vec{r}_0)e^{-jk\hat{s}\cdot\vec{r}_0} \overleftrightarrow{S^{(3)}}(\hat{s}) \vec{E}^i(\vec{r}_0) ,$$
where the wave number $k=\frac {2\pi }{\lambda }$, $\vec {r}=r\hat {s}$ with $\hat {s}$ the unit direction vector (in the spherical coordinator, $[s_x, s_y, s_z]=[\sin \theta \cos \phi , \sin \theta \sin \phi , \cos \theta ]$), $F(\vec {r}_0)$ is the scattering potential given by the refractive index distribution
$$F(\vec{r}_0)=\left\{ \begin{array}{cc} \frac{1}{4\pi}k^2[n^2(\vec{r}_0)-1], & \vec{r}_0 \in V \\ 0, & \vec{r}_0 \notin V \\ \end{array} \right.$$
and $\overleftrightarrow {S^{(3)}}$ is a matrix
$$\overleftrightarrow{S^{(3)}}(\hat{s})= \begin{bmatrix} 1-s_x^2 & -s_x s_y & -s_x s_z \\ -s_x s_y & 1-s_y^2 & -s_y s_z \\ -s_x s_z & -s_y s_z & 1-s_z^2 \\ \end{bmatrix} ,$$
From the unified theory of polarization and coherence [50], one can describe a stochastic electromagnetic field by its cross-spectral density matrix at a pair of points $\vec {r}_1$ and $\vec {r}_2$
$$\overleftrightarrow{\mathbf{W}}^s(\vec{r}_1,\vec{r}_2)=\left[\mathbf{W}^s_{\alpha,\beta}(r_1\hat{s}_1,r_2\hat{s}_2)\right] =\left[\langle E^{s*}_{\alpha}(r_1\hat{s}_1)E^s_{\beta}(r_2\hat{s}_2)\rangle\right] ,$$
where $\alpha =x,y,z$, $\beta =x,y,z$, and $\langle \cdots \rangle$ represents the ensemble average.

Now, considering the ghost scattering scheme, we are interested with the correlation matrix of intensity fluctuation ($\overleftrightarrow {\mathbf {G}}$) between the scattered field from the reference scatterer and the test scatterer. The components of $\overleftrightarrow {\mathbf {G}}$ take the form

$$ \mathbf{G}_{\alpha,\beta}(r_1\hat{s}_1,r_2\hat{s}_2)=\langle \Delta I^s_{t,\alpha}(r_1\hat{s}_1)\Delta I^s_{r,\beta}(r_2\hat{s}_2)\rangle ,$$
where $\Delta I^s_{p,\alpha }(r\hat {s})= E^{s*}_{p,\alpha }(r\hat {s})E^s_{p,\alpha }(r\hat {s}) -\langle E^{*s}_{p,\alpha }(r\hat {s})E^s_{p,\alpha }(r\hat {s})\rangle$ are the scattering intensity fluctuation ($p=r,t$ for different paths and $\alpha =x,y,z$ for different electric field components).

Experimentally often the total intensity is measured, $I_t(\vec {r})=I_x(\vec {r})+I_y(\vec {r})+I_z(\vec {r})$, then the corresponding correlation of intensity fluctuation (CIF) is given by

$$\mathbf{C}(r_1\hat{s}_1,r_2\hat{s}_2)=\langle \Delta I^s_{t}(r_1\hat{s}_1)\Delta I^s_{r}(r_2\hat{s}_2)\rangle =\sum_{\alpha,\beta}\mathbf{G}_{\alpha,\beta}(r_1\hat{s}_1,r_2\hat{s}_2) .$$
Since the stochastic electromagnetic fields obey the Gaussian statistics [50], from the moment theorem of the complex Gaussian random process, we have
$$\mathbf{G}_{\alpha,\beta}(r_1\hat{s}_1,r_2\hat{s}_2) =\left|\langle E^{s*}_{t,\alpha}(r_1\hat{s}_1)E^s_{r,\beta}(r_2\hat{s}_2)\rangle \right|^2 =\left|\mathbf{W}^{s}_{t\alpha,r\beta}(r_1\hat{s}_1,r_2\hat{s}_2) \right|^2 .$$
Based on the scattering integral Eq. (1), the far-zone cross-spectral density matrix has the form
$$\begin{aligned}\mathbf{W}^{s}_{t\alpha,r\beta}(r_1\hat{s}_1,r_2\hat{s}_2) &=\frac{e^{-jkr_1+jkr_2}}{r_1r_2} \int_V d^3 r_a d^3 r_b F^{*}_t(\vec{r}_a)F_r(\vec{r}_b)e^{jk\hat{s}_1\cdot\vec{r}_a-jk\hat{s}_2\cdot\vec{r}_b} \\ & \quad\times \sum_{\alpha'\beta'} S^{(3)}_{\alpha\alpha'}(\hat{s}_1)S^{(3)}_{\beta\beta'}(\hat{s}_2)\langle E^{i*}_{\alpha'}(\vec{r}_a)E^{i}_{\beta'}(\vec{r}_b)\rangle,\end{aligned}$$
then we obtain the relation between the scattered field and the incident electromagnetic stochastic beam as
$$\overleftrightarrow{\mathbf{G}}(r_1\hat{s}_1,r_2\hat{s}_2) =C_0 \left|\int_V d^3 r_a d^3 r_b F^{*}_t(\vec{r}_a)F_r(\vec{r}_b)e^{jk\hat{s}_1\cdot\vec{r}_a-jk\hat{s}_2\cdot\vec{r}_b} \overleftrightarrow{S^{(3)}}(\hat{s}_1) \overleftrightarrow{\mathbf{W}}^i(\vec{r}_a,\vec{r}_b) \overleftrightarrow{S^{(3)}}^T(\hat{s}_2)\right|^2 ,$$
with $C_0$ a constant coefficient. From Eq. (5) it is clear to see that the CIF contains the scattering potential information and can be used to study the scatterer.

The electromagnetic wave is a kind of transverse waves, so that in the spherical coordinator the far-zone scattered fields only have two components $E^s_{\theta }$ and $E^s_{\phi }$. Suppose the incident beam propagates along z direction and has no z component ($E_z^i=0$), under the weak scattering condition, the far-zone scattered field has the form [1]

$$\vec{E}^s(\vec{r}) = \frac{e^{jkr}}{r} \int_V d^3 r_0 F(\vec{r}_0)e^{-jk\hat{s}\cdot\vec{r}_0}\overleftrightarrow{S^{(2)}}(\hat{s}) \vec{E}^i(\vec{r}_0) ,$$
in which $\vec {E}^i(\vec {r}_0)=\begin {bmatrix} \vec {E}^i_x & \vec {E}^i_y \\ \end {bmatrix}^T$, $\vec {E}^s(\vec {r})=\begin {bmatrix} \vec {E}^s_{\theta } & \vec {E}^s_{\phi } \\ \end {bmatrix}^T$, and the matrix
$$ \overleftrightarrow{S^{(2)}}(\hat{s})= \begin{bmatrix} \cos(\theta)\cos(\phi) & \cos(\theta)\sin(\phi) \\ -\sin(\phi) & \cos(\phi) \\ \end{bmatrix},$$
then the far-zone correlation matrix of intensity fluctuation is a $2\times 2$ matrix $\mathbf {G}_{mn}$ (with $m,n=\theta ,\phi$) and takes the form
$$\overleftrightarrow{\mathbf{G}}(r_1\hat{s}_1,r_2\hat{s}_2)= C_0\left|\int_V d^3 r_a d^3 r_b F^{*}_t(\vec{r}_a)F_r(\vec{r}_b)e^{jk\hat{s}_1\cdot\vec{r}_a-jk\hat{s}_2\cdot\vec{r}_b} \overleftrightarrow{S^{(2)}}(\hat{s}_1)\overleftrightarrow{\mathbf{W}}^i(\vec{r}_a,\vec{r}_b) \overleftrightarrow{S^{(2)}}^T(\hat{s}_2) \right|^2 .$$
To make a comparison with the scalar ghost scattering theory [15], let’s consider only the two dimensional scatterers $F(\vec {\rho })$ (with $\vec {\rho }=\left [x,y\right ]$). For the two dimensional test and reference scatterer located at $z_a$ and $z_b$, the far-zone correlation matrix of intensity fluctuation can be simplified as
$$\overleftrightarrow{\mathbf{G}}(r_1\hat{s}_1,r_2\hat{s}_2) =\left| \overleftrightarrow{S^{(2)}}(\hat{s}_1) \begin{bmatrix} \widetilde{\mathbf{F}}_{xx}(k\hat{s}_{\perp1},k\hat{s}_{\perp2}) & \widetilde{\mathbf{F}}_{xy}(k\hat{s}_{\perp1},k\hat{s}_{\perp2}) \\ \widetilde{\mathbf{F}}_{yx}(k\hat{s}_{\perp1},k\hat{s}_{\perp2}) & \widetilde{\mathbf{F}}_{yy}(k\hat{s}_{\perp1},k\hat{s}_{\perp2}) \\ \end{bmatrix}\overleftrightarrow{S^{(2)}}^T(\hat{s}_2) \right|^2 ,$$
in which $\hat {s}_{\perp }=\left [s_x,s_y\right ]$ and $\widetilde {\mathbf {F}}_{\alpha \beta }(k\hat {s}_{\perp 1},k\hat {s}_{\perp 2})$ relates to $\mathbf {W}^i_{\alpha \beta }(\vec {\rho }_a,\vec {\rho }_b)= \mathbf {W}^i_{\alpha \beta }(\vec {\rho }_a,z_a,\vec {\rho }_b,z_b)$ through the transform
$$\widetilde{\mathbf{F}}_{\alpha\beta}(k\hat{s}_{\perp1},k\hat{s}_{\perp2}) =\int_V d^2 \rho_a d^2 \rho_b e^{jk\hat{s}_{\perp1}\cdot\vec{\rho}_a-jk\hat{s}_{\perp 2}\cdot\vec{\rho}_b} F^{*}_t(\vec{\rho}_a)F_r(\vec{\rho}_b){\mathbf{W}}^i_{\alpha\beta}(\vec{\rho}_a,\vec{\rho}_b) .$$
As in the case of scalar ghost scattering, suppose the incident field is x-polarized, only ${\mathbf {W}}^0_{xx}\neq 0$, then the CIF is
$$\begin{aligned}\mathbf{C} &= C_0 \left[(\cos\theta_1\cos\phi_1\cos\theta_2\cos\phi_2)^2+(\cos\theta_1\cos\phi_1\sin\phi_2)^2\right.\\ &\quad\left.+(\sin\phi_1\cos\theta_2\cos\phi_2)^2 +(\sin\phi_1\sin\phi_2)^2\right] \left|\widetilde{\mathbf{F}}_{xx}\right|^2 .\end{aligned}$$
Under the paraxial approximation $\cos \theta \sim 1$, so that $\mathbf {C}\sim \left |\widetilde {\mathbf {F}}_{xx}\right |^2$, the scalar ghost scattering formula in Ref. [15] is retrieved from the present electromagnetic ghost scattering theory. It is also very clear to see that at the large scattering angles, even linearly polarized ghost scattering may lead to deviation from the case of scalar theory.

From Eq. (13), we can see that the scattering properties of the scatterers are contained in the 4 different $\widetilde {\mathbf {F}}_{\alpha \beta }$. Due to the statistical correlation of the stochastic electromagnetic fields, these $\widetilde {\mathbf {F}}_{\alpha \beta }$ may be different each other. Including the angle dependent factors $\overleftrightarrow {S^{(2)}}$, the CIF in the electromagnetic ghost scattering may be very complicated and the ghost scattering results may be modified.

Finally, we briefly discuss the differences between our work and the theory of ghost imaging with electromagnetic stochastic beams in Ref. [60]. Since we are concerned with light scattering in the far-zone, the free-space outgoing Green’s function is approximated by the simple form of $\frac {e^{jkr}}{r}e^{-jk\hat {s}\cdot \vec {r}_0}$ in Eq. (1) (see Eqs. (2.10) and (5.2) in Ref. [1]). It is this $\hat {s}\cdot \vec {r}_0$ term leading to the Fourier transform like formulas in Eqs. (11,12). On the other hand, for ghost imaging, the Green’s function in the paraxial region can be simplified as the Fresnel diffraction, leading to the response functions (Eqs. (8,9)) in Ref. [60]. Thus our results on ghost scattering are different with the case of ghost imaging.

3. Numerical examples

Now, we use numerical examples to demonstrate the electromagnetic ghost scattering properties. To be compared with the case of scalar ghost scattering, we choose a 8-rectangle scatterer shown in Fig. 2(a) as the test scatter, which has been used in Ref. [15]. The reference scatterer is assumed to be a uniformly transmissive plane, i.e., $F_r\propto 1$. The wavelength used in calculations is set to be $\lambda =632$ nm. The distances from the source to the test scatterer and reference scatterer are the same value 100mm. The parameters of the incident electromagnetic Gauss-Schell model beams are varied to see how these factors can affect the behavior of electromagnetic ghost scattering. In following figures, the length unit is mm, and the frequency unit is $k=2\pi /\lambda$. The incident stochastic field along the Z direction is supposed to be described by the electromagnetic Gauss-Schell model (EMGS) beam [50], with the cross-spectral density matrix in the source plane ($z_1=z_2=0$) given by

$$\mathbf{W}^0_{\alpha,\beta}(\vec{\rho}_1,\vec{\rho}_2) =\sqrt{S^0_{\alpha}(\vec{\rho}_1)}\sqrt{S^0_{\beta}(\vec{\rho}_2)}\mu^0_{\alpha \beta}(\vec{\rho}_1-\vec{\rho}_2) ,$$
in which $\vec {\rho }_1,\vec {\rho }_2$ are transverse coordinators, $\alpha ,\beta =x,y$ correspond to the polarization. In this equation, $S^0_{\alpha }(\vec {\rho })=\mathbf {W}^0_{\alpha ,\alpha }(\vec {\rho },\vec {\rho })$ is the spectral density, and $\mu ^0_{\alpha \beta }(\vec {\rho }_1-\vec {\rho }_2)$ is the spectral degree of coherence. Both of them are Gaussian functions, i.e.,
$$S^0_{\alpha}(\vec{\rho})= A^2_{\alpha}\exp\left(-\frac{|\vec{\rho}|^2}{2\sigma^2_{\alpha}}\right),$$
$$\mu^0_{\alpha \beta}(\vec{\rho}_1-\vec{\rho}_2)= B_{\alpha \beta}\exp\left(-\frac{|\vec{\rho}_1-\vec{\rho}_2|^2}{2\delta^2_{\alpha \beta}}\right),$$
then from Ref. [50], we know the cross spectral density matrix at the scatterers ($z_a=z_b=z=100$ mm) under the condition $\sigma _x=\sigma _y=\sigma$ (the correlated parameters can be set as $B_{xx}=B_{yy}=1$, $B_{xy}=B_{yx}\le 1$),
$$\overleftrightarrow{\mathbf{W}}^i(\vec{\rho}_a,\vec{\rho}_b)_{\alpha \beta} =\frac{A_{\alpha} A_{\beta} B_{\alpha \beta}}{\Delta^2_{\alpha \beta}(z)} \exp\left[-\frac{|\vec{\rho}_a+\vec{\rho}_b|^2}{8\sigma^2\Delta^2_{\alpha \beta}(z)}\right] \exp\left[-\frac{|\vec{\rho}_a-\vec{\rho}_b|^2}{2\Omega^2_{\alpha \beta}\Delta^2_{\alpha \beta}(z)}\right] \exp\left[-\frac{ik(\rho^2_b-\rho^2_a)}{2R_{\alpha \beta}(z)}\right] ,$$
in which
$$\begin{aligned} \frac{1}{\Omega^2_{\alpha \beta}}&=\frac{1}{4\sigma^2}+\frac{1}{\delta^2_{\alpha \beta}} , \nonumber \\ \Delta^2_{\alpha \beta}(z)&= 1+\left(\frac{z}{k\sigma\Omega_{\alpha \beta}}\right)^2 , \nonumber \\ R_{\alpha \beta}(z)&= \left[1+\left(\frac{k\sigma\Omega_{\alpha \beta}}{z}\right)^2\right]z.\end{aligned}$$

 

Fig. 2. (a)The two dimensional test scatterer $F_t(x,y)$ used in numerical simulations, length unit in mm. (b) The corresponding spatial spectrums of (a) shown as the ideally scattering distribution. (c) The calculated DSP with the parameters $A_x=1$, $A_y=0.5$, $B_{xy}=0.3$, $\sigma =20$, $\delta _{xx}=5\times 10^{-4}$, $\delta _{xy}=7.5\times 10^{-4}$, $\delta _{yy}=6\times 10^{-4}$. (d) The calculated GSP with the same parameters in (c). (e) The calculated GSP with the parameters used in (c) except $\delta _{xy}=17.5\times 10^{-4}$, $\delta _{yy}=26\times 10^{-4}$, corresponding to the case of very different coherence lengths. (f) The normalized $s_x$ axial distributions in (c,d,e), corresponding to the blue solid, red dashed, and black dotted lines respectively.

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Based on these equations, we can numerically calculate the results of electromagnetic ghost scattering and discuss the effects of different parameters such as the coherence lengths $\delta _{\alpha \beta }$, beam widths $\sigma$, polarization amplitudes $A_{x,y}$, and degree of coherence $B_{xy}$. From Eqs. (5,12,13), the CIF is the function of both $\hat {s}_{\perp 1}$ in the test path and $\hat {s}_{\perp 2}$ in the reference path. As in Ref. [15], we define two kinds of ghost scattering outputs, the ghost scattering pattern (GSP) and the direct scattering pattern (DSP). The GSP is $I_G(s_{rx},s_{ry})=\mathbf {C}(r_1\hat {s}_{\perp 1}=(0,0),r_2\hat {s}_{\perp 2}=r_2(s_{rx},s_{ry}))$ corresponding to the correlation between the scattered field in the test path detected only at the forward direction ($\hat {s}_{\perp 1}=(0,0)$) and the arbitrary scattered fields scanned in the reference path $(s_{rx},s_{ry})$, so that the output seems to be emerged from the reference path in which contains no test scatterers to be studied. Similarly, the DSP is $I_D(s_{tx},s_{ty})=\mathbf {C}(r_1\hat {s}_{\perp 1}=r_1(s_{tx},s_{ty}),r_2\hat {s}_{\perp 2}=(0,0))$, and the output can be intuitively regarded as the results in the direct scattering configuration contains the test scatterer.

Firstly, in Fig. 2(a,b), we plot the test scatterer and its spectrum. Then in Fig. 2(c) we show that the DSP is quite similar as the ideal spectrum under the used parameters, while the GSP in Fig. 2(d) is degraded with the outer tiny structures suppressed. Here, the coherent lengths are very similar ($\delta _{xx}=5\times 10^{-4}$ mm, $\delta _{xy}=7.5\times 10^{-4}$ mm, $\delta _{yy}=6\times 10^{-4}$ mm), so that the changes of $\widetilde {\mathbf {F}}_{\alpha \beta }$ in Eq. (13) may be not very obvious, then the main structures are similar as the scalar cases in Ref. [15]. However, when $\delta _{\alpha \beta }$ are very different from each other, $\widetilde {\mathbf {F}}_{\alpha \beta }$ may have noticeable changes, then the GSP obtained from the combinations in Eq. (5) should be degraded. As shown in Fig. 2(e), with $\delta _{xx}=5\times 10^{-4}$ mm, $\delta _{xy}=17.5\times 10^{-4}$ mm, $\delta _{yy}=26\times 10^{-4}$ mm, the GSP deviates from the scalar case significantly. In Fig. 2(f), we plot the $s_x$ axial distributions in Fig. 2(c,d,e) to see their differences more clearly. The DSP is more accurate compared with the ideal spectrum because the output is measured in the direct test path. The GSP with similar $\delta _{\alpha \beta }$ is degraded to some degree, while the very different $\delta _{\alpha \beta }$ lead to significant distortion of the ghost scattering results.

Now we know the coherent lengths $\delta _{\alpha \beta }$ can affect the electromagnetic ghost scattering. In Fig. 3, we choose two sets of coherent length parameters (very similar and very different $\delta _{\alpha \beta }$), then change other parameters to see the dependence of GSPs on the amplitude $A_{x,y}$, the degree of coherence parameter $B_{xy}$, and the beam width parameter $\sigma$. For simplicity, we set $A_x=1$.

 

Fig. 3. Normalized GSP $I_G(s_{x},0)$ to see the effects of parameters $A_y$, $B_{xy}$ and $\sigma$ on electromagnetic ghost scattering, with $A_x=1$. The coherence lengths in the left figures (a,c,e) are $\delta _{xx}=5\times 10^{-4}$, $\delta _{xy}=7.5\times 10^{-4}$, $\delta _{yy}=6\times 10^{-4}$, and in the right figures (b,d,f) are $\delta _{xx}=5\times 10^{-4}$, $\delta _{xy}=17.5\times 10^{-4}$, $\delta _{yy}=26\times 10^{-4}$. (a,b) $s_x$ axial distributions with $A_y=0$, 0.25, 0.5, 1, corresponding to the black dotted, red dashed, blue dash-dot, and magenta solid curves, $B_{xy}=0.3$, $\sigma =20$. (c,d) $s_x$ axial distributions with $B_{xy}=0.1$, 0.3, 0.6, 0.9, corresponding to the black dotted, red dashed, blue dash-dot, and magenta solid curves, $A_{y}=0.5$, $\sigma =20$. (a,b) $s_x$ axial distributions with $\sigma =5$, 10, 20, 50, corresponding to the black dotted, red dashed, blue dash-dot, and magenta solid curves, $A_y=0.5$, $B_{xy}=0.3$.

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In Fig. 3(a,b), $A_{y}$ is varied from $A_y/A_x=0$ to $A_y/A_x=1$. In the case of similar $\delta _{\alpha \beta }$, the GSPs have almost the same distributions (Fig. 3(a)) because $\widetilde {\mathbf {F}}_{\alpha \beta }$ have similar distributions so that the combinations from Eq. (5) only lead to very tiny and almost unobservable differences in this figure. But for very different $\delta _{\alpha \beta }$, $A_{y}=0$ leads to the best behavior of the scattering distribution since only the most accurate component $\widetilde {\mathbf {F}}_{xx}$ affects the GSP and the other two worse components are not included in the CIF. When $A_y$ increases, the influences of $\widetilde {\mathbf {F}}_{xy}$ and $\widetilde {\mathbf {F}}_{yy}$ will be more and more important, so that the quality of GSPs will be degraded (Fig. 3(b)).

The findings in Fig. 3(c,d) can be understood with the similar discussions. Now, the changes of $B_{xy}$ only changes the influences of $\widetilde {\mathbf {F}}_{xy}$ in Eq. (5) in Eq. (5), and the contributions from $\widetilde {\mathbf {F}}_{xx}$ and $\widetilde {\mathbf {F}}_{yy}$ are fixed, so that the variations in Fig. 3(d) is relatively small. Further we find the larger $B_{xy}$ corresponding to the better GSP, which can be interpreted from the fact that $\delta _{xy}$ is smaller than $\delta _{yy}$, making $\widetilde {\mathbf {F}}_{xy}$ better than $\widetilde {\mathbf {F}}_{yy}$, so that the increase of $B_{xy}$ will increase the contribution of the relatively accurate component $\widetilde {\mathbf {F}}_{xy}$ in the GSPs, as shown in Fig. 3(d).

Finally, in Fig. 3(e,f), we compare the results with different beam widths. Here, for similar $\delta _{\alpha \beta }$ in Fig. 3(e), the larger $\sigma$ leads to the better scattering distribution, similar as the results in the scalar ghost scattering. On the other hand, in Fig. 3(f), the curves with different $\sigma$ are very similar and highly degraded. This can be understood from the observation that these very different $\delta _{\alpha \beta }$ already lead to the significant suppression of the scattering distributions so that the further influences from the change of $\sigma$ are not important.

4. Conclusion

In conclusion, we have derived general expressions of ghost scattering with stochastic electromagnetic fields under the first-order Born approximation. With the help of these formulas, using the stochastic electromagnetic Gaussian Schell-model beam as the incident field, we have numerically obtained the far-zone correlation of scattering intensity fluctuations and demonstrated the electromagnetic ghost scattering properties. We have discussed how the polarization properties and other parameters of the incident EMGS beams can modify the ghost scattering results compared with the early investigated scalar cases. If the coherence lengths of different components in the cross-spectral density matrix of the EMGS beam are very different, the ghost scattering patterns may be significantly degraded. We can retrieve the scalar ghost scattering theory under the conditions of linear polarization and paraxial approximation.

Funding

National Natural Science Foundation of China (NSFC) (11774097).

Acknowledgments

The authors thank the supports from the National Natural Science Foundation of China (11774097).

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10. J. M. Geffrin et al., “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012). [CrossRef]  

11. S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013). [CrossRef]  

12. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B , 107(3), 668–677 (2003). [CrossRef]  

13. P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006). [CrossRef]  

14. B. Draine, “Discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]  

15. J. Cheng, “Theory of ghost scattering with incoherent light,” Phys. Rev. A 93(4), 043808 (2016). [CrossRef]  

16. J. Cheng, “Theory of ghost scattering with biphoton states,” Photon. Res. 5(1), 41–45 (2017). [CrossRef]  

17. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2(4), 405–450 (2010), [CrossRef]   and references therein.

18. J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004). [CrossRef]  

19. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004). [CrossRef]  

20. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005). [CrossRef]  

21. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005). [CrossRef]  

22. D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30(18), 2354–2356 (2005). [CrossRef]  

23. G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006). [CrossRef]  

24. L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006). [CrossRef]  

25. M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A , 75(2), 021803 (2007). [CrossRef]  

26. J. Cheng and S. Han, “Classical correlated imaging from the perspective of coherent-mode representation,” Phys. Rev. A 76(2), 023824 (2007). [CrossRef]  

27. J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78(4), 043823 (2008). [CrossRef]  

28. B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A , 77(4), 043809 (2008). [CrossRef]  

29. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009). [CrossRef]  

30. Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009). [CrossRef]  

31. M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013). [CrossRef]  

32. C. L. Luo and J. Cheng, “Ghost imaging with shaped incoherent sources,” Opt. Lett. 38(24), 5381 (2013). [CrossRef]  

33. C. L. Luo, H. H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-Gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015). [CrossRef]  

34. D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015). [CrossRef]  

35. H. Yu, E. R. Li, W. L. Gong, and S. S. Han, “Structured image reconstruction for three-dimensional ghost imaging lidar,” Opt. Express 23(11), 14541–14551 (2015). [CrossRef]  

36. M. I. Akhlaghi and A. Dogariu, “Compressive correlation imaging with random illumination,” Opt. Lett. 40(19), 4464–4467 (2015). [CrossRef]  

37. L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photon. Res. 4(6), 240–244 (2016). [CrossRef]  

38. Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017). [CrossRef]  

39. R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A , 77(4), 041801 (2008). [CrossRef]  

40. J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009). [CrossRef]  

41. N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84(6), 063824 (2011). [CrossRef]  

42. P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

43. R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012). [CrossRef]  

44. B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013). [CrossRef]  

45. J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87(4), 043810 (2013). [CrossRef]  

46. D. Duan and Y. J. Xia, “Real-time pseudocolor coding thermal ghost imaging,” J. Opt. Soc. Am. A 31(1), 183 (2014). [CrossRef]  

47. H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016). [CrossRef]  

48. D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016). [CrossRef]  

49. Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018). [CrossRef]  

50. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

51. O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E , 75(5), 056609 (2007). [CrossRef]  

52. S. Sahin and O Korotkova, “Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation,” Opt. Lett. 34(12), 1762–1764 (2009). [CrossRef]  

53. Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A , 82(3), 033836 (2010). [CrossRef]  

54. T. Wang and D. Zhao, “Scattering theory of stochastic electromagnetic light waves,” Opt. Lett. 35(14), 2412–2414 (2010). [CrossRef]  

55. Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015). [CrossRef]  

56. X. Wang, Z. Liu, K. Huang, and D. Zhu, “Spectral changes of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry scattered on a deterministic medium,” J. Opt. Soc. Am. A 33(10), 1955–1960 (2016). [CrossRef]  

57. X. Chen and O. Korotkova, “Probability density functions of instantaneous Stokes parameters on weak scattering,” Opt. Commun. 400, 1–8 (2017). [CrossRef]  

58. Y. Ding and D. Zhao, “Correlation between intensity fluctuations of polychromatic electromagnetic light waves on weak scattering,” Phys. Rev. A 97(2), 023837 (2018). [CrossRef]  

59. X. Peng, J. Li, and L. Chang, “Evolution properties of polarization states of far-zone electromagnetic field scattered from an anisotropic medium,” Opt. Express 26(6), 6679–6691 (2018). [CrossRef]  

60. Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010). [CrossRef]  

References

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  1. D. Zhao and T. Wang, “Direct and Inverse Problems in the Theory of Light Scattering,” In E. Wolf ed., Progress in Optics, Vol. 57, 261–308 (Elsevier, 2012).
  2. M. Born and E. Wolf, Principles of Optics, Ch. 13, (Cambridge University Press, 1999).
  3. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, (John Wiley and Sons, 2000).
  4. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small particles, (Cambridge University Press, 2002).
  5. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd ed. (Springer-Verlag, 2006).
  6. H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981).
  7. R. Xu, “Light scattering: A review of particle characterization applications,” Particuology 18, 11–21 (2015).
    [Crossref]
  8. J. Holoubek, “Some applications of light scattering in materials science,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 104–121 (2007).
    [Crossref]
  9. M. Kahnert, T. Nousiainen, and H. Lindqvist, “Review: Model particles in atmospheric optics,” J. Quant. Spectrosc. Radiat. Transfer 146, 41–58 (2014).
    [Crossref]
  10. J. M. Geffrin and et al., “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
    [Crossref]
  11. S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
    [Crossref]
  12. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
    [Crossref]
  13. P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
    [Crossref]
  14. B. Draine, “Discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [Crossref]
  15. J. Cheng, “Theory of ghost scattering with incoherent light,” Phys. Rev. A 93(4), 043808 (2016).
    [Crossref]
  16. J. Cheng, “Theory of ghost scattering with biphoton states,” Photon. Res. 5(1), 41–45 (2017).
    [Crossref]
  17. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2(4), 405–450 (2010), and references therein.
    [Crossref]
  18. J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
    [Crossref]
  19. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
    [Crossref]
  20. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
    [Crossref]
  21. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
    [Crossref]
  22. D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30(18), 2354–2356 (2005).
    [Crossref]
  23. G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006).
    [Crossref]
  24. L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006).
    [Crossref]
  25. M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
    [Crossref]
  26. J. Cheng and S. Han, “Classical correlated imaging from the perspective of coherent-mode representation,” Phys. Rev. A 76(2), 023824 (2007).
    [Crossref]
  27. J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78(4), 043823 (2008).
    [Crossref]
  28. B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A,  77(4), 043809 (2008).
    [Crossref]
  29. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
    [Crossref]
  30. Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
    [Crossref]
  31. M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
    [Crossref]
  32. C. L. Luo and J. Cheng, “Ghost imaging with shaped incoherent sources,” Opt. Lett. 38(24), 5381 (2013).
    [Crossref]
  33. C. L. Luo, H. H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-Gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015).
    [Crossref]
  34. D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
    [Crossref]
  35. H. Yu, E. R. Li, W. L. Gong, and S. S. Han, “Structured image reconstruction for three-dimensional ghost imaging lidar,” Opt. Express 23(11), 14541–14551 (2015).
    [Crossref]
  36. M. I. Akhlaghi and A. Dogariu, “Compressive correlation imaging with random illumination,” Opt. Lett. 40(19), 4464–4467 (2015).
    [Crossref]
  37. L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photon. Res. 4(6), 240–244 (2016).
    [Crossref]
  38. Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
    [Crossref]
  39. R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A,  77(4), 041801 (2008).
    [Crossref]
  40. J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
    [Crossref]
  41. N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84(6), 063824 (2011).
    [Crossref]
  42. P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).
  43. R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
    [Crossref]
  44. B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
    [Crossref]
  45. J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87(4), 043810 (2013).
    [Crossref]
  46. D. Duan and Y. J. Xia, “Real-time pseudocolor coding thermal ghost imaging,” J. Opt. Soc. Am. A 31(1), 183 (2014).
    [Crossref]
  47. H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
    [Crossref]
  48. D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
    [Crossref]
  49. Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
    [Crossref]
  50. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).
  51. O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E,  75(5), 056609 (2007).
    [Crossref]
  52. S. Sahin and O Korotkova, “Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation,” Opt. Lett. 34(12), 1762–1764 (2009).
    [Crossref]
  53. Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A,  82(3), 033836 (2010).
    [Crossref]
  54. T. Wang and D. Zhao, “Scattering theory of stochastic electromagnetic light waves,” Opt. Lett. 35(14), 2412–2414 (2010).
    [Crossref]
  55. Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
    [Crossref]
  56. X. Wang, Z. Liu, K. Huang, and D. Zhu, “Spectral changes of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry scattered on a deterministic medium,” J. Opt. Soc. Am. A 33(10), 1955–1960 (2016).
    [Crossref]
  57. X. Chen and O. Korotkova, “Probability density functions of instantaneous Stokes parameters on weak scattering,” Opt. Commun. 400, 1–8 (2017).
    [Crossref]
  58. Y. Ding and D. Zhao, “Correlation between intensity fluctuations of polychromatic electromagnetic light waves on weak scattering,” Phys. Rev. A 97(2), 023837 (2018).
    [Crossref]
  59. X. Peng, J. Li, and L. Chang, “Evolution properties of polarization states of far-zone electromagnetic field scattered from an anisotropic medium,” Opt. Express 26(6), 6679–6691 (2018).
    [Crossref]
  60. Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010).
    [Crossref]

2018 (3)

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Y. Ding and D. Zhao, “Correlation between intensity fluctuations of polychromatic electromagnetic light waves on weak scattering,” Phys. Rev. A 97(2), 023837 (2018).
[Crossref]

X. Peng, J. Li, and L. Chang, “Evolution properties of polarization states of far-zone electromagnetic field scattered from an anisotropic medium,” Opt. Express 26(6), 6679–6691 (2018).
[Crossref]

2017 (3)

X. Chen and O. Korotkova, “Probability density functions of instantaneous Stokes parameters on weak scattering,” Opt. Commun. 400, 1–8 (2017).
[Crossref]

J. Cheng, “Theory of ghost scattering with biphoton states,” Photon. Res. 5(1), 41–45 (2017).
[Crossref]

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

2016 (5)

J. Cheng, “Theory of ghost scattering with incoherent light,” Phys. Rev. A 93(4), 043808 (2016).
[Crossref]

L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photon. Res. 4(6), 240–244 (2016).
[Crossref]

X. Wang, Z. Liu, K. Huang, and D. Zhu, “Spectral changes of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry scattered on a deterministic medium,” J. Opt. Soc. Am. A 33(10), 1955–1960 (2016).
[Crossref]

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

2015 (6)

Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
[Crossref]

C. L. Luo, H. H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-Gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015).
[Crossref]

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

H. Yu, E. R. Li, W. L. Gong, and S. S. Han, “Structured image reconstruction for three-dimensional ghost imaging lidar,” Opt. Express 23(11), 14541–14551 (2015).
[Crossref]

M. I. Akhlaghi and A. Dogariu, “Compressive correlation imaging with random illumination,” Opt. Lett. 40(19), 4464–4467 (2015).
[Crossref]

R. Xu, “Light scattering: A review of particle characterization applications,” Particuology 18, 11–21 (2015).
[Crossref]

2014 (2)

M. Kahnert, T. Nousiainen, and H. Lindqvist, “Review: Model particles in atmospheric optics,” J. Quant. Spectrosc. Radiat. Transfer 146, 41–58 (2014).
[Crossref]

D. Duan and Y. J. Xia, “Real-time pseudocolor coding thermal ghost imaging,” J. Opt. Soc. Am. A 31(1), 183 (2014).
[Crossref]

2013 (5)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87(4), 043810 (2013).
[Crossref]

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
[Crossref]

C. L. Luo and J. Cheng, “Ghost imaging with shaped incoherent sources,” Opt. Lett. 38(24), 5381 (2013).
[Crossref]

2012 (2)

J. M. Geffrin and et al., “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

2011 (2)

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84(6), 063824 (2011).
[Crossref]

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

2010 (4)

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A,  82(3), 033836 (2010).
[Crossref]

T. Wang and D. Zhao, “Scattering theory of stochastic electromagnetic light waves,” Opt. Lett. 35(14), 2412–2414 (2010).
[Crossref]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2(4), 405–450 (2010), and references therein.
[Crossref]

2009 (4)

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

S. Sahin and O Korotkova, “Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation,” Opt. Lett. 34(12), 1762–1764 (2009).
[Crossref]

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
[Crossref]

2008 (3)

J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78(4), 043823 (2008).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A,  77(4), 043809 (2008).
[Crossref]

R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A,  77(4), 041801 (2008).
[Crossref]

2007 (4)

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

J. Cheng and S. Han, “Classical correlated imaging from the perspective of coherent-mode representation,” Phys. Rev. A 76(2), 023824 (2007).
[Crossref]

J. Holoubek, “Some applications of light scattering in materials science,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 104–121 (2007).
[Crossref]

O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E,  75(5), 056609 (2007).
[Crossref]

2006 (3)

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
[Crossref]

G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006).
[Crossref]

L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006).
[Crossref]

2005 (3)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30(18), 2354–2356 (2005).
[Crossref]

2004 (2)

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

2003 (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
[Crossref]

1988 (1)

B. Draine, “Discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Akhlaghi, M. I.

Bache, M.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Bai, Y.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Basano, L.

L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006).
[Crossref]

Berardi, V.

G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006).
[Crossref]

Body, R. W.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Born, M.

M. Born and E. Wolf, Principles of Optics, Ch. 13, (Cambridge University Press, 1999).

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Brambilla, E.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Cai, Y.

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010).
[Crossref]

Cantelli, V.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

Chan, K. W.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Chang, L.

Chen, X.

X. Chen and O. Korotkova, “Probability density functions of instantaneous Stokes parameters on weak scattering,” Opt. Commun. 400, 1–8 (2017).
[Crossref]

Chen, X. H.

Cheng, J.

J. Cheng, “Theory of ghost scattering with biphoton states,” Photon. Res. 5(1), 41–45 (2017).
[Crossref]

J. Cheng, “Theory of ghost scattering with incoherent light,” Phys. Rev. A 93(4), 043808 (2016).
[Crossref]

C. L. Luo, H. H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-Gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015).
[Crossref]

C. L. Luo and J. Cheng, “Ghost imaging with shaped incoherent sources,” Opt. Lett. 38(24), 5381 (2013).
[Crossref]

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87(4), 043810 (2013).
[Crossref]

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
[Crossref]

J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78(4), 043823 (2008).
[Crossref]

J. Cheng and S. Han, “Classical correlated imaging from the perspective of coherent-mode representation,” Phys. Rev. A 76(2), 023824 (2007).
[Crossref]

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
[Crossref]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

Deacon, K. S.

R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A,  77(4), 041801 (2008).
[Crossref]

Ding, K.-H.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, (John Wiley and Sons, 2000).

Ding, Y.

Y. Ding and D. Zhao, “Correlation between intensity fluctuations of polychromatic electromagnetic light waves on weak scattering,” Phys. Rev. A 97(2), 023837 (2018).
[Crossref]

Dixon, P. B.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Dogariu, A.

Draine, B.

B. Draine, “Discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Du, G. H.

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Duan, D.

Edgar, M. P.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

El-Sayed, I. H.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
[Crossref]

El-Sayed, M. A.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
[Crossref]

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2(4), 405–450 (2010), and references therein.
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A,  77(4), 043809 (2008).
[Crossref]

Fan, H.

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
[Crossref]

Ferri, F.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

Fu, X.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Fukatsu, S.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

Gatti, A.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Geffrin, J. M.

J. M. Geffrin and et al., “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Gong, W. L.

Han, S.

J. Cheng and S. Han, “Classical correlated imaging from the perspective of coherent-mode representation,” Phys. Rev. A 76(2), 023824 (2007).
[Crossref]

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

Han, S. S

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Han, S. S.

H. Yu, E. R. Li, W. L. Gong, and S. S. Han, “Structured image reconstruction for three-dimensional ghost imaging lidar,” Opt. Express 23(11), 14541–14551 (2015).
[Crossref]

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84(6), 063824 (2011).
[Crossref]

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Holoubek, J.

J. Holoubek, “Some applications of light scattering in materials science,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 104–121 (2007).
[Crossref]

Howell, J. C.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Howland, G.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Huang, K.

Jain, M.

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

Jain, P. K.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
[Crossref]

Kahnert, M.

M. Kahnert, T. Nousiainen, and H. Lindqvist, “Review: Model particles in atmospheric optics,” J. Quant. Spectrosc. Radiat. Transfer 146, 41–58 (2014).
[Crossref]

Katz, O.

Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
[Crossref]

Kong, J. A.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, (John Wiley and Sons, 2000).

Korotkova, O

Korotkova, O.

X. Chen and O. Korotkova, “Probability density functions of instantaneous Stokes parameters on weak scattering,” Opt. Commun. 400, 1–8 (2017).
[Crossref]

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A,  82(3), 033836 (2010).
[Crossref]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010).
[Crossref]

O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E,  75(5), 056609 (2007).
[Crossref]

Kuebel, D.

Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
[Crossref]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small particles, (Cambridge University Press, 2002).

Lapin, Z.

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

Lee, K. S.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
[Crossref]

Li, E. R.

Li, H.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Li, H. G.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Li, J.

Li, M. F.

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
[Crossref]

Lin, J.

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87(4), 043810 (2013).
[Crossref]

Lindqvist, H.

M. Kahnert, T. Nousiainen, and H. Lindqvist, “Review: Model particles in atmospheric optics,” J. Quant. Spectrosc. Radiat. Transfer 146, 41–58 (2014).
[Crossref]

Liu, H. L.

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

Liu, Y. F.

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

Liu, Z.

Lu, R. H.

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Lugiato, L. A.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Luo, C. L.

Luo, K. H.

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
[Crossref]

Magatti, D.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

Meyers, R.

R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A,  77(4), 041801 (2008).
[Crossref]

Meyers, R. E.

R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small particles, (Cambridge University Press, 2002).

Nan, S.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Nousiainen, T.

M. Kahnert, T. Nousiainen, and H. Lindqvist, “Review: Model particles in atmospheric optics,” J. Quant. Spectrosc. Radiat. Transfer 146, 41–58 (2014).
[Crossref]

Novotny, L.

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

O’Sullivan-Hale, M. N.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

O-oka, Y.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

Ottonello, P.

L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006).
[Crossref]

Padgett, M. J.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Paganini, D. M.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

Pelliccia, D.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

Peng, X.

Person, S.

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

Qu, L.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Rack, A.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

Rodenburg, B.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Saenz, J. J.

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

Sahin, S.

Scarcelli, G.

G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

Schatz, G. C.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
[Crossref]

Scheel, M.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

Sergienko, A. V.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84(6), 063824 (2011).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2(4), 405–450 (2010), and references therein.
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A,  77(4), 043809 (2008).
[Crossref]

Shaprio, J. H.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Shen, Q.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Shen, X.

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

Sheng, P.

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd ed. (Springer-Verlag, 2006).

Shi, X.

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Shih, Y.

R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A,  77(4), 041801 (2008).
[Crossref]

G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

Shih, Y. H.

R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Simon, D. S.

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

Sun, B.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Tong, Z.

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A,  82(3), 033836 (2010).
[Crossref]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010).
[Crossref]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small particles, (Cambridge University Press, 2002).

Tsang, L.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, (John Wiley and Sons, 2000).

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981).

Visser, T. D.

Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
[Crossref]

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Wang, H. B.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Wang, K. G.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Wang, L.

Wang, S.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Wang, T.

T. Wang and D. Zhao, “Scattering theory of stochastic electromagnetic light waves,” Opt. Lett. 35(14), 2412–2414 (2010).
[Crossref]

D. Zhao and T. Wang, “Direct and Inverse Problems in the Theory of Light Scattering,” In E. Wolf ed., Progress in Optics, Vol. 57, 261–308 (Elsevier, 2012).

Wang, X.

Wang, Y.

Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
[Crossref]

Wei, Q.

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Wicks, G.

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

Wolf, E.

O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E,  75(5), 056609 (2007).
[Crossref]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

M. Born and E. Wolf, Principles of Optics, Ch. 13, (Cambridge University Press, 1999).

Wu, L. A.

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
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D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30(18), 2354–2356 (2005).
[Crossref]

Xia, Y. J.

Xiao, T. Q.

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Xie, H. L.

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Xiong, J.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Xu, H. H.

Xu, R.

R. Xu, “Light scattering: A review of particle characterization applications,” Particuology 18, 11–21 (2015).
[Crossref]

Yan, S.

Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
[Crossref]

Yu, H.

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
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H. Yu, E. R. Li, W. L. Gong, and S. S. Han, “Structured image reconstruction for three-dimensional ghost imaging lidar,” Opt. Express 23(11), 14541–14551 (2015).
[Crossref]

Zhai, Y. H.

Zhang, D.

Zhang, D. J.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Zhang, M. H.

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

Zhang, Y. R.

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
[Crossref]

Zhao, D.

Y. Ding and D. Zhao, “Correlation between intensity fluctuations of polychromatic electromagnetic light waves on weak scattering,” Phys. Rev. A 97(2), 023837 (2018).
[Crossref]

T. Wang and D. Zhao, “Scattering theory of stochastic electromagnetic light waves,” Opt. Lett. 35(14), 2412–2414 (2010).
[Crossref]

D. Zhao and T. Wang, “Direct and Inverse Problems in the Theory of Light Scattering,” In E. Wolf ed., Progress in Optics, Vol. 57, 261–308 (Elsevier, 2012).

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
[Crossref]

Zhao, Q. L.

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Zhao, S. M.

Zhu, D.

Zhu, D. M.

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (5)

G. Scarcelli, V. Berardi, and Y. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006).
[Crossref]

L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

R. E. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

Astrophys. J. (1)

B. Draine, “Discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Phys. Chem. B (2)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B,  107(3), 668–677 (2003).
[Crossref]

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in Biological Imaging and Biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (2)

J. Holoubek, “Some applications of light scattering in materials science,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 104–121 (2007).
[Crossref]

M. Kahnert, T. Nousiainen, and H. Lindqvist, “Review: Model particles in atmospheric optics,” J. Quant. Spectrosc. Radiat. Transfer 146, 41–58 (2014).
[Crossref]

Laser Phys. Lett. (1)

Q. Shen, Y. Bai, X. Shi, S. Nan, L. Qu, H. Li, and X. Fu, “Ghost microscope imaging system from the perspective of coherent-mode representation,” Laser Phys. Lett. 15(3), 035207 (2018).
[Crossref]

Nano Lett. (1)

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref]

Nat. Commun. (1)

J. M. Geffrin and et al., “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Opt. Commun. (2)

X. Chen and O. Korotkova, “Probability density functions of instantaneous Stokes parameters on weak scattering,” Opt. Commun. 400, 1–8 (2017).
[Crossref]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Particuology (1)

R. Xu, “Light scattering: A review of particle characterization applications,” Particuology 18, 11–21 (2015).
[Crossref]

Photon. Res. (2)

Phys. Rev. A (15)

D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. G. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84(6), 063824 (2011).
[Crossref]

P. B. Dixon, G. Howland, K. W. Chan, M. N. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shaprio, D. S. Simon, A. V. Sergienko, R. W. Body, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83(5), 051803 (2011).

R. Meyers, K. S. Deacon, and Y. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A,  77(4), 041801 (2008).
[Crossref]

M. F. Li, Y. R. Zhang, K. H. Luo, L. A. Wu, and H. Fan, “Time correspondence differential ghost imaging,” Phys. Rev. A 87(3), 033813 (2013).
[Crossref]

M. H. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A,  75(2), 021803 (2007).
[Crossref]

J. Cheng and S. Han, “Classical correlated imaging from the perspective of coherent-mode representation,” Phys. Rev. A 76(2), 023824 (2007).
[Crossref]

J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78(4), 043823 (2008).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A,  77(4), 043809 (2008).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

J. Cheng, “Theory of ghost scattering with incoherent light,” Phys. Rev. A 93(4), 043808 (2016).
[Crossref]

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87(4), 043810 (2013).
[Crossref]

Y. Wang, S. Yan, D. Kuebel, and T. D. Visser, “Dynamic control of light scattering using spatial coherence,” Phys. Rev. A 92(1), 013806 (2015).
[Crossref]

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A,  82(3), 033836 (2010).
[Crossref]

Y. Ding and D. Zhao, “Correlation between intensity fluctuations of polychromatic electromagnetic light waves on weak scattering,” Phys. Rev. A 97(2), 023837 (2018).
[Crossref]

Phys. Rev. E (1)

O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E,  75(5), 056609 (2007).
[Crossref]

Phys. Rev. Lett. (6)

H. Yu, R. H. Lu, S. S Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganini, “Experimental X-Ray Ghost Imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Other (7)

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

D. Zhao and T. Wang, “Direct and Inverse Problems in the Theory of Light Scattering,” In E. Wolf ed., Progress in Optics, Vol. 57, 261–308 (Elsevier, 2012).

M. Born and E. Wolf, Principles of Optics, Ch. 13, (Cambridge University Press, 1999).

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, (John Wiley and Sons, 2000).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small particles, (Cambridge University Press, 2002).

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd ed. (Springer-Verlag, 2006).

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981).

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Figures (3)

Fig. 1.
Fig. 1. Geometry of the electromagnetic ghost scattering model. An incident stochastic electromagnetic beam is split into two beams by the beam splitter (BS). An unknown test scatterer is illuminates by one of the beams and the far-zone scattered fields are detected by the test detector $D_t$ located at $\vec {r}_1$. The other beam is scattered by a reference scatterer and considered as a reference beam, with the far-zone scattered fields detected by the reference detector $D_r$ located at $\vec {r}_2$. The scattered signals measured by the test and reference detector $D_t$ and $D_r$ are further processed by the correlator to realize ghost scattering.
Fig. 2.
Fig. 2. (a)The two dimensional test scatterer $F_t(x,y)$ used in numerical simulations, length unit in mm. (b) The corresponding spatial spectrums of (a) shown as the ideally scattering distribution. (c) The calculated DSP with the parameters $A_x=1$, $A_y=0.5$, $B_{xy}=0.3$, $\sigma =20$, $\delta _{xx}=5\times 10^{-4}$, $\delta _{xy}=7.5\times 10^{-4}$, $\delta _{yy}=6\times 10^{-4}$. (d) The calculated GSP with the same parameters in (c). (e) The calculated GSP with the parameters used in (c) except $\delta _{xy}=17.5\times 10^{-4}$, $\delta _{yy}=26\times 10^{-4}$, corresponding to the case of very different coherence lengths. (f) The normalized $s_x$ axial distributions in (c,d,e), corresponding to the blue solid, red dashed, and black dotted lines respectively.
Fig. 3.
Fig. 3. Normalized GSP $I_G(s_{x},0)$ to see the effects of parameters $A_y$, $B_{xy}$ and $\sigma$ on electromagnetic ghost scattering, with $A_x=1$. The coherence lengths in the left figures (a,c,e) are $\delta _{xx}=5\times 10^{-4}$, $\delta _{xy}=7.5\times 10^{-4}$, $\delta _{yy}=6\times 10^{-4}$, and in the right figures (b,d,f) are $\delta _{xx}=5\times 10^{-4}$, $\delta _{xy}=17.5\times 10^{-4}$, $\delta _{yy}=26\times 10^{-4}$. (a,b) $s_x$ axial distributions with $A_y=0$, 0.25, 0.5, 1, corresponding to the black dotted, red dashed, blue dash-dot, and magenta solid curves, $B_{xy}=0.3$, $\sigma =20$. (c,d) $s_x$ axial distributions with $B_{xy}=0.1$, 0.3, 0.6, 0.9, corresponding to the black dotted, red dashed, blue dash-dot, and magenta solid curves, $A_{y}=0.5$, $\sigma =20$. (a,b) $s_x$ axial distributions with $\sigma =5$, 10, 20, 50, corresponding to the black dotted, red dashed, blue dash-dot, and magenta solid curves, $A_y=0.5$, $B_{xy}=0.3$.

Equations (20)

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E s ( r ) = e j k r r V d 3 r 0 F ( r 0 ) e j k s ^ r 0 S ( 3 ) ( s ^ ) E i ( r 0 ) ,
F ( r 0 ) = { 1 4 π k 2 [ n 2 ( r 0 ) 1 ] , r 0 V 0 , r 0 V
S ( 3 ) ( s ^ ) = [ 1 s x 2 s x s y s x s z s x s y 1 s y 2 s y s z s x s z s y s z 1 s z 2 ] ,
W s ( r 1 , r 2 ) = [ W α , β s ( r 1 s ^ 1 , r 2 s ^ 2 ) ] = [ E α s ( r 1 s ^ 1 ) E β s ( r 2 s ^ 2 ) ] ,
G α , β ( r 1 s ^ 1 , r 2 s ^ 2 ) = Δ I t , α s ( r 1 s ^ 1 ) Δ I r , β s ( r 2 s ^ 2 ) ,
C ( r 1 s ^ 1 , r 2 s ^ 2 ) = Δ I t s ( r 1 s ^ 1 ) Δ I r s ( r 2 s ^ 2 ) = α , β G α , β ( r 1 s ^ 1 , r 2 s ^ 2 ) .
G α , β ( r 1 s ^ 1 , r 2 s ^ 2 ) = | E t , α s ( r 1 s ^ 1 ) E r , β s ( r 2 s ^ 2 ) | 2 = | W t α , r β s ( r 1 s ^ 1 , r 2 s ^ 2 ) | 2 .
W t α , r β s ( r 1 s ^ 1 , r 2 s ^ 2 ) = e j k r 1 + j k r 2 r 1 r 2 V d 3 r a d 3 r b F t ( r a ) F r ( r b ) e j k s ^ 1 r a j k s ^ 2 r b × α β S α α ( 3 ) ( s ^ 1 ) S β β ( 3 ) ( s ^ 2 ) E α i ( r a ) E β i ( r b ) ,
G ( r 1 s ^ 1 , r 2 s ^ 2 ) = C 0 | V d 3 r a d 3 r b F t ( r a ) F r ( r b ) e j k s ^ 1 r a j k s ^ 2 r b S ( 3 ) ( s ^ 1 ) W i ( r a , r b ) S ( 3 ) T ( s ^ 2 ) | 2 ,
E s ( r ) = e j k r r V d 3 r 0 F ( r 0 ) e j k s ^ r 0 S ( 2 ) ( s ^ ) E i ( r 0 ) ,
S ( 2 ) ( s ^ ) = [ cos ( θ ) cos ( ϕ ) cos ( θ ) sin ( ϕ ) sin ( ϕ ) cos ( ϕ ) ] ,
G ( r 1 s ^ 1 , r 2 s ^ 2 ) = C 0 | V d 3 r a d 3 r b F t ( r a ) F r ( r b ) e j k s ^ 1 r a j k s ^ 2 r b S ( 2 ) ( s ^ 1 ) W i ( r a , r b ) S ( 2 ) T ( s ^ 2 ) | 2 .
G ( r 1 s ^ 1 , r 2 s ^ 2 ) = | S ( 2 ) ( s ^ 1 ) [ F ~ x x ( k s ^ 1 , k s ^ 2 ) F ~ x y ( k s ^ 1 , k s ^ 2 ) F ~ y x ( k s ^ 1 , k s ^ 2 ) F ~ y y ( k s ^ 1 , k s ^ 2 ) ] S ( 2 ) T ( s ^ 2 ) | 2 ,
F ~ α β ( k s ^ 1 , k s ^ 2 ) = V d 2 ρ a d 2 ρ b e j k s ^ 1 ρ a j k s ^ 2 ρ b F t ( ρ a ) F r ( ρ b ) W α β i ( ρ a , ρ b ) .
C = C 0 [ ( cos θ 1 cos ϕ 1 cos θ 2 cos ϕ 2 ) 2 + ( cos θ 1 cos ϕ 1 sin ϕ 2 ) 2 + ( sin ϕ 1 cos θ 2 cos ϕ 2 ) 2 + ( sin ϕ 1 sin ϕ 2 ) 2 ] | F ~ x x | 2 .
W α , β 0 ( ρ 1 , ρ 2 ) = S α 0 ( ρ 1 ) S β 0 ( ρ 2 ) μ α β 0 ( ρ 1 ρ 2 ) ,
S α 0 ( ρ ) = A α 2 exp ( | ρ | 2 2 σ α 2 ) ,
μ α β 0 ( ρ 1 ρ 2 ) = B α β exp ( | ρ 1 ρ 2 | 2 2 δ α β 2 ) ,
W i ( ρ a , ρ b ) α β = A α A β B α β Δ α β 2 ( z ) exp [ | ρ a + ρ b | 2 8 σ 2 Δ α β 2 ( z ) ] exp [ | ρ a ρ b | 2 2 Ω α β 2 Δ α β 2 ( z ) ] exp [ i k ( ρ b 2 ρ a 2 ) 2 R α β ( z ) ] ,
1 Ω α β 2 = 1 4 σ 2 + 1 δ α β 2 , Δ α β 2 ( z ) = 1 + ( z k σ Ω α β ) 2 , R α β ( z ) = [ 1 + ( k σ Ω α β z ) 2 ] z .

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