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Polarimetric ghost imaging Dongfeng Shi,* Shunxing Hu, and Yingjian Wang Key Laboratory of Atmospheric Composition and Optical Radiation, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China *Corresponding author:
[email protected] Received November 7, 2013; revised December 31, 2013; accepted January 2, 2014; posted January 22, 2014 (Doc. ID 200978); published February 24, 2014 For conventional ghost imaging (GI) systems, the object image is obtained based on the reflective or transmissive character of the object. When the object and its background have the same reflectivity or transmittance, conventional GI is helpless in detecting the object from the background. An improvement is to use the polarization components of the reflected or transmitted light. We propose a polarimetric GI system that employs a polarization state generator and a polarization state analyzer. This feature allows for the first time, to the best of our knowledge, imaging the object buried in the same reflectivity or transmittance background, which represents a breakthrough for GI applications. Using a combination of intensity and polarization information, we are better able to distinguish between the background and the different material objects. © 2014 Optical Society of America OCIS codes: (110.5405) Polarimetric imaging; (110.6150) Speckle imaging; (120.1880) Detection. http://dx.doi.org/10.1364/OL.39.001231
Ghost imaging (GI) [1–9] is an active imaging technique that uses intensity correlation of two light beams to obtain an image of the object. In conventional thermal GI systems, a laser beam propagates through a rotating ground glass in order to produce a speckled light field and two correlated beams are obtained utilizing a beam splitter. One beam, which illuminates the object, is collected by a nonspatially resolving detector, while the other beam is recorded by a spatially resolving detector, e.g., a charge-coupled device (CCD) camera. Recent improvements in GI protocol include computational GI [2,3] which uses computer-controlled spatial light modulators to remove the beam splitter and the spatially resolving detector, compressive sensing GI [4,5] where the algorithm for the data analysis benefits from the sparsity properties of the object, and two-wavelength GI [6,7] where the two beams have different wavelengths. Threedimensional GI [8,9] has been receiving much more attention because it can provide much more information compared with two-dimensional imaging. There are some other techniques, such as multiwavelength GI [10] and differential GI [11]. However, all the previous work on GI is employed to recover the image of the object according to the reflected or transmitted intensity from the object. Ideally, the processor is able to distinguish image pixels containing the object from pixels containing the background. Nevertheless, in some instances, it may create false alarms. For example, when the object is buried in the background (same reflectivity or transmittance), there are ambiguities in the determination of which pixels are on the object. Polarization [12,13] is an intrinsic feature of the light that provides valuable information about the object beyond that provided by the object’s spectral and intensity distributions. Polarization [14] seeks to measure information about the vector nature of the optical field across a scene. It is well known that a promising method for improving the determination of which pixels are on the object is to employ the polarization components of the reflected or transmitted light. The idea is based on the fact that the incident light is less depolarized by the man-made object than the natural background. Depolarization [14] is defined as the process of changing 0146-9592/14/051231-04$15.00/0
polarized light into unpolarized light and reducing the degree of polarization. Therefore, the image encoded by the degree of polarization can be employed to distinguish the man-made object from the same reflective or transmissive natural background. Now, polarimetric laser radar [14–20] has been widely studied and applied in many domains, such as machine vision, biomedical imaging, and remote sensing. To the best of our knowledge, this is the first study about a polarimetric GI system in which the scene is illuminated with purely polarized laser light [12,13] and the reflected or transmitted light is analyzed in the polarization states parallel and orthogonal to the reference axis. In this Letter, we just illuminate the reflective situation. Certainly, a similar analysis can also be achieved for the transmissive situation. A schematic of the experimental setup is shown in Fig. 1. It is a typical thermal reflective GI setup, except for the addition of the polarization state
Fig. 1. The setup for the polarimetric GI system. The laser beam enters a rotating ground glass (RGG) followed by the PSG system that consists of a linear polarizer (LP) and a quarter-wave plate (QWP). Then the beam is split into two beams by the beam splitter (BS). One of the beams is then used to illuminate the object and the reflected light enters the PSA system that consists of a QWP and a polarization beam splitter (PBS) which separates the light into two orthogonal parts. Last, the two parts of light are collected by two nonspatially resolving detectors (NSD). The transverse intensity distribution of the other beam is measured by a CCD camera. The polarization ghost image of the object is produced by the correlation between the outputs of the detectors. © 2014 Optical Society of America
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generator (PSG) and the polarization state analyzer (PSA). In the polarimetric GI system, a laser beam with a known polarization state is transmitted. The Stokes vector S [14], which consists of four parameters I; Q; U; V T , is employed to describe the polarization state. Here, I represents the total intensity of the light, Q is the difference between horizontal and vertical polarization, U is the difference between linear 45° and −45° polarization, and V is the difference between right and left circular polarization. The degree of polarization is a quantity used to describe the portion of an electromagnetic wave which is polarized. Mathematically, in terms of the Stokes vector parameters p Q2 U 2 V 2 : DOP I
2
M PSA1
1 0 6 0 m11 M 6 40 0 0 0
0 0 m11 0
M PSA2
where M is normalized such that the total reflected light m00 is equal to 1, and m11 and m33 are the linear depolarization and the circular depolarization, respectively. Experiments [17] have shown that m11 and m33 are large for man-made surfaces and small for naturally occurring surfaces. In Fig. 1, the laser beam emerged from the rotating ground glass enters a linear polarizer followed by a quarter-wave plate. We suppose S in I; Q; U; V T . Based on Eqs. (2) and (3), we can get S re I; m11 Q; m11 U; m33 V T whose polarization state can be controlled by the incident light S in . When the parameters m11 and m33 are large (small), the reflected light has a high (low) DOP which means the pixel on the man-made surface (naturally occurring surface). If the term V is equal to zero and either Q or U is nonzero, then S re does not contain the circular polarization information and only contains the linear polarization information (vice versa). In order to measure the linear and the circular depolarization information, it is necessary to utilize purely polarized light. Here, we make three variables Q, U, and V equal to nonzero. By setting the linear polarizer parallel to the y axis and the quarterwave plate at 17.632°, we can get a certain polarization state of purely polarized light whose Stokes vector is given by
1 16 1 6 4 2 0 0
(4)
−2∕3 2∕3 0 0
p −p2∕3 2∕3 0 0
2∕3 2∕3 0 0
p p2∕3 2∕3 0 0
p 3 −p3∕3 3∕3 7 7; 0 5
(5)
0
p 3 p3∕3 3∕3 7 7: 0 5 0
(6)
1 1 I 1 1 2m11 m33 ; 2 3
(7)
1 1 1 − 2m11 m33 : 2 3
(8)
I2
3
(3)
p − 3∕3 T ;
Here, the quarter-wave plate of the PSA is fixed at 17.632 90° with respect to the x axis. According to Eqs. (2)–(6), the intensities detected by detectors NSD1 (I 1 ) and NSD2 (I 2 ) are given by
(2)
0 0 7 7; 0 5 m33
1 16 −1 6 24 0 0 2
where M is the Mueller matrix of the object’s surface. For light retroreflected off nonbirefringent materials [15,19], the Mueller matrix can be approximated as 2
p − 2∕3
where the superscript T expresses transpose. The reflected light from the object enters the PSA that consists of a quarter-wave plate and a polarization beam splitter. The Mueller matrices of the PSA at 0° and 90° with respect to the y axis are described by M PSA1 and M PSA2 , respectively,
(1)
DOP 1 corresponds to purely polarized light, DOP 0 corresponds to unpolarized light, and 0 < DOP < 1 corresponds to partially polarized light. The polarization state of the reflected light from the scene is changed relative to that of the incident light. The relationship between the incident light S in and the reflected light S re is given by the following equation: S re M · S in ;
S ain 1 −2∕3
Based on GI theory [1–9], the object image can be reconstructed by correlating intensity distributions obtained by the spatially resolving detector and the nonspatially resolving detector Gx
N N N X X 1X n x − 1 I n I n I n x; B I B 2 N n1 N n1 n1
(9)
where N denotes the total number of measurements, n is the nth measurement, I n x is the intensity collected by the spatially resolving detector for the nth measurement at location x, and I n B is the intensity collected by the nonspatially resolving detector for the nth measurement. In a polarimetric GI system, the nth intensity for the nonspatially resolving detector is obtained by n n I n PGI I 1 − I 2 :
(10)
n Using Eq. (9) and I n PGI I B , a polarimetric GI object image can be achieved. This system also gives conventional GI measurements of the nonspatially resolving detector n n I n CGI I 1 I 2 :
(11)
n Using Eq. (9) and I n CGI I B , a conventional GI object image can be obtained. In the next simulation, we will give the results acquired by the two different GI systems.
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Table 1. Mueller Matrix Elements Steel Stone Wood
m11
m33
0.975 0.385 0.215
0.99 0.35 0.16
Computational simulation experimental comparisons between polarimetric GI and conventional GI are proposed in order to show the striking differences. Measured m11 and m33 values [17] are given in Table 1 and utilized in the described polarimetric GI in this Letter. In ideal situations, we assume that there is no sensor noise, no speckle, and no turbulence. The scene is composed of two objects “A” on the natural structured background (wood). One of the targets “A” (left) is made of steel and the other (right) is made of stone. In the first simulation, we assume the two objects have the same reflectivity which is smaller than that of the background, but the difference is small. The scene is shown in Fig. 2(A). The results are shown in Fig. 3 where (A) and (B), and (C) and (D) are the images obtained by conventional GI and polarimetric GI, respectively. Because the reflectivity between the objects and background in the scene is very close, there are some ambiguities in the conventional GI image. However, for the polarimetric GI image, the steel letter can be clearly recognized. The depolarization of the wood and the stone are very close which makes it difficult to distinguish the stone letter from the wood background in polarimetric GI. When we want to detect the man-made target buried in the background (same reflectivity but different polarization characteristics), the conventional GI is helpless, and nevertheless, the polarimetric GI has great potential. In the second simulation, the difference of the reflectivity between the objects and the background is apparent. The scene is shown in Fig. 2(B). In conventional GI images [Figs. 4(A) and 4(B)], we cannot distinguish the steel letter from the stone one. Nonetheless, polarimetric GI images succeed in detecting the steel object, but the stone one disappears into the background because the difference of the depolarization between the stone and the wood is very small. It is of great interest to combine the different information (intensity and polarization) on a single image. The fusion image is featured by the red channel (equal to the polarimetric GI image), the green channel (equal to the conventional GI image), and the blue channel (equal to the sum of the polarimetric GI and the conventional GI images). Figures 4(E) and 4(F) show the fusion color RGB images where both kinds of
Fig. 2.
Original scenes are used in the simulation experiments.
Fig. 3. Experimental results for the first simulation. Top row: conventional GI reconstruction with (A) 50,000 realizations and (B) 100,000 realizations. Bottom row [(C) and (D)]: polarimetric GI reconstruction using the same experimental condition as in (A) and (B).
Fig. 4. Experimental results for the second simulation. Top row: conventional GI reconstruction with (A) 30,000 realizations and (B) 60,000 realizations. Middle row [(C) and (D)]: polarimetric GI reconstruction using the same experimental condition as in (A) and (B). (E) Fused images (A) and (C), and (F) fused images (B) and (D) are the fusion color RGB images which show combination information.
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information (intensity and polarization) can be easily interpreted. We can clearly distinguish between the background and different material objects in the fusion images. In this Letter, we first propose polarimetric GI described by theories and experiments. In simulation experiments, the application of this system in the detection of the man-made object buried in the background was presented. It was clearly demonstrated that polarimetric GI could lead to an increase in the detection performance. The connection between polarization and GI opens up significant pathways for improving the performance of GI. When the compressive sensing method is employed, the imaging quality will be better. We believe that this new technique will pave the way to the use of GI in several fields, including computer vision, target detection, particularly in imaging targets in scattering media, such as water and fog, in feature extraction, and in material classification. Further studies are focused on the sensitivity of the technique to the detection noise, the effects of a rough surface, and its performance under atmospheric turbulence. The work was supported by the programs of the National Natural Science Fund (Grant Nos. 41127901, 41205020, 4005015, and KJCX2-EW-N07). References 1. J. H. Shapiro and R. W. Boyd, Quantum Inf. Process. 11, 949 (2012). 2. J. H. Shapiro, Phys. Rev. A 78, 061802 (2008). 3. Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
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