Polarization difference ghost imaging Yongchao Zhu,1 Jianhong Shi,1,* Ying Yang,1 and Guihua Zeng1,2 1
State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Key Laboratory on Navigation and Location-based Service, and Center of Quantum Information Sensing and Processing, Shanghai Jiao Tong University, Shanghai 200240, China 2
College of Information Science and Technology, Northwest University, Xi’an 710127, Shanxi, China *Corresponding author:
[email protected] Received 13 October 2014; revised 9 January 2015; accepted 11 January 2015; posted 12 January 2015 (Doc. ID 224822); published 12 February 2015
We propose the polarization difference ghost imaging method and experimentally demonstrate that polarization properties can provide additional information in conventional ghost imaging for object discrimination with contrast enhancement. In our experiment, two kinds of visually similar objects with different polarization properties can be separated for imaging. Meanwhile, an improved polarization difference algorithm is presented, fully utilizing the polarization discrepancy between objects and background, to further enhance the image contrast. Our work facilitates practical applications of ghost imaging. © 2015 Optical Society of America OCIS codes: (110.1758) Computational imaging; (260.5430) Polarization; (120.1880) Detection. http://dx.doi.org/10.1364/AO.54.001279
1. Introduction
Since it was experimentally demonstrated in 1995, ghost imaging (GI) has received much attention and achieved considerable development [1–3]. As an intriguing method, GI is providing a novel and powerful imaging tool. The traditional thermal ghost image is usually retrieved in a “nonlocal” manner by measuring the intensity correlation between two light fields, during which process only a single-pixel detector is needed to collect the object information without any imaging lens [4,5]. Applications that benefit from these advantages are x-ray imaging [6], fluorescence microscopy [7], three-dimensional imaging [8], and lidar detection [9,10]. Also, GI displays great potential for imaging of objects immersed in optically harsh or noisy environments, e.g., in a scattering medium [11–13] or turbulent atmosphere [14–16]. In recent years, the focus of GI has increasingly shifted from fundamental research to practical applications such as remote sensing and biomedical imaging. 1559-128X/15/061279-06$15.00/0 © 2015 Optical Society of America
However, in conventional GI, a bucket detector in the signal beam indiscriminately collects all the reflected light from objects and background. When different material objects with similar reflectivities are in the same field of view (FOV), it is difficult for GI to distinguish between them. Similarly, consider the situation where there exist other objects with higher reflectivity (e.g., specular reflection), then the information of the real target may be overwhelmed. Hence, conventional GI can hardly retrieve the desired target. In addition, strong interference from a complex background will also degrade object visibility and image contrast. Such problems hamper the practical applicability of GI in a variety of fields. Over the past few decades, there has been much effort on the analysis of the imaging quality of GI [17–22], and many improved algorithms have been proposed [17,23–27]. However, almost all the previous work focused on the improvement after signal data have already been collected by a bucket detector. All of the object and background information is included in the same intensity data. In other words, these methods still have little effect on the above challenges. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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Polarization is an inherent property of light. The polarization properties between the objects and the background, such as man-made objects and natural background in remote sensing, are in general dissimilar due to the different materials or surface features. This provides additional information that can be exploited [28–34]. Recently, a polarimetric GI system was theoretically proposed [35]. We also proposed and experimentally demonstrated a different but simpler and more practical method— polarization difference ghost imaging (PDGI) [36]. The object and background information can be separated for imaging during the data acquisition process, and the object visibility and image contrast can be improved by the polarization difference algorithm. In this paper, we experimentally demonstrate that PDGI can provide a means to separate different material objects where they would otherwise appear similar in conventional GI. To further enhance the image contrast, we propose an improved polarization difference algorithm which can remove the interference of background (or other different objects) by fully exploiting the difference of polarization properties between them.
distribution Si x; y. Then it passes through a linear polarizer (P) and a lens (L1) to be incident on the objects. The polarizer is set to transmit only the horizontally polarized light. In our experiment, only linearly polarized light is used because it is easy to handle and calibrate. Certainly, a similar system with the circularly polarized light can also be designed based on our system prototype [35]. Another lens (L2) is positioned approximately 5° off the backscattering direction to collect the reflected light. A polarization beam splitter (PBS) separates the light into two photodiodes (PDs) after the narrowband 632.8 nm filters (F). PD1 and PD2, respectively, detect the copolarized light I ∥i and cross-polarized light I ⊥i (I ∥i is the intensity of the backscattered light, which is linearly polarized in the same direction as the incident light, whereas I ⊥i is the intensity of the backscattered light in the perpendicular direction). The DMD and the two detectors are synchronously computer controlled. In spite of slight losses, the sum of the signals of PD1 and PD2 gives the total light intensity I i in conventional GI. Then the image of the object can be retrieved by correlation imaging arithmetic [10,12,23,25–27]:
2. Experiment and Results
where Si x; y is the speckle pattern modulated by the DMD, I i is the bucket signal collected P by the PDs in each iteration, and h·i 1∕N i ·. N 10; 000 is the total iterations in our experiment. The degree of polarization (DOP) is introduced with the Stokes–Mueller formalism, which describes the interaction between light and matter [30]. It is defined as the ratio of the averaged intensity of the polarized portion of light to its total (averaged) intensity. Depolarization is a process of changing polarized light into unpolarized light and reducing the degree of polarization. In our case, the incident light is linearly polarized, and in a monostatic configuration, we can give a simple definition of the linear degree of polarization of the reflected light:
The schematic of the implementation is shown in Fig. 1. The 632.8 nm output from a He–Ne laser is expanded to 15 mm through a beam expander (E) and illuminates a digital micromirror device (DMD). The DMD is a microelectromechanical system consisting of hundreds of thousands of tiny switchable mirrors with two stable mirror states (12° or −12°). The mirrors are highly reflective and have higher refreshing speed and broader spectral response compared with ordinary spatial light modulators (SLMs) [23]. These features make DMDs attractive for GI since the reference beam can be removed and no array detector (e.g., the charge coupled device (CCD) camera in [35]) is needed [8]. Moreover, the efficiency of DMD extends well beyond the visible spectrum, making our system suitable for imaging fields where current pixelated sensors are unavailable or expensive. For the ith iteration, the light beam modulated by the DMD has the spatial
Fig. 1. Experimental schematic of PDGI. Beam expander, E; digital micromirror device, DMD; linear polarizer, P; lenses, L1 and L2; polarization beam splitter, PBS; narrowband filters, F; photodiodes, PD1 and PD2. 1280
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GI hΔIΔSi hI i − hI i iSi x; y − hSi x; yii; (1)
DOP
I∥ − I⊥ : I∥ I⊥
(2)
DOP is 0 when the reflected light is unpolarized, whereas it is 1 when the light is still linearly polarized as the incident light. The totally depolarized light will be equally detected by PD1 and PD2, and the nondepolarizing light will be mostly detected by PD1. The objects are depicted and illustrated in Fig. 2. Objects 1 are made up of four aluminum sheets in different geometrical shapes, which resemble the English letters “LOVE.” They have high-reflectivity and low-depolarization characteristics. In the center of each sheet, a thin double-sided tape in the shape of capital letter “S, J, T, or U” is pasted, collectively called Objects 2. They have similar reflectivity as Objects 1 since the tapes are pretty transparent.
iobj − ibg ; C iobj ibg
Fig. 2. Experimental objects. (a) Photo: objects 1 and objects 2 will be visually similar under traditional illumination. (b) Objects 1: four aluminum sheets of different geometrical shapes. (c) Objects 2: four transparent double-sided tapes pasted on the aluminum sheets, respectively. (d) Background: white paperboard in the shape of a dialog box.
Thus, Objects 1 and Objects 2 will be visually similar under traditional illumination. In such a case, conventional GI, even with the previous improved algorithms [17,23–27], is incapable of distinguishing between them. However, the double-sided tapes are coated with polyacrylate adhesive on both sides, which will highly depolarize the incident light. The different polarization properties provide a means for separate imaging of Objects 1 and Objects 2. In addition, the two kinds of objects share the same background, which is a white paperboard in the shape of a dialog box. The background also has a depolarizing property similar to that of Objects 2. The reflected light will be strongly depolarized when the incident light is linearly polarized light. Compared with Objects 1 and Objects 2, the background has lower reflectivity due to the different materials. The imaging results are shown in Fig. 3. Figure 3(a) is retrieved by using the I I ∥ I ⊥ in Eq. (1). In this case, it is just the same as the conventional GI. Since the reflectivities of Objects 1 and Objects 2 are similar, they are indistinguishable. Only four geometrical shapes (“LOVE”) can be identified, and the background interference strongly degrades the objects visibility and contrast. In Fig. 3(b), I ∥ of PD1 is used in Eq. (1) instead of I. Almost half of the reflected light from the background and Objects 2 is filtered out, whereas most reflected light from Objects 1 is collected by PD1. Thus it can be observed that there are four letters (“SJTU”) with relatively lower intensities in the centers of Objects 1. Meanwhile, the image contrast is enhanced by reducing the interference of the background. For a quantitative comparison, we calculated the visibility or contrast of the object by
(3)
where iobj and ibg , respectively, represent the average intensity of the object or background areas. The contrast C of Objects 1 in Figs. 3(a) and 3(b) are 0.1372 and 0.2320. Similarly, if we use I ⊥ of PD2 in Eq. (1), only the reflected light from Objects 2 and the background will be detected by PD2, and the reflected light of Objects 1 will be mostly filtered out. The result is depicted in Fig. 3(c). The four letters “SJTU” are clearly visible in spite of the background interference. These results indicate that our method provides a means to separate different material objects where they would otherwise appear similar under unpolarized light. The background interference could be reduced during the data acquisition process. What is noteworthy is that the component of the background noise in I ∥ is commensurate with that in I ⊥ . This indicates that, in our particular case, the background removal may be achieved by simply using I d I ∥ − I ⊥ in Eq. (1) [35,36]. In many cases, however, the reflected light of the background (or the other different material objects) may not be perfectly depolarized. A more general method is required for complex situations in practical applications. We exploit this phenomenon by proposing an improved polarization difference algorithm, which enhances object contrast by optimally separating the object and background components. 3. Improved Polarization Difference Algorithm
In general, both PD1 and PD2 detect the light intensity reflected from objects and background: I ∥ I ∥obj I ∥bg ; I ⊥ I ⊥obj I ⊥bg :
(4)
The DOP of the reflected light from object Dobj and the background Dbg can be defined as Dobj Dbg
I ∥obj − I ⊥obj I ∥obj I ⊥obj I ∥bg − I ⊥bg I ∥bg I ⊥bg
;
:
(5)
Combining Eq. (5) with Eq. (4), the following equations can be derived: I ∥ I ⊥ I ∥obj I ⊥obj I ∥bg I ⊥bg I obj I bg ; I ∥ − I ⊥ Dobj I obj Dbg I bg : ∥
⊥
(6)
(7)
∥
Fig. 3. Experimental results using (a) I I I , or (b) I of PD1 or (c) I ⊥ of PD2 in the correlation imaging arithmetic of Eq. (1).
The solution to this equation set is 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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Iˆ obj
1 I ⊥ 1 Dbg − I ∥ 1 − Dbg ; Dbg − Dobj
(8)
Iˆ bg
1 I ∥ 1 − Dobj − I ⊥ 1 Dobj : Dbg − Dobj
(9)
This is a general result, enabling separation of I obj and I bg from the original data of the two PDs, given the DOPs Dobj and Dbg . A very important property of Eq. (8) is that Dobj contributes only a scale factor to the signal reconstruction Iˆ obj . For purposes of contrast enhancement, the scaled Iˆ obj is sufficient. Thus the estimation of parameter Dbg is the crux in our algorithm. It is reasonable to expect the measured Dbg to be nonuniform. However, it is found empirically that the value of Dbg is constant across the field of view in many practical applications, such as remote sensing or underwater imaging. As Dbg is practically uniform, it is easy to measure. Designing the modulated information S of DMD to make the incident light illuminate only the background area, then I ∥ I ∥bg and I ⊥ I ⊥bg . Thus, ∥ ⊥ ˆ bg I − I D I∥ I⊥
We will further discuss the effectiveness or accuracy of the improved polarization difference algorithm. Our algorithm provides a way to separate the object component from the background component (or other objects). As we can see from its derivation process, Eq. (8) gives the pure object component after removing background information.
10
yields an estimation of Dbg for the background. Similarly, Dobj can also be estimated, if necessary, by modulating the incident light to illuminate only the object area. In general, such estimation of DOP applies to most practical applications where the locations of objects and background can be observed or are known in advance. If location information is inadequate, but the types of objects and background are predictable, the empirical DOP based on the previous research data could be used for the estimation of I obj and I bg . The measured Dbg and Dobj in our experiment are, respectively, 0.10 and 0.75. Using these values in Eqs. (8) and (9) yields an optimal reconstruction of I obj and I bg . These values are substituted into Eq. (1) for the ghost imaging. Figure 4 depicts the imaging results of Objects 1 and the background. As shown in Fig. 4(a), the background is removed and the contrast of Objects 1 is improved (C 0.3522). Actually, the DOP of the reflected light of Objects 2 is 0.23. Thus Objects 2 will be regarded as the background and removed during the estimation of I obj. For this reason, Objects 2 in Fig. 4(a) will appear as negative images, which have relatively lower intensities, and they can be retrieved as the background in Fig. 4(b). This reveals that, aside from background removal, the improved polarization difference algorithm can also be applied to the contrast enhancement of objects with different polarization properties. 1282
Fig. 4. Imaging results with the improved polarization difference algorithm. (a) Contrast enhancement of Objects 1 due to the background removal. (b) Recovered background component. Objects 2 have a depolarization property similar to that of the background and will be removed during the estimation of I obj, so they appear as negative images in (a) but are recovered in (b).
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Fig. 5. Imaging results using I I∥ I ⊥ (conventional GI), I∥ or I ⊥ (simple PDGI), and Iˆ obj or Iˆ bg (improved polarization difference algorithm) in Eq. (1) (from top to bottom), with the decrease of the difference of polarization properties between Objects 1 and the background (from left to right).
Therefore, theoretically we can separate the object from the background as long as there exists difference between their polarization properties (no matter how small it is), which can be demonstrated by our following simulation experiments. For simplicity, the reflected light of Objects 2 (“SJTU”) in our simulation experiments has the same DOP as the background (the dialog box). Thus Objects 2 can also be viewed as part of the background. We investigate the most challenging situation in which Objects 1 (“LOVE”) have the same reflectivity as the background. In this case, conventional GI cannot distinguish Objects 1 from the background, as shown in the results (first row of Fig. 5) that are retrieved using I I ∥ I ⊥ in Eq. (1). The difference of polarization properties between Objects 1 and the background decreases from Experiment I to Experiment III. The DOP of the reflected light from Objects 1 and the background are 0.80 and 0.20 in Experiment I, 0.65 and 0.35 in Experiment II, 0.55 and 0.45 in Experiment III. Therefore, it becomes increasingly difficult to distinguish between them by simply using the I ∥ or I ⊥ in Eq. (1) for imaging, as shown in the second and third rows of Fig. 5. However, the fourth and fifth rows in Fig. 5 show that, with our improved polarization difference algorithm, we can always retrieve Objects 1 and the background clearly utilizing the Iˆ obj or Iˆ bg component, which agrees well with the theoretical analysis, i.e., our algorithm can separate object from background even when their difference is very small. The clarity of imaging results can be further improved by increasing the iteration N or combining the previous improved GI algorithms [17,23–27]. 4. Conclusion
In conclusion, polarization difference ghost imaging (PDGI) was proposed and experimentally demonstrated in this paper, providing an imaging method for object discrimination with contrast enhancement. Compared with conventional ghost imaging and previous improved algorithms based on only intensity information, PDGI took full advantage of the polarization properties to distinguish between different objects and background. We also proposed the improved polarization difference algorithm, which can further reduce the interference of background (or other different objects) and enhance the image contrast. Its effectiveness or accuracy was discussed and demonstrated by simulation experiments, which showed that our algorithm could retrieve object information from background even when the difference between their polarization properties was very small. In many cases, increasing the dimension of polarization information (e.g., circularly polarized light) may significantly enhance the difference between the objects and background [30–32]. Moreover, by combining with other advanced techniques (e.g., compressive sensing [23] or range-gated technology
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