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Light-field-camera imaging simulation of participatory media using Monte Carlo method
International Journal of Heat and Mass Transfer 102 (2016) 518–527
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Light-field-camera imaging simulation of participatory media using Monte Carlo method Yuan Yuan, Bin Liu ⇑, Sai Li, He-Ping Tan ⇑ School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China
a r t i c l e
i n f o
Article history: Received 29 January 2016 Received in revised form 6 April 2016 Accepted 20 June 2016
Keywords: Radiative transfer Light field camera Monte Carlo method Participating medium High-temperature flame
a b s t r a c t In this study, we use the Monte Carlo method to analyze the light-field camera imaging of various participating media (absorbing, scattering and emitting media), along with refocused and sub-aperture images, during the process of reconstructing the temperature field of a high-temperature combustion flame. Hence, the optical field of the participating medium is analyzed. We found that if the participating medium does not have active emission capability, the absorptive and scattering capacity can be regarded as attenuation capacity. However, if the medium has active emission capability, it is difficult to obtain the emission characteristics corresponding to the depth of field through refocusing, and the medium’s temperature field can only be reconstructed using sub-aperture images. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction High-temperature combustion is widely employed in aerospace technology, power and energy generation, ferrous metallurgy, and the chemical industry, in applications such as rocket engines, gas turbines, engines, station boilers, coal gasification rectors, and other high-temperature devices [1–4]. The mechanism and apparent characteristics of the combustion of fuel have been investigated through both theoretical and experimental research; this has helped in revealing the core parameters of combustion phenomena and the laws governing the combustion process. Such research can also help in developing and facilitating the optimized design and operation of combustion systems. The measurement of a flame’s three-dimensional (3D) radiant energy field [5] is primarily based on readings from a single camera and a polyphaser. Such a one-camera measuring system is simple, inexpensive, and easy to install. This system can be used to reconstruct the flame cross section directly and three dimensions. However, single-camera image measurement systems are generally limited and can only be applied to stable, axially symmetric flames [6]. This prevents their application to unsteady and turbulent flame measurement. An increasing number of studies on polyphasers have been conducted in recent years. The polyphaser system is derived from the ⇑ Corresponding authors. E-mail addresses: [email protected] (B. Liu), [email protected] (H.-P. Tan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.06.053 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
computed tomography (CT) measurement method, through which a combustion flame is imaged using a number of cameras at different positions and angles. Hence, flame images at different projections are obtained. This approach can yield better spatial resolution compared to that yielded by single-camera techniques; the greater the projection, the better is the resolution [7]. However, an increased number of cameras results in greater system complexity and cost. Further, as strict centering of the spatial position of the optical axis of the polyphaser system is required, along with synchronization and calibration of more than one camera, the installation and operation of such systems is technically difficult [7]. In contrast, light-field imaging technology can theoretically achieve the synchronous acquisition of optical-field information at large projection angles [8]. Therefore, light-field imaging is more suitable than a polyphaser system for detecting the temperature of an exhaust plume, as it virtually divides the main aperture into many sub-apertures, each one of which can obtain the radiation intensity image at its specific view angle. However, because of various limitations related to imaging mechanisms, arithmetic, and other factors, existing light-field imaging techniques are limited to the acquisition of light-field information under surface radiation conditions, and radiated light-field information cannot be obtained for participating media with complex anisotropy (such as an exhaust-plume flow field) [9–11]. To realize the precise reconstruction of the 3D temperature field of a large-scale combustion flame, the flame temperature must be obtained, and a reconstruction algorithm for optical radiation information that can be applied to participatory flame media with
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model facilitating the imaging of the participating medium that was developed in the present study.
complex anisotropy must be constructed. The latter step is very important. In establishing the reconstruction algorithm to yield the effective light-field radiation information, the aim is to facilitate the accurate imaging of the characteristics of the participating medium. Since the publication of Ren’s study in 2005 [12], lightfield camera research has primarily been focused on the imaging of non-participating media (i.e., media without absorption, scattering, or active emission). For example, Su et al. [13] utilized the characteristics of a light-field camera to obtain the spatial information of rays, used the light-field camera theory to develop a snapshot imaging spectrometer, and proved that a camera based on a microlens array shows superior performance compared to a device based on a pinhole array. Further, Liang et al. [14] constructed the ray transmission model of a light-field camera to analyze the fundamental limitations of the camera resolution and, thereby, evaluated design concepts of light-field cameras. Apelt et al. [15] used focus and depth-of-field images obtained using a light-field camera to observe the morphology of plant growth and to acquire related information. Further, Kim et al. [16] used a light-field camera to detect facial activity, while Marwah et al. [17] proposed a compression light-field camera structure, which can extract a light field with a better resolution from a single image as well as compress and de-noise a 4D light field. The nonlinear attenuation of radiation intensity in participating media makes it difficult to reconstruct the radiation intensity of medium elements. Therefore, the influence of the radiative characteristics of the medium needs to be clarified. However, very few studies have been published on the light-field imaging of participating media, and therefore, further study is required. Focusing on this problem, in this study, we use a Monte Carlo method (MCM) to construct a computer simulation model, and we simulate a microlens-array imaging process for a high-temperature participating medium. We analyze the imaging performance for light-field information for a pure absorbent medium, a scattering medium, and a medium with active emission ability. In addition, we analyze the differences between sub-aperture and refocus imaging using the obtained imaging results to identify the appropriate imaging technique for reconstructing the temperature-field of the medium. Finally, we simulate a physical model of a typical flame.
2.1. Light-field camera model The common light-field camera caliber is not sufficiently large to cause small distance changes between various sub-apertures, and the perspective changes of the objects are not significant. In addition to factors such as insufficient numbers of pixels, insufficient distance between the objects, and the objects being substantially located within the depth of field, a significant factor also led to the small differences in the refocusing results. This paper considered the use of a lens of larger caliber to increase the distance between the main lens and the objects to simulate the perspective changes and refocusing more accurately. The reflecting telescope caliber is easy to modify while maintaining a constant focal length. Fig. 1 shows a model of the camera structure. The hook faces on the two sides of the main lens are spherical surfaces with radius R ¼ 0:2 m. The lens thickness along the optical axis is L ¼ 0:02 m, the main lens diameter is D = 120 mm, the focal length of each main lens is f = 304.0987 mm, and the corresponding minimum aperture F-number is F = 2.534. The distance between the adjacent microlens centers is 0.5 mm, the diameter of each microlens is d = 0.48 mm, the hook faces on the two sides of the microlens are spherical surfaces with radius r = 1.15 mm, the microlens thickness is 0.1 mm, and the refractive index of the microlens medium is n = 1.5. For these microlens parameters, the focal length of each microlens is f = 1.1669 m, as calculated from
1 1 1 ðn 1ÞL : þ ¼ ðn 1Þ f R1 R2 nR1 R2
ð1Þ
Therefore, the minimum aperture of the microlens is F = 2.431 for a microlens array located outside the focal length of the main lens. Further, the F of the microlens and main lens meet the requirements of Eq. (2), where
ðL þ f Þ=D P f =d: 2. Model and algorithm
ð2Þ
A single lens, rather than a group of lenses, is used as the main lens as this yields superior imaging performance. In general, the aperture is reduced in order to reduce lens aberration. In this example, the aperture diameter is 100 mm and F 3.04. A total of 60 60 microlenses are employed, the pixel size of the charge-coupled device (CCD) camera is 0.05 mm, and the number of pixels is 600 600. Therefore, each microlens corresponds to 10 10 pixels, each of which records the directional information of the light.
In a previous study, we constructed a simulation calculation model [18,19] that can be used for light-field camera imaging simulations employing an MCM [20–22]. Related information can be found in reference [12]. In the previous study, only the surface radiation of objects was imaged, and participating media were not considered [23]. Therefore, we will briefly introduce the light-field camera simulation model below, before discussing the
y
D
x
0 z
x = 4m Fig. 1. Camera structure.
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2.3. Simulation algorithm
Table 1 Temperature and radiative parameters of medium sub-blocks. Number
Blackbody radiation temperature (K)
Attenuation coefficient
Scattering albedo
1 2 3
300 900 1500
2.0 1.5 1.0
0.5 0.5 0.5
3 3 1 1
1 1 2 2
2 2 a
3
2 2
31 3
3
12 31 1
2
3
2 3 1
1 1
2
2 3 3
2 2 3
3 3
12 31 1
2 12
1
2
3
3 1
3 1 2
2 2 3 3 1 1
b
3 3
2 12 2
1 2 2
1 1
3 3 3 1
3 1 2
y
1 2 3
x z
c
Fig. 2. Medium sub-block arrangements, where the numbers correspond to the parameter sets given in Table 1.
2.2. Participating medium model We construct a model of the participating medium to illustrate the effect of the characteristics of the participating medium on the imaging process. The concrete structure and parameters are given below, and the calculations performed in this study are based on this model with no specialized adjustments. We set the cube medium dimensions to 0.7 m 0.7 m 0.7 m, which is then equidistantly divided into 3 3 3 sub-blocks. The physical properties of each sub-block correspond to one of three conditions (numbered 1–3) and, in order to increase the differences in radiation energy for the various experimental conditions, we set three significantly different temperatures for these condition sets. The parameters corresponding to each set of conditions are listed in Table 1. Further, we assume that the CCD completely absorbs all of the radiation wavelength energy from the simulated medium and translates it into an image signal. The centers of the medium block arrangements were positioned on the optical axis of the light-field camera, with the blocks facing the camera. The front and rear surfaces of the block arrangement were positioned 9.35 and 10.05 m from the photocenter of the main camera lens, respectively. The camera was focused at 10 m to facilitate the comparison of the imaging results obtained for different block configurations. Fig. 2 shows various sub-block arrangements. The physical parameters of the model can be changed as required for different calculations, as will be shown in the calculations discussed in the next section.
MCMs are usually applied to simulate radiation transfer based on a physical model of the geometrical optics of the medium and excluding the wave optics [24–26]. Although some Monte Carlo simulation methods involve interference, diffraction, and other optical wave phenomena, they utilize existing physical equations to construct a probabilistic model of correlated phenomena, rather than to simulate the wave optics mechanism. By using an MCM based on geometrical optics, the transfer of photons (light beams, rays, radiation, energy beams) is decomposed into several processes in this study, as described below, and a corresponding random model is constructed [27]. The processes are: (1) Surface (interface): Emission, absorption, reflection, projection, and refraction [28,29]; (2) Medium or medium with particles (dispersion): Emission, decay (including absorption and scattering of the medium or particles). The employed technique compares the magnitude of the homogeneous random number Rh in the [0, 1] range [30], and the equations that describe the physical processes indicate whether or not the various physical processes occur. In other words, Rh is used to calculate the physical process conditions. Using the MCM to simulate ray transfer in a complex geometric region requires the following steps:
Fig. 4. Sub-aperture images for a pure absorbent medium.
Fig. 3. Light-field imaging results for a pure absorbent medium with different attenuation coefficients.
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Fig. 5. Refocused images for different object distances (m).
Fig. 6. Light-field imaging results for absorbing or scattering medium for different scattering albedo values.
Fig. 7. Refocusing results for different scattering albedo values and a refocusing distance of 9.35 m.
(1) If the medium in the region has decaying characteristics, then the transmission distance L should be given in advance, or the process should move to the next step. (2) Calculate the distance Lt for the ray separately from the former starting point to the possible intersection points for every surface in the region; exclude the surface if there is no intersection point, and let Lt ¼ 0. (3) Exercise caution: there may be two points on the quadric surface, but only one of them is actually a possible intersection point. After the distances to the intersection points are obtained, check whether the incident direction is the reverse surface-normal direction; if not, then exclude the possible point. (4) Further, check if the direction of the intersection point is the same as the ray direction; if not, then again exclude the point. (5) The intersection points of every surface should then be checked because the actual surface is not infinite and has certain boundary constraints. If the intersection point exceeds the surface boundary, then the point does not exist, and Lt ¼ 0.
(6) Find the value of Lt > 0 that has the minimum value among the surplus intersection points. That point is the actual intersection surface, and the intersection point coordinates can then be given. (7) If the medium in the region has decaying characteristics, the sizes of L in step one and Lt should be compared: If L P Lt , then the ray touches the region surface, and the ray’s absorption, reflection, or refraction characteristics can be calculated based on the surface physical properties; if L < Lt , then the ray interacts with the medium of the region, and the ray’s absorption or scattering can be calculated based on the surface physical properties [31]. 3. Calculation results and analysis From previous studies [31], we know that refocused images for different object distances can be obtained in the case of attenuation-free surface radiation (a normal imaging process). However, it is unclear whether the information on object distance can be extracted for the refocused light-field information images of
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Fig. 8. Image of radiative medium blocks (without micro-lens array).
Fig. 11. Light-field camera image of radiative medium blocks.
Fig. 9. Light-field camera image of radiative medium blocks.
a participating medium. To answer this question, we investigate the light-field imaging of a participating medium in this section. 3.1. Pure absorbent medium The light-field imaging calculation model for a pure absorbent medium is constructed stepwise in this subsection. We consider
both setups b and c of Fig. 2, such that the medium blocks represent a pure absorbent medium with a scattering albedo x = 0. Further, there is no emission from the medium itself; thus, the emissivity e = 0. We set the attenuation coefficients je of the two planes to 1.0, 3.0, or 5.0. Recall that Table 1 lists the physical properties of the three different medium sub-block types utilized in the b and c horizons. This model corresponds to medium horizons with active ability for energy transfer in the direction of the camera after the absorptive action by b and c. Fig. 3 shows the simulated results for the light-field camera. Considerable differences can be seen between the imaging results for the different medium absorption conditions shown in Fig. 3. With the increase in the medium absorption ability, the energy emitted by the medium blocks and arriving at the camera lens generally decreases. For je = 5, the lower-temperature medium block energy does not exceed the set camera detection threshold, and imaging cannot be performed. Through comparison with these calculation results, there is very little difference between the radiation characteristic imaging performance of traditional and light-field imaging for the modeled medium layer. However, unlike the traditional method, light-field
Fig. 10. CCD image refocusing results for refocusing distances from the main lens of (a) 9.35, (b) 10, and (c) 10.05 m.
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Sub-aperture image B
...... ......
Sub-aperture image A Fig. 12. Sub-aperture image as a projection of the radiative field.
Fig. 13. Flame shapes.
Table 2 Temperature and radiative parameters of cylindrical flame layers. Number
Blackbody radiation temperature (K)
Decay factor
Scattering albedo
1 2 3 4
1500 1200 1000 800
1.0 1.3 1.6 2.0
0.5 0.5 0.5 0.5
camera imaging allows refocusing to be applied to images with different depths of field. Therefore, in what follows, we use a selfprogrammed sub-aperture imaging calculation program to compound each of a set of recorded sub-aperture images. As an example, the sub-aperture imaging results for je = 1 are shown in Fig. 4. The main lens is a single lens with spherical surfaces at both sides; as a result, the imaging performance is not as good as expected, especially at the edge of image. A main lens consisting of a group of multiple lenses will be modeled in the future.
Fig. 14. (a) Direct and (b) light-field images of cylindrical layered flame.
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Y. Yuan et al. / International Journal of Heat and Mass Transfer 102 (2016) 518–527 Table 3 Temperature and radiative parameters of ellipsoid flame layers. Number
Blackbody radiation temperature (K)
Decay factor
Scattering albedo
1 2 3
1200 1000 800
1.0 1.3 1.6
0.5 0.5 0.5
Fig. 5 shows images obtained for different object distances using a refocusing calculation. This figure indicates that the refocusing distance results are 9.35, 9.58, and 9.81 m, which correspond to the optical axis distances from the main camera lens of the three medium layers, a, b, and c, respectively. For this figure, the front surface of every medium layer was selected as the refocus location. Regarding the adjustment of the refocus location, superior image focusing is obtained closer to the initiative emission layer medium. However, obvious defocusing phenomena appear for focusing at 9.35 m. 3.2. Absorbing and scattering medium Fig. 15. Sub-aperture image of cylindrical layered flame.
3
2
4.8cm
1
2cm
The light-field imaging characteristics for a scattering medium are examined in this subsection. In contrast to the previous subsection, we set the medium blocks of both the b and c planes to represent absorbing and scattering media; therefore, x – 0. Further, e = 0, as self-emission is neglected. Fig. 6 shows the results obtained by incorporating absorption and scattering, which were simulated for je = 1 and x = 0.01, 0.5, and 0.99. The other parameters are identical to those in the previous subsection. From these results, it is apparent that altering the scattering phase function is not sufficient to cause significant changes in the light-field imaging results for constant je. Regardless of the scattering phase function value, the light-field information distribution entering the camera does not significantly vary. For further analysis, we present the refocused images for the three x conditions. Therefore, Fig. 7 shows the results obtained for a refocusing object distance of 9.35 m and x = 0.01, 0.5, and 0.99. From the images shown in Fig. 7, no significant differences in the brightness, definition, and edge contour of refocusing data results are obtained for the different x conditions. This is because the energy entering the camera accounts for a very small solid angle relative to the medium in 4p space with energy emission. Once ray scattering and the corresponding changes in direction occur, the energy does not enter the field range. At that point, the scattering and absorption play consistent roles. That is, the scattering albedo alters the scattering and absorption ability of the medium, but the total attenuation ability does not change. Therefore, changes in x do not affect the characteristics of the light-field imaging. 3.3. Active emission medium
Fig. 16. Sketch of ellipsoid layered flame.
We know that the different sub-aperture images represent different zones of the energy received at the main lens, which has been focused. Fig. 4 shows that increased differences are obtained between different sub-aperture images if there are greater differences between the incident angles. For example, there is little difference between the four sub-aperture images in the center location because the incident angles are very similar. However, when the angle of incidence is increased towards the exterior of the lens, the sub-aperture images are distorted, with the outermost images exhibiting very significant distortion.
An actual high-temperature flame is an active emission medium, rather than just a participating attenuating medium; that is, the medium itself can radiate energy outward. Therefore, in this subsection, we simulate light-field imaging that includes absorption, scattering, and emission. Fig. 1 shows the model employed here, and the medium is modeled based on the sets of physical properties listed in Table 1. Fig. 8 shows the results for the main lens imaging directly to the CCD in the absence of a microlens array. A combination of parameter sets 1–3 is considered in all medium planes from front to back (ca in Fig. 2); therefore, there is considerable variety in the energy values that arrive at the camera. This is especially true for cases
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Fig. 17. Direct and light-field images of ellipsoid layered flame.
Fig. 18. Sub-aperture image of ellipsoid layered flame.
where medium blocks with parameter set 1 are positioned near the lens. As a result of the low temperature, low energy radiation transmission, and strong radiation attenuation, the lower left to upper right diagonal blocks have low brightness in Fig. 8. Fig. 9 shows the light-field images obtained after the addition of a microlens array. Fig. 10 shows the refocus results obtained for Fig. 9, where Fig. 10(a)(c) are the results corresponding to refocusing at distances from the main lens of 9.35, 10, and 10.05 m. In addition, the coordinate axis shows the number of the pixels of the image. Note that the results shown in Fig. 10 are closest to the commonly obtained imaging results for participatory media. As the distance from the focus point increases, the images become blurred. With reference to the radiation parameter arrangement in Fig. 2, the difference from the refocused surface image processing results can be explained. That is, we cannot directly obtain the radiance at the focus point because of the forward lap of the medium radiation. The different depth-of-field images only indicate the varying degrees of refocusing performed to obtain the apparent radiation information.
Fig. 11 shows sub-aperture images obtained for different perspectives and for a large depth of field. The coordinate axis shows the number of the pixels of the sub-aperture images. The energy value obtained for each pixel of the image is equal to the integral value of the radiation energy for that micro-unit in that direction and on a straight line. A sub-aperture image is equivalent to the projection of a 3D medium in the sub-aperture direction. If D is sufficiently large, the obtained sub-aperture images are projections of the 3D medium in different sub-aperture directions, as shown in Fig. 12. Therefore, we are of the view that the interior radiation information cannot be retrieved in this manner in the case of a participating medium with active emission ability. In this case, the sub-aperture images that contain information for multiple detection angles reflect the apparent radiation, but they contain more information on independent-direction radiation intensity compared to images obtained after a refocusing process, and are more suitable for the reconstruction of a high-temperature flame light field. The principle of temperature-field reconstruction using subaperture information is as follows. Because of the overlapping of the projection directions, equations that relate to the micro-unit radiation energy values can be derived. When the apparent radiation of the micro-unit is isotropic and the light is not attenuated in the medium, we can obtain the apparent radiation in all parts of the 3D medium simply by using a digital computer-imaging algorithm. Then, we can obtain the temperature field of the medium by inverting the radiation transfer of this apparent radiation field.
3.4. Stratified flame model imaging On the basis of the above findings, we consider an actual flame model in this subsection. Simulated light-field camera imaging and two images of actual flames are used in the investigation of the radiation temperature inversion. As shown in Fig. 13, there are two common flame shapes: high-speed jet flames and lowvelocity flow flames. In the former type, an example of which are aircraft jet flames, the radiation properties and temperature have less variation along the jet direction and over a longer length, with the only obvious change being along the radial direction. This is because of the high jet velocity. A simplified model consists of a cylindrical flame model with finite length constructed using concentric cylinders stratified along the radial direction. In contrast,
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in the case of low-velocity flow flames such as candle flames and natural convection, an ellipsoid shape can be approximated. We first simulate the light-field imaging of cylindrical flame radiation. The flame height is 1.0 m, the maximum radius is 0.4 m, and the cylindrical flame is divided into quarters according to the radius. The medium blocks are arranged such that the numbers increase in the outward direction; thus, isotropic scattering is considered. The radiation properties of the medium blocks are listed in Table 2. Note that the flame is 10 m from the main lens. Fig. 14 shows the direct and light-field camera imaging results for the cylindrical stratified flame, while Fig. 15 shows a subaperture image of a simulated CCD image obtained after postprocessing. The coordinate axis shows the number of the pixels of the sub-aperture images. Fig. 16 shows the simulated ellipsoid flame, in which the three ellipsoid centers do not overlap. Because of the small flame size, it is positioned only 1 m from the main lens to ensure sufficient imaging size. However, this leads to an increase in the distance between the microlens array and the main lens. Eq. (1) shows that the image space F-number increases, while the spot radius behind each microlens decreases accordingly. Table 3 lists the temperature and physical parameters of thermal radiation of the ellipsoid flame for each layer in Fig. 16, from the interior (1) to the exterior (3). Fig. 17 shows the simulated imaging results for direct and lightfield camera imaging. The spot in Fig. 17(b) is obviously smaller than that in the former simulated results, confirming the changing rules for increased F. With the decreased spot size, the utilization of CCD pixels behind the microlens is efficiently reduced. The number of sub-aperture images after processing is also reduced, as shown in Fig. 18. The coordinate axis shows the number of pixels of the sub-aperture images. Considerable differences can be seen between the imaging information obtained in Figs. 15 and 18 for the different imaging angles and flame types. Therefore, regarding the refocusing method (which can only present the surface radiation), it would be more effective to utilize information obtained for different sub-apertures to reconstruct the temperature field of the hightemperature flame medium.
4. Conclusion In this paper, we used a Monte Carlo method to construct a simulation model for light-field camera imaging calculations so as to simulate a microlens-array imaging process for a hightemperature participating medium. The light imaging information obtained for a pure absorbent medium, scattering medium, and active emission medium was analyzed. Further, through a comparison of the differences between sub-aperture and refocusing imaging based on the imaging results, we identified the imaging method most suitable for the reconstruction of a participating medium’s temperature field. Finally, we simulated a physical model of a typical flame and performed the associated calculations. From these investigations, we came to the following conclusions: (1) By comparing the simulated imaging results for different participating media, it was found that the change in the optical depth of an inactive participating medium directly affects the imaging results. Further, for 4p space, only a small component of the medium scattering energy can enter the camera lens. Therefore, the majority of the light is scattered from the optical path of the system such that it exits the system and does not reach the lens. In this case, the scattering and absorption have almost the same effect, with no special consideration being awarded to the scattering energy.
(2) By comparing the refocusing and sub-aperture imaging results for different conditions, it was shown that the subaperture result can reflect the object for which the emission energy is being detected at different angles. Moreover, the imaging results obtained at different angles are mutually independent and can be used for inversion. Regarding the refocusing in the case of an inactive participating medium, the use of this technique can effectively improve the clarity of the imaging results. However, the brightness calculated at a refocused point does not correspond to the radiance at that point. Therefore, an effective algorithm needs to be developed for the reconstruction of radiance fields and, therefore, temperature fields.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 51327803 & 51406041), and the Postdoctoral Science Foundation of China (Grant No. 2014M551239). A very special acknowledgement is made to the editors and referees who made important comments to improve this paper.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Light-field-camera imaging simulation of participatory media using Monte Carlo method Yuan Yuan, Bin Liu ⇑, Sai Li, He-Ping Tan ⇑ School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China
a r t i c l e
i n f o
Article history: Received 29 January 2016 Received in revised form 6 April 2016 Accepted 20 June 2016
Keywords: Radiative transfer Light field camera Monte Carlo method Participating medium High-temperature flame
a b s t r a c t In this study, we use the Monte Carlo method to analyze the light-field camera imaging of various participating media (absorbing, scattering and emitting media), along with refocused and sub-aperture images, during the process of reconstructing the temperature field of a high-temperature combustion flame. Hence, the optical field of the participating medium is analyzed. We found that if the participating medium does not have active emission capability, the absorptive and scattering capacity can be regarded as attenuation capacity. However, if the medium has active emission capability, it is difficult to obtain the emission characteristics corresponding to the depth of field through refocusing, and the medium’s temperature field can only be reconstructed using sub-aperture images. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction High-temperature combustion is widely employed in aerospace technology, power and energy generation, ferrous metallurgy, and the chemical industry, in applications such as rocket engines, gas turbines, engines, station boilers, coal gasification rectors, and other high-temperature devices [1–4]. The mechanism and apparent characteristics of the combustion of fuel have been investigated through both theoretical and experimental research; this has helped in revealing the core parameters of combustion phenomena and the laws governing the combustion process. Such research can also help in developing and facilitating the optimized design and operation of combustion systems. The measurement of a flame’s three-dimensional (3D) radiant energy field [5] is primarily based on readings from a single camera and a polyphaser. Such a one-camera measuring system is simple, inexpensive, and easy to install. This system can be used to reconstruct the flame cross section directly and three dimensions. However, single-camera image measurement systems are generally limited and can only be applied to stable, axially symmetric flames [6]. This prevents their application to unsteady and turbulent flame measurement. An increasing number of studies on polyphasers have been conducted in recent years. The polyphaser system is derived from the ⇑ Corresponding authors. E-mail addresses: [email protected] (B. Liu), [email protected] (H.-P. Tan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.06.053 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
computed tomography (CT) measurement method, through which a combustion flame is imaged using a number of cameras at different positions and angles. Hence, flame images at different projections are obtained. This approach can yield better spatial resolution compared to that yielded by single-camera techniques; the greater the projection, the better is the resolution [7]. However, an increased number of cameras results in greater system complexity and cost. Further, as strict centering of the spatial position of the optical axis of the polyphaser system is required, along with synchronization and calibration of more than one camera, the installation and operation of such systems is technically difficult [7]. In contrast, light-field imaging technology can theoretically achieve the synchronous acquisition of optical-field information at large projection angles [8]. Therefore, light-field imaging is more suitable than a polyphaser system for detecting the temperature of an exhaust plume, as it virtually divides the main aperture into many sub-apertures, each one of which can obtain the radiation intensity image at its specific view angle. However, because of various limitations related to imaging mechanisms, arithmetic, and other factors, existing light-field imaging techniques are limited to the acquisition of light-field information under surface radiation conditions, and radiated light-field information cannot be obtained for participating media with complex anisotropy (such as an exhaust-plume flow field) [9–11]. To realize the precise reconstruction of the 3D temperature field of a large-scale combustion flame, the flame temperature must be obtained, and a reconstruction algorithm for optical radiation information that can be applied to participatory flame media with
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model facilitating the imaging of the participating medium that was developed in the present study.
complex anisotropy must be constructed. The latter step is very important. In establishing the reconstruction algorithm to yield the effective light-field radiation information, the aim is to facilitate the accurate imaging of the characteristics of the participating medium. Since the publication of Ren’s study in 2005 [12], lightfield camera research has primarily been focused on the imaging of non-participating media (i.e., media without absorption, scattering, or active emission). For example, Su et al. [13] utilized the characteristics of a light-field camera to obtain the spatial information of rays, used the light-field camera theory to develop a snapshot imaging spectrometer, and proved that a camera based on a microlens array shows superior performance compared to a device based on a pinhole array. Further, Liang et al. [14] constructed the ray transmission model of a light-field camera to analyze the fundamental limitations of the camera resolution and, thereby, evaluated design concepts of light-field cameras. Apelt et al. [15] used focus and depth-of-field images obtained using a light-field camera to observe the morphology of plant growth and to acquire related information. Further, Kim et al. [16] used a light-field camera to detect facial activity, while Marwah et al. [17] proposed a compression light-field camera structure, which can extract a light field with a better resolution from a single image as well as compress and de-noise a 4D light field. The nonlinear attenuation of radiation intensity in participating media makes it difficult to reconstruct the radiation intensity of medium elements. Therefore, the influence of the radiative characteristics of the medium needs to be clarified. However, very few studies have been published on the light-field imaging of participating media, and therefore, further study is required. Focusing on this problem, in this study, we use a Monte Carlo method (MCM) to construct a computer simulation model, and we simulate a microlens-array imaging process for a high-temperature participating medium. We analyze the imaging performance for light-field information for a pure absorbent medium, a scattering medium, and a medium with active emission ability. In addition, we analyze the differences between sub-aperture and refocus imaging using the obtained imaging results to identify the appropriate imaging technique for reconstructing the temperature-field of the medium. Finally, we simulate a physical model of a typical flame.
2.1. Light-field camera model The common light-field camera caliber is not sufficiently large to cause small distance changes between various sub-apertures, and the perspective changes of the objects are not significant. In addition to factors such as insufficient numbers of pixels, insufficient distance between the objects, and the objects being substantially located within the depth of field, a significant factor also led to the small differences in the refocusing results. This paper considered the use of a lens of larger caliber to increase the distance between the main lens and the objects to simulate the perspective changes and refocusing more accurately. The reflecting telescope caliber is easy to modify while maintaining a constant focal length. Fig. 1 shows a model of the camera structure. The hook faces on the two sides of the main lens are spherical surfaces with radius R ¼ 0:2 m. The lens thickness along the optical axis is L ¼ 0:02 m, the main lens diameter is D = 120 mm, the focal length of each main lens is f = 304.0987 mm, and the corresponding minimum aperture F-number is F = 2.534. The distance between the adjacent microlens centers is 0.5 mm, the diameter of each microlens is d = 0.48 mm, the hook faces on the two sides of the microlens are spherical surfaces with radius r = 1.15 mm, the microlens thickness is 0.1 mm, and the refractive index of the microlens medium is n = 1.5. For these microlens parameters, the focal length of each microlens is f = 1.1669 m, as calculated from
1 1 1 ðn 1ÞL : þ ¼ ðn 1Þ f R1 R2 nR1 R2
ð1Þ
Therefore, the minimum aperture of the microlens is F = 2.431 for a microlens array located outside the focal length of the main lens. Further, the F of the microlens and main lens meet the requirements of Eq. (2), where
ðL þ f Þ=D P f =d: 2. Model and algorithm
ð2Þ
A single lens, rather than a group of lenses, is used as the main lens as this yields superior imaging performance. In general, the aperture is reduced in order to reduce lens aberration. In this example, the aperture diameter is 100 mm and F 3.04. A total of 60 60 microlenses are employed, the pixel size of the charge-coupled device (CCD) camera is 0.05 mm, and the number of pixels is 600 600. Therefore, each microlens corresponds to 10 10 pixels, each of which records the directional information of the light.
In a previous study, we constructed a simulation calculation model [18,19] that can be used for light-field camera imaging simulations employing an MCM [20–22]. Related information can be found in reference [12]. In the previous study, only the surface radiation of objects was imaged, and participating media were not considered [23]. Therefore, we will briefly introduce the light-field camera simulation model below, before discussing the
y
D
x
0 z
x = 4m Fig. 1. Camera structure.
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2.3. Simulation algorithm
Table 1 Temperature and radiative parameters of medium sub-blocks. Number
Blackbody radiation temperature (K)
Attenuation coefficient
Scattering albedo
1 2 3
300 900 1500
2.0 1.5 1.0
0.5 0.5 0.5
3 3 1 1
1 1 2 2
2 2 a
3
2 2
31 3
3
12 31 1
2
3
2 3 1
1 1
2
2 3 3
2 2 3
3 3
12 31 1
2 12
1
2
3
3 1
3 1 2
2 2 3 3 1 1
b
3 3
2 12 2
1 2 2
1 1
3 3 3 1
3 1 2
y
1 2 3
x z
c
Fig. 2. Medium sub-block arrangements, where the numbers correspond to the parameter sets given in Table 1.
2.2. Participating medium model We construct a model of the participating medium to illustrate the effect of the characteristics of the participating medium on the imaging process. The concrete structure and parameters are given below, and the calculations performed in this study are based on this model with no specialized adjustments. We set the cube medium dimensions to 0.7 m 0.7 m 0.7 m, which is then equidistantly divided into 3 3 3 sub-blocks. The physical properties of each sub-block correspond to one of three conditions (numbered 1–3) and, in order to increase the differences in radiation energy for the various experimental conditions, we set three significantly different temperatures for these condition sets. The parameters corresponding to each set of conditions are listed in Table 1. Further, we assume that the CCD completely absorbs all of the radiation wavelength energy from the simulated medium and translates it into an image signal. The centers of the medium block arrangements were positioned on the optical axis of the light-field camera, with the blocks facing the camera. The front and rear surfaces of the block arrangement were positioned 9.35 and 10.05 m from the photocenter of the main camera lens, respectively. The camera was focused at 10 m to facilitate the comparison of the imaging results obtained for different block configurations. Fig. 2 shows various sub-block arrangements. The physical parameters of the model can be changed as required for different calculations, as will be shown in the calculations discussed in the next section.
MCMs are usually applied to simulate radiation transfer based on a physical model of the geometrical optics of the medium and excluding the wave optics [24–26]. Although some Monte Carlo simulation methods involve interference, diffraction, and other optical wave phenomena, they utilize existing physical equations to construct a probabilistic model of correlated phenomena, rather than to simulate the wave optics mechanism. By using an MCM based on geometrical optics, the transfer of photons (light beams, rays, radiation, energy beams) is decomposed into several processes in this study, as described below, and a corresponding random model is constructed [27]. The processes are: (1) Surface (interface): Emission, absorption, reflection, projection, and refraction [28,29]; (2) Medium or medium with particles (dispersion): Emission, decay (including absorption and scattering of the medium or particles). The employed technique compares the magnitude of the homogeneous random number Rh in the [0, 1] range [30], and the equations that describe the physical processes indicate whether or not the various physical processes occur. In other words, Rh is used to calculate the physical process conditions. Using the MCM to simulate ray transfer in a complex geometric region requires the following steps:
Fig. 4. Sub-aperture images for a pure absorbent medium.
Fig. 3. Light-field imaging results for a pure absorbent medium with different attenuation coefficients.
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Fig. 5. Refocused images for different object distances (m).
Fig. 6. Light-field imaging results for absorbing or scattering medium for different scattering albedo values.
Fig. 7. Refocusing results for different scattering albedo values and a refocusing distance of 9.35 m.
(1) If the medium in the region has decaying characteristics, then the transmission distance L should be given in advance, or the process should move to the next step. (2) Calculate the distance Lt for the ray separately from the former starting point to the possible intersection points for every surface in the region; exclude the surface if there is no intersection point, and let Lt ¼ 0. (3) Exercise caution: there may be two points on the quadric surface, but only one of them is actually a possible intersection point. After the distances to the intersection points are obtained, check whether the incident direction is the reverse surface-normal direction; if not, then exclude the possible point. (4) Further, check if the direction of the intersection point is the same as the ray direction; if not, then again exclude the point. (5) The intersection points of every surface should then be checked because the actual surface is not infinite and has certain boundary constraints. If the intersection point exceeds the surface boundary, then the point does not exist, and Lt ¼ 0.
(6) Find the value of Lt > 0 that has the minimum value among the surplus intersection points. That point is the actual intersection surface, and the intersection point coordinates can then be given. (7) If the medium in the region has decaying characteristics, the sizes of L in step one and Lt should be compared: If L P Lt , then the ray touches the region surface, and the ray’s absorption, reflection, or refraction characteristics can be calculated based on the surface physical properties; if L < Lt , then the ray interacts with the medium of the region, and the ray’s absorption or scattering can be calculated based on the surface physical properties [31]. 3. Calculation results and analysis From previous studies [31], we know that refocused images for different object distances can be obtained in the case of attenuation-free surface radiation (a normal imaging process). However, it is unclear whether the information on object distance can be extracted for the refocused light-field information images of
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Fig. 8. Image of radiative medium blocks (without micro-lens array).
Fig. 11. Light-field camera image of radiative medium blocks.
Fig. 9. Light-field camera image of radiative medium blocks.
a participating medium. To answer this question, we investigate the light-field imaging of a participating medium in this section. 3.1. Pure absorbent medium The light-field imaging calculation model for a pure absorbent medium is constructed stepwise in this subsection. We consider
both setups b and c of Fig. 2, such that the medium blocks represent a pure absorbent medium with a scattering albedo x = 0. Further, there is no emission from the medium itself; thus, the emissivity e = 0. We set the attenuation coefficients je of the two planes to 1.0, 3.0, or 5.0. Recall that Table 1 lists the physical properties of the three different medium sub-block types utilized in the b and c horizons. This model corresponds to medium horizons with active ability for energy transfer in the direction of the camera after the absorptive action by b and c. Fig. 3 shows the simulated results for the light-field camera. Considerable differences can be seen between the imaging results for the different medium absorption conditions shown in Fig. 3. With the increase in the medium absorption ability, the energy emitted by the medium blocks and arriving at the camera lens generally decreases. For je = 5, the lower-temperature medium block energy does not exceed the set camera detection threshold, and imaging cannot be performed. Through comparison with these calculation results, there is very little difference between the radiation characteristic imaging performance of traditional and light-field imaging for the modeled medium layer. However, unlike the traditional method, light-field
Fig. 10. CCD image refocusing results for refocusing distances from the main lens of (a) 9.35, (b) 10, and (c) 10.05 m.
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Sub-aperture image B
...... ......
Sub-aperture image A Fig. 12. Sub-aperture image as a projection of the radiative field.
Fig. 13. Flame shapes.
Table 2 Temperature and radiative parameters of cylindrical flame layers. Number
Blackbody radiation temperature (K)
Decay factor
Scattering albedo
1 2 3 4
1500 1200 1000 800
1.0 1.3 1.6 2.0
0.5 0.5 0.5 0.5
camera imaging allows refocusing to be applied to images with different depths of field. Therefore, in what follows, we use a selfprogrammed sub-aperture imaging calculation program to compound each of a set of recorded sub-aperture images. As an example, the sub-aperture imaging results for je = 1 are shown in Fig. 4. The main lens is a single lens with spherical surfaces at both sides; as a result, the imaging performance is not as good as expected, especially at the edge of image. A main lens consisting of a group of multiple lenses will be modeled in the future.
Fig. 14. (a) Direct and (b) light-field images of cylindrical layered flame.
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Blackbody radiation temperature (K)
Decay factor
Scattering albedo
1 2 3
1200 1000 800
1.0 1.3 1.6
0.5 0.5 0.5
Fig. 5 shows images obtained for different object distances using a refocusing calculation. This figure indicates that the refocusing distance results are 9.35, 9.58, and 9.81 m, which correspond to the optical axis distances from the main camera lens of the three medium layers, a, b, and c, respectively. For this figure, the front surface of every medium layer was selected as the refocus location. Regarding the adjustment of the refocus location, superior image focusing is obtained closer to the initiative emission layer medium. However, obvious defocusing phenomena appear for focusing at 9.35 m. 3.2. Absorbing and scattering medium Fig. 15. Sub-aperture image of cylindrical layered flame.
3
2
4.8cm
1
2cm
The light-field imaging characteristics for a scattering medium are examined in this subsection. In contrast to the previous subsection, we set the medium blocks of both the b and c planes to represent absorbing and scattering media; therefore, x – 0. Further, e = 0, as self-emission is neglected. Fig. 6 shows the results obtained by incorporating absorption and scattering, which were simulated for je = 1 and x = 0.01, 0.5, and 0.99. The other parameters are identical to those in the previous subsection. From these results, it is apparent that altering the scattering phase function is not sufficient to cause significant changes in the light-field imaging results for constant je. Regardless of the scattering phase function value, the light-field information distribution entering the camera does not significantly vary. For further analysis, we present the refocused images for the three x conditions. Therefore, Fig. 7 shows the results obtained for a refocusing object distance of 9.35 m and x = 0.01, 0.5, and 0.99. From the images shown in Fig. 7, no significant differences in the brightness, definition, and edge contour of refocusing data results are obtained for the different x conditions. This is because the energy entering the camera accounts for a very small solid angle relative to the medium in 4p space with energy emission. Once ray scattering and the corresponding changes in direction occur, the energy does not enter the field range. At that point, the scattering and absorption play consistent roles. That is, the scattering albedo alters the scattering and absorption ability of the medium, but the total attenuation ability does not change. Therefore, changes in x do not affect the characteristics of the light-field imaging. 3.3. Active emission medium
Fig. 16. Sketch of ellipsoid layered flame.
We know that the different sub-aperture images represent different zones of the energy received at the main lens, which has been focused. Fig. 4 shows that increased differences are obtained between different sub-aperture images if there are greater differences between the incident angles. For example, there is little difference between the four sub-aperture images in the center location because the incident angles are very similar. However, when the angle of incidence is increased towards the exterior of the lens, the sub-aperture images are distorted, with the outermost images exhibiting very significant distortion.
An actual high-temperature flame is an active emission medium, rather than just a participating attenuating medium; that is, the medium itself can radiate energy outward. Therefore, in this subsection, we simulate light-field imaging that includes absorption, scattering, and emission. Fig. 1 shows the model employed here, and the medium is modeled based on the sets of physical properties listed in Table 1. Fig. 8 shows the results for the main lens imaging directly to the CCD in the absence of a microlens array. A combination of parameter sets 1–3 is considered in all medium planes from front to back (ca in Fig. 2); therefore, there is considerable variety in the energy values that arrive at the camera. This is especially true for cases
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Fig. 17. Direct and light-field images of ellipsoid layered flame.
Fig. 18. Sub-aperture image of ellipsoid layered flame.
where medium blocks with parameter set 1 are positioned near the lens. As a result of the low temperature, low energy radiation transmission, and strong radiation attenuation, the lower left to upper right diagonal blocks have low brightness in Fig. 8. Fig. 9 shows the light-field images obtained after the addition of a microlens array. Fig. 10 shows the refocus results obtained for Fig. 9, where Fig. 10(a)(c) are the results corresponding to refocusing at distances from the main lens of 9.35, 10, and 10.05 m. In addition, the coordinate axis shows the number of the pixels of the image. Note that the results shown in Fig. 10 are closest to the commonly obtained imaging results for participatory media. As the distance from the focus point increases, the images become blurred. With reference to the radiation parameter arrangement in Fig. 2, the difference from the refocused surface image processing results can be explained. That is, we cannot directly obtain the radiance at the focus point because of the forward lap of the medium radiation. The different depth-of-field images only indicate the varying degrees of refocusing performed to obtain the apparent radiation information.
Fig. 11 shows sub-aperture images obtained for different perspectives and for a large depth of field. The coordinate axis shows the number of the pixels of the sub-aperture images. The energy value obtained for each pixel of the image is equal to the integral value of the radiation energy for that micro-unit in that direction and on a straight line. A sub-aperture image is equivalent to the projection of a 3D medium in the sub-aperture direction. If D is sufficiently large, the obtained sub-aperture images are projections of the 3D medium in different sub-aperture directions, as shown in Fig. 12. Therefore, we are of the view that the interior radiation information cannot be retrieved in this manner in the case of a participating medium with active emission ability. In this case, the sub-aperture images that contain information for multiple detection angles reflect the apparent radiation, but they contain more information on independent-direction radiation intensity compared to images obtained after a refocusing process, and are more suitable for the reconstruction of a high-temperature flame light field. The principle of temperature-field reconstruction using subaperture information is as follows. Because of the overlapping of the projection directions, equations that relate to the micro-unit radiation energy values can be derived. When the apparent radiation of the micro-unit is isotropic and the light is not attenuated in the medium, we can obtain the apparent radiation in all parts of the 3D medium simply by using a digital computer-imaging algorithm. Then, we can obtain the temperature field of the medium by inverting the radiation transfer of this apparent radiation field.
3.4. Stratified flame model imaging On the basis of the above findings, we consider an actual flame model in this subsection. Simulated light-field camera imaging and two images of actual flames are used in the investigation of the radiation temperature inversion. As shown in Fig. 13, there are two common flame shapes: high-speed jet flames and lowvelocity flow flames. In the former type, an example of which are aircraft jet flames, the radiation properties and temperature have less variation along the jet direction and over a longer length, with the only obvious change being along the radial direction. This is because of the high jet velocity. A simplified model consists of a cylindrical flame model with finite length constructed using concentric cylinders stratified along the radial direction. In contrast,
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in the case of low-velocity flow flames such as candle flames and natural convection, an ellipsoid shape can be approximated. We first simulate the light-field imaging of cylindrical flame radiation. The flame height is 1.0 m, the maximum radius is 0.4 m, and the cylindrical flame is divided into quarters according to the radius. The medium blocks are arranged such that the numbers increase in the outward direction; thus, isotropic scattering is considered. The radiation properties of the medium blocks are listed in Table 2. Note that the flame is 10 m from the main lens. Fig. 14 shows the direct and light-field camera imaging results for the cylindrical stratified flame, while Fig. 15 shows a subaperture image of a simulated CCD image obtained after postprocessing. The coordinate axis shows the number of the pixels of the sub-aperture images. Fig. 16 shows the simulated ellipsoid flame, in which the three ellipsoid centers do not overlap. Because of the small flame size, it is positioned only 1 m from the main lens to ensure sufficient imaging size. However, this leads to an increase in the distance between the microlens array and the main lens. Eq. (1) shows that the image space F-number increases, while the spot radius behind each microlens decreases accordingly. Table 3 lists the temperature and physical parameters of thermal radiation of the ellipsoid flame for each layer in Fig. 16, from the interior (1) to the exterior (3). Fig. 17 shows the simulated imaging results for direct and lightfield camera imaging. The spot in Fig. 17(b) is obviously smaller than that in the former simulated results, confirming the changing rules for increased F. With the decreased spot size, the utilization of CCD pixels behind the microlens is efficiently reduced. The number of sub-aperture images after processing is also reduced, as shown in Fig. 18. The coordinate axis shows the number of pixels of the sub-aperture images. Considerable differences can be seen between the imaging information obtained in Figs. 15 and 18 for the different imaging angles and flame types. Therefore, regarding the refocusing method (which can only present the surface radiation), it would be more effective to utilize information obtained for different sub-apertures to reconstruct the temperature field of the hightemperature flame medium.
4. Conclusion In this paper, we used a Monte Carlo method to construct a simulation model for light-field camera imaging calculations so as to simulate a microlens-array imaging process for a hightemperature participating medium. The light imaging information obtained for a pure absorbent medium, scattering medium, and active emission medium was analyzed. Further, through a comparison of the differences between sub-aperture and refocusing imaging based on the imaging results, we identified the imaging method most suitable for the reconstruction of a participating medium’s temperature field. Finally, we simulated a physical model of a typical flame and performed the associated calculations. From these investigations, we came to the following conclusions: (1) By comparing the simulated imaging results for different participating media, it was found that the change in the optical depth of an inactive participating medium directly affects the imaging results. Further, for 4p space, only a small component of the medium scattering energy can enter the camera lens. Therefore, the majority of the light is scattered from the optical path of the system such that it exits the system and does not reach the lens. In this case, the scattering and absorption have almost the same effect, with no special consideration being awarded to the scattering energy.
(2) By comparing the refocusing and sub-aperture imaging results for different conditions, it was shown that the subaperture result can reflect the object for which the emission energy is being detected at different angles. Moreover, the imaging results obtained at different angles are mutually independent and can be used for inversion. Regarding the refocusing in the case of an inactive participating medium, the use of this technique can effectively improve the clarity of the imaging results. However, the brightness calculated at a refocused point does not correspond to the radiance at that point. Therefore, an effective algorithm needs to be developed for the reconstruction of radiance fields and, therefore, temperature fields.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 51327803 & 51406041), and the Postdoctoral Science Foundation of China (Grant No. 2014M551239). A very special acknowledgement is made to the editors and referees who made important comments to improve this paper.
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