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Abstract
The Risley prism's compact structure, dynamic responsiveness, and high tracking accuracy make it ideal for photoelectric image tracking. To realize fast and high-precision tracking of the target, we propose an image-based closed-loop tracking cascade control (IBCLTCR-F) system using a single image detector that integrates the Risley prism and fast steering mirror (FSM). Firstly, We propose a cascade control input-decoupling method (CCIDM) for the IBCLTCR-F system to solve the complex problem of coarse-fine control input decoupling in traditional single detector cascaded control systems. Moreover, the CCIDM method ensures that the FSM deflection angle is small and does not exceed its range during the fine tracking process, by using the Risley prism to compensate for the FSM deflection angle. Next, we design the image-based closed-loop tracking controllers of the Risley prism system and FSM system and analyze the stability of the IBCLTCR-F system. Finally, we track static and moving targets through experiments. The experimental results verify the feasibility of the IBCLTCR-F system, the effectiveness of the decoupling method, and the fast and high-precision tracking of the targets.
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1. Introduction
Photoelectric imaging tracking equipment can be used to acquire, track, and point the target. It is often applied to astronomical telescope observation, photoelectric reconnaissance, photoelectric fire control tracking, and laser communication [1–4]. Fast, high-precision, and stable tracking targets are important photoelectric imaging tracking system indices. Conventional photoelectric imaging tracking equipment includes a gimbal and FSM. However, the gimbal exhibits significant rotational inertia, which hinders its ability to achieve fast and high-precision target tracking. Although the FSM has a small rotational inertia, it has a limited deflection range, which poses challenges in tracking wide-range targets [5,6]. The traditional method to solve the problem of fast and high-precision target tracking is to combine the gimbal and the FSM to form a cascaded control system [7–9]. However, in some application scenarios, such as tracking some high-speed aircraft, the cascaded control system may have limitations due to the high rotational inertia issue associated with the gimbal. On the other hand, because the gimbal needs to be mounted in a protruding position, it will be subjected to airflow interference when installed on an aircraft and will be subjected to wave impact when installed on a ship.
In 1960, Rosel proposed the Risley prism scanner [10]. The Risley prism consists of two prisms with the same structure that rotates synchronously to achieve beam control, as shown in Fig. 1. The Risley prism has been studied by many scholars so far. Its operation mode has been extended from beam scanning to the field of target tracking. Application scenarios include optical detection, infrared countermeasures, biomedicine, and LIDAR [11–18].
Fig. 1. Risley prism system beam deflection. ${\alpha _1}$ and ${\alpha _2}$ are the apex angles of prism1 and prism2, ${\theta _1}$ and ${\theta _2}$ are the rotation angles of prism1 and prism2, $\Theta $ is the azimuth angle, and $\Phi $ is the pitch angle.
In previous studies, researchers have presented various methods to enhance the scanning and tracking accuracy of the Risley prism system. Some scholars have investigated the composite axis technique with two pairs of Risley prisms. In 2015, Roy proposed a new scanner that utilizes two pairs of Risley prisms. The first pair of Risley prisms exhibit a narrower field of view compared to the second pair. The second pair of Risley prisms is used to position the first pair of Risley prisms scan patterns within its large field of view to achieve continuous high-precision scanning [19]. In 2017, Neptec Technologies in collaboration with Defence Research and Development Canada has developed a unique LiDAR using two pairs of Risley prisms. The first pair of prisms defines a small field of view of 30°, which is then shifted to a large field of view of 90° by using the second pair of prisms [20]. In 2018, Sun proposed a laser coarse-fine coupling tracking method utilizing two pairs of Risley prisms, enabling both forward and reverse tracking capabilities for the target [21]. The method based on two pairs of Risley prisms present challenges due to the complex system structure and difficult solution. Some scholars have investigated the composite axis technique with the Risley prism and FSM. In 2010, Lu Wei et al. investigated the composite axis control system for satellite laser communication. The system employed the Risley prism for coarse pointing and the FSM for fine pointing. Then the relationship between the bandwidth ratio of the Risley prism and the FSM and the pointing accuracy was analyzed. However, the feasibility of this method has not been experimentally verified in their study [22]. In 2022, Ma et al. used the RBF neural network model to predict the tracking error of the next control cycle of the Risley prism coarse tracking platform in advance, and the error is compensated in real-time through the FSM fine tracking platform. This method solved the coarse-fine control coupling problem of single detector composite axis system of Risley prism and FSM. However, the neural network approach will increase the algorithm complexity. Moreover, this method has only been implemented within a simulation system and has not undergone experimental validation [23]. In 2023, Wang et al. proposed the two detectors beam composite tracking technique based on the Risley prism and FSM. The Risley prism is used for coarse control and the FSM is used for fine control [24]. The two detectors composite axis system features one detector each in the coarse tracking loop and fine tracking loop, necessitating coordination in the operation and data processing of both detectors during coarse-fine control. In contrast, the single-detector system, which shares a single image detector for both coarse and fine tracking loops, exhibits a simpler system structure and incurs lower design and manufacturing costs.
In our team's previous work, we focused on the Risley prism image-based closed-loop control algorithm. It mainly solves the coupling problem between the target’s miss distance and the prism rotation angle in the image-based closed-loop tracking control [14,25]. We then studied the nonlinear problem of the Risley prism system and the influence of the nonlinear problem on the image-based closed-loop tracking control. We achieved smooth tracking of diverse targets through controller design in image-based closed-loop tracking [15]. However, the previous work only used the Risley prism to achieve target tracking, and did not involve the cascaded control system of the Risley prism and FSM. As a mechanical structure system, the Risley prism is inevitably affected by system friction, which leads to limited tracking accuracy. Moreover, despite the Risley prism's superior dynamic response compared to the gimbal, it still exhibits a notable disparity when compared to FSM. Notably, these issues remained unaddressed in the prior studies.
The innovation of this paper lies in the proposal of an image-based closed-loop tracking cascade control (IBCLTCR-F) system using a single image detector that integrates the Risley prism system and the FSM system. Additionally, we investigate the cascade control input-decoupling method (CCIDM) to address the issue of coarse-fine input coupling. The image detector and the FSM form a closed-loop control system, compensating for the FSM's deflection angle using the Risley prism. The CCIDM ensures that the FSM's deflection angle remains within a narrow range (if the FSM operates at a large deflection angle, its control capability decreases sharply). Subsequently, we design the image-based closed-loop tracking controller and analyze system stability. We verify the feasibility of the IBCLTCR-F, the effectiveness of the CCIDM, and the realization of fast and high-precision target tracking.
This paper is organized as follows. Section 2 is analysis of the coupling problem in a cascaded control system. Section 3 is working principle of the IBCLTCR-F system. Section 4 is experimental verification. Finally, conclusions are presented in Section 5.
2. Analysis of coupling problem in cascaded control system
The cascaded control system is a special case of a two-dimensional, orthogonal, feedback control system [26,27].
2.1 Traditional single image detector cascaded control system
The structure of the traditional image-based closed-loop tracking cascade control system using a single image detector is shown in Fig. 2 [28].
In Fig. 2 R is the input information and C is the output information. ${G_{ccd}}$ is the output characteristic of the image detector. ${G_{FC}}$ is the controller for the image-based closed-loop tracking of the fine control system. ${G_F}$ is the output characteristic transfer function of the fine control system. ${G_{RC}}$ is the image-based closed-loop tracking controller for the coarse control system. ${G_R}$ is the output characteristic transfer function for the coarse control system. ${G_{dec}}$ is the decoupling controller for the coarse-fine control. The transfer function ${G_{close}}$ of the image-based closed-loop tracking cascaded control system in Fig. 2 is shown as follows:
The image-based closed-loop transfer function of the fine control system is shown as follows:
The fine control error transfer function of image-based closed-loop tracking is described as
The image-based closed-loop transfer function of the coarse control system is shown as follows:
The image-based closed-loop error transfer function of the coarse control system is described as
According to the two-dimensional, orthogonal, feedback control system, the conditions for achieving full decoupling in a cascaded control system is as follows [27]:
That is, the decoupling controller is required to be equal to the output characteristic of the image detector. The error transfer function of the cascaded control system is shown as follows:
It can be seen from Eq. (7) that the order of the error transfer function without differentiation for the cascaded control system is equal to the sum of the orders of the error transfer functions without differentiation for the fine control system and the coarse control system. Therefore, the cascaded control system shown in Fig. 2 has a high error rejection capability and tracking accuracy. However, the decoupling controller has to be designed to match the image detector output characteristics, which is difficult to achieve in a real system. Therefore, this paper proposes a new cascaded control system and coarse-fine control decoupling method based on the structure of Fig. 2 for the Risley prism system and the FSM system.
2.2 IBCLTCR-F system
The structure of the IBCLTCR-F system is shown in Fig. 3.
The image-based closed-loop transfer function ${G_{R\_F\_close}}$ in Fig. 3 is shown as follows:
The image-based closed-loop transfer function of the FSM system is shown as follows:
Equation (8) can be simplified as
According to Eq. (10), the conditions for achieving full decoupling in the IBCLTCR-F system are as follows:
According to Fig. 3 and Eq. (11), it can be seen that to make the FSM system and Risley prism system decoupled, it is only necessary to use the FSM deflection angle as the input information of the Risley prism system. Then the Risley prism controller calculates the Risley prism compensation rotation angle. The deflection angle of the FSM is always kept near the zero position of the range. The cascade control input-decoupling method (CCIDM) effectively reduces the design difficulty of the decoupling controller.
The error transfer function of the decoupled IBCLTCR-F system is shown as
The closed-loop Bode diagrams of the image-based closed-loop control of the Risley prism and FSM systems are shown in Fig. 4.
As can be seen in Fig. 4, the image-based closed-loop control bandwidth of the Risley prism system is about 0.25 Hz, and the image-based closed-loop control bandwidth of the FSM system is about 2.82 Hz. The image-based closed-loop control bandwidth of the FSM is 11 times that of the Risley prism system, which meets the requirement of a coarse-fine control bandwidth ratio in the cascaded control system [29]. And the image-based closed-loop control bandwidth of the FSM is much larger than the Risley prism system, so we can have ${G_{F\_close}} \approx 1$ in Eqs. (10) and (12). The error transfer function of the IBCLTCR-F system can thus be simplified as
It can be seen from Eqs. (7) and (13) that the order of the error transfer function without differentiation for the IBCLTCR-F system is equal to the order of the error transfer function without differentiation for the traditional cascaded control system. This shows that the IBCLTCR-F system can achieve the traditional cascaded control system's tracking accuracy and error rejection capability.
3. Working principle of the IBCLTCR-F system
The IBCLTCR-F system model is shown in Fig. 5.
The light source simulates the target. The Risley prism system is an achromatic Risley prism, and this achromatic Risley prism model is derived from the literature [30]. From left to right are prism 11, prism 12, prism 21, and prism 22, with apex angles ${\alpha _{11}}$, ${\alpha _{12}}$, ${\alpha _{21}}$, ${\alpha _{22}}$, and refractive indices ${n_{11}}$, ${n_{12}}$, ${n_{21}}$, ${n_{22}}$, respectively. Prism 11 and prism 12 are combined to form prism 1. Prism 21 and prism 22 are combined to form prism 2.
Beam deflection angles ${\delta _1}$, ${\delta _2}$ by prism 1 and prism 2 are as follows:
The workflow of the IBCLTCR-F system is fundamentally consistent with that of the traditional cascaded control system [31]. The specific workflow is shown in Fig. 6.
First, the coarse control system (Risley prism) continuously rotates to scan and capture the target. Or the target guidance information is known and goes directly to the coarse tracking stage. Upon successful target acquisition and imaging on the detector, the coarse control system (Risley prism) transitions into the coarse tracking mode. This mode utilizes the miss distance from the image detector as an input, employing the rotation matrix error-decoupling method [14] to calculate the Risley prism's rotation angle. At the coarse tracking mode, the image detector adopts full window ($1024 \times 1024$) and low frame frequency mode. Subsequently, when the target's tracking error on the image detector falls within the FSM's designated range, the fine control system is activated. At the fine tracking mode, the image detector adopts small window ($128 \times 128$) and high frame frequency mode.
However, the difference between the IBCLTCR-F system and the traditional single image cascaded control system is that when the fine control system is working, the coarse control system is also working at the same time. According to the CCIDM, the deflection angle of the FSM serves as the input information to the Risley prism system to solve the coarse-fine control system coupling problem.
- 1. Firstly, when the tracking error on the image detector falls within the range of the FSM, due to the larger closed-loop bandwidth of the FSM compared to the Risley prism, the FSM can respond more quickly, adjusting the deflection angle to reduce the target's tracking error.
- 2. Then, the FSM deflection angle is transmitted to the Risley prism system in real-time. This angle information is the input information of the Risley prism closed-loop control, and the compensated rotation angle to bring the FSM back to the zero position is calculated through the closed-loop control algorithm (Rotation matrix error-decoupling method).
- 3. Finally, because the FSM deflects the angle, the Risley prism also rotates the angle, causing the target's tracking error to increase in the opposite direction. In order to reduce the tracking error to the set value, the FSM will deflect in the opposite direction of the previous deflection direction, and these two deflections will cancel the deflection angle, making the FSM move around the zero of its range.
These are all done in a closed-loop cycle. The reason for keeping the FSM near zero is that if the FSM operates at a large deflection angle, its control capability decreases sharply. If the FSM is kept near the zero position, then when the next cycle of closed-loop control starts the FSM has enough capacity to respond. Thus, fast and high-precision target tracking is achieved.
4. Experiment
In this section, the output characteristic transfer functions of the Risley prism system and FSM system are first carried out. Then, we proceed to analyze the stability of the IBCLTCR-F system. Finally, the IBCLTCR-F system is employed to track static and moving targets.
4.1 Experimental platform
Figure 7 shows the experimental platform of the IBCLTCR-F system, and Fig. 7(b) shows the experimental diagram of the fine control system in the IBCLTCR-F system. The lamp, collimator, and FSM2 are used to simulate the target in the experiment. The motion of FSM2 is controlled to simulate the moving target. The achromatic Risley prism serves as the coarse control device in the IBCLTCR-F system, primarily for coarse control of the target and compensating the deflection angle of FSM1 during the fine control process. The method used for target tracking and calculating the compensated rotation angle of the Risley prism is based on the rotation matrix error-decoupling method. FSM1 is employed for fine control. In the IBCLTCR-F system, FSM1 and the image detector constitute a closed-loop control system. During the fine control process, the deflection angle of the FSM1 is continuously transmitted to the achromatic Risley prism system in real-time, ensuring decoupling between the input of the FSM1 and the Risley prism system. This approach guarantees that the deflection angle of the FSM1 remains close to the zero position, enabling fast and high-precision target tracking.
Fig. 7. Experimental platform. (a) Photograph of the IBCLTCR-F system. (b) Photograph of the fine control system. (c) Experimental platform optical path diagram.
In the experimental platform, the deflection angle range of FSM2 is ${\pm} {1.5^ \circ }$. The field of view of the achromatic Risley prism is ${0^ \circ } \sim {3^ \circ }$. FSM1 has a deflection angle range of ${\pm} 2062$″. The sampling frequency of the image detector is 50 Hz, the field of view of the image detector is ${0.2^ \circ }$, and the array format of the image detector is 1024 × 1024. The target image should be captured with a delay of 3 frames (The process of imaging on an image detector typically takes one frame for image buildup, one frame for image processing, and the same for sampling and transmission. Thus, the total time delay is 3 frames.). The output characteristic of the image detector is as follows:
4.2 Stability analysis of experimental platform
Initially, we conduct measurements of the frequency response curves for both the achromatic Risley prism system and FSM1 employing a frequency response analyzer. Figure 8 depicts the frequency response curves acquired using the frequency response analyzer, along with the corresponding fitted frequency response curves.
The frequency response curves were fitted to obtain the output characteristic transfer function ${G_R}$ for the achromatic Risley prism system and ${G_F}$ for the FSM1.
Furthermore, we have designed the image-based closed-loop tracking controller ${G_{RC}}$ for the achromatic Risley prism system and the image-based closed-loop tracking controller ${G_{FC}}$ for the FSM1 system. ${G_{RC}}$ is designed as a proportional-integral controller, and ${G_{FC}}$ designed as an integral controller.
Figure 9 shows the open-loop Bode diagrams of the image-based closed-loop tracking for the achromatic Risley prism system and the FSM1. Gm is the magnitude margin, and Pm is the phase margin (the stability of the closed-loop system is related to the magnitude margin and phase margin of the open-loop characteristics, which usually need to fulfill Gm ≥ 6 dB and Pm ≥ 45°). As depicted in Fig. 9, Gm of FSM1 system is 11.8 dB, and Pm of FSM1 system is 95°. Gm of achromatic Risley prism system is 12.6 dB, and Pm of achromatic Risley prism system is 69°. So, the image-based closed-loop tracking controllers of the achromatic Risley prism system and the FSM1 meet the requirements of system stability.
Fig. 9. Open-loop Bode diagram of the image-based closed-loop tracking. (a) The achromatic Risley prism system. Gm = 11.8 dB, Pm = 95deg. (b) The FSM1 system. Gm = 12.6 dB, Pm = 69deg.
Figure 10 shows the open-loop and closed-loop Bode diagrams of the IBCLTCR-F system. Observing Fig. 10(a), Gm of the IBCLTCR-F system is 11 dB, and Pm of the IBCLTCR-F system is 49.4°. It is evident that both the magnitude margin and phase margin conform to the stability criteria of the IBCLTCR-F system. Furthermore, Fig. 10(b) reveals that the closed-loop bandwidth of the IBCLTCR-F system is approximately 2.55 Hz. This bandwidth closely aligns with that of the FSM1 system in Fig. 4, in agreement with the theoretical analysis of the IBCLTCR-F system.
Fig. 10. The IBCLTCR-F system Bode diagram of the image-based closed-loop tracking. (a) The open-loop Bode diagram. Gm = 11 dB, Pm = 49.4deg. (b) The closed-loop Bode diagram.
4.3 Static target experiment
Four static targets were tracked using the IBCLTCR-F system. The pitch and azimuth information of the four targets are as follows: target1 (1.06°, 45°), target2 (1.06°, 135°), target3 (1.06°, 225°), and target4 (1.06°, 315°). Table 1 shows the pitch and azimuth angles of the four targets. Figure 11 shows the location of the four static targets in the system's field of view.
Table 1. Pitch and azimuth angles
The division of the system field of view can be referred to this paper [15]. The system's field of view ranges from ${0^ \circ } \sim {3^ \circ }$ in pitch and ${0^ \circ } \sim {360^ \circ }$ in azimuth. Region I represents the blind area of the achromatic Risley prism system’s field of view (the field of view is less than 0.1°) [32], region II represents the region with the small pitch angle of the field of view (the field of view is between 0.1° and 0.5°), region III field of view is between 0.5° and 2.1°, and region IV is the large pitch angle of the field of view (the field of view is between 2.1° and 3°).
Figure 12 shows the tracking errors of the IBCLTCR-F system and Risley prism system while tracking different static targets. Figure 13 illustrates the deflection angles of FSM1 during the tracking of static targets in the IBCLTCR-F system. Figure 14 illustrates the rotation angle deviation of prism 1 and prism 2 when using the Risley prism system and the IBCLTCR-F system to track different static targets. Table 2 shows the dynamic response time (i.e., the time required to reduce the initial tracking error from 90% to 10%) ${t_{r\_R}}$ during image-based closed-loop tracking of four static targets with the Risley system, and the dynamic response time ${t_{r\_R\_F}}$ during image-based closed-loop tracking of four static targets with the BCLTCR-F system.
Fig. 13. FSM1 deflection angles during the tracking of target1,target2, target3 and target4 in the IBCLTCR-F system.
Fig. 14. Rotation angle deviations while tracking target1, target2, target3 and target4 using the Risley prism system and the IBCLTCR-F system. (a) Prism1 rotation angle deviation. (b) Prism2 rotation angle deviation.
Table 2. Dynamic Response Time
As shown in Fig. 12 and Table 2 the dynamic response time of the Risley prism system is approximately twice that of the IBCLTCR-F system, indicating that the IBCLTCR-F system possesses a faster dynamic response capability. Figures 13 and 14 demonstrate that deflection angle of FSM1 near the zero position after the image-based closed-loop tracking reaches stability, and the rotation angle deviation of both prism 1 and prism 2 remains within ${\pm} 0.\textrm{03}$°. The experimental results validate the correctness of CCIDM and the successful decoupling of the BCLTCR-F system.
4.4 Moving target experiment
The image-based closed-loop tracking experiments of sinusoidal moving and circular moving targets are conducted using the Risley prism system and IBCLTCR-F system, respectively. The sinusoidal moving target5 has an amplitude of 180″ and a frequency of 0.1 Hz. The circular moving target6 has an amplitude of 360″ and a frequency of 0.04 Hz. The trajectory of the moving targets is depicted in Fig. 15.
Figure 16 and Fig. 17 show the time-domain and frequency-domain analyses of the image-based closed-loop tracking experiments for targets5 and targets6, respectively, using the Risley prism and IBCLTCR-F systems.
Fig. 16. Image-based closed-loop tracking error of sinusoidal moving target. (a) Time-domain analysis. (b) Frequency spectrum analysis
Fig. 17. Image-based closed-loop tracking error of circular moving target. (a) Time-domain analysis. (b) Frequency spectrum analysis.
It can be observed from Fig. 16, Fig. 17, Table 3, and Table 4 that the IBCLTCR-F system demonstrates high-precision tracking and strong error rejection capability for moving targets. The tracking precision is at least 27 times higher than that of the Risley prism system.
Table 3. Image-Based Closed-Loop RMS Tracking Error
Table 4. Error Rejection Ability
Figure 18 illustrates the deflection angles of FSM1 during the tracking of target5 and target6 in the IBCLTCR-F system. Figure 19 depicts the rotation angle deviations of prism1 and prism2 while tracking different moving targets using the Risley prism system and the IBCLTCR-F system.
Fig. 18. FSM1 deflection angle during the tracking of target5 and target6 in the IBCLTCR-F system. (a) Tracking sinusoidal moving target (target5). (b) Tracking circular moving target (target6).
Fig. 19. Rotation angle deviations of prism 1 and prism 2 while tracking target5 and target6 using the Risley prism system and the IBCLTCR-F system. (a) Tracking sinusoidal moving target (target5). (b) Tracking circular moving target (target6).
It can be observed from Fig. 18 that the deflection angle of FSM1 does not exceed 10% of the full range when the IBCLTCR-F system tracks different moving targets. From Fig. 19 that the rotation angle deviations of prism1 and prism2 are within ${\pm} 1.5$°. These experimental results indicate the correct decoupling of the IBCLTCR-F system.
Regarding the IBCLTCR-F system and experiments, there are several aspects that warrant particular emphasis. Firstly, in the experiments involving the tracking of moving targets, we selectively employed sinusoidal and circular motions as the tracked targets. However, it is essential to note that the scope of moving targets extends beyond these two patterns. We will continue to use the IBCLTCR-F system to track other trajectory targets in our future work. Secondly, in the conducted experiments, the maximum pitch angle of the achromatic Risley prism was limited to 3°. To extend the tracking capabilities to targets with broader ranges of motion, consideration may be given to substituting the current prism with a Risley prism system possessing a larger field of view. Thirdly, the primary focus is the IBCLTCR-F system. Controller design is not the central emphasis. In experiments, we have chosen relatively straightforward PI and integral controllers to validate the feasibility of the IBCLTCR-F system. It is noteworthy that in the future, both our research team and other teams have the flexibility to explore alternative controller options. However, it is imperative that any controller design ensures system stability as a prerequisite.
5. Conclusion
In this paper, we proposed the IBCLTCR-F system based on previous studies. The Risley prism system serves as the coarse control system in the IBCLTCR-F system, while the FSM is used as the fine control system. We introduced a cascade control input-decoupling method (CCIDM) to address the coupling issue between coarse and fine control inputs under a single image detector setup. During the image-based closed-loop fine tracking process, the miss distance of the target is employed as the FSM's input information, and the FSM's displacement information is used as the input for the Risley prism system. The Risley prism controller calculates the compensating rotation angle to bring the FSM back to the zero position based on the FSM deflection angle. The CCIDM ensures that the FSM deflects within a small angle range during the fine target tracking process, leading to fast and high-precision tracking in the IBCLTCR-F system. Subsequently, We designed image-based closed-loop tracking controllers for the Risley prism system and FSM system, and analyzed the stability of the IBCLTCR-F system. Experimental trials were conducted on both static and moving targets using the IBCLTCR-F system and Risley prism system, and the results validated the correctness of the CCIDM and demonstrated the IBCLTCR-F system's capability for fast and high-precision tracking.
Funding
West Light Foundation, Chinese Academy of Sciences; Youth Innovation Promotion Association of the Chinese Academy of Sciences (2019367).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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