Focal plane array detector design in the presence of vibration for intersatellite optical communications

Optik 124 (2013) 1948–1951

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Focal plane array detector design in the presence of vibration for intersatellite optical communications Xin Li ∗ , Jing Ma, Siyuan Yu, Liying Tan, Tao Shen Freespace Optical Communication Technology Research Center, National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin 150001, China

a r t i c l e

i n f o

Article history: Received 10 January 2012 Accepted 30 May 2012

Keywords: Satellite vibration Focal plane array detector CMOS Fine tracking Adaptive window

a b s t r a c t A single focal plane array (FPA) detector to operate both for all beacon acquisition, beacon tracking, and pointing functions simplifies the pointing acquisition tracking (PAT) systems. CMOS photodetector is a good FPA candidate by feature of window adaptive. For intersatellite optical links, it is critical to design an appropriate size of fine tracking subwindow (FTSW) especially in the presence satellite vibration. An optimum design of FTSW could ensure the received beacon jitter with the desired exceeding error, as well as maximize the frame rate of FPA. In this paper, a stochastic model of the beacon spot jitter is given considering satellite vibration induced angle of arrival fluctuation. And then the probability density function of the distance moved by beacon spot in the frame period has been derived. Moreover the optimum tracking window design is proposed taking consideration of the combined influences of detector frame rate and beacon spot jitter. © 2012 Elsevier GmbH. All rights reserved.

1. Introduction Optical satellite networks, which have attracted considerable attention, are considered to be a promising way to provide realtime high-speed data communication globally [1–4]. Intersatellite optical links (IOLs) offer the potential advantages over microwave links of smaller size and weight of the terminal, less transmitter power, high immunity to interference as well as larger data rate [5]. For IOLs it is important to keep the incoming beam properly mapped on the tracking detector to maintain the optical link throughout the data transmission period especially in the presence of satellite vibration. With growing demand for lighter weight, lower power for more efficient satellites, recent pointing acquisition tracking (PAT) system designs utilize a combined arrangement for optical terminals which employs a single focal plane array (FPA) to operate both for all beacon acquisition, beacon tracking, and pointing functions instead of traditional individual detectors [6]. The novel architecture of using a single FPA was first proposed by Jet Propulsion Laboratory in design of the Optical Communications Demonstrator (OCD), the feasibility of which is validated by a series of experiments [7,8]. As the next generation of smart sensors, CMOS active pixel sensor is a good candidate which can be adaptively windowed with low power, on-chip control, timing and digital output [9]. The area of interest feature of CMOS-based photodetector allows

∗ Corresponding author. E-mail address: [email protected] (X. Li). 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.05.026

acquisition and tracking subsystems to specify different size of windows on detector arrays [10]. However, the specific subwindow design has never been reported as far as the authors’ knowledge, which matters the tracking stability and the tracking loop bandwidth. In practice, optical terminals operate in the presence of satellite vibrations, which could cause the beacon spot jitter resulting in a large burst error. So it is critical to design an appropriate size of subwindow for fine tracking. An optimum design of fine tracking subwindow (FTSW) could ensure the received beacon jitter with the desired exceeding error, as well as maximize the frame rate of FPA. A novel design of FTSW is of concern in this paper for single FPA PAT systems. The structure of this paper is arranged as follows. First, the single FPA detector scenario is illustrated in Section 2. Subsequently, the characteristic of satellite vibration is analyzed, and a stochastic model of bacon spot jitter is derived in Section 3. Then the optimum FTSW design is proposed considering the vibration induced angle of arrival fluctuation based on CMOS photodetector in Section 4. Moreover, the optimum FTSW design criteria are given taking OLYMUPS as an example in Section 5. The results of the optimization of FTSW will aid intersatellite optical system design theoretically. 2. Single FPA detector scenario A single focal plane array (FPA) detector to operate both for all beacon acquisition, beacon tracking, and pointing functions simplifies the PAT systems. Generally, PAT system consists of acquisition subsystem, coarse tracking subsystem, and fine tracking

X. Li et al. / Optik 124 (2013) 1948–1951

Y

1949

where E[•] denotes the mean value and * denotes the complex conjugate operation. And Eq. (2) yields

Acquisition Detection

Coarse Tracking Detection

Rff () = 2R() +

n 

˛2i cos(ωi t)

(3)

i=1

with assumption of that Rxx () = Ryy () = R() and E(A2i ) = E(Bi2 ) = ˛2i . Eq. (3) suggests that f(t) is a stationary stochastic process. We define the distance shifted by the beacon spot on the CMOSarrays in  due to satellite vibration as

Fine Tracking Detection

X FTSW

r(t, ) = rx (t, ) + jry (t, )

CTSW

(4)

where ASW

rx (t, ) = x(t + ) − x(t) +

Pixel address

ry (t, ) = y(t + ) − y(t) + subsystem [11]. Accordingly for the single FPA PAT system, there should be acquisition subwindow (ASW), coarse tracking subwindow (CTSW) and fine tracking subwindow (FTSW) designed on the detector arrays as illustrated in Fig. 1. In the beginning, once the incidence beacon spot enters the ASW, the control loop turns the normal vector to the direction of the impinging optical field according to the calculated deviation angle. And then the close tracking loop is established. Therefore the incoming beacon spot would move gradually to the center approaches the CTSW until enters the FTSW where the communication begins. For the sake of tracking stability and communication quality, it is critical to design an appropriate size of FTSW, which matters the system response characteristic with respect to the tracking loop bandwidth.

In this section the satellite vibration induced beacon spot jitter is analyzed and the stochastic model of beacon spot jitter is presented. Subsequently, the variance of spot moving distance is also derived. For intersatellite optical link we can assume that the beacon energy is large enough compared to background and other noise, then satellite vibration is the only reason causing beacon spot jitter as a result of variance of the arrival angle of beacon beam. Thus the characteristic of beacon spot jitter inherits from satellite vibration. The spot moving from pixel to pixel in the focal plane detector is a random process which has two degrees of freedom relative to the line of sight [12]. And the spot jitter can be modeled as having two components: the first one has a continuous spectrum whose bandwidth is relatively narrow around the origin which arises from satellite base motion disturbances; and the other is modeled as discrete sum of random sinusoids which arises from certain resonance frequencies in the spacecraft [13]. Therefore the spot jitter is expressed as



[Ai cos(ωi t) + jBi sin(ωi t)]

(1)

i=1

where f(t) is the 2-dimensional spot jitter represented in complex form. x(t) and y(t) are uncorrelated, identical zero mean Gaussian process with variance of 0 . Ai and Bi are also independent random variables. The characteristic of beacon spot in Eq. (1) inherits from satellite vibration. The autocorrelation function of f(t) is evaluated as [14] Rff () = E[f (t)f ∗ (t − )]

(2)



(5) Bi {sin[ωi (t + )] − sin(ωi t)}

i=1

According to Eq. (5) we got that E[rx (t, )] = E[ry (t, )] = 0

(6)

And accordingly the variance can be calculated as n 

E[rx2 (t, )] = E[ry2 (t, )] ≤ 202 − 2R() + 4

˛2i

(7)

i=1

Given Eqs. (6) and (7), the distance moved by the beacon spot in x and y directions in time  is followed Gaussian distribution, with zero mean and the upper bound on the variance which is dependent on interval time . Based on the analysis above the probability density function (PDF) of beacon spot jitter on detector arrays can be written as

3. Vibration induced beacon spot jitter analyses

f (t) = [x(t) + j y(t)] +

Ai {cos[ωi (t + )] − cos(ωi t)}

i=1 n

Fig. 1. Illustration of combined PAT system FPA working scheme.

 n 

n 

1 f (rx , ry ) = exp 2 2

 −

rx2 + ry2

 (8)

2 2 n 

where  2 = 202 − 2R() + 4

˛2i which represent the worse jitter

i=1

of beacon spot. We should notice that all the variables analyzed above could be all on the detector arrays counted in ␮m or mapped on the field of view counted in ␮rad. For example, the acquisition field of view is 8.64 mrad × 8.64 mrad, which is mapped on to 1024 × 1024 pixels. Hence, each pixel corresponds approximately to 8.5 ␮rad × 8.5 ␮rad field of view [15]. 4. Optimum fine tracking subwindow design In this section the optimum design of FTSW is proposed for CMOS-based photodetector taking consideration of the PDF of spot jitter derived in Section 2. In adaptive windowed mode for tracking process, only pixels in the area of interest (AOI), which determines the maximal frame rate, are used. And the relation is given by T = TE + M 2 c

(9)

where T is the minimum frame period, TE denotes the exposure time, c represents the readout time parameters for pixels array of M × M, and the number of pixels in horizontal and vertical direction are all M. It is obvious that the maximum allowed frame rate increases as the size of the AOI decreases. However, the maximum frame rate is limited by factors of the exposure time and the readout time.

1950

X. Li et al. / Optik 124 (2013) 1948–1951 900

The distance of beacon spot moving in detector arrays, which follows Eq. (8) in time of frame period T , for a given exceeding probability Pe , can be expressed as

−r



−

rx2 + ry2 2 2



700

drx dry

(10)

n

where  2 = 202 − 2R(T ) + 4 i=1 ˛2i , it should be pay attention to that the longer the frame period the larger the variance will be. And 2r is the edge distance corresponding to Pe . Eqs. (9) and (10) suggest that as the window size reduces the variance of the beacon spot jitter also decreases, and as a result the edge distance for a same Pe will be smaller, due to lesser frame period. And they also imply the need to optimize tracking window, which of course also arise from the requirement to improve the response time of tracking subsystem, is that without drag the beacon spot to the center of the detector it would escape the tracking window resulting from the accumulative effect of random process. To maintain the optical link in case of re-acquisition, the beacon spot should be in the tracking window with exceeding probability of Pe , taking consideration of tracking accuracy T . The optimum tracking window obtained as m = T + 2r,

2r + T M= L FOV

(11)

2

−r

1 exp 2 2

σ (μrad2)

r

In this section we take the jitter power spectral density (PSD) of OLYMPUS as an example to illustrate the relationship between factors mention above, as well as to present design criteria based on the proposed optimum design theory. The PSD consists of two components: the continuous spectrum has a 3 dB bandwidth of 5 Hz; the discrete frequencies chosen correspond to 2 Hz, 10 Hz and 300 Hz, respectively. And the peak value of the PSD is taken as 240 ␮rad2 . The three discrete components have mean square jitter values equal to 1 ␮rad2 , 4 ␮rad2 , and 16 ␮rad2 , respectively. Then the PSD and the autocorrelation function of jitter can be described as [15]

200 100 -4 10

480 1 + ((/3)f )

2

-3

-2

10

-1

10

10

τ (s) Fig. 2. Variance of beacon spot jitter  2 vs. interval time . 30 25 20 15 10 5 0 0

200

400

600

800

1000

M (pixels) Fig. 3. The minimum frame period T vs. the size of AOI M.

pixels array in AOI is shown in Fig. 3, when the exposure time is set for 2 ms. It is obvious that the frame period T monotonically increases as pixels array M rises. It is suggested that the less the AOI is, the higher the frame rate will be. Taking consideration of the tracking stability, for the required exceeding probability 10−7 , 10−6 and 10−4 , the dependence of the corresponding field of view of beacon spot moving distance r to the variance of beacon spot jitter  2 is depicted in Fig. 4 according to Eq. (10). It is shown that for a given exceeding probability, r is increasing with rising in  2 . And for a specific  2 , the less the exceeding probability is the bigger the r is. It means that for a higher tracking stability, the field of

110

+ 2ı(f − 2) + 8ı(f − 10) + 32ı(f − 300)

(12)

R() = 1440 exp(−6||) + 2 cos(4) + 8 cos(20) + 32 cos(300)

Pe=1e-7

100

Fig. 2 depicts the variance of beacon spot jitter according to Eq. (7) given Eq. (12), for interval time  ranging from 0.1 ms to 100 ms. As can be seen from Fig. 2,  2 rises as  increases with periodically fluctuation which is resulting from the discrete frequencies of satellite vibration. It is implied that the less the interval time, the less the beacon spot jitter is. In other words, given enough higher tracking loop bandwidth, the impact of satellite vibration would dramatically decrease. The motivation of this paper is to find the optimum size of FTSW, which could ensure the tracking stability as well as minimize the frame rate of optical sensor. As to the frame rate, we take BASLER A620f CMOS camera as the FPA detector [16]. And the relation between frame period and

Pe=1e-6 Pe=1e-4

90

2

r (μrad)

S(f ) =

500

300

where M is the number of pixels per row or line in the optimum tracking window, which mapped on the field of view is m . And L is the number of pixels per row or line in the effective detector arrays, which mapped on the field of view is FOV . Therefore, for a desired exceeding probability, the optimum size of tracking window is M × M given by Eq. (11). And the result of Eq. (11) may not be an integer, then the next higher odd integer value should be chosen as the pixels number of the square window. Since the selection of an odd integer helps in placing the location of the beacon spot at the center of the window. 5. Numerical results and analysis

600

400

T (ms)

 r

Pe = 1 −

800

80 70 60 50 40 100

150

200

σ

2

250

300

350

400

2

(μrad )

Fig. 4. The corresponding field of view of beacon spot moving distance r vs. variance of beacon spot jitter  2 for various exceeding probability Pe .

X. Li et al. / Optik 124 (2013) 1948–1951

view of FTSW should be bigger enough to tolerate the satellite vibration. And then we would interpret how to find the available optimum FTSW. Taking the exceeding probability 10−7 as an example, according to Eq. (10) the dependence of r to  2 is



r = 3.8547

2 2

(13)

For a tracking accuracy of 2 ␮rad PAT system, based on Eq. (11) the optimum size of FTSW can be calculated as M=

2r + 2 ␮rad 8.5 ␮rad

(14)

From Eqs. (13), (14) and (7), we can get the relation of M and . Finally across the relation between M and  and the relation between T and M of A620f, we can find the optimum size of FTSW is 15 × 15. 6. Conclusion For intersatellite optical communication systems, the characteristic of beacon spot on focal plane detector at the mercy of satellite vibration has been addressed. A stochastic model has been given which describe the beacon spot jitter. And then the PDF of distance moved by beacon spot has been developed. The frame period is analyzed based on CMOS photodetector which owns the outstanding adaptive windowed advantage. Subsequently the optimum tracking window design has been proposed taking consideration of the combined influences of detector frame rate and beacon spot jitter. Finally the numerical example is presented taking the vibration model of OLYMOUS. It is shown the optimum FTSW is 15 × 15 for the required exceeding probability of 10−7 . The proposed optimum tracking window could improve the response time of tracking subsystem and promise the link tracking stabilization keeping the beacon spot within the tracking window. The results obtained in this paper should be useful in tracking subsystem design for intersatellite.

1951

Acknowledgment This work was supported by program of excellent team in Harbin Institute of Technology. References [1] J. Ma, M. Li, L.Y. Tan, Y.P. Zhou, S.Y. Yu, C. Che, Space radiation effect on EDFA for intersatellite optical communication, Optik 121 (2010) 535–538. [2] L.Y. Wan, L.R. Liu, J.F. Sun, On-ground simulation of optical links for free space laser communications, Optik 121 (2010) 263–267. [3] V.W.S. Chan, Optical satellite networks, J. Lightwave Technol. 21 (2003) 2811–2827. [4] N. Karafolas, S. Baroni, Optical satellite networks, J. Lightwave Technol. 18 (2000) 1792–1806. [5] R.G. Marshalek, G.A. Koepf, Comparison of optical technologies for intersatellite links in a global telecommunication network, Opt. Eng. 27 (1988) 663–676. [6] M. Jeganathan, A. Portillo, C. Racho, S. Lee, D. Erickson, J. Depew, S. Monacos, A. Biswas, Lessons learnt from the optical communications demonstrator, Proc. SPIE 3615 (1999) 23–30. [7] C. Chen, J.R. Lesh, Overview of the optical communications demonstrator, Proc. SPIE 2123 (1994) 85–95. [8] S. Lee, J.W. Alexander, M. Jeganathan, Pointing and tracking subsystem design for optical communications link between the international space station and ground, Proc. SPIE 3932 (2000) 150–157. [9] R.C. Stirbl, B. Pain, T.J. Cunningham, B.R. Hancock, K.P. McCarty, Next generation CMOS active pixel sensors for satellite hybrid optical communications imaging sensor systems, Proc. SPIE 3498 (1998) 255–264. [10] B.R. Hancock, R.C. Stirbl, T.J. Cunningham, B. Pain, C.J. Wrigley, P.G. Ringold, CMOS active pixel sensor specific performance effects on star tracker imager position accuracy, Proc. SPIE 4284 (2001) 43–53. [11] G. Baister, P.V. Gatenby, Pointing acquisition and tracking for optical space communications, J. Electron. Commun. Eng. 6 (1994) 271–280. [12] P.R. Chakravarthi, C.C. Chen, Spatial acquisition in the presence of satellite vibrations for free space optical communication link, Proc. SPIE 2221 (1994) 248–259. [13] S. Arnon, Power versus stabilization for laser satellite communication, Appl. Opt. 38 (1999) 3229–3233. [14] K.J. Aström, Introduction to Stochastic Control Theory, Academic Press, New York, 1970 (Chapter 2). [15] M. Witting, L. van Holtz, D.E.L. Tunbridge, H.C. Vermeulen, In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS, in: Selected Papers on Free Space Laser Communication II, 1994, pp. 389–398. [16] Basler Vision Technologies, Basler A620f User’s Manual, Document, Number: DA00069601 (release date 22.10.04).