HU Xiaodong,DING Xiaokun

(The Flight Automatic Control Research Institute of AVIC,Xi’an 710065,China)

Abstract: During the operation of the airborne star sensor,star image is caused to be blurred by the atmosphere disturbance or carrier vibration,which influences measurement precision and decreases observation efficiency.The Fast-steering Mirror based image stabilization system in star sensor is presented to compensate the image motion to keep the optical path stable.First of all,the centroid of the star target is calculated by the barycenter method in a certain window,which is determined by searching from the star image acquired by star sensor in an improved centroid calculating method.Consequently,the miss distance between star target and image center could be obtained.According to this,the controlling system drives the voice coil motor to ensure the fast-steering mirror moving to compensate the carrier motion,which keeps the star staying at the center of the image and enhances the image stability.The experimental results show that,when the correcting frequency of the system is about 100 Hz and the exposure time is 8 ms,the vibration amplitude reduced by about 3 pixels.The influence of carrier vibration is mostly eliminated,and the impact of atmospheric disturbance has also been improved.Thus the observation efficiency is obviously increased.

Key words: fast-steering mirror;image stabilization;star sensor;atmospheric disturbance;carrier vibration

As an important device of attitude measurement,the star sensor is generally operating statically[1].The relative position between the stellar and the star sensor keeps still.However,for airborne star sensor that operates within aerosphere,due to the vibration of aircraft and atmospheric turbulence,the star spot on CCD trembles,which degenerates the image quality,contrast and resolution.This degradation could hardly be solved by improving imaging device resolution or image processing[2].Therefore,eliminating or depressing negative effects deriving from environment interference becomes the key to image stabilization technology.

Presently,common image stabilization technology concludes optical image stabilization technology,electrical image stabilization technology,micromechanical image stabilization technology and so on[3].Optical image stabilization technology is limited to lightly vibration condition,besides both of the configuration and manufacture for the compensator are too complex.Electrical image stabilization technology compensates images with digital image processing which could not work during CCD integration time.Micro-mechanical image stabilization technology demonstrates high-speed detection and high-precision compensation depending on compensating mirror steering or focal plane adjusting.It is upgraded from conditional optical image stabilization with lots of advantages such as small size,light weight and low power.Moreover,there is nearly no negative effect for the imaging quality.Above all,micro-mechanical image stabilization technology is considered as the most commonly used method for high precision application.

Fast-steering Mirror(FSM),which manipulates mirror by piezoelectric driver or voice coil motor,could control light beam fast rotating within small range but high precision between the light source and the receiver.Compared to conditional motor driven,fast-steering mirror demonstrates small inertia,quick response and high regular resolution.It is widely used in astronomical telescope,laser communication,laser weapon,image stabilization and adaptive optics[4].In this paper,the application of fast-steering mirror based micro-mechanical image stabilization technology in star sensor is introduced.

1 System fabrication

In order to enhance the detection capability of star sensor,CCD with big pixel was chosen.Besides,the focal length of optics needs to be long and the diameter of optics needs to be large so as to improve measurement resolution.Furthermore,the space requirement of mechanic frame,focal length adjusting device,electro circuit and detector should be fully considered during the design of optics[5].Therefore the optics has to be compact,lightweight and integrated.Compared to transmission optics and off-axis reflection optics,coaxial reflection optics seems to meet the space requirement much better[6].Considering the sky background luminance,the field of view of the airborne star sensor was usually set to be narrow.Thus,the exterior servo mechanism is needed to shift the star sensor to aim the target stellar.

Fig.1 The diagram of system compositionof the fast-steering mirror based micro-mechanical image stabilization system

The diagram of system composition of the fast-steering mirror based micro-mechanical image stabilization system is shown in figure 1.It consists of imaging optics(1),fast-steering mirror(2),large array focal plane detector(3)and FPGA processing unit(4).

The imaging optics employs coaxial reflection telescope with diameter 150 mm,focal length 1800 mm,angular resolution 5''.The field of view is 0.95 °.

As shown in figure 2,the fast-steering mirror includes motor,plane mirror,mirror bracket,bearing,bearing housing,motor support frame,motion detector and so on.

Fig.2 Picture of the fast steering mirror

Considering the volume restriction,the structure of fast-steering mirror must be light and small.Thus,the material of plane mirror is chosen as aluminum alloy,and the mirror is connected to the bracket directly by bolts.The diameter of mirror is 40 mm.The distance between the mirror and the focal plane is 80 mm.The weight of moving parts of fast steering mirror is 30g.The surface accuracy of mirror is better than λ/10.The closed loop slope angle is +2 mrad.The angular resolution is 0.05 μrad.The resonance frequency is 33 kHz.

In order to increase the compensation precision and rapidity of the fast-steering mirror,voice coil motor(VCM)was chosen as the executive device,which could reduce the influence on mirror moving caused by friction moment.The stabilization system includes two voice coil motors.One is for pulling,and the other is for pushing.The gyration radius of mirror is 20 mm.The weight of moving parts of fast steering mirror is 30g.Considering the maximum angular acceleration of the mirror should be no less than 800 rad/s2,the maximum thrust should be calculated as Eq.1.

Consequently,TMEC0003-003-00A voice coil motor is selected.The parameters are as follows:resistance(RΩ)is 3Ω,inductance(L)is 0.24 mH,force constant(Kf)is 1.8 N/A,peak force(Fp)is 3 N,consecutive force(Fc)is 1.3 N,maximum stroke(S)3 mm,loop weight(m)7g,total weight of the voice coil motor 41g.

The electrical time constant could be obtained by Eq.2.

The mechanical time constant is as follows:

The consecutive angular acceleration could be calculated by Eq.4.

The maximum angular acceleration could be got by Eq.5.

Both of the parameters meet the requirement of fast-steering mirror maximum angular acceleration.

The large array focal plane detector employs a monochromatic CCD with global shutter.The response wavelength range is 400～1000 nm.The pixel size is 6.5 μm× 6.5 μm.The active pixel resolution is 2048 × 2048 supporting 2 × 2 binning.The frame frequency is up to 100 fps.The integral time could be adjustable.In the 10-bit ADC global shutter mode,the dynamic range could reach 60 dB,which could be up to 70 dB by internal CDS combining with HDR.

The logic unit of FPGA is 12060 Les,within 2 PLL 234 Kbits RAM.The external clock is 40 MHz.

2 Operation processing

The flow diagram of procedure is shown in figure 3.It consists of parameters setting,CCD camera and FSM controller initializing,image capturing,star centroid extraction,fast-steering mirror controller setting and so on.At the beginning of the procedure,the CCD exposure time,gain and binning mode should be set during parameters setting process firstly.

Fig.3 The flow diagram of procedure

Fig.4 The sketch map of window search

When the star sensor is operating,stellar signal is captured by CCD through optics,and then the star target starts to be searched in the image.Subsequently the centroid of the star target spot is calculated.Before the fast-steering mirror based micro-mechanical image stabilization system working,it is essential to adjust the star sensor by exterior servo mechanism to ensure the star target spot located in the center of the image,according to the above calculated centroid.Considering the center of the image guarantees the best image quality and could endure the largest oscillation,it is set as the reference location.During the image stabilization procedure,the offset between the centroid of the star target spot and the center of the image is calculated by the controlling software.Furthermore,the adjustment of fast-steering mirror controller could be acquired.So that,the controller drives the fast-steering mirror to keep the star target spot steady around the center of the image.Thus,the measurement stability is enhanced and the imaging quality is also improved.However,when the offset is beyond the adjusting range of the fast-steering mirror,it is essential to re-adjust the star sensor to aim at the stellar by exterior servo mechanism.

In order to calculate the offset,the centroid of the star target spot for every frame needs to be extracted in real time.Convectional algorithms include normalized phase correlation method,barycenter method,Hough transform method,Gauss fitting method,circular fitting method and so on.Hereinto,both the normalized phase correlation method and barycenter method guarantee higher precision and better stability.Although the precision of normalized phase correlation method is a little higher,the calculation speed of barycenter method is much faster.Considering both of the precision and the stability,barycenter method is chosen.

Consider the gray scale data of star image isf(x,y),x= 1…M，y= 1…N.The traditional barycenter method calculated the star centroid coordinates(x0,y0)according to Eq.6

In order to improve the precision,some optimization was investigated based on the traditional barycenter method.The threshold barycenter method seems to be an outstanding choice.The notable amelioration of this improvement was introducing the threshold of the background(T).The star centroid coordinates were calculated after background deduction according to Eq.7.Compared to the traditional method,the threshold barycenter method could depress the disturbance of background noise effectively,consequently the precision is improved[9].

2×2×M×N times operation would be needed when the centroid of the star target is calculated by the barycenter method[7].However,for a real star image,the star target spot occupies a quite small area.Most operation was wasted for the useless area.The improved method searches the whole star image for the star target spot firstly.The star detection begins by forming 2×2 pixel windows,so that there are(M-1)×(N-1)overlapping windows on the star image.We start searching the whole star image from left to right and bottom to top window by window,as viewed in figure 4 and compute the mean gray scale value,Sw(x,y)for every window.We also compute the signal for a "reference" window,Sr,which is the average value of the whole star image for pixels around the perimeter.For each window,we then compute the net signalS(x,y)=Sw(x,y)-Sr.When we encounter a window that exceeds a search threshold,the window is expanded from 2×2 to 4×4,including more pixels on the right and top.Because we scanned from the left and bottom,any additional signal energy appears in the enlarged window.As before,we compute a net signalS(x,y)for the enlarged window and check to see if it exceeds a track threshold.If not,we go back to continue searching.If so,we calculated by the threshold barycenter method during this window.This improved method requires no more than(M-1)×(N-1)+ 2×2×42times operation,which is much fewer than the conventional method,especially when the size of image(M/N)is bigger.Furthermore,owing to computation only operating in the selected window,the impact caused by noise from area except for the selected window is eliminated,thus the precision is improved.

Fig.5 The comparison of operation times between conventional method and improved method

In general,the star image is influenced by various kinds of noise such as CCD dark noise,circular read out noise,A/D conversion noise,and quantization noise [8].Especially for the dim stellar,the signal-noise-ratio is much worse,which impacts the precision of star centroid extraction seriously.Therefore filtering and noise reduction seem to be necessary before the centroid extraction.After analyzing the star image,it is proved that the image contains much salt and pepper noise.The gray scale value of some noise pixel is even greater than that of the star target pixel,which would influence star centroid extraction seriously.Therefore,the median filteringto be necessary in order to eliminate the salt and pepper noise[10].

3 Experiment results

Fig.6 Experiment setup

In order to verify the stabilization effect,comparative experiment is executed.The experiment setup is shown in figure 6.A two-axis turntable is used to simulate the aircraft vibration.The amplitude is 1' and the frequency is 300 Hz.A collimator is introduced to simulate the stellar.The magnitude is +2.5 mag.The experiment was executed as follows.First,shut down the stabilization system and save the star spot centroid.Second,startup the stabilization system and save the star spot centroid.During the whole comparative experiment,the stellar target and CCD parameters keep constant.The exposure time of CCD is set 8 ms.The sample number is 250.Considering the data collection time stands short,the influence caused by weather variation could be ignored.The image center pixel coordinate(20,20)is chosen as the reference position.

The variations of the stellar centroid positionsxandywith stabilization(bottom)and without stabilization(up)are shown in figure 7.The scale of the two figures is set the same.When the stabilization is shut down,it could be easily got that most star spot centroid positions gather around the reference position in a small range with random distribution,which is mainly caused by atmospheric disturbance.There are also other star spot centroid positions distributing far away from the reference position,which is mostly caused by carrier vibration.However,when the stabilization is turned on,star spot centroid positions distributing far away from the reference position disappeared.Besides,the shaking range of star spot centroid positions also decreases.

Fig.7 The variations of star spot centroid positions x and y with stabilization(bottom)and without stabilization(up)

Fig.8 Temporal variation of the star spot centroid positions x with stabilization(bottom)and without stabilization(up)

Analyzing the star spot centroid position data fromxandydimension independently,we could get figure 8 and figure 9.When the stabilization is shut down(Fig.8 up and Fig.9 up),the standard variance of positionxis 3.65 and the standard variance of positionyis 4.5.When the stabilization is turned on(Fig.8 bottom and Fig.9 bottom),the standard variance of positionxbecomes 0.63 and the standard variance of positionybecomes 0.75.Moreover,the great vibration disappeared.

Fig.9 Temporal variation of the star spot centroid positions y with stabilization(bottom)and without stabilization(up)

Fig.10 The probability distribution of the star spot centroid positions x with stabilization(bottom)and without stabilization(up)

As shown in figure 10 and figure 11,after turning on the stabilization,the probability distribution of the star spot centroid positions demonstrates more concentrated.It is proved that the stabilization system makes the light path more stable and the observation efficiency is obviously increased.

Fig.11 The probability distribution of the star spot centroid positions y with stabilization(bottom)and without stabilization(up)

4 Conclusion

In conclusion,the application of fast-steering mirror based on micro-mechanical image stabilization system in star sensor is introduced and analyzed in this paper.The experiment results demonstrate the stabilization system could mostly eliminate the effect of carrier vibration,and the impact of atmospheric disturbance has also been improved.It could reduce the centroid hysteresis and also improve the ability of the sensor to keep up with fast-moving stars.This image stabilization system is suitable to airborne star sensor with great dynamic and has great potential in high resolution measurement system with atmospheric disturbance or carrier vibration.