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ON RANDOM AND SYSTEMATIC ERRORS OF A
STAR TRACKERMaxim Tuchin, Anton Biryukov,
Mikhail Prokhorov, Andrey Zakharov
Space Project Laboratory,Sternberg Astronomical Institute,
Lomonosov Moscow State University
2
Comparing real and estimated random errors
D ω NN x,y
BOKZ, IKI (Russia)
SED26, Sodern (France)
S3S, (Canada)
ST-200, BST (Germany)
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Random error sources
The effect of shot noise of star fluxdecreases with the increase of signal from star ~
Shot noise of background (light scattering)
Random dark signal componentcan be reduced by cooling the sensor
Readout noise of the sensorreading out with a lower frequency
Estimation of random error
𝛿𝑟𝜃
𝑆𝑁𝑅
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Systematic error sources Image pixelization Limitation of the analyzed area while measuring coordinates Different sensitivity of the sensor elements (PRNU) Inhomogeneous sensitivity within a sensor element Dark current non-uniformity (DCNU) Effect of "hot" pixels Displacing effect of electron traps Various aberrations Differences in the spectral sensitivity of elements
(SRNU) Non-uniformity of gains, bias Degradation of sensor and optics Etc.
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Pixelization and bounded area errors
Using integrated signal from pixels rather then signal distribution function across focal plane
Using limited area instead of whole focal plane i.e. using instead of
~𝑥𝑐=∑𝑖 , 𝑗
𝑥 𝑗𝐹 𝑖 , 𝑗
∑𝑖 , 𝑗
𝐹 𝑖 , 𝑗𝑥𝑐=
∬−∞
+∞
𝑥𝑓 (𝑥−𝑥𝑐 , 𝑦− 𝑦𝑐 )𝑑𝑥𝑑𝑦
∬−∞
+∞
𝑓 (𝑥−𝑥𝑐 , 𝑦− 𝑦 𝑐)𝑑𝑥𝑑𝑦
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Error of star image position depending on image size
Using PSF ,where S – signal from the star, – radius with 80% of signal within
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Shift of measured coordinatesdepending on position within pixel
Small size star images Large size star images
Pixelization effect Bounded area effect
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Dark current non-uniformity Sensor elements have different levels of
thermo generation rate of electrons Non-uniformity is high (up to 20-30%) It leads to increased errors
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Effect of DCNU on the position error
Note: SNR is signal-to-noise ratio with DCNU=0 and reflects the signal’s strength
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Effect of DCNU on the star image detection
Note: SNR is signal-to-noise ratio with DCNU=0 and reflects signal’s strength
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DCNU changes with Total Dose Irradiation and after annealing
High Accuracy Star Tracker (HAS)Version 2 CMOS Active Pixel image Sensor (CMOS APS)
Source: HAS2 Detailed Specification - ICD
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Solutions to DCNU problem Cooling the sensor
+ We can forget about DS (except “hot” pixels)─ Additional elements to design─ More power consumption─ Heat dumping problem─ Increased effects of electron traps
Dark signal estimation─ Increasing requirements to calculation capabilities─ Less accuracy due to additional noise─ Recalibrations are highly recommended
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Conclusions
To achieve the high accuracy one shouldDo ground-based calibrationsStore fair-sized calibration data (like bias or
sensitivity maps) onboardProvide for various corrections during data
reductionCool the sensor or calculate dark signalDo some space-based calibrations