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)

3

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

4

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.

5

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

6

Error of star image position depending on image size

Using PSF ,where S – signal from the star, – radius with 80% of signal within

7

Shift of measured coordinatesdepending on position within pixel

Small size star images Large size star images

Pixelization effect Bounded area effect

8

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

9

Effect of DCNU on the position error

Note: SNR is signal-to-noise ratio with DCNU=0 and reflects the signal’s strength

10

Effect of DCNU on the star image detection

Note: SNR is signal-to-noise ratio with DCNU=0 and reflects signal’s strength

11

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

12

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

13

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