Development of the Arcsecond Pico Star Tracker (APST)*

Vishnu Anand MURUGANANDAN,1) Ji Hyun PARK,1) Sangyoon LEE,1) In-Seuck JEUNG,1)†

Sangkyun KIM,2) and Gwanghyeok JU3)

1)Institute of Advanced Aerospace Technology, Department of Mechanical and Aerospace Engineering, Seoul National University,Seoul 08826, Korea

2)Laboratory of Space Environment Interaction Engineering, Kyushu Institute of Technology, Kitakyushu 804–8550, Japan3)Lunar Exploration Program Office, Korea Aerospace Research Institute, Daejeon 34133, Korea

The second-generation star tracker estimates pointing knowledge of a satellite without a-priori knowledge. Butstar trackers are larger in size, heavier, power hungry and expensive for nanosatellite missions. The Arcsecond Pico StarTracker (APST) is designed based on the limitations of nanosatellites and estimated to provide pointing knowledge in anarcsecond. The APST will be used on the SNUSAT-2, Earth-observing nanosatellite. This paper describes the require-ments of APST, trade-off for the selection of image sensor, optics, and baffle design. In addition, a survey of algorithmsfor star trackers and a comparison of the specifications of APST with other Pico star trackers are detailed. The field of view(FOV) estimation shows that 17° and 22° are suitable for APST and this reduces stray light problems. To achieve the 100%sky coverage, the FOV of 17° and 22° should able to detect the 5.85 and 5.35 visual magnitude of stars, respectively. It isvalidated by estimating the signal to noise ratio of APST and night sky test results. The maximum earth stray light angle isestimated to be 68° and a miniaturized baffle is designed with the exclusion angle of 27°.

Key Words: Nanosatellite, Attitude Determination, Pico Star Tracker, APS Camera, Baffle

1. Introduction

The SNUSAT-2 is a technology demonstration missionfor the nanosatellite platform. One of the technical objectivesof this mission is to develop a pico star tracker that can esti-mate the attitude of a satellite with arcsecond accuracy. Thestar trackers in the commercial market are heavy, larger insize, power consuming, and costly for nanosatellites. Hence,an optimized Arcsecond Pico Star Tracker (APST) forSNUSAT-2 is under development at Seoul National Univer-sity. The APST is designed based on the mission require-ments and limitations of nanosatellites. The main componentsof the APST are image sensor, imaging lens, and a processorthat are selected from commercially-off-the-shelf (COTS)products. The baffle for the star tracker has been designedand fabricated in-house. The selection of image sensor,imaging lens, processor and baffle design are interconnectedand, this determines the capability and performance of thestar tracker. This paper describes the important parametersto consider for selecting the image sensor, imaging lens, pro-cessor, and baffle design. In addition, the design of variouspico star trackers and their algorithms are analyzed in detail.

2. Current Pico Star Trackers

The star trackers for pico and nanosatellites are developed

by various institutions around the world. The most prominentfive pico star trackers that have produced results during theground based testing is discussed in this section. Table 1shows the important parameters of the pico star trackersand their corresponding imaging sensor and lens.

In general, pico star trackers weigh up to 90 g but this doesnot include the weight of the baffle. The STC-2 has the low-est weight of 65 g, developed by Sternberg AstronomicalInstitute, Lomonosov Moscow State University.1) The sizeof the pico star tracker is designed to fit within 0.5U(50� 100� 100mm) which is half the size of a cubesat plat-form. The ST-200 is the smallest pico star tracker at30� 30� 38:1mm3 without including the baffle developedby Berlin Space Technologies, Germany. The ST-200 hasthe lowest nominal power consumption of 220mW.2) TheST-16 has the highest accuracy of 7 arcseconds (pitch/yaw) and a 70 arcsecond (roll) developed by Ryerson Uni-versity, Canada.3) When lost in space (LIS) a-priori informa-tion about satellite is unknown; hence, the update rate is low-er. However, when in tracking mode (TM) a-prioriinformation about satellite is known using other sensors;hence, there is a higher update rate. The nominal requiredslew rate in LEO is 0.1° to 0.3°/s. When conducting a satel-lite maneuver higher than the nominal slew rate, the image ofstar will blur. But ST-16 is operational up to 3°/s by post-processing the image. Most pico star trackers use a low res-olution image sensor having 1 mega pixel (MP) resolution orless. However, the ST-16 and ST-200 have high resolutionimage sensor of 4MP and 5MP, respectively. The selectionof image sensor includes various aspects, which will be de-tailed in the next sections.

Due to the limitation in size the pico star tracker uses an

© 2017 The Japan Society for Aeronautical and Space Sciences+Presented at Asia Pacific International Symposium on AerospaceTechnology, October 25, 2016, Toyama, Japan.Received 1 December 2016; final revision received 26 June 2017;accepted for publication 18 July 2017.†Corresponding author, enjis@snu.ac.kr

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imaging lenses with a low focal number, which comparablyproduces brighter images. The focal ratio of 1.2 to 1.8 is op-timum for pico star tracker. Most pico star trackers are de-signed with a FOV of less than 20 but the CubeStar devel-oped by the University of Stellenbosch, South Africa useswide FOV (WFOV) of 42° that requires fewer stars to be cat-aloged but has relatively low accuracy and is vulnerable tostray light.4) Based on the FOV requirement, the focal lengthof the imaging lens varies from 6 to 16mm. The focal lengthof 16mm would be the upper limit due to the constraints likeweight, size and accuracy. The limiting magnitude of the startracker is the magnitude of the faintest star detectable by thestar tracker. The pico star tracker developed by the Univer-sity of Wuerzburg, Germany has a high sensitivity imagesensor; hence, it can detect stars up to a magnitude of6.46.5) Based on a literature review and mission require-ments, the possible design requirements for APST are listedin Table 2.

The ST-16 pico star tracker was launched into space aspart of SkySat-1 in 20133); however, it performed lower thanthe expectations due to chromatic aberration of the lens. TheST-16 RT, a modified version equipped with a customizedlens, was launched as part of skySat-2 and skySat-2C in2014 and 2016, respectively.6) It produced better results afterimplementing the customized lens. The ST-200 and CubeStar will be launched into orbit for the QB50 mission.

3. FOV Estimation

The High Precision Parallax Collecting Satellite (HIP-PARCOS-2) catalog is used for APST. The catalog contains

118,218 stars in total, and the accuracy of star magnitude isup to a factor of 4.7) In APST, the stars of magnitude brighterthan 6 are used. Hence, for initial analysis, only 4,558 starsare used. Figure 1 shows the number of stars brighter thanthe magnitude of 6. The number of stars increases exponen-tially as the apparent magnitude of the star increases. Thestars are non-uniformly distributed over the sky becausethe star density is higher in the galactic plane and lower atthe galactic poles. Figure 2 shows the distribution of starsof magnitude brighter than 6 in June 2016, clearly implyingthat the stars nearer the poles have a relatively lower magni-tude compared to those nearer the equator. The average den-sity of stars brighter than a magnitude of 6 over entire sky,galactic plane, and galactic poles is 0.15, 0.32, and0.13 per square degree, respectively.8)

The FOV of a star tracker is a crucial factor that deter-mines the requirements for the image sensor, optics, and baf-fle. A star tracker with a WFOV ranging from 15° to 40° isthe optimum range for the nanosatellites. The WFOV has ad-vantages like lower memory, less processing time, and mod-erate accuracy. In general, star tracker need two stars to de-termine the attitude of the satellite. We use a sub-graphmethod that applies the angular distance between stars to

Table 2. Requirements of Arcsecond Pico Star Tracker (APST).

Parameters Requirements

Weight including baffle (g) < 150

Size including baffle (mm3) 48� 48� 90

Nominal power (mW) < 500

Accuracy 3� (arcsecond) < 50 (PY), < 200 (R)Update rate LIS (Hz) 1Slew rate (°/s) 0.1 to 0.3

Fig. 1. Number of stars corresponding to their magnitude.

Table 1. Parametric study of current Pico star trackers.

Parameters ST-16 ST-200 Cube star STC-2 Pico star

Weight (g) 90 74 90 65 70Size (mm) 60� 46� 58 30� 30� 38:1 46� 33� 70 57� 23� 73:5 30� 38� 80

Power (mW) 250 220 350 250 250Accuracy (arcsec) PY-7, R-70 PY-30, R-200 PY-36 PY-10, R-50 PY-36, R-144Update rate (Hz) LSM-1 LSM-1, TM-4 LSM-1 TM-10 LSM-4Max Slew rate (deg/s) 3 0.3 0.3 2 0.3

Image sensor specifications

Resolution (MP) 5 4 0.5 0.6 0.3Pixel size (Lm) 2.2 2.2 5.6 10 5.6Sensitivity (V/lux.s) 1.4 1.4 — — 16.5

Imaging lens specifications

Focal ratio 1.2 — 1.2 1.17 1.8Focal length (mm) 16 — 6 10.5 16CFOV (deg) 20.03° — 42.33° 19.64° 12.51°Limiting magnitude 5.75 6 3.8 5.5 6.46

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identify stars. When there are only two or three stars in aFOV, there is a high probability of mistakenly identifyingor not identifying the stars. If the angular measurement errorof the star tracker is 0.005° and there are a minimum of fourstars in the FOV, then all the four of the stars can be success-fully identified. There is always a possibility of false starsbeing in a FOV and to compensate for this, we used five starsfor the FOV estimation. The larger the number of stars in theFOV, the higher the accuracy and success rate; however, thisconsumes more operation time. Therefore, we should make atrade-off based on the accuracy and update rate requirement.Accordingly, a minimum of five stars is required in the FOVto identify the real stars. The APST is required to have a min-imum of 99% sky coverage containing a minimum of fivestar in a FOV to determine the attitude of the satellite.

The simulations are performed in MATLAB to determinethe required FOV containing minimum five stars in any partof the sky. The stars of brighter than a magnitude of 6 areused for this simulation. The Circular FOVs (CFOVs) of17°, 20°, 22°, 25°, 30°, 35° and 40° are used for analysis.In order to estimate the FOV, a unit celestial sphere is createdusing real star coordinates and the star tracker is assumed tobe in the center of the unit sphere. The simulation also gen-erates a random location on a unit sphere which representsthe pointing direction of the star tracker. Then the numberof stars present in the FOV is estimated for 10,000 iterations,which are randomly selected sky locations. This programperforms many iterations to collect statistics about howmanystars lie within the FOV of the star tracker. The error in theapproach is 1=

ffiffiffiffiN

p, where N is the number of iterations.

Hence, result contains an error of 1 in every 100 random lo-cations. This means the higher the number of iterations, thehigher the accuracy of identifying the number of stars inthe location. The simulation method and codes for FOV es-timation were made by ‘‘Scott Mulligan” and readers can gothrough for the details of this simulation and code.9)

Figure 3 shows the required star magnitudes for differentFOV and their corresponding sky coverage. Based on the re-quired sky coverage, the limiting magnitude can be deter-mined. The minimum sky coverage required for APST is99% and maximum is 100%. Table 3 shows the required lim-iting magnitude for sky coverage of 99% and 100% for var-

ious CFOV. To acquire 100% sky coverage, the CFOV of17° requires a limiting magnitude of 5.85, whereas the limit-ing magnitude is 4.4 at 40°. This implies that a wider FOVrequires the minimum of number of stars and processing timecan be significantly reduced. However, wide FOVs of 40°and 30° is more vulnerable to stray light from the sun, earth,and moon. Therefore, the CFOV of 17° and 22° are selectedfor initial analysis because they are less vulnerable to straylight and relatively accurate. Either one of these FOVs canbe selected for APST. The selection of imaging sensor andoptics for a star tracker should be based on the FOV and lim-iting magnitude requirement. The image sensor and optics ofthe APST are selected based on the CFOV 17° and 22° andlimiting magnitude of 5.85.

4. Selection of Image Sensor and Imaging Optics

The image sensor contains various parameters that deter-mine its function and performance. The active pixel sensor(APS)-based CMOS sensor is preferred instead of a CCDdue to the advantages of windowing, lower power consump-tion, and lower price. The fabrication of the radiation-tolerantCMOS APS image sensor using standard CMOS processesprovides a considerable cost advantage over other image sen-sors fabricated using specialized radiation tolerant processes.Moreover, other radiation tolerant electronics can be inte-grated with CMOS APS image sensors using the same designand standard CMOS fabrication process. This enables mini-aturization of the radiation tolerant imaging system. Theseadvantage makes CMOS APS a viable alternative to CCDfor space applications.

Fig. 2. Distribution of stars over the sky. Fig. 3. Sky coverage for various FOV and required star magnitude.

Table 3. Required limiting magnitude for sky coverage of 99% and 100%for various CFOVs.

CFOV(deg)

Limiting magnitude forsky coverage of 99%

Limiting magnitude forsky coverage of 100%

17 5.5 5.8520 5.25 5.522 5.1 5.3525 4.9 5.330 4.55 535 4.35 4.5540 4.05 4.4

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The image sensor can either be monochrome or color.Monochrome is preferred because its quantum efficiency ishigher than a color sensor, and a star tracker does not needcolor information of the star. The usage of a color sensorfor star tracker will be one of the research topics in the future.Table 4 shows three CMOS-based monochrome image sen-sors and the important parameters to be considered.10) Thesensor size of 1/3AA to 1/2AA is suitable for APST. The pixelsize is the important factor for determining the accuracy ofthe sensor; the smaller the pixel size, higher the accuracy.The star tracker usually has an image sensor with a resolutionless than 1MP.

The problem with a high-resolution sensor is it takes alonger processing time, which will reduce the update rateof the star tracker. The higher the quantum efficiency, thelower the read noise and dark noise is better because it ena-bles the imaging of faint stars. The full well capacity deter-mines the brightest star it can image. The dynamic range isthe ability to image the brightest and faintest star in thesky. The star tracker needs an images sensor with higher dy-namic range. The CMOS sensor usually has a rolling shutterbut the latest CMOS sensors have a global shutter. The glob-al shutter can image without smearing even if a satellite ma-neuvers at a relatively high rate, whereas the rolling shutterwill smear the image. Therefore, the global shutter is pre-ferred over the rolling shutter. The final important thing isthe availability of the image sensor in the market.

The first preference is the AR1034 because among thethree it has highest sensitivity, quantum efficiency, and dy-namic range. However, only the MT9P031 is the only oneavailable, and it satisfies most of the requirements. TheON-Semi MT9P031 has already been used in the ST-16 startracker developed by University of Ryerson, Canada andhave been successfully operated in many missions since2013. Accordingly, the MT9P031 monochrome image sen-sor was selected for APST. Based on the MT9P031 imagesensor, an imaging lens was selected. The S-mount lenseswere chosen because they weigh less. The lens with a lowfocal ratio (1.2 to 1.8) maximizes the light collection, butaberration increases rapidly as the focal ratio decreases.Spherical and chromatic aberration in the lens may causefailure during the execution of star identification. The equa-tions (1 to 3) shows the relationship between the aberrationand focal ratio. The focal length of 16mm and 12mm pro-vides the FOVs of 15° and 20°, respectively. Additionally,the focal length determines the accuracy of the star tracker;

higher the focal length the better the accuracy of the startracker. Using 16 and 12mm focal lengths, the theoreticalpixel accuracies of 28.4 arcsec and 37.8 arcsec are obtained,respectively.

Spherical aberration / 1=ðfocal ratioÞ3 ð1ÞComa / 1=ðfocal ratioÞ2 ð2ÞAstigmatism / 1=ðfocal ratioÞ ð3ÞField of view / arctan ðsensor size=focal lengthÞ ð4ÞPixel accuracy / arctan ðpixel size=focal lengthÞ ð5Þ

The resolution of the image sensor lens should be in high-resolution MP, otherwise the image that is output will beblurred. This means the magnitude of the signal is reducedin the image sensor. A lens with a resolution of 1 to 3MPis chosen. Theoretically, the 1MP and 3MP lenses can re-solve at 8.9 Lm/line and 5.9 Lm/line, respectively. Thesecharacteristics will be studied in detail during laboratoryand night sky testing. Based on the testing results,B3M16018 lens in Table 5 is chosen. Distortion is one ofthe important factors in determining the quality of the lens.There are three types of distortion: barrel, pincushion andmustache. We use a distortion correction algorithm in thepost-processing to overcome the error due to distortion inthe lens. This enables distortion to be compensated. TheB3M16018 lens has a pincushion distortion of 0.65%. Basedon the suggestions from experts, we opted for lens with lessthan 1% distortion. An antireflection coating for the lens in-creases transmission of the light. An imaging lens with filtersand customized lenses would enhance the quality and per-formance of the star tracker, but these are expensive and willbe considered for development in the future.

5. Sensitivity of APST

The previous sections have established the required FOV,available image sensor, and optics. The signal to noise ratio(SNR) of the APST is one of the factors for verifying if theimage sensor and imaging lens meets the FOV requirements.If the APST has a minimum SNR of 8, it can easily detectstars. The signal of the APST is estimated using Eq. (6),where R is the radius of the lens, t is exposure time (0.1 s),

Table 4. Important parameters of image sensors.

Parameters MT9P031 AR0134 Python 1300

Sensor size (inch) 1/2.5 1/3 1/2Pixel size (Lm) 2.2 3.75 4.8Resolution (MP) 5 1.2 1.3QE at 525 nm (%) 63 77 59Sensitivity (V/lux�s) 1.4 7.7 6.1Read noise (e¹) 7.64 6.58 9.28Full well capacity (e¹) 6,693 5,542 6,057Dynamic range (dB) 58.3 64 55.84Shutter Rolling Global Global

Table 5. Important parameters of imaging lenses.

ParametersBHR16012

BL16014

B3M16018

BSM12016

Optical format (inch) 1/2AA 1/3AA 1/2AA 1/2AAFocal length (mm) 16 16 16 12Focal ratio 1.2 1.4 1.8 1.6FOV (deg) 15 15 15 19.6Resolution (MP) 1 1 3 < 1

Resolution (Lm/line) 8.98 5.96 5.18 9.21Weight (g) 12 16 — 5

Picture ofthe imaginglenses

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F0 ¼ 21,161 ph/s/mm2 is the theoretical flux of the zeromagnitude star detected by the MT9P031 image sensor(based on the quantum efficiency of the image sensor),11)

m is the limiting magnitude of the star tracker (m ¼ 5:35,5.85). The noise estimation of the MT9P031 image sensoris shown in Table 6. A detailed method for estimating thenoise of the APS-based image sensor is given12–14) and esti-mated using Eq. (7)

Total signal ðSeÞ ¼ ð3:14R2 t F0Þ=ð2:5mÞ ð6ÞTotal noise ðNeÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðS þDþ DCNUþ R2 þQ2Þ

pð7Þ

The number of pixels included in the star image is basedon the Point spread function (PSF), by increasing the PSF,the number of pixels that contribute to the noise increases,whereas the magnitude of the signal decreases. The symmet-ric PSF is considered for analysis, and due to the slew rate ofthe satellite, the noise in the pixels increases, which is a func-tion of focal length. The total number of pixels in the PSF isestimated using Eq. (8)14)

Np ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3:14P2 þ 2PðF tanð!tÞ=�Þ

pð8Þ

Where P is the PSF radius in pixels, F is the focal length(mm), ½ is the slew rate (0.1°/s), t is the exposure time (0.1 s)and £ is pixel size (2.2 Lm). The SNR for various PSF radiiand for the corresponding focal ratio of the lens are estimatedin Eq. (9). The graph in Fig. 4 implies that the PSF radius of0.5 has higher SNR when compare to a PSF radius of 3.Focal ratio is another important factor increasing the SNR,the lower the focal ratio the better than signal, so it has higherSNR.

SNR ¼ Se=ðNeNpÞ ð9ÞThe stars can be easily detected with a SNR of 8. The anal-

ysis shows that the lenses with a focal ratio of 1.2 to 1.8 havea SNR higher than 8 for the PSF radius of 0.5 to 3. The focal

ratio of 1.2 with a PSF radius of 0.5 has the highest SNR,84.6, and whereas focal ratio of 1.8 and PSF radius of 3has the lowest SNR, 13.4. The higher the PSF radius, the bet-ter the centroiding ability; however, the higher PSF reducesthe SNR, which leads to the inability to detect faint stars.Therefore, SNR and PSF should be chosen based on the re-quirements of the star tracker.

Table 7 shows the estimated SNR for star magnitudes of5.85 and 5.35 using 16mm and 12mm lens respectively.The PSF of 0.5 is when a star is focused in a single pixeland a PSF of 3 is when a star is defocused at around six pix-els. In APST we prefer focal ratio of 1.8 and PSF of 1 to 2(PSF 0.5 is practically not achievable). For example, whenimaging 5.85 magnitude, the SNR is 72.8 (using 16mm lens,PSF 1, and focal ratio 1.2) and the SNR decreases to 34(using a focal ratio of 1.8), whereas the same lens withPSF 3 reduces the SNR to 13.4.

Based on the analysis from previous sections, two possibledesign for the star tracker are chosen. The MT9P031 imagesensor with a focal length of 16 and 12mm have CFOVs of17° and 22°. Based on the sensitivity analysis of APSTs withCFOV of 17° and 22° can detect stars with magnitudes of5.85 and 5.35, respectively, which assures sky coverage of100%. Table 8 lists the two possible designs for the APST.The both design ¡ and ¢ have their own advantages and dis-advantages. Design ¡ has better accuracy, but the total num-ber of stars is higher. Therefore, the algorithm execution timewould be relatively longer. The total number of stars indesign ¢ is less. Therefore, the execution time is relativelyless, but accuracy is lower as well. Both of this design aresuitable for an APST, based on night sky results, the design¡ is chosen.

6. Operational Algorithms

The star tracker image processing consists of four impor-tant steps,

Table 6. Noise estimation for MT9P031 image sensor.

Parameters Noise (e)

Dark current (D) 0.39Dark current non-uniformity 0.04Read noise (R) 3.5Quantization noise (Q) 0.46Photon shot noise (S)

ffiffiffiffiffiSe

p

Fig. 4. SNR vs focal ratio of various PSFs.

Table 7. Estimation of SNR for various focal ratio and PSF.

Focal length(mm)

Focalratio

SNRPSF 0.5

SNRPSF 1

SNRPSF 2

SNRPSF 3

16 1.2 84.6 72.8 41.2 28.81.4 63.9 55.1 31.1 21.81.6 50.3 43.3 24.5 17.11.8 39.6 34 19.2 13.4

12 1.6 50.2 38.8 21.5 14.9

Table 8. Two possible design for APST.

Parameters Design ¡ Design ¢

Min. no. of stars in a FOV 5 5CFOV (deg) 17 22Limiting magnitude 5.85 5.35Total no. of stars 3,897 2,237Focal length (mm) 16 12Focal ratio 1.2, 1.4, 1.6, 1.8 1.6Accuracy (arcsecond) 28 38Execution time Longer Shorter

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i) Star detectionii) Centroidingiii) Identificationiv) Attitude determinationStar detection is based on the sensitivity of the APST and

background threshold. The previous section of this paper de-tailed the theoretical estimation of star detection. The pixelsize and focal length limit the star tracker accuracy. To obtainsub-pixel accuracy, the star tracker is purposely defocused tospread over many pixels (i.e., the PSF of the star image is en-hanced). A centroid algorithm is then used to identify thecentroid of the star image. Basically, centroiding has twotypes of algorithms: Centre of mass or weight, which usesthe number of pixels, and light intensity to estimate the cen-ter point of a star.

The accuracy is up to 1/10 of a pixel. The Gaussian distri-bution method produces an accuracy of 1/100 of a pixel, butit’s complex to implement. Therefore, the centre of mass orweight is easier to implement and achieve reasonable accu-racy.15) Centroiding without defocusing would be advanta-geous for achieving higher SNR and to overcome aberrationissues.

Using the centroid coordinates of star images, the identifi-cation algorithm is implemented. The identification algo-rithm identifies stars in the image by matching them withthe onboard star catalog. The identification algorithm con-tains two main classifications: pattern recognition and sub-graph. The pattern recognition is based on the patterns pro-duced by connecting the stars (e.g., star constellations) usinggrid algorithm or ring algorithm, but the pattern recognitionmust have higher star density, which means more faint stars.The sub-graph method uses the distance and angle informa-tion between the stars for identification. Table 9 contains alist of important identification algorithms and their character-istics. The main characteristics of an efficient identificationalgorithm are being highly robust, less complex, having asmall database, and requiring less time for execution.

Comparing the four algorithms in Table 9,16) geometricvoting is more suitable for APST because it is highly robust,has a high success rate and require only small database, butone disadvantage is it requires more time for execution whencomparing to other algorithms. The second option would bea pyramid algorithm (K-Vector search) due to its well-knownsuccess rate, robustness and shorter execution time. Grid al-gorithm or any other based on pattern recognition would bethe option for future development because pattern recogni-tion requires a lower percentage of trigonometrical informa-tion of stars. This could be a serious problem due to aberra-

tion in lens, noises, and stray light and this can be overcomeusing pattern recognition but it requires higher star density.Further work on developing optimized pattern based algo-rithm would be efficient. The triangle algorithm is wellknown for its lower complexity and smaller database but itdoes not have a high success rate. The pyramid algorithmwill be used for star identification.17,18)

The final operation is determining the 3-axis attitude solu-tion from star vector observation. The triad algorithm will beused by APST to determine the attitude of the satellite. It’ssimple to execute, requires less memory and reduces compu-tation time. The star tracker is basically a camera that imagesthe part of the celestial sphere and post-process the image todetermine the attitude of the satellite.

Figure 5 shows the inverted projection of a celestialsphere on a sensor frame. In the sensor frame, the stars arelocated based on sensor origin and focal distance (x; y; f).Therefore, the rotation between the sensor frame and inertialframe (celestial sphere) has to be determined to estimate theattitude of the satellite.

Using identification algorithm inertial coordinates of twovectors, (ai bi) is obtained from the mission catalog. Thenthe two corresponding star vectors in the sensor frame (as bs)are estimated. Using these four star vectors, the rotationmatrix (Rsi) is determined using a triad equation shownEq. (10). The rotation matrix is converted to represent Eulerangles.

as ¼ Rsiai and bs ¼ Rsibs ð10Þ

7. Night Sky Testing

Based on the theoretical estimation of sensitivity of the im-age sensor and imaging lens, a MT9P031 demonstration kitand Lensation lenses are used for the testing, which is shownin Fig. 6 and Fig. 7. The MT9P031 demonstration kit con-tains a wide angle lens, which has been replaced with a len-sation lens, using an adapter as shown in Fig. 6. The parame-ters of the MT9P031 image sensor and lensation lenses areshown in Table 4 and Table 5 respectively. In this night skytesting, the hardware is tested to see if it can image stars of5.85 magnitude with an exposure time of less than 200msto ensure APST has 100% sky coverage. But the algorithmsfor star detection, centroiding, and identification have notbeen implemented yet. First night sky testing is performed

Table 9. Comparison of various identification algorithms.

Parameters Triangle PyramidGeometricvoting

Grid

Robust Low High High HighComplexity Normal High Normal NormalDatabase Small Small Small LargeAccuracy Sub-pixel Sub-pixel Sub-pixel PixelTime Less Less Normal Less

Fig. 5. Celestial sphere projection in a pinhole camera.

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at the Seoul National University and around Seoul but, thetest results were poor due to the city lights. Therefore, wetraveled 160 km southeast of Seoul to Yongjin-ri which is lo-cated in the state of Danyang-gun. This location is a remotearea and there are no artificial lights in the surrounding area.Based on the Accu Weather forecast there were no clouds(i.e., 100% clear sky) on August 12, 2016 at 1:00 a.m. Thehumidity was above 90%, but dry weather is a better condi-tion for star imaging.

The stars near the zenith have a brightness loss of 0.2 vis-ual magnitude and stars near the earth surface have a bright-ness loss of 1 visual magnitude due to the high atmosphericair mass. Therefore, stars within the zenith angle of 45° areimaged during the night sky testing. which have a brightnessloss of 0.3 visual magnitude.19) If APST can detect 5.7 visualmagnitude stars in orbit, it can detect visible 6 magnitudestars. All four of the lenses in Table 5 are tested using theMT9P031 demonstration kit for the exposure time of200ms and using the maximum gain value. Two of thelenses are selected based on night sky testing. TheBHR16012 is the brightest lens having a focal number of1.2 and resolution of 1MP. Figure 8 and Fig. 10 are imagesof the Cassiopeia and Lyra constellations imaged using theBHR16012 with a 200ms exposure.

The numbers in Figs. 8 to 11 shows the visual magnitudeof the stars. The BHR16012 lens imaged stars with a visualmagnitude of 6.1, which means in orbit it can detect starswith a magnitude of 6.4. The APST only requires visualmagnitude of 5.85; therefore, it can operate with an exposuretime less than 200ms. The disadvantages of BHR16012 arelow resolution and aberration. In Fig. 10, the star vega showsaberration (unsymmetrical) and in Fig. 8 stars with magni-

Fig. 6. MT9P031 demonstration kit.

Fig. 7. Lensation imaging lenses for the APST.

Fig. 8. Cassiopeia constellation imaged using the BHR16012 lens with anexposure time of 200ms and maximum gain.

Fig. 10. Lyra constellation imaged using the BHR16012 lens with an ex-posure time of 200ms and maximum gain.

Fig. 9. Cassiopeia constellation imaged using the B3M16018 lens withexposure time of 200ms and maximum gain.

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tudes of 2.25, 2.65 and 3.35 show aberration and distortion inthe lens. The B3M16018 has a focal number of 1.8 and res-olution of 3MP. Figure 9 and Fig. 11 contain images usingthe image of B3M16018, are not as bright as BHR16012,it can still image a star with a magnitude of 6 using an expo-sure time of 200ms.

But the B3M16018 produced symmetric images withoutaberration and distortion in Fig. 9 and Fig. 11 which is betterthan BHR16012. The stars imaged using the B3M16018 aremore symmetrical than those imaged using the BHR16012and this will help to accurately define the centroid of the starand high success rate of identifying the stars. Therefore,B3M16018 lens is chosen for APST. These tests confirmedthat existing hardware can detect stars of 5.85 magnitudewith an exposure time of less than 200ms. This shows thatthe APST will have 100% sky coverage during static imag-ing, but the sky coverage will be decreased under dynamiccondition (high slew rate). This night sky testing is donewithout the operation of algorithms and baffle. A night skytest with various slew rate will be performed.

8. Baffle Design

The stray light from the Sun, Earth and Earth’s moon isone of the major factors in lowering the performance of thestar tracker. It could even lead to failure in certain conditions.As APST will be operating in a Low-Earth orbit, the dom-inant stray light source is the Earth. The SNUSAT-2 orbitalaltitude will be around 400 to 700 km, which is far less thanthe radius of the Earth. Therefore, the Earth is viewed as anextended stray light source. However, the bright stray lightsources like the Sun and Earth’s moon are viewed as pointsources due to their long distance from the LEO satellites.To successfully image the faint stars of 5.85 magnitude,the background stray light must be lower than the magnitudeof 5.85. The optical axis of the star tracker should be orientednormal to the Sun to reduce the stray light intensity. Since theEarth is an extended surface, the effective stray light regionof the Earth is calculated. Figure 12 shows the orientationof APST, which is almost normal to the Sun and Earth. It alsoshows the effective stray light region of the Earth. The max-imum stray light angle is due to the Earth, incident on theAPST is known as �max.20) The average radius of the EarthRearth is 6,370 km, H is the altitude of the orbit (500 km) andthe �max is 68°. The maximum radius of the effective stray

light region Rmax,

�max ¼ arcsin ðRearth=ðRearth þHÞÞ ð11ÞRmax ¼ Rearth cos�max ð12Þ

The �max is useful when designing the baffle and startracker orientation. The maximum irradiancy from the sunis 918.1W/m2 and the Earth reflects 35% of the Sun’s light,which is known as albedo.

The maximum irradiancy from the Earth is 321.3W/m2.The irradiance of the Earth’s moon when it’s full is 1.4mW/m2.21) The function of the baffle is to prevent stray lightfrom bright objects (i.e., Sun, Earth and Earth’s moon) out-side the FOV from directly reaching the lens surface and toreduce the intensity of stray light so that the star trackercan identify the stars effectively. A single-stage, diffused cy-lindrical baffle with straight vanes has been designed for theAPST. A two-stage baffle is efficient for reducing stray, lightbut due to volume constraints, a single stage baffle is used forAPST. Baffles can be designed in either cylindrical or conicalshape. A baffle with specular reflection is highly dependenton low reflective paint and precise machining, and becauseof this reason diffused baffle is easier to fabricate. The bafflewith a straight vane has a lower Point Source Transmittance(PST) of 10�6, whereas baffle that are grooved vanes andhave no vanes have PST of 10�5 and 10�3, respectively.22)

It has a half FOV of 7.5° and exclusion angle of 27°. The de-tailed method for baffle design is explained by Jacobs.23)

The baffle design should consider the following guidelines,which were suggested by Heinisch.24) The star tracker FOVshould not interfere with the baffle wall or edges. At least tworeflections from a blackened surface are required betweenstray light source and the optical elements. The stray lightwithin the baffle is required to have a maximum number ofreflections before it enters the sensor. Minimum number ofedges should be exposed to the Sun. The vanes of the baffleshould have sharp edges. The baffle is to be designed basedon the required star tracker FOV and exclusion angle. Theexclusion angle is the minimum angle at which light froma bright object outside the FOV can reach the lens surface.The lower the exclusion angle the better the attenuation tostray light. A baffle with higher length to diameter (L=D)ratio has a lower exclusion angle, but a baffle with a higher(L=D) ratio becomes heavier and larger. The baffle being

Fig. 12. Extended stray light source from Earth.

Fig. 11. Lyra constellation imaged using the B3M16018 lens with an ex-posure time of 200ms and maximum gain.

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used is designed based on the MT9P031 image sensor andB3M16018. The baffle design for the APST, shown inFig. 13, has a diagonal FOV of 22°, baffle length of50mm, diameters of the lens and baffle are 10.9mm and46mm, respectively.

The next step is the vane placement in the baffle. TheAPST baffle design in Fig. 13 contains three straight beveledvanes. In order to reduce the reflecting surface of the vaneedge, the edges of the vanes are sharpened, which is knownas beveled vanes. The vanes are designed with a constantbeveled angle of 45° because it easier to manufacture. A vaneedge thickness of 0.1mm is achievable. The number of vanesand depth of the vanes in the baffle determine the spacing be-tween the vanes. The number of vanes should be optimizedbecause it enhances the risk of reflecting the stray light di-rectly to the optics. The thickness of the baffle and vanes is1mm. The details regarding vane design and placement havebeen reported by Fest.22) Another important factor is the re-flectivity of the black paint; the inner surface of the baffle ispainted to reduce scattering of the stray light. The paints 3Mblack velvet, Aero glaze Z306, Martin black, Parson black,3M 401-C10 have very low reflectivity. But due to lack ofavailability, black anodized is easier to obtain. Figure 14shows the APST design. The total length of APST is87mm and its breadth is 48mm, without the baffle the di-mension are 37:5� 48mm. The left side of Fig. 14 containsoptics, image sensor and other electronics. The electronicsare shielded by aluminum of 2mm thickness to protect itfrom space radiation. In Fig. 13, the maximum stray light

angle in the baffle is shown.If the orientation of the APST optical axis is normal to the

Sun, it’s estimated that only the Sun directly illuminates thefirst vane. If the orientation of the APST optical axis is nor-mal to the Earth, it illuminates up to the third vane directly.The illumination of stray light attenuates as it undergoes mul-tiple reflections within the baffle before it reaches the lenssurface. The maximum stray light angle from the earth is68°, which is shown in Fig. 12 and Fig. 14. The APSTshould maintain a minimum offset angle of 42° and 68° fromthe Sun and Earth respectively, to efficiently identify the starswith a visual magnitude of 5.85. Based on this design, a baf-fle for the APST will be manufactured and tested using a so-lar simulator.

9. Radiation Tolerance

The APST will be installed in the SNUSAT-2 Earth obser-vation nanosatellite. It’s planned to be operated in a Sunsynchronous polar orbit. The altitude of the orbit has notbeen fixed but it will be around 400 to 600 km. The elec-tronics in a satellite are always vulnerable to charged par-ticles from radiative sources. The energy, flux, and fluencyof these charged particles varies based on the altitude and in-clination of the orbit. Due to the radiation, electronics in sat-ellite malfunctions and can even lead to functional failure.This is overcome by using radiation-hardened devices. How-ever, due to high cost and limited availability, it’s not acces-sible for nanosatellites.

The COTS components are accessible for nanosatellite,but they are not qualified for space environment. Therefore,the components are qualified by radiation ground testing todetermine the lifetime in the target orbit. The main radiationsources are trapped charged particles in Van Allen’s Beltwhich extends from 300 to 36,000 km. The South AtlanticAnomaly is one of the main problems faced by satellites inLEO. Next, solar particle events like solar flares and coronalmass ejection occurrence are based on an 11 year solar cycle.Finally, galactic cosmic rays which are dominant over thepoles due to the weak magnetic field. In SPace ENVIronmen-tal Software (SPENVIS), all of these radiative sources aregiven as inputs and the radiation exposure in the target orbitis estimated. The ionizing particles lose their energy whentraveling through matter and the energy is deposited in thematter. Over time, the charge accumulates, and this is knownas total ionizing dose (TID). The TID for silicon for a periodof one year at the orbital altitude of 400 to 600 km and incli-nation of 90° is estimated using SPENVIS.25)

Table 10 shows the TID accumulation for different shield-ing thicknesses over one year. By increasing shielding thick-ness, the accumulated dose is reduced; however due toweight constraints, a thickness of 2 to 3mm is feasible.Based on the literature review, at high inclination orbit(705 km, 98°) with shielding of 2.54mm, the component ac-cumulates a TID of 4 krad25) and this data is close to our es-timation using SPENVIS. In general, COTS componentshave a radiation tolerance of 1–10 krad/year and silicon

Fig. 13. Baffle design for the APST.

Fig. 14. APST design with stray light illumination.

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has a dose limit of 5 krad/year.25) These numbers conveythat, if the APST has (Al) shielding of 3mm, it can survivein orbit for a period of one year.

10. Conclusion

This paper details the hardware requirements of Pico startrackers. The focus of this paper is selection of an image sen-sor and imaging optics based on the estimation of FOV,SNR, PSF, focal ratio because most current research paperson Pico star trackers have not revealed information on the de-tails of selecting images sensor, and optics, which are themost important factors for a star tracker. The next importantfactor is baffle design, since the current research paper illus-trates baffle design for a larger scale, a proper design isneeded to reduce the size of the baffle. Therefore, importantaspects in baffle design and estimation of maximum Earthstray light angle are estimated. In addition, the feasible algo-rithms for star trackers and their characteristics are briefed.Finally, two possible design for the Arcsecond Pico startracker are established.

Based on this analysis, it’s estimated that the ON-SemiMT9P031 image sensor combined with Lensation low focalratio lenses of 1.2 to 1.8 can achieve the required limitingmagnitude of 5.85 and 5.35 for the CFOVs of 17° and 22°,respectively. The night sky test results show that theBHR16012 lens with a focal ratio of 1.2 (1MP) andB3M16018 with a focal ratio of 1.8 (3MP) detect stars of6 magnitudes with exposure time of less than 200ms. Thefocal number of 1.2 shows unsymmetrical images of stars(aberration and distortion), whereas 1.8 focal lens showsmore symmetric images, which will help in accurate cen-troiding and successful identification of the stars. Therefore,the MT9P031 image sensor and B3M16018 imaging lenswere selected for the APST. The test results shows that theAPST will be able to detect stars with a magnitude of 5.85with an exposure time of less than 200ms. Accordingly, thisensures 100% sky coverage during static imaging. However,the sky coverage will decrease during dynamic imaging (i.e.,due to high slew rate). The night sky test to estimate the skycoverage at slew rate of 0.1 to 0.5°/s will be tested in the fu-ture. The author detailed two possible designs, ¡ and ¢ forAPST in Table 8. Design ¡ has been selected for the APSTbased on the availability of a quality lens (i.e., focal ratio of1.8) that can produce symmetric images without aberrationand doing so with high accuracy. However, the authors alsosuggest readers to select either design ¡ or ¢ based on mis-sion and system requirements, which is explained in the fifthsection of this paper.

The maximum stray light angle from Earth is estimated tobe 68°. A baffle with a length of 50mm and exclusion angleof 27° has been designed with beveled vanes. The advan-tages of an APST include a small size that fits in pico-, nano-and micro-satellites, light weight, and low power consump-tion, while providing high accuracy. The software develop-ment and testing of an engineering model will be conductedby the end of 2017 and the flight model will be ready by thefirst quarter of 2018.

Acknowledgments

This research is financially supported by the Space TechnologyDevelopment Program (NRF-2015M1A3A4A01065787) throughthe National Research Foundation of Korea (NRF) grant fundedby the Korean government (MSIP) and J.H. Park, V.A. Muruganan-dan, S.Y. Lee were supported by the Brain Korea 21 program in2016 (F14SN02D1310).

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Table 10. Total mission dose for one year.

Aluminum shielding thickness (mm) Total ionizing dose (krad)

0.0001 3,0401.4 5.92 3.043 1.39

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S. MatunagaAssociate Editor

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