IN-FLIGHT CALIBRATION OF THE OSIRIS-REX OPTICAL NAVIGATION IMAGERS

IN-FLIGHT CALIBRATION OF THE OSIRIS-REX OPTICAL NAVIGATION IMAGERS John Y. Pelgrift, Eric M. Sahr, Derek S. Nelson, Coralie D. Jackman, Lylia Benhacine, Brent J. Bos, Bashar Rizk, Christian d Aubigny, Dathon Golish, Daniella DellaGiustina, Dante S. Lauretta INTRODUCTION Navigation for solar system exploration missions often requires optical navigation techniques in order to achieve the orbit determination precision necessary to fulfill mission science objectives. Optical navigation relies heavily on the imaging instruments on-board the spacecraft, which each need to be individually calibrated to characterize and model their optical properties. While a preliminary calibration of the instruments is completed on the ground before launch, an in-flight calibration is necessary to refine the results of the preliminary calibration and achieve the post-launch accuracy levels necessary for optical navigation. This paper presents the procedure and results of the in-flight calibration of the optical navigation imagers on-board NASAs OSIRIS-REx spacecraft. This spacecraft is currently en route to the asteroid Bennu (101955), which will be the smallest body that NASA has ever attempted to orbit. Orbiting such a small body presents unique challenges and requires high-precision optical navigation, which is not possible without proper camera calibration. In this paper we will introduce the OSIRIS-REx optical navigation camera parameters and designs, the concepts of geometric distortion modeling in optical systems, and the preferred calibration models used to characterize the optical properties of the cameras. We will then outline the procedure for processing images taken in-flight to calibrate each optical navigation camera on the spacecraft. Finally, we will present our calibration results and discuss the differences between the cameras on-board the spacecraft and each of their unique challenges with respect to calibration. The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission was launched in September 2016 and will rendezvous with near-earth asteroid Bennu (101955) in late 2018. OSIRIS-REX, a NASA New Frontiers mission, will conduct an extensive campaign of observations at Bennu, collect a sample of regolith, and return it to Earth. Bennu will be the smallest body NASA has ever attempted to orbit, which presents unique navigational challenges and requires optical navigation techniques for successful execution of the mission. Optical Navigation (OpNav) uses information extracted from images taken by the spacecraft to assist in the orbit determination (OD) of the spacecraft. Radiometric tracking data are used for OD throughout the mission, however these data are most useful in determination of spacecraft position relative to Earth. Current ephemeris knowledge for Bennu is relatively large when compared to the scale of the body so Earth-based radiometric tracking is insufficient to ensure accurate determination of the spacecraft position relative to the asteroid. Therefore, optical navigation techniques are required in order to meet mission objectives and ensure spacecraft safety. 1 OpNav for the OSIRIS-REx mission will nominally utilize four of the six imagers on-board the spacecraft: NavCam1, NavCam2, PolyCam, and MapCam. The optical and radiometric properties of these imagers are Space Navigation and Flight Dynamics Practice, KinetX, Inc., 21 W. Easy Street Ste. 108, Simi Valley, California 93065, U.S.A. Contributed while interning for KinetX. Current affiliation: Draper Laboratory, 17629 El Camilo Real, Ste. 470, Houston, TX 77058 NASA Goddard Spaceflight Center, Greenbelt, MD 20771, U.S.A. Lunar and Planetary Laboratory, University of Arizona, 1415 N. 6th Ave, Tuscon, AZ 85705 1

Table 1: OpNav Imager Optical and Radiometric Properties 1 NavCams 1 & 2 PolyCam MapCam FOV ( ) 44 x 32 0.8 x 0.8 4 x 4 IFOV (µrad/px) 280 13.5 68 Detector size (px) 2592 x 1944 1024 x 1024 1024 x 1024 Aperture (mm) 2.28 175 38 F/# 3.5 3.5 3.3 Focal length (mm) 7.6 630 125 Pixel size (microns) 2.2 x 2.2 8.5 x 8.5 8.5 x 8.5 shown in Table 1. In order to effectively and accurately extract optical navigation information from the images taken by these cameras, a variety of calibrations need to be performed to characterize and model their physical and optical properties. In-flight calibrations are performed to refine the pre-launch calibrations and achieve the required optical navigation accuracy levels. These in-flight calibrations have been performed using images taken during the two-year cruise phase of OSIRIS-REx while it has been en-route to Bennu. This paper will present the results of two of the calibrations performed geometric distortion modeling and boresight alignment analysis for each of the four cameras. Details of the cameras are presented here, followed by an introduction to each of these two calibrations. NavCam 1 and NavCam 2, part of the Touch and Go Camera System (TAGCAMS), are redundant, identically designed cameras specifically dedicated to optical navigation. They were designed and constructed by Malin Space Science Systems based on requirements developed by Lockheed Martin and NASA. These cameras feature a 2592 x 1944 pixel complementary metal-oxide-semiconductor (CMOS) detector array and a wide field of view (FOV) of 44 x 32 degrees. 2 PolyCam and MapCam are scientific cameras in the OSIRIS-REx Camera Suite (OCAMS), which was designed and constructed at the University of Arizona Lunar Planetary Lab. They have identical focal planes containing the same model 1024 x 1024 pixel active charge-coupled device (CCD) detector array. PolyCam is a narrow angle, high resolution F/3.5 Ritchey-Chretien telescope with a 0.8 x 0.8 degree FOV. PolyCam is the primary optical navigation imager during the early approach phase of the mission. In addition, it is one of the prime scientific instruments and will provide high-resolution close-range imaging of Bennu. MapCam is a F/3.3 5-element refractive telescope with a FOV of 4 x 4 degrees and an 8-element filter wheel. For optical navigation, MapCam will be configured to use its panchromatic filter that is focused for ranges of 125 m to infinity, which is the filter used for all the calibrations presented here. MapCam s other main function is to image the asteroid to contribute to the science team s development of topographic maps of Bennu for landmark navigation. 3 The inherent geometric optical distortion of each on-board imager directly affects optical navigation performance and needs to be accurately modeled post-launch. In order to calibrate this distortion in-flight, star images were acquired and analyzed to calculate a set of star center residuals that can be minimized in a leastsquares sense to determine a best-fit estimate of the distortion model parameters. Several image mosaics of dense star fields were acquired with each imager in order to ensure that the entire FOV of each camera was adequately sampled. The distortion calibration for each imager was used to estimate a variety of algebraic distortion coefficients, as well as the focal length and intersection point of the optical axis with the detector. These calibrations were performed at various temperatures that are expected throughout the OpNav operational profile. The effective focal length of the cameras was found to have a significant dependence on temperature, especially in NavCam 1 and NavCam 2, therefore a linear focal length temperature-dependence coefficient was also estimated for each camera. Once the geometric optical distortion of each camera was adequately modeled, the camera s alignment 2

with respect to the spacecraft could be calibrated. The star fields in each image were used to determine the camera s boresight attitude at each image epoch. This was then compared to the camera boresight attitude as determined on-board by the GNC system. The GNC system uses the spacecraft s star trackers to determine the spacecraft attitude. It then uses the spacecraft-to-instrument matrix, a pre-defined rotation matrix that describes the offset between the camera boresight and the spacecraft frame, to convert this spacecraft attitude into a camera boresight attitude. An update to this rotation matrix was estimated in a least squares sense to calibrate the alignment of the instrument with respect to the spacecraft. CALIBRATION PROCEDURES KXIMP Star-based OpNav Software The first step in calibration is processing the star field images using the KinetX Image Processing (KXIMP) software suite to perform star center-finding and attitude determination. In this process, the centroids of the stars are calculated and used to determine the inertial attitude of the camera boresight at the image epoch. A predicted centroid position is first calculated for each star using data from the UCAC4 star catalog. A 2D Gaussian function is then fit to each star s point-source image data in a least squares sense in order to determine the best estimate for the centroid. The predicted star center positions are then fit to the observed star center positions to determine the boresight attitude. Without calibrating for optical distortion, the residuals between the observed and predicted star centers should be higher at the edges of the field of view where the distortion effect is the greatest. After distortion calibration, the residuals should be relatively constant throughout the field of view. Geometric Optical Distortion After star center finding is completed and an initial attitude solution is determined for each star field image, the star center residuals are again minimized to estimate the distortion parameters by recalculating the predicted star locations and fitting them to the observed star locations. This calibration used the OpenCV distortion model with 10 different parameters being estimated: three parameters to model radial distortion (k 1, k 2, and k 3 ), two parameters to model tangential distortion (p 1 and p 2 ), two parameters for the camera s focal length at 0 C pixels in each of the two image dimensions (f x and f y ), two parameters to describe the intersection point of the optical axis with the image plane (c x and c y ), and one parameter to model the focal length s temperature dependence (a 1 ). The algebraic formulation of the OpenCV model (with the introduction of a temperature-dependent focal length) is as follows: 4 [ ] x y = 1 [ ] x z y r 2 = x 2 + y 2 [ ] [ ] [ ] x y = (1 + k 1 r 2 + k 2 r 4 + k 3 r 6 x 2p1 x ) y + y + p 2 (r 2 + 2x 2 ) p 1 (r 2 + 2y 2 ) + 2p 2 x y [ [ ] x u fx (1 + a = 1 T ) 0 c x v] y 0 f y (1 + a 1 T ) c y 1 where T is the camera temperature in degrees Celsius. A unit vector ([x, y, z] T ) describing the star s position is found for each star using its inertial position according to the UCAC4 star catalog rotated into the instrument frame using the camera boresight attitude. This unit vector is then normalized by its z-component and the distortion model described above is applied. The resulting unitless coordinates (x, y ) are converted to pixels by multiplying by the focal length for each dimension (which is adjusted based on the camera temperature). These coordinates are relative to the optical axis intersection point so they are then added to the coordinates of the optical axis intersection point to finally 3

get the star s location within the image (u, v). The star center residual then is the difference between this predicted star location and the observed star location from the centerfinding performed with KXIMP. A Levenberg-Marquart least squares algorithm was implemented to estimate these 10 camera parameters as well as to re-estimate the camera boresight attitude for each image so that the star center residuals were minimized. The criteria for an ideal distortion calibration result is two-fold. First, the residuals should show a zero-mean Gaussian distribution with a standard deviation less than 0.1 pixels in both image dimensions. Second, the residuals should be at random directions throughout the FOV, showing no systematic structure related to the stars positions in the image. Boresight Alignment Analysis Once a final solution is reached for the optical distortion model parameters that minimizes the star centerfinding residuals, the images are re-processed in KXIMP to generate a final solution for the camera boresight attitude at each image epoch. This boresight attitude is then compared to the attitude solution given by the GNC system at the same epoch. The difference between the KXIMP and GNC attitude solutions is expressed as a delta-rotation defined by three Euler angles. The axes for these Euler angle rotations were chosen such that the first rotation is about the instrument y-axis (which corresponds to an offset in the pixel direction in the image), the second rotation is about the instrument x-axis (which corresponds to an offset in the line direction in the image), and the third rotation is about the instrument z-axis, representing the camera roll about its own boresight. These three Euler angles have been labeled pixel, line, and roll, respectively, in this paper. As described above, the GNC system determines the boresight attitude by first determining the spacecraft attitude and then applying the spacecraft-to-instrument rotation matrix to determine the corresponding boresight attitude. This spacecraft-to-instrument matrix is initially inaccurate, resulting in a constant offset between the GNC and KXIMP boresight attitude solutions. The GNC attitudes are fit to the KXIMP attitudes in a least squares sense to estimate a more accurate spacecraft-to-instrument rotation matrix. The remaining residuals show the uncertainty in the boresight alignment. RESULTS NavCam 1 Optical Distortion Both NavCam 1 and NavCam 2 exhibited a relatively large amount of distortion due to their wide field of view compared to the other imagers. This can be clearly seen in the star center residuals when no distortion model is applied, shown in Figure 1. There is obvious strong radial distortion, especially Table 2: OpNav Imagers Final Distortion Parameter Results Parameter NavCam 1 NavCam 2 MapCam PolyCam k 1-0.5372-0.5384 0.91096 3.29134 k 2 0.3739 0.3826-14.480-8.376 10 3 k 3-0.1839-0.2041-0.01717-1.962 10 3 p 1-2.3050 10 4-6.2311 10 4-4.2536 10 3 5.8877 10 3 p 2-9.1007 10 4-1.2370 10 4-1.1334 10 3 4.8654 10 3 f x (pixels) 3473.260 3462.596 14729.888 73858.704 f y (pixels) 3473.321 3462.446 14728.590 73858.743 c x 1269.082 1310.530 513.000 513.000 c y 950.746 969.487 513.000 513.000 a 1 2.526 10 5 2.018 10 5 1.094 10 5-2.849 10 6 4

Figure 1: Star center residuals for NavCam 1 when no distortion model is used, shown at each star s image location. Figure 2: Post-calibration star center residuals for NavCam 1 shown at each star s image location. 5

Figure 3: Post-calibration star center residuals for NavCam 1 as a function of star magnitude. Figure 4: Post-calibration star center residuals for NavCam 1 as a function of camera temperature. 6

at the edges and corners of the FOV. The length of each vector is equal to the magnitude of the residuals, which are larger than 150 pixels at the corners. After calibrating, the star center residuals become much smaller and the radial pattern is removed. Figure 2 shows the post-calibration star center residuals for NavCam 1 at each star s location in the image. The length of the vectors has been magnified by a factor of 200 so that they are visible. The vectors are mostly pointing in random directions throughout the field of view showing that the residual error is random and not due to incorrect modeling of the optical distortion, which would show structure in the residual vectors similar to Figure 1. Star center finding error from KXIMP and star catalog position error from the UCAC4 catalog contribute to the remaining error. There does appears to be some slight radial structure appearing in the top left corner of the FOV that has not been perfectly corrected and requires further investigation, however the other three corners do not seem to exhibit this same behavior. Figure 3 shows the same residuals plotted over star magnitude. This shows us that the residuals have a Gaussian-like distribution with a near zero mean and standard deviation below 0.1 pixels. This is an ideal result and, along with Figure 2, shows that the distortion has been adequately modeled. Figure 5: Distortion map for NavCam 1. Contour lines show the magnitude of the distortion in pixels. NavCam 1 had issues with acquiring usable data at the hot end of the operational temperature spectrum due to the way it is mounted on the spacecraft instrument deck. For hot calibrations, the sun is used to heat the instrument deck. The NavCam 1 boresight is angled 6 degrees compared to the rest of the instruments on the spacecraft instrument deck. This is done to simplify the planning and execution of OpNav images while in orbit, but results in NavCam 1 receiving significantly more stray light from the sun than the other imagers during hot calibration runs. This stray light was so significant that every image taken during NavCam 1 s first hot calibration campaign was completely saturated and unusable. For the second hot calibration campaign, the exposure time was reduced from 10 seconds to 1.6 seconds. This resulted in an image that was partially saturated but still had some usable data. About 8-10 stars were used from each image compared to at least 50 stars from images without stray light. The extreme stray light in the images degraded the star center finding results. This effect can be seen 7

in Figure 4, which shows the star center residuals plotted over camera temperature. Larger residuals are observed in the images taken at higher temperatures. It can also be seen that there is less data at the hot end of the temperature spectrum due to there being less usable stars in these images. The final results for each distortion parameter are given in Table 2. Figure 5 shows a map of the distortion generated from these parameters. This distortion map shows the same pattern observed in Figure 1 when no distortion model is used. The optical center marked in this distortion map is the optical axis intersection point (c x, c y ). Figure 6: NavCam 1 alignment error as a function of camera temperature expressed as Euler angles when using the previous spacecraft-to-instrument rotation matrix. Figure 7: NavCam 1 alignment error as a function of camera temperature expressed as Euler angles when using the updated spacecraft-to-instrument rotation matrix. 8

Figure 8: Star center residuals for NavCam 2 when no distortion model is used, shown at each star s image location. Boresight Alignment Figure 6 shows the error in NavCam 1 s boresight alignment before correcting the spacecraft-to-instrument rotation matrix. As described above, this alignment error is expressed as three Euler angle rotations. The left y-axis is in units of milliradians while the right y-axis is in units of NavCam pixels. One NavCam pixel is 0.28 milliradians. Figure 7 shows the effect of updating the spacecraft-to-instrument matrix. The alignment error has been greatly reduced. There seems to be a slight temperature dependence, however the alignment error remains less than one pixel over the expected operational temperature range. This amount of alignment error is acceptable so there is no need to model this temperature dependence and a constant spacecraft-to-instrument matrix can be used across the temperature range. NavCam 2 Optical Distortion The optical distortion observed in NavCam 2 was similar to that of NavCam 1. There is strong radial structure observed in the star center residuals when no distortion model is applied, shown in Figure 8. The post-calibration residuals for NavCam 2 show that the distortion has been adequately modeled. Figure 9 shows that there is no remaining distortion structure, and Figure 10 shows that the residuals exhibit a Gaussian-like distribution with near zero mean and standard deviations less than 0.1 pixels. NavCam 2 did not have the same issues as NavCam 1 with acquiring data at hot temperatures because it is mounted differently and receives much less stray light when the instrument deck is being heated by the sun. As a result, NavCam 2 was able to acquire images during its hot calibrations using 10 second exposures with only a moderate amount of stray light. This allowed for better star centerfinding results and lower postcalibration residuals. This can be seen in Figure 11, which shows that there are similar residuals across the temperature spectrum. This also shows that the temperature-dependent focal length is adequately modeling 9

Figure 9: Post-calibration star center residuals for NavCam 2 shown at each star s image location. Figure 10: Post-calibration star center residuals for NavCam 2 as a function of star magnitude. 10

Figure 11: Post-calibration star center residuals for NavCam 2 as a function of camera temperature. Figure 12: Distortion map for NavCam 2. Contour lines show the magnitude of the distortion in pixels 11

the change in distortion over the temperature range. NavCam 2 s final distortion parameter results are shown in Table 2. The distortion map generated from these parameters is shown in Figure 12. The distortion is very similar to that observed in NavCam 1, differing most noticeably in the optical axis intersection point. Figure 13: NavCam 2 alignment error as a function of camera temperature expressed as Euler angles when using the previous spacecraft-to-instrument rotation matrix. Figure 14: NavCam 2 alignment error as a function of camera temperature expressed as Euler angles when using the updated spacecraft-to-instrument rotation matrix. 12

Boresight Alignment NavCam 2 s boresight alignment results were again very similar to NavCam1 s alignment results. Figure 13 shows the error before correcting the spacecraft-to-instrument rotation matrix, and Figure 14 shows alignment error after correcting the spacecraft-to-instrument matrix. Like NavCam 1, a slight temperature dependence can be seen, but the error is less than one pixel over the operational temperature range. This shows that a constant spacecraft-to-instrument matrix can be used across the temperature range for NavCam 2 as well. MapCam Figure 15: Star center residuals for MapCam when no distortion model is used, shown at each star s image location. Optical Distortion MapCam s star center residuals before calibration show moderate radial distortion. In addition, it is clear that the distortion pattern is not centered exactly on the center of the image. This decentering distortion was modeled using the tangential distortion terms (p 1 and p 2 ) as discussed later. There are also some clear outliers in the middle of the FOV. Some of these are finger region stars, as discussed later, and the rest are removed using an outlier detection routine and not included in the calibration solution. MapCam s post-calibration star center residuals show a near-ideal calibration result. Figure 16 shows the residual vectors pointing in random directions throughout the FOV, indicating that there is no distortion structure left. Figure 17 shows that the residuals follow a Gaussian-like distribution with near zero means and standard deviations less than 0.1 pixels in both image dimensions. This shows that the optical distortion present in the imager has been adequately modeled and corrected. The OCAMS detectors exhibit a behavior where certain regions of the field of view have their stars distorted such that the star s light bleeds into the pixels above the star. All stars from these regions were excluded 13

Figure 16: Post-calibration star center residuals for MapCam shown at each star s image location. Red bands mark the detector s finger regions. Figure 17: Post-calibration star center residuals for MapCam as a function of star magnitude. 14

during calibration because they would otherwise cause an upwards bias in the final solution. These regions dubbed finger regions because the stars appear to have fingers extending upwards are the vertical red bands marked in Figure 16. Figure 18: Distortion map for MapCam. Contour lines show the magnitude of the distortion in pixels. The final results for MapCam s distortion parameters are given in Table 2. Figure 18 shows a map of the distortion generated from these parameters. MapCam s distortion parameter results differ from the other imagers in that the optical axis intersection point (c x, c y ) was constrained to the center of the image and not estimated. This was done because the least squares algorithm did not seem to be estimating it well and the results would differ wildly between calibration runs. We were able to obtain a result that adequately modeled the distortion even when keeping the coordinates for this point constrained so there was no need for it to be estimated exactly. Any distortion caused by the optical axis not being aligned with the center of the image was sufficiently modeled by the tangential distortion terms, p 1 and p 2. Their effect can be seen in the distortion map where the distortion contours are asymmetrical and not centered on the center of the image. Boresight Alignment Figure 19 shows MapCam s alignment error before correcting the spacecraft-toinstrument rotation matrix, and Figure 20 shows the alignment error after correcting the spacecraft-to-instrument matrix. This shows shows the alignment error for MapCam to be within about ±2 MapCam pixels. Unlike NavCams 1 and 2, the OCAMS were heated using electronic heaters instead of the sun for their hot calibrations, which does not heat the rest of the spacecraft in the same way that the sun does. The alignment changes based on the temperature gradients throughout the spacecraft, so using the heaters, which only heat the camera and not the rest of the spacecraft, does not affect the alignment in the same way. For this reason we did not observe temperature dependent alignment in MapCam like we did in NavCams 1 and 2. 15

Figure 19: MapCam alignment error as a function of camera temperature expressed as Euler angles when using the previous spacecraft-to-instrument rotation matrix. Figure 20: MapCam alignment error as a function of camera temperature expressed as Euler angles when using the updated spacecraft-to-instrument rotation matrix. 16

Figure 21: Star center residuals for PolyCam when no distortion model is used, shown at each star s image location. PolyCam Optical Distortion The PolyCam optical distortion calibration proved to more challenging than the analysis of the other imagers. Systemic bias in the residuals suggests that some distortion has not been accounted for in the distortion model, and work on the PolyCam imager remains ongoing. Figure 21 shows the star center residuals for PolyCam before the distortion calibration knowledge was applied. A small number of stars have significant residuals against the trend of the rest of the image (discussed below), but the overall structure is largely radial as expected. Figure 22 shows the star center residuals for PolyCam after the distortion calibration knowledge was applied. A clear systemic bias is present in this quiver plot, with a tendency for the residuals to be pointing upwards and to the left. While the distortion and bias are obvious, the residual errors were not large. Figure 23 shows the same post-calibration star center residuals as a function of star magnitude. Similar to the quiver plot, this plot shows a clear bias in the line direction, especially in the lower magnitudes. The bias appears to be benign or nonexistent in the brightest stars, but as the dimmer stars are examined, the bias in the positive direction grows. The mean of the data in both the pixel and line directions is approximately at zero, but the standard deviations of the residual errors in both directions are high at over 0.2 pixels. The root cause of this systemic bias is still under investigation. Figure 24 shows the distortion map for PolyCam, which shows slight decentering distortion. This was modeled by the the tangential distortion terms, p 1 and p 2, and, like with MapCam, their effect can be seen in the distortion map by the distortion contour lines not being perfectly centered on the center of the image. 17

Figure 22: Star-center residuals for PolyCam, with distortion model applied. Red bands mark the finger regions. Figure 23: Final PolyCam residual errors as a function of star magnitude. 18

Figure 24: Distortion map for PolyCam. Contour lines show the magnitude of the distortion in pixels. As noted and seen in the figures above, there is an apparent magnitude-driven bias in the residual errors after the distortion calibration is applied. The bulk of the stars analyzed are between 8.5 and 12.5 magnitude. No apparent bias exists in the pixel direction of the detector. Around 8.5 magnitude, the line residuals are overwhelmingly negative. As the magnitude increases, the line residuals slowly creep up, and by 12.5 magnitude the residuals are biased in the positive direction. This indicates that the processing of the images and the distortion calibration is not capturing some aspect of the optical system. Discussion with the OCAMS Instrument Engineers has indicated that there are a number of potential root causes, many of which require additional imagery from the spacecraft which will be captured and downlinked in July 2018. Boresight Alignment Figure 25 shows PolyCam s alignment error before correcting the spacecraft-toinstrument rotation matrix, and Figure 26 shows the alignment error after correcting the matrix. This shows that the post-calibration alignment error for PolyCam is about ±0.1 mrad or 8 PolyCam pixels. PolyCam also used the camera s electronic camera heaters (rather than the sun) for its hot calibration, which do not heat the rest of the spacecraft. For this reason, as well as having much less hot alignment data, we did not observe clear temperature dependence in the alignment of PolyCam. 19

Figure 25: PolyCam alignment error as a function of camera temperature expressed as Euler angles when using the previous spacecraft-to-instrument rotation matrix. Figure 26: PolyCam alignment error as a function of camera temperature expressed as Euler angles when using the updated spacecraft-to-instrument rotation matrix. CONCLUSION This paper presented the in-flight optical distortion and boresight alignment calibration results for four of the imagers on-board OSIRIS-REx. An ideal optical distortion calibration result was attained for NavCam 1, NavCam 2, and MapCam. PolyCam exhibited an upward bias that was unable to be corrected, but it still was able to achieve sub-pixel error levels. These distortion models will be utilized by OpNav during OSIRIS-REx Proximity Operations to allow for sub-pixel star and target centerfinding accuracy. The boresight alignment was also calibrated and an updated spacecraft-to-instrument rotation matrix was estimated for each camera. 20

This updated spacecraft-to-instrument matrix minimized the alignment error for each camera. NavCams 1 and 2 showed alignment error less than one pixel across the operational temperature spectrum. This boresight alignment calibration will allow for accurate camera pointing throughout the mission. ACKNOWLEDGEMENTS The authors would like to acknowledge the following individuals and teams for their support: Andrew Liounis from NASA Goddard Spaceflight Center for supporting the calibrations of all four imagers and independently verifying our results. Chris Norman from Lockheed Martin for supporting the calibration imaging campaigns for NavCam 1 and NavCam 2. This material is based upon work supported by the National Aeronautics and Space Administration under Contract NNG13FC02C issued through the New Frontiers Program. REFERENCES [1] C. D. Jackman, D. S. Nelson, L. K. McCarthy, T. J. Finley, A. J. Liounis, K. M. Getzandanner, P. G. Antreasian, and M. C. Moreau, Optical Navigation Concept of Operations for The OSIRIS-REx Mission, American Astronomical Society, 2017. [2] B. J. Bos, M. A. Ravine, M. Caplinger, J. A. Schaffner, J. V. Ladewig, R. D. Olds, C. D. Norman, D. Huish, M. Hughes, S. K. Anderson, D. A. Lorenz, A. May, C. D. Jackman, D. Nelson, M. Moreau, D. Kubitschek, K. Getzandanner, K. E. Gordon, and A. Eberhardt, Touch And Go Camera System (TAGCAMS) for the OSIRIS-REx Asteroid Sample Return Mission, Space Science Reviews: The Origins, Spectral Interpretation, Resource Identification, Security - Regolith Explorer (OSIRIS-REx) Mission, 2017. [3] B. Rizk, C. d Aubigny, D. Golish, D. D. Giustina, C. Fellows, C. Merrill, P. Smith, J. Hancock, R. Tanner, R. Burt, M. Whiteley, T. Connors, J. Chen, D. Hamara, T. McMahan, M. Williams, A. Lowman, W. Verts, B. Williams, L. Harrison, W. Black, M. Read, and A. Dowd, OCAMS: the OSIRIS-REX Camera Suite, Space Science Reviews: The Origins, Spectral Interpretation, Resource Identification, Security - Regolith Explorer (OSIRIS-REx) Mission, 2017. [4] Camera Calibration and 3D Reconstruction, OpenCV Dev Team, 2014. 21