PDS_VERSION_ID = PDS3 RECORD_TYPE = STREAM PRODUCER_ID = "ISAS/JAXA" LABEL_REVISION_NOTE = " 2016-10-18, K. McGouldrick, S. Murakami: Initial version; 2017-02-09, K. McGouldrick: cleaned to conform to PDS format requirements; 2017-05-05, S. Murakami: Revised; 2017-06-26, S. Murakami: Revised; 2018-08-15, S. Murakami: Revised; " OBJECT = INSTRUMENT INSTRUMENT_HOST_ID = "VCO" INSTRUMENT_ID = "IR2" OBJECT = INSTRUMENT_INFORMATION INSTRUMENT_NAME = "2-MICRON CAMERA" INSTRUMENT_TYPE = "CAMERA" INSTRUMENT_DESC = " This summary of the IR2 camera is compiled primarily from [SATOHETAL2016]. Instrument Overview =================== IR2, the 2 micron camera, is intended to study the meteorology of Venus by utilizing near-infrared (NIR) 'windows' of the CO2 atmosphere discovered in 1983 (ALLEN&CRAWFORD1984). Contrast features at 1.74 and 2.3 micron on the night-side disk are the silhouette of spatially inhomogeneous scatterers/absorbers, back-illuminated by the glow of the hot (300 -- 500 K) lower atmosphere (KAMP&TAYLOR1990). IR2, one of the key instruments onboard Akatsuki, is intended to image Venus in these NIR windows. Specification of IR2 -------------------- The specification of IR2 are summarized as follows: - Wavelength (band width) 1.65 um (0.30 um) 1.735 um (0.04 um) 2.02 um (0.03 um) 2.26 um (0.06 um) 2.32 um (0.03 um) - Field of View (FOV) 12 degrees x 12 degrees - IFOV 0.21 mrad (0.012 degrees) - Optics (triplet optics) - F-number 4 - Focal length 84.2 mm - Detector PtSi Schottky barrier sensor array (CSD/CCD) - Pixels 1040 x 1040 (IR-sensitive area is 1024 x 1024) 17-um pitch with a fill factor 0.59 - Quantum efficiency 4.6% at 1.65 um 5.2% at 1.735 um 4.5% at 2.02 um 3.9% at 2.26 um 3.8% at 2.32 um - MTF (at Nyquist Freq.) > 0.4 (1.65 um) > 0.7 (1.735, 2.02, 2.26, 2.32 um) - Detector control - Exposures 6.97 s (1.735, 2.26, 2.02 um) 18.97 s (2.32 um) 122.83 s (1.65 um) - A/D Converter 14 bits - Operating temperature < 68 K (PtSi) < 190 K (optics) - Cryocooler / cooling efficiency Single-stage Stirling-cycle 1.3 W at 65 K (50 W power) - Mass 1.35 kg (camera + wire harness) 2.32 kg (baffle) 6.8 kg (cryocooler + radiator) 3.6 kg (cooler driver) - Power 40.4 W (IR-AE when imaging) 74.4 W (cryocooler at 50 W) Scientific Objectives ===================== The main role of IR2 is to probe the middle-to-lower atmosphere for dynamics, aerosols, and trace gases, by utilizing the NIR spectral transparency ``windows.'' Atmospheric dynamics -------------------- To understand the production and maintenance mechanisms of super- rotation on Venus, it is essential to quantitatively characterize the atmospheric motions in 4-D space (3 spatial plus 1 temporal). Previous entry probe missions acquired mainly 1-D (vertical) profiles, in which westward zonal winds increase from ~0 m/s at the ground to ~100 m/s near the cloud top (~70 km) (SCHUBERT1983). For the cloud-top region, another dimension, the ``temporal'' variability, was studied using VEX/VMC data [MOISSLETAL2009, KOUYAMAETAL2013]. While Moissl et al. indicated short- term variability of day scale, Kouyama et al. suggested longer and periodic changes of zonal wind velocity with an amplitude of ~20 m/s and a time-scale of a few hundred days. Other periodicities are suggested by [KHATUNTSEVETAL2013] and by [PATSAEVAETAL2015]. At altitudes of 1.74- or 2.3-um opacity sources (~48 -- 50 km) [GRINSPOON1993], the velocity is ~60 m/s with substantial variability (SANCHEZLAVEGETAL2008), although a periodicity similar to that at the cloud top has not yet been detected. Investigating such, to enhance our knowledge about the atmospheric motions in 4-D, will certainly be the most important mission of IR2. VEX/VIRTIS-M images revealed numerous meso-scale waves in the upper and lower atmosphere (PERALTAETAL2008), confined to poleward of 40 degrees south. because of VEX's polar orbit, however, detection of waves might have been biased to higher southern latitudes. IR2, from an equatorial orbit, complements the VEX/VIRTIS-M observations, as it will allow a more intensive search for such waves at low latitudes than was possible with VEX. together with the previous data, IR2 will allow us to better understand the origins and roles of these waves. CO as a tracer of atmospheric circulation ----------------------------------------- CO is thought to be a good tracer of the atmospheric circulation. After photochemical production in the upper atmosphere via CO2 photodissociation (VONZAHNETAL1983). CO2 + hv -> CO + O CO will be transported poleward by the Hadley cell and descend to the lower atmosphere. Grassi et al. (2014) suggested that the region of maximum CO above the clouds (60 degrees south), as retrieved from VEX/VIRTIS-M spectra, is consistent with such circulation. Once in the lower atmosphere, CO, while transported, thermodynamically equilibrates with other gases and aerosols (YUNGETAL2009). Therefore, mapping and long-term monitoring of sub-cloud CO will yield valuable information about the meridional circulation. While the volume mixing ratio of sub-cloud CO is believed to be nearly constant for the altitudes from 0 to 50 km, the CO absorption band at 2.32 um is most sensitive to the CO abundance at a ~35 km altitude. Previous studies show more CO (~40 ppmv) at high latitudes than near the equator (~25 ppmv), suggestive of equatorward transport of CO (TAYLOR&CRISP1997, TSANGETAL2008). IR2 allows differential photometry of CO absorption by acquiring 2.26-um (free of CO absorption) and 2.32-um (with CO absorption) images. We define the CO absorption index in the following form: (I_2.26um - I_2.32um ) D_CO = ------------------------------------ (I_2.26um - alpha * I_2.32um )**beta (I_2.26um: radiance at 2.26 um, I_2.32um : radiance at 2.32 um, and alpha and beta are constants). Such a quantity is expected to be less affected by uncertainties of radiometric calibration. We have found a combination of (alpha, beta) = (0.5, 1.03) renders D_CO nearly independent of overlaying cloud opacities up to 30. We will derive pixel-by-pixel maps of CO absorption indices to study the hypothetical return flow of the Hadley cell (or indirect cell) (SCHUBERT1983), which may not be detected by cloud tracking results. Cloud-top altimetry ------------------- [HAUSETAL2014] performed a comprehensive study of mesospheric temperature and cloud parameters while demonstrating usefulness of analyzing multi-window (1.74-, 2.3-, and 4.3-um) spectra of the Venus night-side disk (VEX/VIRTIS-M). On Akatsuki, longwave infrared camera (LIR) can replace 4.3-um observations by mapping the cloud-top temperatures at 8 -- 12 um (FUKUHARAETAL2011), while IR2 provides 1.74- and 2.3-um cloud opacity data. IR2 also measures the cloud-top altitudes by imaging the sunlit side of Venus in the CO2 absorption band (2.02 um). In the CO2 absorption band, the reflected sunlight is attenuated by a factor proportional to the column abundance of CO2 at the cloud top. Therefore, if the cloud albedo and the cloud-top structure are spatially uniform, contrast features at 2.02 um reflect the undulation of the cloud top. Such cloud-top altimetry has been performed using VEX/VIRTIS-M data (IGNATIEVETAL2009) in a different CO2 band (1.6 um), revealing stable cloud-top altitudes of 74 km at latitudes up to ~50 degrees and lower (63 -- 69 km) in the polar regions. The sensitivity of the 2.02-um images to various cloud-top altitudes is examined as follows. A simple reflecting surface is located at Z_RS = 72, 70, and 68 km altitudes to indicate how much contrast we expect to see in the 2.02-um images. An additional curve is for a model with a diffuse aerosol layer (2-km thick) added on top the reflecting surface at 70 km. This demonstrates how limb-darkening curves change according to the cloud-top structure. Because IR2 almost always takes full-disk Venus images, the limb-darkening curves enable determination of the typical structure at the cloud-top level and then local contrasts can be interpreted as the undulations. UVI, LIR, and IR2 altogether provide the cloud-top dynamics, temperatures, and altitude data with which we investigate transportation of energy and materials in the upper cloud layer. Ground-based observations of cloud-top temperatures, as demonstrated with Subaru/COMICS (SATOETAL2014), may also be combined. Aerosol properties ------------------ The Venus cloud layer has an enormous vertical extent, from its top at ~70 km to the bottom at ~50 km with a few distinctive layers within it (KNOLLENBERG&HUNT1980, ESPOSITOETAL1983D). Studying the properties of aerosols will tell us how they are produced and maintained in the atmosphere. Based on the analysis of Galileo/NIMS data, the following empirical formula has been proposed to describe the cloud size parameters (CARLSONETAL1993): m = (I_1.74um )/(I_2.3um )**0.53 (Eq. 1) (m: size parameter, I_1.74um: radiance at 1.74 um, I_2.3um: radiance at 2.3 um). This simple yet useful formula has been used as a convenient tool to classify the clouds of different particle sizes (CARLSONETAL1993, WILSONETAL2008). Carlson et al. identified five branches of m parameter in Galileo/NIMS data and interpreted them as variations in mixing ratio of two distinctive modes of particles (one is ~3 um and another is ~7 um in diameter). Cloud condensation depends on local conditions (temperature, vapor pressure, motion of air parcels, existence of condensation nuclei, etc.) that may not be understood with snapshot data. Statistical analysis is therefore essential (CARLSONETAL1993, WILSONETAL2008). IR2 will provide spatially resolved 1.74- and 2.3-um images continuously from a retrograde and near-equatorial orbit to allow statistical studies. Interplanetary dust ------------------- IR2 studies the distribution of interplanetary dust in the 0.7 -- 1.0 AU region from the Sun by observing the zodiacal light at 1.65 um (astronomical H-band). Sensitivity is required to detect the typical flux of ~4 x 10**-7 (W m**-2 sr**-1) in the H-band (MATSUMOTOETAL1996). Measured Parameters =================== The radiance from 1.74- and 2.3-um ``windows'' of the CO2 atmosphere on the night side are measured by the detector. The spatial and temporal variability of CO below the clouds is also studied by differentiating 2.32-um CO-band images from simultaneous 2.26-um images. Images of the night-side disk in these wavelengths will enable us to determine the zonal and meridional winds near the cloud-base altitudes. IR2 also images at 2.02 um, the center of a CO2 absorption band. Such images can visualize the variation of the cloud-top altitudes as contrast features due to different absorption path lengths of the reflected sunlight. Tracking of the 2.02-um features will also enable us to obtain wind information at the cloud-top level. During cruise, IR2 observed zodiacal light with a broad-band H filter (1.65 um), imaged the Earth-moon remotely from a distance of ~30 million km, and determined Venus's phase curves at small phase angles. Subsystems ========== The hardware components of IR2 are summarized as follows. Component Sub-component T Weight Power consumption and remarks --------- ---------------- --- ------- ----------------------------- IR2-CMR IR2-SNS 66 1100 g 5.0 W (17-um pitch (from IR-AE, when imaging) 1M pix. PtSi) IFOV = 0.20 mrad, FOV = 12 deg IR2-OPT 172 f = 84.6 mm (170 K), (triplet lens) F / 4 IR2-STR - (structure) IR2-FWH 172 7.2 W (filter wheel) (from IR-AE, when in motion) IR2-FLTR 83 Fixed short-wavelength pass filter IR2-ELC 250 A set of wire harness IR2-THRM CP 2500 g AlBeMet162 alloy metal (Radiator plate) IR2-CMP 3500 g 50 W (from IR2-CDE) (compressor) IR2-CHD 800 g (cold head) IR2-CDE 3600 g 74.4 W (50 W to IR2-CMP) IR2-H 2320 g Box-shape baffle IR-AE 3300 g 40.4 W (when imaging) 33.4 W (when FWH in motion) IR-AE-WHN 200 g A set of wire harness Total 17570 g 114.8 W (when imaging) 107.8 W (when FWH in motion) Detectors ========= IR2 utilizes a platinum silicide (PtSi) Schottky-barrier (SB) detector. The characteristics of IR2-SNS are as follows. Although quantum efficiency (QE) is not high, about 4% at 2 um, the uniformity and stability of PtSi SB are superb owing to its monolithic structure (AKIYAMAETAL1994). For applications in which shot noise of incoming photon dominates (e.g., Venus observations), the advantage of PtSi overcomes the disadvantage of low QE. Domestic availability of large format arrays was another major reason why the PtSi SB was chosen for IR2. The IR2-SNS (a 1-Mpixels PtSi SB detector), manufactured by Mitsubishi Electric, Corp. (MELCO), has all design details disclosed to us. On 1040x1040 pixels (17-micrometers pitch) of IR2-SNS, the PtSi SB covers the middle 1024 x 1024 pixels, leaving 8 lines around the imaging area not sensitive to IR. Such non-sensitive pixels are used to precisely calibrate the zero level for low-signal observations. Pixels of IR2-SNS are read through the CSD (charge sweep device) / CCD architecture identical to the Si CSD/CCD of IR1 (IWAGAMIETAL2011). Because the CSD channel (vertical in the sensor) holds electrons only from a single pixel at a time, it can be very narrow (AKIYAMAETAL1994), contributing to a good fill factor, ~59%, without microlenses. The current density in PtSi, J [A m**-2], due to thermal electrons, is governed by the following Richardson's equation: J = A * T**2 * exp( - phi_b * e / ( k * T ) ) (T: temperature, phi_b: barrier height, e: elementary charge, k: Boltzmann constant, and A: Richardson constant, 1.20173 x 10**6 [A m**-2 K**-2]). The barrier height, phi_b, of IR2-SNS is ~0.197 (eV) which yields thermal electrons at a rate of 135, 2960, and 4.2 x 10**4 (s**-1 pix**-1) at T_SNS = 60, 65, and 70 K, respectively. Since the full well is approximately 10**6 electrons per pixel, the dark current saturates a pixel in a few tens of seconds at T_SNS = 70 K. Therefore, the sensor needs to be cooled to below 70 K with stability (Delta T < 1 K/h). Electronics =========== IR2 and IR1 (IWAGAMIETAL2011) are controlled by IR-AE. The output from the sensor is digitized at 14-bit depth with one count corresponding to 70 electrons. The full well is, therefore, 14,000 counts, just under the largest 14-bit integer. Filters ======= A 6-position filter wheel (IR2-FWH), of which one is for dark current measurements, holds five observing filters selected by referring to the science objectives and typical spectrum of Venus. IR2-FWH/FLTR/OPT are all cooled to suppress the radiation. - Two prominent NIR windows, the primary target of IR2, are probed with filters at 1.735 and 2.26 um, with respective bandwidths of 0.043 and 0.058 um. - To map the distribution of sub-cloud CO, the absorption band at ~2.32 um is chosen. This will be differentiated with 2.26 um (free of CO absorption) to evaluate the CO absorption index (Eq. 1). - For the cloud-top altimetry, we have chosen 2.02 um, center of a strong CO2 absorption band. - The last filter is an astronomical H-band (1.65 um). This broad-band filter is dedicated to the zodiacal light observations. A blocking filter (IR2-FLTR), a short-wavelength pass filter (SWPF) which effectively blocks unwanted infrared radiation, lambda > 2.46 um, is fixed in front of IR2-SNS. Note that the ``Avg. trans.'' in the table below are calculated with the following definite integral: Rbar = Integral_lambda1^lambda2 R(lambda) * dlambda / b.w. (Rbar: average transmission, lambda: wavelength, R(lambda): transmission as a function of lambda, [lambda1, lambda2]: interval for integral, b.w.: band width given in the table below). Channel Wavelength [um] Avg.trans. Day/Night Scientific targets Center Width (%) ------- ------ ----- ---------- --------- --------------------- 1.74 um 1.742 0.041 85 N Dynamics and clouds 2.26 um 2.270 0.052 67 N Dynamics and clouds 2.32 um 2.320 0.036 67 N CO distribution 2.02 um 2.020 0.039 6.0 D Cloud-top altimetry 1.65 um 1.650 0.283 93 - Zodiacal light (dust) Optics ====== The IR2 optics (IR2-OPT) is a triplet type (F=4), with the following characteristics. - With a focal length of 84.2 mm, IR2-OPT yields a field of view (FOV) of 12 degrees x 12 degrees. The IFOV is 0.20 mrad. In order to reduce difficulty of optical alignment in developing phases, while increasing robustness, IR2-OPT employs a rather simple design: a triplet of ZnS (G1), quartz (G2), and quartz (G3). Geometrical distortion is well corrected, and this was confirmed with star-field images during the cruise. - The optics is designed so as to achieve diffraction-limited spatial resolution at lambda = 1.735, 2.02, 2.26, and 2.32 um. The modulation transfer function (MTF) for the Nyquist frequency (30 lines per mm) is ~0.65 at 2.32 um and is better at other three wavelengths. IR2-OPT maintains MTF > 0.5 within plus or minus 80 um of defocusing. As IR2 defocuses at a rate of 4.5 um/K, as T_OPT changes, good optical performance is expected for T_OPT range of plus or minus 18 K. The low-temperature focal length is 84.6 mm at 170 K. - In order to use the triplet type, we relaxed the requirement for chromatic aberration correction and allowed slight focus shifts for different filters. The best focus positions (170 K), relative to that at 1.735 um, are +76.7 um at 2.02 um, +7.0 um at 2.26 um, and -20.6 um at 2.32 um, respectively. To compensate for the large focus shift at 2.02 um, the 2.02-um filter was made thinner by 100 um. - The chromatic aberration becomes more noticeable for the H-band (1.65 um): The relative focus is -60 um and the MTF > 0.45 across 80% of the FOV. The H-band images are, however, primarily used to study the large-scale features of the zodiacal light, so the highest spatial resolution is not required. We therefore decided not to correct the chromatic aberration in the H-band, but to 2 x 2 bin the H-band images on board. Thermal control =============== IR2-SNS needs to be cooled to ~65 K, and IR2-OPT/FWH/FLTR to T < 195, 180, and 85 K, respectively. To achieve these, a single-stage Stirling- cycle cryocooler is employed. The cooler, manufactured by Sumitomo Heavy Industries, Ltd., has heritage from previous Japanese space missions (HASEBEETAL2008), with reliability and long lifetime (> 50,000 hours on the laboratory test model). When IR2-CMP is driven at 50-W power by IR2-CDE, 1.3 W of heat is continuously removed from an object at the cold tip (at 60 K) of IR2-CHD. The 50,000-hours (or longer) lifetime of the cryocooler would allow ~2000 Earth days of continuous cooling of IR2. However, to survive the severe thermal condition in the Venus orbit, we plan to lower the power or even to switch off the cooler when it is appropriate (long-duration umbra passages, for example). The cold tip is in contact, via a flexible thermal path of copper, to the detector housing, achieving the required cooling of IR2-SNS. IR2-FLTR, directly mounted on the detector housing, is cooled together with IR2-SNS. The thermal coupling of the detector housing to IR2-OPT/FWH is optimized such that the optics are also cooled to the desired temperatures (< 195 K). Actually, ~90% of the heat removed by the cold tip comes from IR2-OPT/FWH. To efficiently dispose of the heat from IR2-CMP and IR2-CHD by utilizing the entire surface of radiator (CP), the material needs to be of high heat conductivity. By using a large, 500 mm (W) x 735 mm (D), ribbed plate of AlBeMet162 (aluminum-beryllium alloy metal), the desired thermal control of IR2 is achieved. Onboard Data processing ======================= The nominal ``day-side'' observing sequence is to acquire 3 Dark images (``pre'' Darks), 3 Venus images at 2.02 um, and 3 Dark images again (``post'' Darks). Each set of 3 consecutive images is median processed and the resultant ``pre'' and ``post'' Darks are averaged for subtraction from the medianned Venus image. These are done on the spacecraft and ``pre'' and ``post'' Darks as well as the Venus image are stored on the data recorder (DR) for downlink to the ground. The nominal ``night-side'' observing sequence is divided to 2 steps. In the first step, 3 ``pre'' Darks, 3 Venus images at 1.735 um, 3 Venus images at 2.26 um, and 3 ``post'' Darks are acquired. The image processing is essentially the same as the ``day-side'' sequence. The second step of the ``night-side'' observing sequence is, with longer exposures due to CO absorption, to acquire 3 ``pre'' Darks, 3 Venus images at 2.32 um, and 3 ``post'' Darks. On DR, the ``Venus data'' partition is shared with other cameras and is most prioritized for the downlink. The IR2 Darks are stored in a dedicated partition and they will be downlinked when something wrong is suspected by the Venus images. The ``zodiacal-light'' observing sequence acquires a series of 120-s exposure images: 1 ``pre'' Dark, 3 star-field images at 1.65 um, and 1 ``post'' Dark. As already mentioned in the above, the adjacent 2 x 2 pixels are binned and the resultant 520 x 520 pixels per frame are stored on DR. To study very faint emission in the interplanetary space, detailed examination of Darks is required so that all 5 images are stored in the same partition as ``Venus data'' for prioritized downlink. Calibration =========== A set of ``flat-field'' data was obtained in the laboratory. The flight model of IR2, including IR2-CMR, IR2-CHD, and IR2-CMP, is placed in a vacuum chamber. The chamber has a viewing port (a quartz window) which faces to the window of the laboratory. We use a diffuser to further flatten the incident light. The gain variation between the four quadrants is canceled out to a level that the brightness discontinuity between the adjacent quadrants disappears. In-flight calibration --------------------- While in space, we have acquired three datasets that were used for the photometric calibration of IR2: A: Imaging of star fields: October 22 -- 23, 2010, at 1.65 um in the high-gain mode (10 times more sensitive than the normal gain) and 122.8-s integration. B: Imaging of the Earth and the moon: October 26, 2010, at 2.02 um (normal gain and 6.97-s integration). C: Disk-integrated photometry of Venus: February -- March 2011 at 2.02 um (normal gain and 6.97-s integration) (SATOHETAL2015). Dataset A is a full-longitude scan of the ecliptic plane to study zodiacal light in the H-band. The results of aperture photometry on seven stars of Pleiades are compared with the published H-band magnitudes (STAUFFERETAL2007), and it is found that a 3.68 H-band magnitude star would yield 10,000 counts. This compares favorably to the estimated sensitivity, based on design parameters of IR2, which expects 10,000 counts for a 3.28 H-band magnitude star. A small difference (~13%) may be attributed to ripples in the filter transmission, to the quantum efficiency (measured using a different sensor), and to uncertainties in the star brightness. It should be mentioned that dataset A was rather noisy, due to insufficient cooling of the sensor (59 K at its best), to detect the zodiacal light of which typical flux is ~4 x 10**-7 (W m**-2 sr**-1). Considering the IFOV of 0.20 mrad, 6.4 x 10**-14 (W m**-2) is expected to fall in one 2 x 2-binned pixel. This translates to ~10 counts in the 122.8-s integrated image and may well be masked by the noise at the level of tens of counts. Dataset C was converted to Venus albedos by correcting for the radii and distances with dataset B as a reference (SATOHETAL2015), but neither was treated as absolute radiance. At the time of acquisition of B, the absolute flux from the moon at Akatsuki is estimated to be 2.5 x 10**-12 (W cm**-2 um**-1) for the conditions given in [SATOHETAL2015]. Based on the IR2 design parameters, this translates to an expectation of 475 counts which agrees very well with the actual measurement, 477 counts. The calibration coefficients, including results from A and B, are summarized the table below. Wavelength (um) Q.E. (%) Calib. coefficients. Flags (J cm**-2 um**-1 ADU**-1) --------------- -------- ------------------------- ----- 1.735 5.2 2.6 x 10**-15 E 2.260 3.9 2.6 x 10**-15 E 2.320 3.8 3.8 x 10**-15 E 2.020 4.5 3.7 x 10**-14 C 1.650 4.6 4.0 x 10**-17 C,H Description of value of Flags: E: estimated, C: in-flight calibrated, H: high-gain mode Using a star-field image of A, astrometry is performed. As is mentioned in the above, the image was 2 x 2 binned onboard. In the 12 degrees squared FOV, we measured the position of 5 stars: Maia, epsilon Tau, 36A and 37A Tau, and BD+16 560. We used the ccmap task in IRAF (Image Reduction and Analysis Facility) to locate the centroid of each star and fit their celestial coordinates. The obtained plate scale is 82.12 (arcsec pix**-1 ) in X and 82.10 (arcsec pix**-1) in Y with r.m.s. residuals of 13.2 arcsec in X and 8.9 arcsec in Y. This implies that the focal length is 85.42 mm, or +1.0% of the designed value (84.6 mm at 170 K). Since the fitting residual is ~1/6 pixel, it is confirmed that the geometrical distortion of IR2 is negligibly small. 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