Introducing the Condor Array Telescope. 1. Motivation, Configuration, and Performance

The prototype element of Condor is comprised of of six Telescope Engineering Company (TEC) 180 mm-diameter f/7 refracting telescopes of focal length 1260 mm. The telescopes feature diffraction-limited, apochromatic, oil-spaced, triplet objective lenses with multi-layer coatings on all surfaces and a CaF₂ middle element. Each optical assembly sits within a lightweight aluminum tube coated with an anti-reflection coating, and each tube assembly contains custom-designed and -fabricated sharp-edged baffles throughout the interior. The baffles of two of the telescopes are coated with a standard black paint, while the baffles of four of the telescopes are coated with Singularity Black carbon-nanotube paint, thus allowing for the possibility of assessing the performance of very black carbon-nanotube paint on the telescope baffles.

Each TEC telescope is equipped with an Astro-Physics (A-P) 0.72x QUADTCC-TEC180 four-element telecompressor corrector. These correctors when used with the TEC 180 mm-diameter telescopes yield an effective focal length of 907 mm and an effective focal ratio of f/5.0. The effective focal ratio of the six telescopes together, considered as a single telescope, is f/2.0.

Each TEC telescope is equipped with a ZWO ASI6200MM monochrome CMOS camera, which is based on the large-format Sony IMX455 back-illuminated detector. The cameras feature USB3.0 interfaces and 256 MB DDR3 caches. The cameras use Peltier coolers to cool the detectors to as much as 40 C below the ambient temperature. Specifications of the CMOS camera detectors are summarized in Table 1.

Each TEC telescope is equipped with a ZWO EFW 7/2” seven-position filter wheel. Each filter wheel is capable of holding seven 2-inch round filters.

Each TEC telescope is equipped with (1) a Sloan $g^{\prime}$ filter, (2) a Sloan $r^{\prime}$ filter, (3) a Sloan $i^{\prime}$ filter, (4) a luminance filter, and (5) a narrow-band filter, each manufactured by Chroma Technology Corp. The six narrow-band filters are tuned to emission lines of (1) He II 468.6 nm, (2) [O III] 500.7 nm, (3) He I 587.5 nm, (4) H$\alpha$ 656.3 nm, (5) [N II] 658.4 nm, and (6) [S II] 671.6 nm. The six narrow-band filters have widths of $\approx 4$ nm. Typical response functions of the various filters (as measured by the manufacturer) are shown in Figure 1. The peak transmission of each filter approaches 100%. The Sloan $i^{\prime}$ and luminance filters exhibit infrared leak, which is more significant for the luminance filters.

Each TEC telescope is also equipped with a Star Analyzer 200 diffraction grating distributed by Field Tested Systems, LLC. The gratings are ruled at 100 lines mm^-1 and blazed in first-order at a wavelength of 550 nm and provide a resolution of $R\equiv\lambda/\Delta\lambda\approx 200$. The dispersion directions of the various diffraction gratings are oriented in such a way that they are rotated with respect to one another, which can significantly aid in untangling the various overlapping spectra of the various sources in the field of view.

Each TEC telescope is equipped with an Optec TCF-Leo low-profile motorized focuser. The focusers have a step size of 0.08 $\mu$m and a maximum range of travel of $\approx 9$ mm.

Each TEC telescope is equipped with an Optec Alnitak motorized dust cover.

The six TEC telescopes are mounted onto a Planewave L-600 half-fork mount with equatorial wedge. The mount features direct-drive motors and precision encoders on each axis and slew speeds of up to 50 deg s^-1 and is not subject to backlash or periodic error. The telescopes are attached to the mount using a custom-designed and -fabricated bracket that allows the telescopes to be independently collimated with respect to each other.

Condor is located at a very dark astronomical site in the southwest corner of New Mexico, at the Dark Sky New Mexico observatory near Animas, roughly midway between (and more than 100 miles from either) Tucson and El Paso, at an elevation of 1341 m. Details of the site are summarized in Table 2.

The telescope is housed in an observatory building with a roll-off roof. Images of Condor in its observatory building at the Dark Sky New Mexico observatory are shown in Figure 2.

The CMOS cameras, filter wheels, focusers, dust covers, mount, and observatory roof are controlled by and data are acquired by eight Raspberry Pi 4 “control and acquisition” computers running Ubuntu 20.04, which are located in a control room adjacent to the telescope. Each Raspberry Pi 4 computer is equipped with a 128 GB SATA III solid-state drive connected via USB3.0, and each computer and drive assembly is mounted into a custom-designed and -fabricated 3-D-printed enclosure, and the eight computer and drive enclosures are mounted into a server rack. The server rack also contains a router, a 1 TB solid-state drive, and environmental monitor, an IP power distribution unit, a power distribution unit, and three focus controller hubs. The 1 TB solid-state drive is used to stage data, the environmental monitor is used to monitor temperature and humidity and the state of the observatory roof, the IP power distribution unit is used to remotely cycle power to the computers and other peripherals, and the focus controllers are used to control the focusers. An image of the Raspberry Pi 4 computers and the server rack is shown in Figure 3.

Each CMOS camera is connected to a Raspberry Pi 4 computer via USB3.0. The other peripherals (filter wheels, focusers, dust covers, mount, and observatory roof) are connected to Raspberry Pi 4 computers via USB2.0 or Ethernet. In operation, one Raspberry Pi 4 computer acts as a “sequencer” and sends instructions to other Raspberry Pi 4 computers, which in turn send instructions to the various peripherals. As images are acquired, they are temporarily staged to the 128 GB solid state drives and then promptly transferred to storage and analysis computers on the campus of Stony Brook University (described in § 3.11) and from there to storage and analysis computers at the American Museum of Natural History. The Raspberry Pi 4 computers continuously report information (related to status of the observations, status of the peripherals, status of the computers themselves, and weather) to a database running on one of the storage and analysis computers; these communications are cached locally, ensuring that they are not lost in the event of a disruption to the storage and analysis computers or a loss of Internet connectivity. Current and predicted weather is continuously monitored via the Tomorrow.io weather API; these weather observations are used to assess local conditions bearing on whether the observatory roof should be opened or closed and are recorded for later use in science analysis.

Data acquired by Condor are stored on and analyzed by six Dell PowerEdge R720xd “storage and analysis” computers running Ubuntu 20.04, which are located at the Data Center on the campus of Stony Brook University. Each Dell R720xd computer is equipped with one or more solid-state drives, which are used to store the operating system and local scratch space; several high-capacity (14 to 18 TB) hard disk drives, which are used to store data; and 768 GB DDR3 memory. The various Dell R720xd computers each run MinIO, which is an open-source object storage system that is functionally compatible with AWS S3, and data acquired by Condor are ultimately stored under MinIO clusters. The various MinIO clusters are configured for a factor two redundancy, and the system is robust against loss of drives and loss of computers. One Dell R720xd computer hosts the Condor web site and runs a PostgreSQL database, and all six Dell R720xd computers participate in the analysis of data.

Here we describe characteristics of the Sony IMX455 detectors used in the ZWO ASI6200MM monochrome CMOS cameras.

Considering the 3.76 $\mu$m pixel size of the $9576\times 6388$ format Sony IMX455 detector together with the nominal effective focal length 907 mm of the TEC 180 mm telescope with the A-P 0.72x four-element telecompressor corrector yields a nominal plate scale of 0.86 arcsec pixel^-1 and a nominal field of view $2.29\times 1.53$ deg². The measured values after astrometric calibration are very close to the nominal values. (See § 4.4 for a brief discussion of our astrometric calibration techniques.) The solid angle subtended by the field of view is 3.50 deg². Details of the plate scale and field of view are summarized in Table 3.

The Rayleigh limit of a 180 mm-diameter aperture ranges from $\approx 0.5$ arcsec at wavelength $\lambda=350$ nm to $\approx 1.0$ arcsec at $\lambda=700$ nm, which when convolved with a seeing profile of width, say, ${\rm FWHM}=1.2$ arcsec typical of a good astronomical site yields a point-spread function (PSF) of width ranging from ${\rm FHWM}\approx 1.3$ arcsec at $\lambda=350$ nm through ${\rm FWHM}\approx 1.6$ arcsec at $\lambda=700$ nm. The 0.86 arcsec plate scale of the telescope Nyquist samples a PSF of ${\rm FWHM}\approx 1.7$ arcsec, hence Condor slightly undersamples the PSF under seeing conditions typical of a good astronomical site, by a factor ranging from as much $\approx 25$% at $\lambda=350$ nm through as little as $\approx 6$% at $\lambda=700$ nm. We conclude that Condor can obtain nearly Nyquist-sampled images at a good astronomical site.

An image of the twilight sky obtained with one of the six telescopes is shown in Figure 10. From Figure 10 it is apparent that: (1) The detector response is very uniform over the field of view, and the detector exhibits no obvious blemishes or cosmetic flaws. (As is expected, several out-of-focus dust motes are clearly visible in the image of Figure 10.) (2) The image circle is well centered on the detector, which indicates that the optical beam is well collimated. And (3) the detector is nearly but not quite fully illuminated by the image circle, with vignetting evident at the corners of the image. Similar results are obtained for other twilight images and for twilight images obtained by the other telescopes.

A diagonal cut across the image of Figure 10 running from the upper left corner to the lower right corner is shown in Figure 11. From Figure 11 it is apparent that the illumination of the detector is very flat across most of the field of view, with vignetting again evident at the corners of the image. The maximum vignetting at the very corners of the image reaches $\approx 15$%. Similar results are obtained for other twilight images and for twilight images obtained by the other telescopes.

Details of the astrometric calibration of Condor images will be described elsewhere, but here we present a brief summary of our procedures and results.

Accurate astrometric calibration is crucial for all of the science objectives of Condor. Yet determining an accurate astrometric calibration over the wide field of view of Condor is not straightforward, especially in the presence of geometric distortions and field curvature at the corners of the images. Accordingly, we developed a technique of measuring astrometric calibration that is appropriate to Condor images. Briefly, the technique proceeds as follows: First, we start with a science image for which bias subtraction and field flattening and background subtraction have already been performed. Next, we process the image through SExtractor (Bertin & Arnouts, 1996a), which is a program that identifies sources in astronomical images. This processing produces a list of pixel coordinates of sources detected in the image. Next, we query the Gaia DR3 catalog (Gaia Collaboration et al., 2017, 2018, 2021) to obtain a list of sources in the field, noting in particular the celestial coordinates and proper motions of the sources. Next, we fit for parameters of the affine transformation that best matches the pixel and celestial coordinates (corrected for proper motions) of a subset of the sources, and we construct a list of matched pixel and celestial coordinates of the sources. Finally, we fit for parameters of a higher-order model that best matches the pixel and celestial coordinates, taking as parameters the affine transformation parameters and the coefficients of a seventh-order geometric distortion polynomial including radial terms, in the “TPV” projection. (The TPV projection is similar to the TAN projection described by Calabretta & Greisen, 2002 but includes a seventh-order geometric distortion polynomial.)

By applying this technique, we consistently obtain an astrometric calibration with systematic differences between the transformed pixel and celestial coordinates of $\lesssim 0.1$ arcsec.

Details of the field flattening and background subtraction of Condor images will be described elsewhere, but here we present a brief summary of our procedures and results.

Field flattening and background subtraction are critical to many of the science objectives of Condor. Yet there are no obvious flat sources of illumination to which Condor could be pointed to produce field-flattening calibration images. We experimented with producing “sky flat” images by median combining unregistered science images (after scaling to account for difference in background level). But we note two very significant problems with this approach: (1) the night sky is itself not flat, and (2) photon noise in a sky flat image can never be made insignificant in comparison to photon noise in the (combined) science images, because the number of photons recorded by the sky flat image grows only in direct proportion to the number of photons recorded by the science images.

Instead, we have developed a technique of field flattening and background subtraction that is based on forming a quotient with a twilight image. Briefly, the technique proceeds as follows: First, the science image is divided by a twilight image (obtained by the same telescope with the same detector). This quotient is devoid of all instrumental effects (including all telescope and detector effects) but contains the signatures of the (different and unknown) sky backgrounds of the science and twilight images. Next, the quotient is fitted by a high-order (typically eighth-order) two-dimensional polynomial, rejecting regions around sources present in the science image. This polynomial fit accounts for the backgrounds of both the science and twilight images. Finally, the polynomial fit is subtracted from the quotient. This sequence of steps produces a version of the science image that is simultaneously corrected for field flattening and background subtraction.

By experimenting with pairs of twilight images (i.e. by substituting another twilight image for the science image), we found that we are able to carry out field flattening and background subtraction to within fundamental physical limitations. In particular, we found that the residuals of the quotients after the polynomials are subtracted result from (1) rapidly-varying (i.e. with times scales less than $\approx 10$ s) stochastic fluctuations of the atmosphere on scales of several hundred pixels and (2) photon statistics on scales of one pixel. We used this technique, for example, to determine the gain of each CMOS detector by measuring photon statistics on scales of one pixel of pairs of twilight images, as described in § 4.1.3.

Details of the photometric calibration of Condor images will be presented elsewhere, but here we present a brief summary of our procedures and results.

Exquisite photometric calibration is not critical to many of the science objectives of Condor. Accordingly, our current efforts have concentrated on obtaining an approximate photometric calibration suitable for quantifying sensitivity and for identifying variable and transient sources. Briefly, the technique proceeds as follows: First, we start with science images for which bias subtraction, astrometric calibration, and field flattening and background subtraction have been performed. Next, we query the Gaia DR3 catalog (Gaia Collaboration et al., 2017, 2018, 2021) to obtain a list of sources in the field, noting in particular the celestial coordinates and $g^{\prime}$ magnitudes of the sources. Next, we use aperture photometry techniques to measure brightnesses of sources in the list of sources, excluding very bright or very faint sources. Finally, we compare the measured brightnesses to the $g^{\prime}$ magnitudes across the ensemble to derive a rough photometric calibration.

The distributions of the “photometric calibration” (i.e. the energy flux density that corresponds to 1 ADU s^-1) and the “magnitude zero point” (i.e. the $g^{\prime}$ magnitude that corresponds to 1 ADU s^-1) measured for a large number of images obtained through the luminance filter are shown in Figure 12. From Figure 12 it is apparent that under the clearest conditions ever experienced by Condor, the photometric calibration is $\approx 3.5$ $\mu$Jy ADU^-1 s and the magnitude zero point $m_{0}$ is $m_{0}\approx 22.7$ through the luminance filter. Measurements of the photometric calibration and magnitude zero point through other filters are given in Appendix A.

An image of Vega obtained by one telescope is shown in Figure 13. This image demonstrates that the Condor PSF is exceptionally clean and that the only apparent features of the PSF are (1) a very faint reflection visible to the lower left of the star in the left panel and (2) very low-level “spikes” that emanate radially from the star (which are more easily seen in the right panel). Following AvD, we tentatively attribute these spikes to diffraction from striae in the glass elements and lattice imperfections in the crystalline CaF₂ elements of the lenses. The left panel of Figure 13 may be directly compared to Figure 8 of AvD, which is a similar image of Venus on a logarithmic stretch over a scale of 50 arcmin. (But we note that Venus is, of course, not a point source.) The Condor image appears substantially cleaner than the Dragonfly image, and the Condor image does not show the multiple reflections, “ghosts,” and halos evident in the Dragonfly image. Similar results are obtained for other images of Vega (and other bright sources) and for images of Vega (and other bright sources) obtained by the other telescopes.

The Condor PSF pieced together from the image of Figure 13 and other similar images of exposure times 0.1, 1, 10, and 100 s is shown in Figure 14. In Figure 14, the vertical axis gives surface brightness $\mu_{\rm PSF}$ of a zero-magnitude source in units mag arcsec^-2, and the horizontal axis gives angular distance $r$ in units arcsec on a logarithmic scale. In Figure 14, the PSF on scales $r>10$ arcsec was estimated by determining the median values within circular annuli centered on Vega. The median values in ADU units were converted to surface brightness units using the photometric calibration described in § 4.6, but otherwise these values were not scaled in any way. This is appropriate because Vega is the primary photometric standard. On scales $r<10$ arcsec the image of Vega was saturated even in the 0.1 s exposure, so the PSF was estimated by determining the median values within circular annuli of a fainter star. Figure 14 also shows the Dragonfly PSF from Liu et al. (2022). The two PSFs are very similar on scales $r\lesssim$ 50 arcsec but appear to deviate on scales $r\gtrsim 50$ arcsec. But it is important to note that: (1) the Condor PSF on scales $r\lesssim 5$ arcsec is set by seeing conditions and (2) both the Condor and Dragonfly PSFs on scales $r\gtrsim 10$ arcsec depend on weather and atmospheric conditions. We defer a detailed comparison between the Condor and Dragonfly PSFs until later.

The distribution of the “image quality” FWHM of a large number of images obtained through the luminance filter are show in Figure 15. We define the “image quality” FWHM of an image to be the FWHM of the central core of the autocorrelation function of the image. We found through experimentation that the FWHM of the central core of the autocorrelation function of an image is $\approx 2$ times the typical FWHM of point sources in the image. Hence the image quality FWHM is an easily-measured statistic that characterizes the typical FWHM of point sources in the image. We note that the typical FWHM of point sources in the image is set by a combination of seeing, focus, tracking errors, and field curvature (in the sense that focus may not be completely uniform across the field). Hence the distribution of Figure 15 represents the sum of these effects. In the months immediately following first light, when methods of controlling focus, tracking errors, and field curvature were still being developed, these effects contributed significantly to image quality. But by several months later, when these effects were better controlled, image quality was set primarily by seeing. The mode of the image quality FWHM distribution is 1.6 arcsec, and the median of the distribution is 2.0 arcsec. Because Condor Nyquist samples a PSF of ${\rm FWHM}\approx 1.7$ arcsec (as described in § 4.2), its configuration is well matched to the typical image quality obtained at the Dark Sky New Mexico observatory site.

The distributions of the “night-sky background rate” (in units e^- s^-1 pix^-1) and the “night-sky surface brightness” $\mu_{\rm sky}$ (in units mag arcsec^-2) measured for a large number of images obtained through the luminance filter are shown in Figure 16. (The night-sky surface brightness $\mu_{\rm sky}$ was determined from the night-sky background rate using a photometric zero point $m_{0}=22.7$ appropriate for clear conditions, as described in § 4.6.) In Figure 16a, the large peak results from images obtained under dark conditions, and the long tail (which continues substantially beyond the right-hand edge of the plot) results from images obtained under brighter conditions. In Figure 16b, the prominent peak near $\mu_{\rm sky}=21.5$ mag arcsec^-2 results from images obtained when the Moon is below the horizon, and the prominent peak near $\mu_{\rm sky}=18.5$ mag arcsec^-2 results from images obtained when the full Moon is above the horizon. From Figure 16 it is apparent that under the darkest conditions ever experienced by Condor, the night-sky background rate is $\approx 0.5$ e^- s^-1 pix^-1 and the night-sky surface brightness is $\mu_{\rm sky}\approx 21.7$ mag arcsec^-2 through the luminance filter. The Condor site is as dark as any ground-based astronomical site, including Muana Kea, of which we are aware (see Figure 5 of Barentine, 2022). Measurements of the night-sky background rate and night-sky surface brightness through other filters are given in Appendix A.

Over a 60-s exposure, a night-sky background rate of $\approx 0.5$ e^- s^-1 pix^-1 produces a sky background of $\approx 30$ e^- per pixel, which corresponds to a sky noise of $\approx 5.5$ e^- per pixel, which dominates the read noise 1.2 e^-. We conclude that Condor is sky-noise limited through the luminance filter in 60-s exposures under the darkest conditions it ever experiences. In fact, given the very low read noise of the CMOS detectors, Condor would be sky-noise limited through the luminance filter in exposures as short as 20 or even 10 s (which correspond to sky noises of 3.2 or 2.2 e^- per pixel, respectively) under the darkest conditions it ever experiences. Hence if called for by the science case, Condor could operate at a cadence as rapid as 20 or even 10 s through the luminance filter while remaining sky-noise dominated. Condor is easily sky-noise limited through the luminance filter under brighter conditions.

The point-source and surface-brightness sensitivities of Condor may be directly determined from the measurements of the CMOS detector read noise described in § 4.1.2, the CMOS detector gain described in § 4.1.3, the plate scale described in § 4.2, the photometric calibration and magnitude zero point described in § 4.6, and the night-sky background rate described in § 4.7. Various point-source and surface-brightness sensitivities are presented in Table 4 as functions of lunar phase. In Table 4, the point-source sensitivities are $5\sigma$ determined for a 60-s exposure summing all six telescopes, assuming optimally-weighted measurements and a seeing ${\rm FWHM}=1.2$ arcsec (and so a PSF ${\rm FWHM}=1.6$ arcsec at $\lambda=700$ nm, as described in § 4.2) under dark, grey, and bright conditions. And in Table 4, the surface-brightness sensitivities are $3\sigma$ determined for exposure times ranging from 1 to 300 h summing all six telescopes averaged over $10\times 10$ arcsec² regions of the sky under dark, grey, and bright conditions. Measurements of the sensitivity through other filters are given in Appendix A.