Auroral meridian scanning photometer calibration using Jupiter

Observations of astronomical sources provide information that can significantly enhance the utility of auroral data for scientific studies. This report presents results obtained by using Jupiter for field cross calibration of four multispectral auroral meridian scanning photometers during the 2011–2015 Northern Hemisphere winters. Seasonal average optical field-of-view and local orientation estimates are obtained with uncertainties of 0.01 and 0.1, respectively. Estimates of absolute sensitivity are repeatable to roughly 5 % from one month to the next, while the relative response between different wavelength channels is stable to better than 1 %. Astronomical field calibrations and darkroom calibration differences are on the order of 10 %. Atmospheric variability is the primary source of uncertainty; this may be reduced with complementary data from co-located instruments.

). Fan shapes indicate 4 • optical beam width for altitudes of 110 and 220 km at elevations of 10 • above the horizon. Contours indicate magnetic dipole latitude (IGRF 2010). Table 1. Canadian meridian scanning photometer site information. Geographic latitude, longitude, and altitude are in degrees North, degrees East, and metres above mean sea level (WGS-84). L-shell and magnetic declination obtained from the IGRF model.  filter bandpass drift, decreased detector sensitivity) or abruptly (eg. damage during shipping). Such problems could be identified with calibration of instruments in the field. This process must be completely automatic, as many remote sites do not have fulltime technical staff. It should be repeated frequently in order to identify abrupt changes in system response, but without interrupting or degrading normal data acquisition. A regular schedule of measurements with portable low-brightness sources (LBS) might satisfy some of these requirements, but would involve a substantial allocation of resources for repeated site visits.

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In this report we examine some of the strengths and limitations of astronomical calibration for auroral instruments. We focus on issues related to field cross-calibration of MSPs which have been used extensively for auroral research (see §2 for details).
However, many of these topics can also be applied more generally to other instruments used to study the optical aurora, such as all-sky imagers (ASIs).
A single ground-based instrument may measure photons with wavelengths λ arriving from angular locations θ, φ. External luminosity I is convolved with the instrument response function f to product a measurement M with error M M (θ, φ, λ) = f (θ, φ, λ) I(θ , φ , λ ) + M (θ, φ, λ) (1) 5 For an ideal device f would be a delta function and M = I, but any real measurement will have limited resolution. The goal of calibration or characterization is to determine the instrument response function f in order to better understand the "true" source properties.
The general response function in Equation 1 can be separated into a product of geometric sensitivity f G and spectral sensi- This approximation is not always valid (eg. wide-angle optics coupled to a narrow-band interference filter) but can be usefully applied to many auroral instruments. For convenience we introduce relative response functions (f ) that are normalized to a maximum of one, and combine all scaling into a single system constant C C ×f G (θ, φ) ×f S (λ) We show that using Jupiter for field calibration of MSPs provides detailed knowledge aboutf G (θ, φ), estimates of C that are comparable to darkroom calibration, and useful information about relative spectral responsef S (λ) at different wavelengths.

Geometric
Calibration for auroral instruments with moderate (∼ 1 • ) angular resolution can be achieved using point-like sources located sufficiently far from the entrance aperture. Angular response can be measured by either moving the source or rotating the 20 instrument. The effective field-of-view (or "beam shape") is often azimuthally symmetric around an optical axis with angular polar coordinates θ 0 , φ 0 , in which case relative response can be expressed in terms of off-axis angle γ f G (θ, φ) ≈f G (γ; q 1 , .., q N ) and some set of instrument parameters q i (eg. full-width half-max).
Ideally, each instrument would arrive at a field site in exactly the same condition as it left the darkroom. It would be operated 25 exactly as intended (ie. perfectly level and aligned North/South) without changes for the entire design lifetime. In practice it may be difficult to achieve desired alignment to better than a few degrees. The initial orientation may subsequently drift to some more stable state over months or years, or can change abruptly as new instruments are installed nearby. In general, the rotation matrix R required to properly transform from device to local coordinates (eg. azimuth & zenith angle) must be updated regularly in order to ensure that data are scientifically useful.

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Determining Euler angles and geometric response model parameters in the field is relatively straightforward for auroral instruments that can detect and resolve at least a few of the brightest stars. Accurate GNSS site location and measurement timing can be combined with astronomical catalogs to predict the local orientation of each star. These can be converted into device coordinates and used to calculate observable quantities such as transit time and zenith angle. Discrepancies between predictions and observations can be minimized to determine optimal parameter values. A single night of good data may be 5 sufficient to achieve sub-degree accuracy, which is adequate for many auroral instruments.
Although stars are essentially point sources at infinity, other immutable properties (eg. location, apparent motion, spectral radiance) may make them somewhat less tractable than darkroom calibration sources. Any given object will not always be visible in the night sky or pass through any specific location in an instrumental field of view. However, a substantial amount of useful information can be gathered over several days or months. 10

Spectral
The relative spectral response of an instrument is essential for quantitative multi-wavelength analysis, such as estimating precipitation energy (Rees and Luckey, 1974;Strickland et al., 1989). Spectral response can be most effectively determined with a monochromatic sourcê 15 that can scan through the wavelength range of interest. For narrow-band devices it may be sufficient to observe a broad-band source S(λ) with known absolute spectral flux density. If the source flux is roughly constant near some wavelength λ j for each device channel then the throughput for each channel may be expressed in terms of the effective bandwidth ∆λ k .

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Measurements of an absolutely calibrated low-brightness source (LBS) provide estimates of the differential sensitivity to a continuum source characterized in terms of Rayleighs per nanometer. For discrete emission lines the effective bandwidth is also required in order to determine the sensitivity to brightness as expressed in Rayleighs. The equipment necessary for comprehensive calibration (eg. LBS and monochromator) is not always available at remote field sites, so different methods must be established. Many stellar sources provide spectra which are apparently broad-band at typical auroral instrument resolutions 25 on the order of 1 nm. Only relatively bright stars may be above the detection threshold, and absolute flux calibrated spectra are not available for all sources. Still, in certain cases it may be possible for astronomical calibration to produce accurate and repeatable estimates of differential sensitivity.
There does not appear to be a corresponding strategy to determine effective bandwidth in the field. Most stellar spectra are essentially constant in time, so individual sources cannot be used to determine a fixed instument response. Combining 30 many different spectra might in principle allow us to distinguish between changes in effective bandwidth and total sensitivity.
However, this would require nearly simultaneous observation of multiple absolutely calibrated sources with different spectral types. Low signal levels might also limit the accuracy of any estimates.
For this study we proceed under the assumption that absolute spectral response cannot be independently determined in the field using only astronomical sources. We presume that normalized transmission integrated across each pass-band can be obtained in some other way, and acknowledge that simultaneous changes across multiple channels may not be detected using methods considered here. For these reasons, we shall tend to focus on the differential calibration coefficientĊ which 5 can be determined using only astronomical methods. This quantity can also be directly compared to the results of darkroom calibration with an LBS. For auroral studies data numbers D must be converted to Rayleighs R, and effective bandwidth is required in order to calculate C R/D .

Photometry
A point source with total power output (radiant flux) P 0 and isotropic radiant intensity will produce radiance S which falls off 10 as distance squared.
An observer at some distance r will intercept an amount of power proportional to the effective receiver surface area A eff .

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Power from an extended source can be expressed in terms of a volume emission rate ρ(r, θ, φ) integrated over the entire source region weighted by the receiver angular sensitivity G(θ, φ) where the radial integral L has units of radiance (watt · meter −2 · sr −1 ) and is often referred to as the "column emission rate".
For a uniform source radiance the total received power depends on the product of the effective area and the effective solid angle. When signals are detected from some point source, we might ask what equivalent volume emission would produce the same observed power. For a uniform emission region the result 25 depends only on the effective solid angle. Auroral intensities are customarily expressed in units of Rayleighs (Hunten et al., 1956;Baker, 1974;Baker and Romick, 1976;Brändström et al., 2012) 4πL γ (λ) ≡ I(λ) where the subscript E indicates energy flux and γ is photon number flux. For narrow-band channels converting differential radiant spectral densityṠ to equivalent Rayleighs per nanometerİ requires only the effective solid angle, which can also be estimated from observations of a point source. Working with Rayleighs requires some additional knowledge in the form of the effective bandwidth ∆λ. As this is also true for darkroom LBS calibration, we focus here on relatingİ in Rayleighs per nanometer toṠ in Watts per metre-squared per nanometer.

Astronomical sources
10 Extra terrestrial objects have many properties which are required for accurate calibration. Locations in the celestial sphere are known to arc-second resolution or better, which is more than enough to determine the orientation and geometric response of auroral instruments. Absolute spectral irradiance profiles are available for many sources, providing opportunities for photometric calibration of narrow-band instruments. Total visible intensity of most sources is essentially constant, allowing for long term monitoring of system performance. A single object can be viewed simultaneously by multiple instruments at nearby sites, 15 facilitating quantitative inter-comparisons.
Most astronomical objects are effectively point sources, which is convenient for geometric calibration, but can introduce complications for auroral instruments designed to observe extended emission regions. Only the brightest stars can produce count rates comparable to background contributions such as airglow. Celestial source brightness spans a wide range and is usually expressed in terms of logarithmic magnitude m so that the relative intensity of two sources can be determined from the difference of their magnitudes. Absolute flux distributions as a function of wavelength are available for most of the brightest stars, including Vega (Colina et al., 1996), Sirius (Bohlin, 2014), and Arcturus (Blackwell et al., 1975;Griffin and Lynas-Gray, 1999). Other catalogs contain many other stars (Hayes, 1985;Alekseeva et al., 1996Alekseeva et al., , 1997Bohlin, 2007Bohlin, , 2014, but the majority may be too dim for reliable observation by 25 typical auroral instruments. Conversely, the sun is so bright that direct observation will saturate detectors designed for relatively faint aurora.     (Thuillier et al., 2003) and Jupiter albedo (Karkoschka, 1998 Although direct sunlight is unsuitable as a calibration source for most auroral instruments, scattering from other bodies in the solar system can provide more reasonable levels of brightness. The irradiance of an arbitrary body x can be modeled by isotropic emission from the sun incident on a sphere with radius R x at distance D Sx , followed by scattering and absorption leading to some fraction of flux travelling a distance D xE to arrive at the top of Earth's atmosphere. We can group terms that depend on wavelength and time into B(λ) and A(t) respectively where the solar power P s (λ) and planetary albedo are both assumed to be time independent to 1% or less. We may express irradiance in terms of the total solar irradiance (TSI ∼ 1360 watts/metre-squared) at a fixed distance of 1 AU.
A phase correction term Φ(ϕ) accounts for any non-Lambertian scattering as a function of angle ϕ between illumination 10 and observer.
For example, illumination from a full moon (φ = 0) is reduced by a factor of 3e-6 (m ∼ 14) relative to direct sunlight.
Despite this substantial decrease, the equivalent brightness of roughly one megaRayleigh per nanometer (Table 2) is still a hundred times brighter than the brightest aurora. For many instruments the angular size of the moon is neither point-like 15 nor beam-filling, requiring careful attention to details such as wavelength dependent albedo varying across the disk (Kieffer and Stone, 2005), and making phase calculations more complicated. For these reasons, the moon is not commonly used for calibrating auroral instruments.
After the moon, Jupiter is currently the brightest celestial object that can be regularly observed well past astronomical twilight. Peak visible magnitude is nearly four times Sirius (the brightest star), making Jupiter easy to identify in the night 20 sky. A detailed spectral distribution of Jupiter's albedo is given by Karkoschka (1998). This can be combined with the solar spectrum of Thuillier et al. (2003) to predict the wavelength dependence of reflected light given in Table 3.
Other bodies in our solar system are less suitable as calibration sources. Mercury is only visible from Earth during the daytime when looking near the sun. Venus can often be seen near dawn or dusk, but always with excessive amounts of indirect sunlight. Mars can be visible at night for several months in a row, but this ideal configuration only occurs on alternate years.

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( Figure 5). Albedo can vary considerably during dust storms and a wide range of ϕ means that the phase function Φ must be very precisely determined (Mallama, 2007). Saturn is roughly one-tenth as bright as Jupiter, with complex albedo variations due to ring geometry (V = −0.62 to +1.31) (Mallama, 2012). The remaining outer planets are simply too dim for reliable detection by most auroral instruments.
As Jupiter and Earth each orbit around the Sun, their relative motion produces significant variations in apparent magnitude   (-9.40) and calculations in this study (-9.426). Middle: declination, which is effectively the same for any terrestrial observer (parallax≈ 0). Bottom: relative air mass for transit at Fort Smith, Gillam, Athabasca, and Pinawa.
During in this study we identified a systematic difference between our flux calculations for Jupiter and the corresponding magnitude value provided by widely available astronomy software (Downey, 2015) using the formula V = V (1, 0) + 5 log 10 (dr) + ∆m(i) where V (1, 0) is the magnitude at 1 AU with i = 0 and ∆m(φ) is the magnitude phase correction. Our results were calculated by entering standard distances into Equation 18 with irradiance and reflection from Thuillier et al. (2003) and Karkoschka (1998).
Eventually we discovered that the widely used lower value came from the 2nd edition of the Explanatory Supplement to the Astronomical Almanac (Seidelmann, 1992) but the most recent 3rd edition (Table 15.8 Seidelmann, 2005) now indicates 5 V (1, 0) = −9.40, which differs from our results by only 2%. This exemplifies the level at which we were able to cross-check our results against other references. It also demonstrates that even astronomical "constants" may be a work in progress.

Jan
July Jan July Jan July Jan July Jan July Jan July 0 Yellow contours correspond to daytime between nautical sunrise and sunset (6 • below horizon). Size of small circles are proportional to lunar phase with yellow indicating daytime.

Atmospheric effects
Light arriving at the top of the Earth's atmosphere may undergo significant changes by the time it arrives at a ground-based observer. Gradients in the refractive index will bend ray paths, changing the apparent arrival angle. The magnitude of this 10 effect increases with zenith angle but is only on the order of 5 arc-minutes at 10 • elevation above the horizon. This might be important for astronomical applications, but is negligible for most optical auroral devices with precision requirements on the order of 1 • .
In contrast, variations in atmospheric transmission can be important even at moderate zenith angles. Atmospheric scattering and absorption processes will reduce the radiant flux detected by a ground-based observer (Sterken and Manfroid, 1992 where the relative air mass X as a function of zenith angle ζ is equal to one at the zenith (ie. X(0) = 1) and increases by a factor of 5 at 10 • elevation above the horizon (Tomasi and Petkov,5 2014). For convenience we may separate zenith angle and wavelength effects where E k is the transmission through one standard air-mass (ie. at zenith).
Empirical results from several nights of astronomical observations near sea level (Vargas et al., 2002) show  Table 3. Spectral variation of solar irradiance at Earth (Thuillier et al., 2003), albedo of Jupiter (Karkoschka, 1998), and atmospheric extinction at Cerro Paranal (Patat et al., 2011). Column 5 is the product of solar irradiance at 1AU and Jupiter albedo (defined as B(λ) in Equation 18) with units of watts per metre-squared per nanometre. Atmospheric transmission E k at zenith is related to extinction κ by Equation 22a. Column 8 is the product of solar irradiance, Jupiter albedo, and atmospheric transmission with units of watts per metre-squared per nanometre. in brightness of a few percent or more depending on the latitude offset ∆Λ and extinction E k Calibration using Jupiter (or any other planet) will be further complicated by corrections for varying declination. Figure 4 shows several years variation of air mass for Jupiter transit at the four field sites considered in this study. A significant transition occurs between large latitude dependent extinction before 2011 to relatively uniform low levels afterward. The effects for this 5 study are only on the order of a few percent, but are clearly evident in results presented in §3.3. This provides some assurance that our analysis procedures are accurate near the 1% level. Of course, calculating the effects of varying declination requires atmospheric extinction coefficients that may not be very well known. This is a challenge, but also an opportunity to test which extinction models produce the best agreement with observations.
Declination differences can even alter the intensity ratio between two different wavelengths (heterochromatic extinction in 10 Sterken and Manfroid (1992)) because extinction is a non-linear function of air mass. This effect is considered in §3.4 and found to be significant.

Meridian Scanning Photometer
Auroral luminosity is often spatially anisotropic, with latitude structuring on scales of 1-100 km and longitudinal features ex- 15 tending from 100s up to 1000s of kilometres. Consequently, some instruments are designed with reduced azimuthal coverage in exchange for improved sensitivity along a latitude profile. These systems may be referred to as meridian imaging spectrographs (MIS) or meridian scanning photometers (MSP) depending on the technology used for spectral discrimination and photon detection. In this paper we explore issues related to field cross-calibration of a specific MSP design that has been used extensively for auroral research in Canada. Many of these topics can also be applied more generally to other auroral optical 20 devices.
Data used for this study were obtained from a network of four multi-spectral auroral meridian scanning photometers. These systems were based on the meridian scanning photometer array (MPA) component of the CANOPUS project (Rostoker et al., 1995) which operated MSPs at three sites in a latitude chain: Rankin Inlet, Gillam, Pinawa (the "Churchill line"), and a fourth auroral zone site two hours to the west in Fort Smith. The primary goal was to detect proton aurora at 486.1 nm and electron 25 aurora at several wavelengths (see Table 4) in order to determine precipitation species, characteristic energy, and energy flux.
The array was operated continuously for nearly 20 years, producing a large high-quality data set which was the foundation for important research on topics including substorms (Samson et al., 1992), the polar cap boundary (Blanchard et al., 1995(Blanchard et al., , 1997, poleward boundary intensifications (Lyons et al., 1999;Zesta et al., 2000), and the B2i isotropy boundary (Donovan et al., 2003).

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Due to bandwidth limitations, most raw instrument output was down-sampled by averaging in space and time in order to produce a uniform data stream for real-time transmission. Full high resolution data were available over a serial "campaign port". In later years, data loggers were used at some sites to record the full resolution data; several years of "high-res" MSP data are available for retrospective re-calibration. The more extensive "low-res" dataset is averaged into 17 latitude bins per scan, which is adequate for auroral science, but diminishes the ability to resolve elevation from individual star transits.
The original CANOPUS MSPs were built by an industrial contractor (Johnston, 1989) based on a series of instruments developed at the National Research Council of Canada (NRCC). Calibration of the prototype was carried out in 1985 by 5 NRCC and the University of Saskatchewan; the results of which led to several design modifications. The first field system was commissioned at Gillam in February 1986, with all four units operational by early 1988. By the late 1990's it was increasingly obvious that the instruments were nearing end-of-life. The primary concern was the mirror motors which had driven several billion steps, but many other issues (eg. data acquisition, high voltage supplies, photomultiplier tubes) were also causing problems. Eventually, a lack of spare parts resulted in significant failures and data loss.

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An MSP revitalization project was carried out at the University of Calgary starting in 2007. The goal was to provide replacement systems with equivalent functionality. System design was based closely on the original instruments in order to minimize risk, with legacy mechanical and optical components reused where possible. Initial development was carried out on the legacy system at Rankin Inlet which was broken beyond repair. The detector was replaced with a new PMT, high voltage supply, and pulse-counting circuit. Anti-reflection coatings were added to several optical elements, with system throughput optimized with 15 predictions from optical modelling software and confirmed with quantitative testing. All of the old filters were replaced, as was the filterwheel motor. The scanning mirror assembly was upgraded to provide 0.09 • elevation steps (4000 steps per 360 • ).
Thermal and power control systems were completely replaced. An FPGA coordinates for low level timing and synchronization, while a Linux PC-104 was responsible for data acquisition and overall system control.
After darkroom calibration and local field trials the new prototype system was deployed at Gillam and operated adjacent to 20 the legacy system which was still functioning intermittently. The original Gillam system was then upgraded and sent to Fort Smith (2009) The new Calgary MSPs use the same filter-wheel design as CANOPUS to acquire data from eight spectral channels, with 486.1 nm duplicated in order to increase SNR for faint proton aurora. Accurate photometry of rapidly varying aurora requires effectively simultaneous measurements of background and signal. This is accomplished by rotating the filter-wheel at 30 1200 RPM (20 Hz) and gating the detector to provide successive 12.5 ms sample spacing. Some details about filter sequencing is given in Table 4; for simplicity all subsequent multi-channel data will presented in wavelength order (blue to red).
Interference filter transmission and blocking as a function of wavelength were provided by the manufacturer and summarized in Table 5. Results were very close to specifications (FWHM 3 nm for the blue filters and 2 nm for the others). Transmission peaks were broad and flat with maxima around 80%, which is the key parameter for optimizing detection of narrow emission 35 is the relevant quantity for broad-band calibration sources ie. converting from Rayleighs per nanometer to Rayleighs. These data suggest typical passband and transmission variations on the order of 5% between different sets of filters. Light which passes through the filters is detected by a photo-multiplier tube (PMT) with photocathode quantum efficiency 5 ranging from 20% at 400 nm to 2% at 750 nm; this response was selected to maximize response for the faint H β emissions.
A dynode chain amplifies each electron to produce a cascade which triggers a pulse-counting circuit. The high-voltage power supply required for this process is quite stable over short intervals under ideal conditions, but may change during extended field operations. Photocathode aging and high-voltage drift are likely to be the primary cause of any long-term reduction in system sensitivity. PMTs dead-time produces a non-linear response at high count-rates. This pulse pile-up effect can be largely removed if the time resolution τ of the system is known and is not significantly longer than the signal count interval. For the PMTs used in this study nonlinearity only becomes important for count rates greater than 10 5 photons per second. These rates can be produced by very bright aurora but are not a problem for any astronomical sources except the Sun and Moon.
Meridian scans are achieved with a 45 • mirror and a stepping motor. Many MSPs rotate the mirror at a fixed rate in order 5 to produce data from evenly spaced elevations. Both the original and refurbished systems instead utilize a sequence of variable steps chosen to produce nearly constant exposure times as a function of linear distance at auroral altitudes. This detail is relevant to this study because Jupiter transit profiles will be measured with different resolution depending on transit elevation.
The effects are expected to be small, but must be kept in mind when considering multi-year variability.

System sensitivity 10
The relationship between incident photon flux P(λ) and measured channel count rate D k depends on the effective aperture allowing photons into the system (A eff ), channel multiplexing efficiency (M k ), filter transmission (T k ), measurement interval (∆t), and the detector efficiency Q(λ).
For wide-band input through narrow-band filters the process can be written in terms of filter peak transmission T k and giving a response k C D/P for each channel 20 in terms of measured D and predicted P for each filter wavelength. We will use the term "calibration coefficient" to refer to differential brightness per count which is the quantity of interest when converting data to physical units. However, we will express subsequent results in terms of the reciprocal "sensitivity" for which higher numbers are better.

Darkroom calibration
All systems have been calibrated at the University of Calgary using a low brightness source (LBS) with spectral radiance measured by the Canadian Institute for National Measurement Standards. Several sets of calibration results for one instrument at different times are shown in Table 6. Results from two sucessive days (November 21 & 22 2014) agree to 1% or better, suggesting that the calibration process is highly repeatable. Earlier results from 2010 indicate that the system was about 5% 5 more sensitive in all channels, but with only two measurements over more than 4 years, it is impossible to determine whether this corresponds to a gradual decline or an abrupt change at some time during shipping or field operations. that range from precise and absolute to uncertain and relative. Optical field of view is considered in §3.1, device orientation in §3.2, magnitude variation in §3.3, spectral ratios in §3.4, and absolute sensitivity in §3.5.
Each of the MSPs considered in this study executes a sequence of repeated scans from the northern to southern horizon.
Every scan consists of multiple steps through a 160 • elevation range, with measurements acquired through multiple filters at each step. The resulting data stream has units of "counts" or simply "data numbers" (D) and can be represented by a Ephemeris software (Downey, 2015) was used to calculate the time and elevation corresponding to the transit of Jupiter through the local meridian containing the zenith and terminated by the celestial poles. To start we assumed that instruments were perfectly level and had azimuths pointing directly north in order to obtain a starting point for identifying actual transits.

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A keogram sub-region centered on the predicted transit was used to fit a two-dimensional generalized Gaussian model  where D 0 and B 0 are signal and background,ȳ = y − y 0 andx = x − x 0 are the elevation and time relative to the transit peak x 0 , y 0 , α x,y are profile widths, and β x,y are scaling parameters. Jupiter transit profiles were initially modelled with a simpler bivariate Gaussian (β x = β y = 2) which could usually achieve model/data differences on the order of 10%. The more general representation in Equation 31 was introduced in an attempt to ensure that model error would not be a limiting factor for analysis at the 1% level. We subsequently found that the coefficients also provided a useful measure for classifying transit quality, and 5 more clearly identified minor azimuthal asymmetry in the optical response.
This significantly increases the number of transits which could be used for estimating orientation and field-of-view, although relatively few of these additional events are suitable for photometric calibration. Figure 7 shows Gillam transit times obtained over three winters. Sequences of good transits correspond to cloudless nights, gaps to periods of poor visibility near full Moon.

Field of view
Stars and distant planets are effectively point sources when viewed with a single pixel detector (PMT) through optics with angular resolution on the order of 1 • . Each MSP elevation sweep over an astronomical source will produce a profile that corresponds to the "vertical" optical angular response. Similarly, a time sequence of observations from a fixed elevation should provide a complementary measure of "horizontal" optical beam shape. This is illustrated in Figure 6 with a full two-dimensional  Table 7. Results are consistent with all instruments having similar horizontal and vertical widths: σ ≈ 1.07 • (FWHM ∼ 3.0 • ). Average beam widths have standard deviations less than 0.05 • and standard errors less than 0.01 • ; typical beam solid angles are approximately 2.30 × 10 −3 steradians with uncertainties of a few percent. 15 The effective solid angle Ω 0 is essential for comparing flux from distant point sources to distributed auroral emissions. For several years of Fort Smith data the average value was 2.07 milliSteradians with standard deviation of 0.12, and standard error of the mean less than 1%.

Orientation
An ideal MSP would be aligned to produce scans with predetermined azimuth and elevation. For outdoor installations at 20 remote field sites it can be difficult to reduce leveling errors below a few degrees. Further complications may arise as the ground freezes in autumn and thaws in spring. Geographic azimuth may be difficult to precisely determine unless a detailed site survey is available. Alignment with magnetic north can also be challenging unless the site is magnetically clean and there are no geomagnetic disturbances. Over longer periods the magnetic declination may change significantly (see Table 1) due to secular variation in the geomagnetic field. 25 Fortunately, it is possible to accurately determine instrument orientation from transit observations. Starting with site locations obtained using GPS, observed transit times were used to calculate the actual elevation and azimuth of Jupiter for each night.
These were interpreted in terms of two device angles. First, azimuth offset was attributed to horizontal orientation of a level instrument. Second, the difference between nominal mirror elevation and actual target elevation was attributed to instrument "tilt" from level.

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Results for three seasons at Gillam are shown in Figure 9. Azimuth estimates are extremely stable over time, with jitter < 1 • and no apparent drift. Tilt estimates from the first two seasons are even less variable, although there appears to be a small jump in early November. Examination of results from the other three sites (not shown) finds a similar feature at Fort Smith (FSMI), a smaller shift at Pinawa (PINA), and no obvious change at Athabasca (ATHA). These results are consistent with "frost heave" occurring in early winter as moisture in the soil freezes. The lack of this effect at ATHA may be be due to better foundations for the instrument platform.
A yearly summary of orientation parameters for each site is presented in Table 7. For cases with 30 or more good transits the standard deviations are less than 1/2 • and uncertainties in the average (standard errors) are less than 0.1 • . This allows data 5 to be accurately mapped into other coordinates (ie. geographic); even minor changes to instrument alignment can be easily identified.

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Geosci. Instrum. Method. Data Syst. Discuss., doi:10.5194/gi-2016-5, 2016 Manuscript under review for journal Geosci. Instrum. Method. Data Syst. Published: 23 March 2016 c Author(s) 2016. CC-BY 3.0 License. Figure 9. Gillam MSP orientation inferred from observations of Jupiter. Each symbol corresponds to one transit during a single night. Large symbols correspond to "good" beam widths with both vertical and horizontal σ ∼ 1 • . Small symbols correspond to all other events.

Magnitude variation
The signal intensity during each transit will depend on source brightness, instrument sensitivity, and atmospheric effects. This is complicated for Jupiter, as the apparent visual magnitude varies due to changes in distance from Earth. Figure 10 illustrates the importance of this effect, with predicted variation in apparent brightness following the upper bound of observations. The lower set of events typically correspond to apparent transit profile widths that are significantly different than the best-case 5 values, and are likely due to non-ideal atmospheric transmission (eg. clouds or ice crystals). There are usually several dozen "good" transits per season; subsequent analysis will focus on these events. Effects due to variation in source brightness can be removed by normalizing all measuredD cases to magnitude m = 0 where m J is the apparent visual magnitude of Jupiter predicted by the ephemeris. The resulting distribution of normalized magnitude at Gillam (not shown) has a fairly narrow peak with a sharp higher cut-off and a long tail of lower values corresponding to non-ideal viewing conditions. The 90th percentile was found to be a simple and robust estimator of peak normalized bright-5 ness, while average and standard deviation are used to estimate uncertainty in seasonal averages. Results for Gillam and Fort Smith are presented in Table 8. Normalized brightness for all Gillam transits over three years are shown in Figure 11. Linear fits to the data give a slight positive slope of roughly 2% per year, but with statistical uncertainty that includes zero. This is consistent with a stable system response at blue wavelengths, although variations on the order of 5% cannot be excluded. If the linear trend were significant, this would mean the instrument was becoming slightly more sensitive over time, which seems unlikely. Closer examination of the data found that most of the variation is due to a 5% jump between 2012 and 2013 after which the signal levels remain essentially constant. The jump did not correspond to any system maintenance or modifications.
A nearly identical pattern was observed at Fort Smith, further suggesting that the underlying cause was not instrumental.
In fact, this appears to be an example of atmospheric effects as discussed in §1.4.1. The apparent declination of Jupiter the change in declination corresponds to transmission differences of 74.9% versus 80.4%. Adding this correction to normalized brightness reduces the linear trend to zero, although with considerable uncertainty.

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Absolute photometric calibration with Jupiter is complicated by variability in observed brightness, and absolute spectral sensitivity is similarly challenging. Working with relative spectral response removes changes in source brightness, allowing us to focus on instrumental and atmospheric effects. In order to reduce statistical uncertainty we have normalized all channels to the average of the twin H β channels and summarized the results in Table 8.
Factoring out external brightness variation provides useful information about internal stability of different wavelength chan-15 nels. Averages for normalized blue channels are essentially constant to within 1% year-to-year. This result provides some reassurance about relative filter stability, but cannot exclude the possibility of any change which might produce identical changes in all channels (eg. high-voltage supply drift, optical defocusing).
Red channels exhibit more variability on both short and longer time scales as shown in Figure 12. One notable feature is a clear drop after the first season, followed by two years of relative stability. This might be attributed to some wavelength depen-20 dent change in sensitivity such as photocathode aging or filter delamination. However, exactly the same pattern is observed at all four sites, suggesting a cause that is external rather than instrumental.
As noted in §1.4.1, apparent changes in wavelength ratios can also be produced by variations in source declination. Extinction at zenith will have a larger effect on shorter wavelengths, thus increasing the red:blue ratio. This effect becomes larger as zenith angle increases with largest red-to-blue ratios observed near the horizon. From 2012 to 2013 Jupiter's declination increased 25 by roughly 10 • and transit zenith angle decreased from 50 • to 40 • . Assuming that observed changes in wavelength ratio are caused by this effect, a simple log-linearized regression gives a slope of κ red − κ blue ≈ 0.38 which is generally consistent with other results considered in §1.4. Since this estimate is produced by combining a large number of transits obtained during a wide range of atmospheric conditions we do not place 30 too much weight on the precise value. The important result is that spurious trends in wavelength ratios can be modelled well enough to allow detection of real changes on the order of 5%.

Absolute sensitivity
The data count rate D produced by one Rayleigh per nanometerṘ of auroral luminosity can be found by using angle Ω is either known a priori or can be estimated from transit profiles. From §3.1 the uncertainty of an unbiased estimate will be less than 1%, but systematic bias on the order of 5% is also a possibility.
The extinction coefficient spectrum κ(λ) can be highly variable, can have a major effect on received signal levels, and cannot be accurately estimated from the MSP data. In the absence of other information, the best we can do is identify an upper envelope containing the brightest events and assume that they correspond to the minimum possible extinction values. This 15 approach seems to produce intrinsic variability less than 5%, but does not address the issue of systematic bias.
Each transit could potentially provide a measured value for D. A simple calculation of Poisson uncertainty for the entire profile would be on the order of 1% assuming good transits with peaks in excess of 2000 counts. This result may be overly optimistic given the complicated nature of many transits. An alternative approach is to examine sequences of transit profiles, focus on clusters of "bright" events in the top quartile or decile, and assume that they provide an overestimate of the intrinsic 20 variability.This approach produces estimated uncertainties ranging from 1-5%.
Data from a single transit can be scaled by model flux density from Equation 18 to obtain an empirical estimate of the system calibration coefficient C. An example is provided in Table 9 for the November 22, 2011 transit at Gillam using the pair of nominally identical 486 nm channels as an example. Fitting a two-dimensional Gaussian model to each channel separately produced very similar peak values: 1501.14 DN and 1501.54 DN. Appropriate model values from Table 3 can be used to 25 predict input photon flux (neglecting atmospheric effects) and estimate a system calibration coefficient relating flux from a point source to measured data numbers.
Calculation up to this point has consisted of multiplying several quantities, each with relative uncertainty of a few percent or less. These errors are negligible in comparison to atmospheric variability. The 486.1 nm extinction factor at zenith could vary between 0.73-0.84 for fair to good visibility, and 0.64-0.78 at ζ = 45 • . Lower elevations and worse viewing conditions 30 will further attenuate incoming flux. Neglecting extinction will provide a lower bound for empirical sensitivity, as reduced flux requires higher sensitivity in order to produce the same observations.
Including more events should provide some combination of additional information and increased variability. We attempt to focus on a sub-set of "high-quality" transits that presumably correspond to good atmospheric viewing conditions. Events including standard least squares estimates of intercept and slope C D/P . Figure 13 shows classification and fitting results for the combined blue channel data. This automated process produces reasonable results for all the data considered in this study. More 5 sophisticated algorithms for further studies could explicitly include the asymmetric nature of extinction ie. hard upper bound on theoretical maximum.

Discussion
When auroral instruments operate unattended for long periods of time at remote locations, frequent comprehensive on-site calibration may not be feasible. If celestial objects can be identified in standard data streams then these may serve as the basis 10 for alternative independent calibration procedures.
There is a long history of using astronomical sources to determine the alignment of auroral instruments (Montbriand et al., 1965). Absolute calibration using stellar spectra appears to be a more recent development Gladstone et al. (2000); Whiter et al.  (2011); Wang et al. (2012). Details discussions of these topics are not always found Figure 13. Total counts in four blue channels (excluding 470.9 nm) as a function of predicted photon flux density. Small "+" indicate all cases, medium "x" for good beam widths, large squares for nearness to robust fit line. Flux model includes solar spectrum, illumination geometry, Jupiter albedo, and terrestrial atmospheric extinction as in Table 3. in the primary scientific literature, but must often be extracted from conference proceedings, technical reports, and theses.
Fortunately, these resources are more easily discovered with modern search engines.
Stars are essentially point sources when viewed using auroral instruments with angular resolution on the order of 1 • . They are stationary in celestial coordinates, and follow predictable paths as the Earth moves during each day and over the course of a year. Absolute flux spectra are increasingly available, although more generally for faint stars that cannot be reliably detected by 5 most auroral devices. Even the brightest stars are only comparable to low-intensity aurora with correspondingly high statistical uncertainty. Light from extra-terrestrial sources must also travel through the Earth's atmosphere before arriving at a detector. The resulting wavelength-dependent reduction in photon flux depends critically on atmospheric properties that may not be well known. Of course, auroral light is also subject to the same atmospheric effects.
Jupiter's peak radiance is greater than the brightest star, but less than the mooon, so there is no risk of saturating most auroral detectors. It is effectively point-like, has a predictable trajectory, and absolute spectral flux can be calculated from existing albedo and solar irradiance measurements. Unlike stars, planets are not fixed in celestial coordinates, meaning that 5 transit altitude is not constant. This minor complication actually provides an opportunity to study the effects of changing zenith angle on atmospheric extinction.

Atmospheric effects
Atmospheric transmission is likely to be the largest source of uncertainty for high SNR applications. Reducing this uncertainty will require estimation of extinction coefficients that are appropriate for each transit. Our preliminary attempts to determine 10 these parameters using multi-spectral MSP data were not successful, but this problem may yield to more sophisticated analysis.
In principle, extinction coefficients can be found simply by measuring the apparent magnitude of a single star at a given wavelength over a range of different zenith angles. Improved precision can be achieved by combining data from multiple stars.
Many auroral observatories include all-sky camera systems which can image dozens or hundreds of stars. However, the optical 31 Geosci. Instrum. Method. Data Syst. Discuss., doi:10.5194/gi-2016-5, 2016 Manuscript under review for journal Geosci. Instrum. Method. Data Syst. Published: 23 March 2016 c Author(s) 2016. CC-BY 3.0 License. response ("flat field") of these systems is also a strong function of axial angle, which for an ASI is usually directed towards the zenith. Accurate flat-fields will be essential for accurate extinction estimates. Recent work by Duriscoe et al. (2007) It is tempting to avoid the compexity of atmospheric variation by using only a small number of "good" days to determine calibration parameters. One obvious limitation of this approach is that it cannot reliably detect short term changes in instrument 5 response. More importantly, all auroral observations are subject to exactly the same atmospheric issues. An arc moving from the horizon to zenith will become brighter, not because of any change in precipitation, but simply due to reduction in total airmass between auroral altitudes and a ground-based observer. Atmospheric effects may be negligible when looking directly upward through clear skies, but critically important at low elevations and non-ideal viewing conditions. These effects would be even more pronounced at shorter wavelengths (eg. 427.8 nm and 391.4 nm) often used in auroral studies.

Retrospective Calibration
Some auroral instruments only acquire data during short-term "campaigns", but many are operated in support of longer term science objectives. Not all devices are fully calibrated before being deployed and few are calibrated on a regular basis. Even when the resulting data overlap in space and time, quantitative comparison may not be possible. Astronomical observations of bright sources such as Jupiter can provide a basis for retrospective cross-calibration of historical data sets. 15 The original CANOPUS meridan scanning photometer array (MPA) is a good example. Digital "low resolution" binned data are available starting in early 1988 and continuing until spring 2005. Some data are available for the transition period from 2005-2010, after which all refurbished instruments were operating in the same high-resolution mode. The 16 years of low-res data alone extend well beyond one solar cycle and could span more than two if merged with newer data.
However, certain kinds of quantitative analysis are limited by the lack of photometric calibration. Some key parameters 20 (eg. filter band-width and channel sensitivity) were determined for each system, but the supporting documentation is very limited. Mechanical and electrical subsystems were regularly maintained and repaired, but there was no corresponding calibration schedule. Some terminal calibration procedures were carried out during the 2005-2010 transition, but by this point the instruments were often not functioning reliably. In order to confidently identify long-term geophysical trends in these data it is essential to have some sense of how instrument performance changed over the same time-scales. 25 A preliminary survey of the CANOPUS MPA data archive has confirmed the feasibility of astronomical calibration and also identified some significant challenges. First, only the brightest few stars are visible even with optimal viewing conditions. Jupiter can be clearly identified, but at count rates much lower than obtained by the newer systems, and consequently with much greater uncertainty. Elevation steps are combined into 17 latitude bins which effectively removes the ability to determine instrument tilt. More generally, it eliminates virtually all information about the optical beam-shape in that direction, including 30 that required to estimate the effective solid angle Ω 0 . Finally, the decreased scan cadence of one-per-minute will slightly reduce the accuracy of azimuth estimates. Despite these limitations it should still be possible to estimate absolute sensitivity using Jupiter transits during extended intervals at both ends of the project: 1989-1993 and 1999-2005. Other bright stars or planets might be used to fill in the intervening period.

Conclusions
In this study we have demonstrated the feasibility of using Jupiter to calibrate a network of auroral meridian scanning photometers. This approach provides an estimate of instrument orientation for each transit with even marginal viewing conditions. Abrupt changes of less than 1 • can be easily identified. If orientation is constant then it can be determined to at least 1/10 • , which exceeds most application requirements. Angular optical response (beam-shape) can be obtained from a sequence of 5 meridian scans obtained during the transit of a point source. Statistical uncertainty may be a limiting factor even for bright stars, so the increased SNR from Jupiter is highly advantageous.