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When we measure color using photometric techniques, the camera integrates all the light that each filter transmits. For each measured star, this sum gives us the star's brightness in that filter, so we reduce all transmitted light to a single number. Then, by comparing it to the brightness in another filter, we get the star's color index.
The same happens when we relate the colors observed through the photometric filters used by a photometric catalog, such as APASS,[1], with the colors observed through our RGB filters. As the two systems have entirely different transmission curves, this simplified color conversion has an implicit uncertainty. To this conversion effect, we should also add the implicit uncertainty in the photometric measurements of the APASS catalog. All these factors lead to a color calibration limited by this color conversion and not by the noise in the image.
So far, we have been basing photometric color calibration on the APASS catalog in PixInsight. APASS was the first stellar catalog fulfilling the requirements for this task by providing measurements made with CCD cameras and filters similar to the photographic RGB filters that we normally use for a significant amount of stars (about 120 million stars in APASS Data Release 10). The availability of APASS led to the development of our PhotometricColorCalibration tool (PCC). With PixInsight's new generation of photometric and color calibration tools, we now take a step forward by basing all measurements on data from the Gaia space mission.[2] [3]
Spectrophotometry consists of applying photometry separately to individual wavelengths. We can achieve this using a spectroscope or a system of juxtaposed narrow filters. With Gaia spectrophotometry, instead of having a few isolated brightness values, we now have a continuous spectrum function for each star, which we can sample arbitrarily from ultraviolet to infrared.
Gaia provides the first accurate, massive spectrophotometric catalog in the history of astronomy. Compared to APASS, Gaia offers unprecedented uniform sky coverage and color homogeneity since the data are based on observations made from space without the varying conditions of the atmosphere. We now have at our fingertips the spectra of about 219 million stars, which, considering that each spectrum is made up of more than 300 measurements, represents a base of 80 billion data. This database is now available for download to all PixInsight users from the PixInsight Software Distribution System as a set of XPSD database files, ready to be used with the new SPCC tool. SPCC, therefore, represents a significant step forward in terms of robustness and reliability, and a new milestone in the definition and expression of color in astrophotography.
Philosophical criteria must always support the definition of a standardized white reference. The definitions of many of the measurement units of the International System of Units follow this reasoning, so we could say that this is a work in the philosophy of science and mathematics field. For example, the definition of the degree Celsius and that of the liter in its origin, are related to one of the essential elements for life: water.
Contrarily to many other imaging disciplines, in the case of astrophotography, the problem of color is not primarily a matter of accuracy. In astrophotography, what we need to be precise about is the concept that supports color in our images. When we designed PCC, we established a new color philosophy based on a reference point more universal than sunlight: an average spiral galaxy.[8] [9] The reasoning behind this conceptual change is based on two principles:
At that time, we decided that this reference spiral galaxy would have an average spectrum between the Sb, Sc and Sd types, avoiding the extreme types and leaving out the lenticular (S0) galaxies. Since the release of the SPCC and PCC tools in November of 2022, we have updated this definition of an average spiral galaxy to be the mean of the spectra of all morphological types: S0, Sa, Sb, Sc, Sd, and Sdm.
The rationale of this decision is that, in this way, we are fairer when averaging the different stellar populations, especially those of galaxies with a high rate of star formation (Sd and Sdm), as we can see in Figure [1].
While the morphological types S0, Sa, Sb and Sc have similar spectra, the types Sd and Sdm have much more emission in the blue part of the visible spectrum. By averaging all of these spectra, the spectrum of the average spiral galaxy (plotted with a dashed line) is very similar to that of a type Sc galaxy, as shown in the graph above. A very representative galaxy of this morphological type is M74 (Figure [2]).
Therefore, this is the new standard white reference on which color calibration will be based in PixInsight, both photometric color calibration with PCC and spectrophotometric color calibration with SPCC.
With the release of version 1.8.8-6 of PixInsight in October 2020, we introduced XPSD (eXtensible Point Source Database), a new database format we have designed and developed for fast and efficient access to massive astrometric and photometric star catalogs. As of writing this document, we have already released XPSD databases with data from the APASS DR9, APASS DR10, Gaia DR2, Gaia EDR3, and Gaia DR3 catalogs.
The new SPCC process requires special Gaia DR3/SP databases. DR3/SP means here Data Release 3 with spectra. These XPSD databases provide astrometric, photometric and sampled mean BP/RP spectrum data for a total of 219,165,266 Gaia DR3 point sources. Available data include equatorial coordinates, proper motions, parallax, mean G, BP and RP magnitudes, and mean spectra from 336 to 1020 nm sampled discretely at 2 nm steps (343 spectrum values) for each star.
Before using the SPCC process, you must configure the Gaia process to use Gaia DR3/SP local database files. First, download the required .xpsd files, either the small or complete set, at your option. Then open the Gaia process from the Process Explorer window, where you'll find it under the StarCatalogs and Astrometry categories:
On Gaia Preferences, select the Gaia DR3/SP data release, click the Select button to select the required .xpsd files, and click the OK button. Now you can use the SPCC process with full access to local XPSD database files.
This section describes the algorithms we have designed and implemented for the new SpectrophotometricColorCalibration process (SPCC) in PixInsight. At a high level, we can decompose the SPCC task into the following main steps:
We begin by detecting a set of point sources in the image. This first step is critical because we want to detect stars, not extended objects or potential bright artifacts such as uncorrected hot pixels, cosmic ray impacts, satellite and plane trail residuals, etc. We already have this task well implemented in our code base and have been improving it for many years.
When the difference between and is larger than the nominal fitting resolution (0.01 pixel in the current implementation), our PSF fitting routines fit an additional parameter, which is the rotation angle of the X axis with respect to the centroid position. varies in the range [0,180). For a rotated PSF, the and coordinates in the above equations must be replaced by their rotated counterparts and respectively:
Each PSF is fitted from pixels inside a square sampling region centered at the approximate central coordinates of the detected source. The size of each sampling region is determined adaptively by a median stabilization algorithm. The sampling region starts at the limits of the detected source structure and grows iteratively until no significant change can be detected in the median calculated from all pixels within the region. This technique improves accuracy and resilience to outliers in fitted local background estimates, which are crucial for the accuracy of fitted PSF models and hence of PSF flux estimates.
Our current implementation supports an automatic mode for selecting an optimal PSF type for each detected source. When this mode is enabled, a series of different PSFs will be fitted for each source, and the fit that leads to the least absolute difference among function values and sampled pixel values will be used for flux measurement. Currently, the following functions are tested in this special automatic mode: Moffat functions with shape parameters equal to 2.5, 4, 6 and 10 (Figure [5]). This limited set represents a compromise between accuracy and efficiency with current computational resources. In future versions, we'll add more sophistication to this adaptive PSF type selection strategy.
where is the elliptical detection region, defined by default at the one tenth maximum level (FWTM) of the fitted PSF, represents a set of image coordinates within , is the pixel sample value at , and is the fitted local background estimate.
Note that fitted (amplitude) parameters are not used for PSF flux evaluation, since flux is calculated exclusively from sampled image pixels. This leads to our hybrid PSF/aperture photometry approach.
The catalog sources are mapped to sources detected on the image by transforming their equatorial coordinates to Cartesian coordinates on the image plane. For this transformation, we first apply the appropriate reduction of positions,[20] [21] which depends on the celestial reference system to which the astrometric solution has been referred:
The filter functions, respectively for the red, green and blue color components. These are three continuous functions of wavelength, where the dependent variable is filter transmission in the [0,1] range. These functions should describe the spectral response of the filters used to acquire raw image data.
A quantum efficiency (QE) curve. This is also a continuous function of wavelength with values in the [0,1] range. This function is optional; by default, it is an ideal QE curve with a constant value equal to 1. Under normal working conditions, a QE curve is only necessary for monochrome sensors. For color sensors and cameras, one assumes that quantum efficiency is being taken into account implicitly by the corresponding filter spectral response curves.
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