Spectrophotometry–based Color Calibration in PixInsight

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.

This is a source of errors. Suppose we have a very red star. Suppose also that our camera is quite insensitive to the extreme range of ​​red light. This will cause the star to appear dimmer in the red filter, despite using the same filters as other observers who own a more red–sensitive camera, which will undoubtedly affect our color measurements.

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]}

Gaia currently represents the state of the art in terms of stellar astrometry and photometry. The star catalogs and auxiliary data generated by Gaia are of the highest quality as they are based on measurements made from space. We at the PixInsight Development Team have already been using and recommending Gaia for all astrometry–related tasks in PixInsight for many years. Now we have implemented a new tool, SpectrophotometricColorCalibration (SPCC), which uses Gaia's mean BP/RP spectra^[4] available since Gaia Data Release 3.^{[5] [6] [7]} SPCC is the first of a series of tools we are developing to exploit the availability of Gaia mean spectrum data in PixInsight.

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.

The great advantage of spectrophotometry is that it allows us to compute the brightness that a star should have through the exact filters we have used to acquire our image. This is done by simply multiplying each filter's transmission curve by the star's spectrum. In addition, we can also synthesize the exact colors that a white reference should have as acquired with our filters. By taking into account the spectra and the transmission curves, we get rid of the important sources of errors mentioned above—when comparing PCC fitting graphs with the corresponding SPCC graphs, in most cases, the uncertainty of computed white balance functions is decreased by more than one order of magnitude.

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:

• The Sun does not illuminate the deep sky astronomical scene.
• A spiral galaxy works as a balance point because, as a whole, it has a significant representation of all stellar populations.

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]).

The formal definition of our average spiral galaxy white reference is then as follows:

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.

Before XPSD, our astrometry and photometry tools and scripts relied on online database access services, such as VizieR.^[12] These online services are excellent in their implementation and capabilities. They have made possible the development of robust, accurate, and feature–rich software products such as our well–known ImageSolver, AperturePhotometry and AnnotateImage scripts, among others. However, for the requirements of most of these tools and many others subject to intense development work in PixInsight, we need much faster access to huge astronomical catalogs. The main advantage of the XPSD format is that it provides efficient access to massive astronomical catalogs using local database files, that is, files stored on the local filesystems of the user's machines or local networks.

The XPSD format is similar to the XISF image format^[13] in the way it stores and organizes metadata—for example, both formats use XML file headers to guarantee flexibility and extensibility in metadata serialization. XPSD files provide fast, multithreaded access to point source data with special quadtree–based index structures to perform search operations on arbitrary regions of the celestial sphere, as well as efficient storage with transparent data decompression. An in–depth, formal description of the XPSD format is beyond the scope of this document, so we'll limit the following subsections to describe the practical usage of XPSD databases with the SPCC process. For interested developers, the implementation of XPSD and currently supported catalogs in XPSD format (APASS and Gaia as of writing this document) is part of our open–source C++ development framework.^[14]

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:

• Star detection. Detect sources separately on each color component of the image.
• PSF fitting. A point spread function (PSF) is fitted for each detected source, also separately for individual RGB channels.
• Signal evaluation. For each detected source, compute three flux estimates, respectively for the R, G and B color components. Evaluate pixel values within the fitted elliptical PSF region (at the one-tenth maximum level (FWTM) by default).
• Database search. Perform a database search to retrieve the set of Gaia DR3 stars with mean spectra within the region of the sky covered by the image. This requires the image to provide a valid astrometric solution.
• Source matching. Find the set of pair matches between Gaia DR3 catalog stars and detected stars on the image.
• Image flux ratios. For each matched image star, compute its R/G and B/G image flux ratios from the corresponding PSF flux estimates.
• Catalog flux ratios. For each matched catalog star, integrate its spectrum multiplied by each color filter and an optional quantum efficiency (QE) curve. Compute the R/G and B/G catalog flux ratios from the values of these integrals.
• White reference ratios. For the selected white reference, integrate its spectrum multiplied by each color filter and an optional quantum efficiency (QE) curve. Compute the R/G and B/G white reference ratios from the values of these integrals.
• White balance functions. Compute robust linear fits from the set of matched catalog and image R/G and B/G flux ratios.
• White balance factors. Use the white reference ratios as input to the white balance functions to find the R, G and B white balance factors. These factors are applied by multiplication with the color components of the image to perform a white balance operation.
• Background Neutralization (optional). Subtract any existing bias in the color components after the white balance operation, measured on a subset of pixel samples representative of the sky background as acquired in the image.

We describe these steps in the following subsections, including some important implementation details.

The main advantage of Gaia over APASS is its greater accuracy and consistency throughout the entire sky. You can easily find images where uncertainty in the APASS catalog is locally quite high, leading to results where the precision of color calibration is quite low. In these cases, color precision is not limited by image noise but by noise in the colors derived from catalog data. Let's see an example with the following wide–field image of NGC 6946.

We will compare the uncertainties in the R scaling factor calculated with the APASS and Gaia catalogs. When we increase the limiting magnitude, we expect to get an increase in uncertainty because the fainter stars are noisier in our image. On the contrary, when we limit calibration to brighter stars, we expect to see a decrease in uncertainty. This is exactly what happens when we vary the limiting magnitude from 14 to 17 using the Gaia catalog (Figure [7]).

As we would expect, limiting catalog stars to 14 magnitude leaves a very well–defined line because we are using stars with a higher signal–to–noise ratio in the image. This is not the case with APASS in this field, as can be seen in Figure [8].

In Figure [8] we observe that the point cloud does not tend to a thin distribution when we limit the catalog magnitude to 14. In other words, we cannot decrease uncertainty by decreasing the limiting magnitude from 15 to 14. Moreover, if you look carefully at the graphs, you will notice that increasing the limiting magnitude increases the dispersion of the points, mainly in the horizontal direction. This means one thing: APASS data are noisier than our image, so color calibration is limited by the precision of APASS and not by the image itself. Note also that, in the graphs of Figure [8], there are clusters of stars that fall entirely out of the main trend, denoting local biases in the APASS catalog.

The Gaia catalog outperforms APASS in all of these aspects. We routinely get much smaller color calibration uncertainties by using Gaia spectrum data. We have compared the R and B scaling uncertainties in a test performed with 21 broadband deep sky images. The graph in Figure [9] shows the decrease in uncertainty achieved using SPCC instead of PCC.

Almost in every case, we find a substantial increase in the precision of color calibration. In some cases, the color adjustment is about ten times less uncertain. On average, we expect a reduction of color calibration uncertainties by 400% and 300%, respectively for the red and blue channels.

Overall, we have found that color calibrations performed using Gaia spectra (SPCC) lead to calibrated images with a slight blue shift compared to calibrations using APASS photometry (PCC). Usually, this blue shift is under 10%. To verify this, we first performed a calibration with PCC and then calibrated again with SPCC. Ideally, SPCC would find 1:1:1 RGB white balance factors, but the calculated ones are systematically lowering the R and G components. This is shown in Figure [10].

The differences in white balance factors and calibration uncertainty between both catalogs are not consistent throughout this set of test images. However, since the precision in color measurements is so higher with Gaia, we are much more confident with this catalog not showing any global or local color shifts, as well as on the vastly superior accuracy of color calibrations performed using Gaia. Gaia mean BP/RP spectra represent the current state of the art for flux measurement and will be the present and future source for photometry calculations in PixInsight.

The user interface of SpectrophotometricColorCalibration (SPCC) is quite similar to the interface of PhotometricColorCalibration (PCC):

Switching from PCC to SPCC is straightforward. In both tools, we have the Catalog Search, Signal Evaluation and Background Neutralization sections. The only significant difference between these tools, for basic usage, is the ability to configure our own filters provided by SPCC. In PCC, we compare stars measured on our RGB image channels to the brightness of the same stars measured with the photometric filters used to build the APASS catalog. With the Gaia spectra database, we calculate the exact brightness of each star in the filters we have used to acquire our image. Hence, in the Calibration section, we can assign a filter for each color channel of the image:

Irrespective of being a color image acquired with a monochrome or color camera, we should always select the three filters separately. As shown above, the default filters are those of a generic Sony color image sensor. The only difference regarding the type of camera is that, for a monochrome camera, we first need to create a color image with the ChannelCombination tool, as explained in the next section.

In the default filter list, we have included the most common filter sets:

• Astrodon E and I series.
• Astronomik.
• Baader.
• Chroma.
• Selected models of Canon, Nikon and Pentax DSLRs.
• A generic Sony color image sensor with three options (sensitivity from UV to IR, with UV-cut filter and with UV and IR-cut filter).
• Astronomical standard photometric filter sets: Johnson UBVRI and Sloan u'g'r'i'z'.

As you can see, most filter sets are split in the three drop–down lists. This is because most of the filters can be assigned only to one primary color. For example, there is no sense in assigning the Baader G filter to the R channel, so the Baader G filter only appears in the Green filter drop–down list. This limitation does not exist for photometric Johnson and Sloan filters since their passbands range from ultraviolet to infrared and are not exactly matched to the RGB visual regions.

In case you're using a monochrome camera, you can also select the sensitivity curve of your sensor in the QE curve parameter. Here we have a selection of curves for some of the most widely used sensors. By default, this parameter is set to Ideal QE curve, which assumes that the camera is equally sensitive to all wavelengths. By selecting the sensitivity curve of your camera, you'll get a more accurate color calibration, but this is not a decisive parameter—or in other words, by not setting your QE curve, you're not going to ruin your color calibration, in general.

If using a color camera, please set QE curve to Ideal QE curve since the filter curves of color sensors have the sensor QE implicitly included.

It could happen that neither your filter set nor your QE curve is listed in SPCC's default filter and QE curve sets. Even in this case, we recommend using SPCC over PCC, since by selecting an ideal QE curve and similar filters to yours it will calibrate your color image with much less uncertainty than PCC using the APASS catalog. Furthermore, by using SPCC and the Gaia catalog, you can be sure that the color of your image is not subject to existing local color shifts in the APASS catalog.

You can always select a QE curve and a filter set similar to the ones you have used to acquire the image. To know how those curves are, you can use the Curve Explorer dialog:

Here you will see the list of filters and camera sensitivity curves:

We can select any element in the list to visualize its curve. We can also select multiple elements in the list with the Control (Cmd in macOS) or Shift keys. For instance, in the figure below, we choose to visualize the Baader RGB set:

If we move the mouse over the graph, we'll get the wavelength and curve readouts:

The same applies to the camera sensitivity curves (or quantum efficiency curves), which are marked with a Q in the first column of the list:

By analyzing these curves, it's easy to decide which ones are the most similar to the equipment we're using. But we can also import our own filters by using the Filter Management dialog.

The narrowband working mode in PCC has been discontinued since the narrowband emission lines can be calculated with much more accuracy in SPCC. This is because SPCC calculates the brightness of each measured star exclusively within the small interval of wavelengths transmitted by narrowband filters. Thus, we no longer need to rely on imprecise star brightness comparisons between broad and narrowband filters.

The most common case is an image where we assign the H-alpha filter to the red channel and the [O III] to the green and blue channels (HOO composition). In this case, the first step is to create a color image with ChannelCombination by assigning each narrowband master image to its corresponding color channel:

To calibrate the color of this image, we enable the Narrowband filters mode option in SPCC. Then, we should fill the filter data: center wavelength and bandwidth. By default, this is set to H-alpha wavelength in R and [O III] wavelength in G and B, all three filters being 3 nm wide.

Since we want an image where the intensity of the nebula in the different filters corresponds to the actual proportions between the emission lines, the white reference in this mode should be set to Photon Flux. Below you can see some examples.

In some cases, the difference from the original image can be subtle. Still, the critical point here is that we know that the proportion between the emission lines in the processed image corresponds to reality. This is a main goal by itself, but we can also use it as a starting point to modify the color palette. For instance, in the WR134 image, we can vary the balance between G and B in [O III] to give this emission line a different hue. If we multiply the G channel by 0.6666 and the B channel by 1.3333, we'll shift the [O III] emission towards the blue since it will be twice more intense in this channel:

Then, if we want to uncover the delicate [O III] emission from inside the strong H-alpha emission, we can multiply [O III] by a factor of 2 by multiplying it in the G and B channels with PixelMath:

Since SPCC gave us a precise starting point, we can now say that the color mapping of this image has been done by placing the H-alpha in the red channel and the [O III] in green and blue with a proportion of 1:2, then enhancing the [O III] component by a factor of 2 with respect to H-alpha.

Remember that all these steps will require a final background neutralization; we can use the same preview we configured in SPCC for this task. This is the final image before and after the background neutralization process:

It is important to point out that a Hubble's palette configuration in SPCC will always give a poorly optimized color rendition. To apply this palette, we first create a color image with ChannelCombination. We assign the S-II image to the red channel, H-alpha to green, and [O III] to blue:

This is the result of applying SPCC to an SHO version of the Rosetta nebula picture:

The result will always look similar when using SPCC for this application. This happens because the S-II emission line is usually much weaker than the H-alpha and [O III] ones. To achieve a good Hubble's palette representation, we recommend using the ColorCalibration tool instead:

In ColorCalibration, we use the entire nebula as the white reference because we want to balance the intensity between the three emission lines. Note that the Structure detection checkbox has been disabled to sum all the light inside the preview; if we leave it checked, ColorCalibration will balance the color of small structures, that is, the stars, which is not what we want in this case.

Below you have two comparisons between SPCC and ColorCalibration results for SHO compositions:

Note that this is not a limitation of SPCC but a limitation imposed by the nature of the objects, requiring a different use of our color calibration tools.

In the PixInsight Development Team, we do think that the artwork of astrophotography is based on the unification of the inner pictorial content of the image with the documentary content of the scene. This defines the aesthetics of astrophotography, which lies at the point where beauty meets authenticity.^[33]

At this point lies SPCC, whose goal is to materialize the above philosophy in the work of art. The color calibration process provides a documentary value to the picture that cannot be undervalued, invalidated, or manipulated in the subsequent operations we apply to the image. This includes arbitrary manipulation of individual hues, incorrect use of the delinearization processes, arbitrary use of the RGB curves, or applying any color transformation process without having a rational documentary argument at its roots. Color calibration gives color meaning by itself in the picture; hence, we should preserve it up to the end of the creative process.

A few processes that can break the meaning of color in the image are:

• A histogram transformation that changes each color channel separately.
• A curves transformation that changes each RGB channel separately.
• A curves transformation that changes the hue curve to arbitrarly modify the hues in the image.
• A curve applied through ColorSaturation to selectively enhance specific hues.
• SCNR applied to remove green tones from the image.

When we designed the PCC tool, we thought it was a temporary solution for the color calibration task. At that moment, PixInsight had only color calibration techniques that were intrinsic to the image, in the sense that it was required to select the white reference inside the image. PCC provided us with the first extrinsic color referencing, and more importantly, it used the first photometric catalog built with modern imaging techniques: the APASS catalog. Moreover, one of the primary goals in the design of the AperturePhotometry script was to provide PixInsight with the ability to perform photometric measurements of the stars, which was absolutely lacking in the platform then. For these reasons, both the AperturePhotometry script and the PCC tool were the perfect test workbench to demonstrate that photometry, along with modern star catalogs, would be the needed platform to allow us to materialize our new philosophy of color: the definition of a new astrophotography color referencing standard based on a spiral galaxy instead of the sunlight. This, obviously, can only be done through star color measurements with photometry, since you cannot have a face–on spiral galaxy in every image.

The success of the implementation of SPCC is due to two decisive features of the PixInsight platform. First is the adequate use of the gigantic database that allows us to access 80 billion data in milliseconds. Second, the new hybrid photometric engine (the same that has been implemented in the LocalNormalization tool) outperforms the capabilities of the AperturePhotometry script in both precision and resource optimization. Both PCC and SPCC run now much faster and more accurately.

PCC was a temporary solution for us because we were waiting for the release of the Gaia spectrophotometric catalog. We knew this catalog would be the definitive solution for our needs. Now, PCC and APASS will be deprecated in most use cases, and we do think SPCC will be the flexible, precise and accurate tool we'll need in the upcoming years. Therefore, SPCC represents the culmination of nearly ten years of work.

Gaia DR3

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

GaiaXPy

This job has made use of the Python package GaiaXPy (https://gaia-dpci.github.io/GaiaXPy-website/), developed and maintained by members of the Gaia Data Processing and Analysis Consortium (DPAC), and in particular, Coordination Unit 5 (CU5), and the Data Processing Centre located at the Institute of Astronomy, Cambridge, UK (DPCI).

[1] AAVSO website: APASS: The AAVSO Photometric All–Sky Survey

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[3] ESA website: the Gaia Archive at ESA

[4] Gaia Data Release 3 Documentation: 5.3.6 Catalogue of BP/RP spectra in Gaia DR3

[5] Gaia Collaboration, A. Vallenari, A. G. A. Brown, et al (2022k). Gaia Data Release 3: Summary of the content and survey properties. arXiv e-prints, pp. arXiv:2208.00211.

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[12] Strasbourg Astronomical Data Center website: The VizieR Catalogue Service

[13] J. Conejero (2017). XISF Version 1.0 Specification

[14] PCL documentation: Star Catalogs and Point Source Databases

[15] Wikipedia article: Levenberg–Marquardt algorithm

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[29] Wikipedia article: Comma-separated values

[30] PixInsight Official YouTube channel: Introduction to PixInsight — 08 ScreenTransferFunction (Part 3)

[31] PixInsight Official YouTube channel: Introduction to PixInsight — 10 Process Windows (Part 1)

[32] Vicent Peris (2020). Fotografiar lo invisible. La estética de la astrofotografía. El arte naturalista en el siglo XXI., p. 175

[33] Vicent Peris (2020). Fotografiar lo invisible. La estética de la astrofotografía. El arte naturalista en el siglo XXI., p. 201