provides a comparison between NISP photometry and PS1 data. In this region,
extinction plays a more significant role with typical values around
$E(B-V)=0.15$ mag, exhibiting spatial variability by approximately a factor of
1.8 across the field (Marleau et al. 2024). Furthermore, the extinction varies
with distance for stars within the Galactic disc. This contributes to
dispersion but mostly at the red end of the stellar colour distribution, which
we avoid in the calibration procedure. The most significant effect is seen for
$H_{\scriptscriptstyle\rm E}$, where an increase of the adopted $A_{V}$ by 0.1
mag decreases the offset between predicted and observed
$I_{\scriptscriptstyle\rm E}$ by 0.011 mag. With $A_{V}=3.1E(B-V)=0.45$ mag,
the average deviation between predicted and observed magnitudes in Perseus is
negligible for $Y_{\scriptscriptstyle\rm E}$, and approximately $+0.1$ mag for
$J_{\scriptscriptstyle\rm E}$ and $H_{\scriptscriptstyle\rm E}$. This analysis
was supplemented with a consistency check using galaxy magnitudes, converted
to $H_{\scriptscriptstyle\rm E}$ from the 2MASS galaxy catalogue, yielding
similar discrepancies. Because the average offset values were finalised after
the images for first ERO data-release were frozen for science production and
distribution as part of the first ERO data release presented in this paper,
the photometric zero points in those first-release NISP image FITS keywords
are not updated;888All the ERO teams were informed, however. we recommend to
subtract 0.1 mag from the header ZPs of the $J_{\scriptscriptstyle\rm E}$ and
$H_{\scriptscriptstyle\rm E}$ stacked images, and to subtract 0.1 mag to all
$J_{\scriptscriptstyle\rm E}$ and $H_{\scriptscriptstyle\rm E}$ magnitudes in
the ERO catalogues delivered with this first release. The next ERO public data
release will integrate this adjustment. For consistency in the first ERO
public data release, Table 2 summaries the dataset’s general properties,
listing the zero points as found in the FITS headers and adopted for catalog
production.

Table 1: Aperture-magnitude corrections for the ERO catalogues. These values should be applied to the catalogue entries for the relevant MAG_APER (from the second to the tenth listed here, with the first not being relevant). Catalogue aperture | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
---|---|---|---|---|---|---|---|---|---
Aperture diameter [arcsec] | 2.0 | 0.3 | 0.6 | 1.2 | 2.4 | 4.8 | 9.6 | 5.85 | 8
VIS diameter [pixels | 20 | 3 | 6 | 12 | 24 | 48 | 96 | 58.5 | 80
NISP diameter [pixels] | 6.7 | 1 | 2 | 4 | 8 | 16 | 32 | 19.5 | 26.7
$I_{\scriptscriptstyle\rm E}$ offset | $-0.039$ | $-0.604$ | $-0.265$ | $-0.120$ | $-0.062$ | $-0.034$ | $-0.017$ | $-0.013$ | $-0.009$
$Y_{\scriptscriptstyle\rm E}$ offset | $-0.050$ | $-1.748$ | $-0.418$ | $-0.130$ | $-0.076$ | $-0.043$ | $-0.025$ | $-0.021$ | $-0.016$
$J_{\scriptscriptstyle\rm E}$ offset | $-0.062$ | $-1.827$ | $-0.520$ | $-0.167$ | $-0.098$ | $-0.053$ | $-0.030$ | $-0.025$ | $-0.019$
$H_{\scriptscriptstyle\rm E}$ offset | $-0.070$ | $-1.962$ | $-0.653$ | $-0.249$ | $-0.120$ | $-0.059$ | $-0.032$ | $-0.027$ | $-0.020$

Overall, the derived ZPs align closely with pre-launch expectations, showing
variations within approximately 0.1 mag across different ERO projects. Such
variations are entirely plausible, considering that the ERO pipeline has not
yet undergone nonlinearity calibration or photometric flat-fielding
adjustments. Furthermore, the absolute quantum efficiency of the NISP
detectors carries an uncertainty of about 5%, due to an entanglement with the
detector gain (Waczynski et al. 2016; Secroun et al. 2018) among other
factors. Finally, the definition of the total stellar flux, encoded in
aperture corrections, may differ between surveys. Subsequent analysis of
photometry in the three NISP bands within the ERO data framework did not
uncover any significant inconsistencies in this calibration, staying within
the broader uncertainties inherent to the ERO pipeline process.

In summary, the uncertainty of the absolute flux calibration of the VIS data
after calibration against Gaia fluxes, is better than 1% on average, with
residual trends versus colour and brightness with joint amplitude of the order
of 10%. In NISP, the absolute calibration is limited to about 10% by the
stronger model-dependence of the colour-transformations to reference data, and
a limited calibration set in the early months of observations.

##  8 Compact source catalogues and general performance of the ERO data set

###  8.1 PSF modelling

For photometric analyses, a PSF model is essential for each image stack. The
PSF model is computed using PSFEx that employs a super-resolution algorithm
along with a simple regularisation scheme to map the PSF at sub-pixel
resolution. To minimise the contribution from spurious Nyquist modes, we
choose a PSF sampling step of 0.45 pixels.

The Euclid PSF shows remarkable homogeneity across the FoV, aligning with the
stringent requirements set for the instrument. A second-degree polynomial
adequately captures the PSF’s subtle variations across the entire image. As
anticipated, the precision of the PSF models derived from the stacks is
limited by aliasing and image resampling, with these effects being
particularly pronounced in the NISP data.

Despite these challenges, the typical $\chi^{2}$ per degree-of-freedom value
for PSF models fitted on bright point sources in VIS stacks remains at a
reasonable level of 1.7. However, for the NISP stacks, this value escalates to
around 10, indicating a higher level of deviation from the ideal PSF model,
primarily due to undersampling.

Table 2: General median properties of the 17 Euclid ERO fields, with a 0.60 deg2 sky coverage for single ROS observations. Table 5 and Table 6 list all properties per ERO field. All magnitudes are instrumental and in the AB system. The range of the sky background reflects the ecliptic latitudes covered across the ERO fields. Band | $I_{\scriptscriptstyle\rm E}$ | $Y_{\scriptscriptstyle\rm E}$ | $J_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$ | Unit / note
---|---|---|---|---|---
FWHM | 0.157 | 0.477 | 0.486 | 0.492 | arcsec
FWHM | 1.57 | 1.59 | 1.62 | 1.64 | pixel
Pixel sampling | 0.1 | 0.3 | 0.3 | 0.3 | arcsec pixel-1
Depth 5 $\sigma$ stars | 27.12 | 24.45 | 24.60 | 24.52 | mag (PSF or aperture photometry)
Depth 10 $\sigma$ galaxies | 25.29 | 22.97 | 23.22 | 23.31 | mag (Kron magnitude)
Limiting surface brightness | 29.9 | 28.2 | 28.4 | 28.4 | mag arcsec-2, $$$\times$$$ scale at 1 $\sigma$
Sky background | 22.3 | 22.1 | 22.2 | 22.3 | mag arcsec-2, range: [-0.5, +0.5]
Photometric zero point | 30.13 | 30.0 | 30.0 | 30.0 | mag, ADU (first ERO public data release)
Astrometry (internal) | 5.1 | 14.9 | 14.9 | 14.9 | mas
Saturation | 20 900 | 141 000 | 107 000 | 111 000 | ADU
Total number of sources | 11 359 274 | 5 257 808 | 5 257 808 | 5 257 808 | All EROs (common detection on NISP)

###  8.2 Production of the science validation catalogues

Rich photometric catalogues were produced using SourceExtractor on both the
VIS and NISP compact-sources stacks, utilising inputs such as PSFs derived by
PSFex, the weight maps, the NISP ${\chi}^{2}$ detection image created by
SWarp, and the updated photometric ZPs as previously described. Source
extraction for the VIS $I_{\scriptscriptstyle\rm E}$-band catalogue was
performed in stand-alone mode, benefiting from its higher depth and
resolution. The deep nominal detection image produced by combining the three
NISP bands led to a uniform source extraction approach across all three bands
and a consistent segmentation map from the three SourceExtractor runs for NISP
for a given field. The ERO collection primarily includes 34 stacks and 17
weight maps and catalogues for VIS, together with 102 stacks and 51 weight
maps and catalogues for NISP.

The ERO catalogues include model-fitting measurements (e.g. SourceExtractor’s
MODEL / SPHEROID / DISK / POINTSOURCE), totalling 163 requested parameters,
with several generating multiple columns in the photometric catalogue.
Consequently, the ERO science-validation catalogues feature a total of 363
parameters per identified source. Table 7 in Appendix E lists all input
parameters along with their descriptions and units.

SourceExtractor was configured with a detection and analysis threshold of
$1.5\,\sigma$, bringing a comprehensive census of compact sources (stars and
galaxies) within the images. The internal background subtraction utilised a
mesh size of $None$, mirroring the precise setting employed by SWarp for the
stacks. The catalogues provide a series of 10 aperture photometry measurements
(MAG_APER). For VIS ($None$ pixel-1) the diameters of the apertures in pixels
are 20, 3, 6, 12, 24, 48, 96, 58.5, and 80, spanning from the 2nd to the 10th
aperture. For NISP, these pixel values are adjusted due to the different pixel
scale of $None$ pixel-1. The initial aperture should be disregarded because it
was an exploratory measure based on FWHM that did not yield useful insights.
The 9th and 10th apertures align with certain apertures used in the DES
official products ($None$, and $None$). The magnitude offsets that must be
applied to the catalogues for each aperture to obtain the total magnitude are
detailed per Euclid band in Table 1, stemming from an analysis of encircled
energy in the PSF discussed later in Sect. 9.2.

While individual ERO teams typically developed photometric catalogues tailored
to their specific scientific objectives, a collaborative effort among the six
teams resulted in the establishment of a general format designed primarily for
compact-sources science. These catalogues are both comprehensive and
versatile, facilitating a wide spectrum of scientific research. Accompanying
the stack images, these catalogues represent a crucial component of the ERO
public data release, enabling diverse astronomical studies.

These catalogues also served to assess the performance attained in each ERO
field as outlined in Table 6, leading to their designation as science-
validation catalogues. To reproduce and verify the work, miscellaneous
configuration files and derived data products from the AstrOmatic tools
(PSFex, SourceExtractor) used to produce the components of the final
catalogues are provided as well. Among these data products is the segmentation
map generated by SourceExtractor, offering a comprehensive suite of resources
for in-depth analysis and validation of the ERO data-processing methodology.

In the first ERO data release, there is no catalogue specifically dedicated to
the photometry of extended sources (extension larger than $None$). The
creation of such a catalogue, based on the extended-emission stacks, is
scheduled for inclusion in the next ERO public data release.

###  8.3 Performance summary of the ERO data set

We used generic depth metrics widely adopted in the field to reflect the
performance of the ERO for compact sources based on the science-validation
catalogues. The Kron magnitude, MAG_AUTO, by SourceExtractor is a robust
estimator for the total magnitude of extended sources. To ensure the estimated
depth is based exclusively on galaxies, a strict CLASS_STAR value of 0.65 was
used for the star-galaxy separation criteria by SourceExtractor. We adopted a
10 $\sigma$ detection limit above the background noise to derive meaningful
physical parameters. For point sources, we first investigated PSF photometry
for both VIS and NISP, exploiting the PSF produced by PSFex in
SourceExtractor. The superior resolution of VIS leads to a clear separation of
compact sources and galaxies, without the use of the CLASS_STAR criteria, and
the depth is derived at the 5 $\sigma$ level for solid detection and
meaningful photometric measurement. This metric is not adequate for NISP due
to the coarse sampling, which does not allow for an effective separation of
stars and galaxies (even with CLASS_STAR $>0.9$). Instead, for robustness, we
adopted a large photometric aperture of $None$ diameter (4 pixels) and derived
the depth on the deepest edge of the population, ensuring we are probing only
the point sources. Figure 22 illustrates these depth metrics adopted for
galaxies and point sources. The LSB metric and performance of the ERO data set
is described in Sect. 9.3. Tables 5 and 6 in Appendix B detail the essential
characteristics of each ERO field, with Table 2 summarising the principal
attributes (sky coverage, etc.) and performance metrics across all 17 fields.

##  9 Performance for extended emission science

###  9.1 The Euclid optical design and the ERO extended-emission science

The selection of Euclid’s Korsch optical design (Korsch 1977; Bougoin et al.
2018) was motivated by the goal of achieving an optimal PSF for the primary
gravitational lensing probe, focusing on maximising the energy concentration
within the PSF’s core across a broad FoV. This optical design is instrumental
in addressing spherical aberration, coma, astigmatism, and field curvature,
and supporting a wide FoV while reducing stray light. The effective
minimisation of scattered light – a direct result of the optical design
complemented by advanced baffling on the instrument platform (Gaspar Venancio
et al. 2016) – underscores the spacecraft and its instruments’ exceptional
capability to investigate the LSB Universe. While this potential was not
initially anticipated in Euclid’s science objectives, subsequent modelling and
simulations have highlighted its significance (Euclid Collaboration:
Scaramella et al. 2022; Euclid Collaboration: Borlaff et al. 2022). The in-
flight science performance concerning the detection of extended emission is
assessed in this section through detailed analysis of real data from ERO
projects that aim to explore Euclid’s capabilities for LSB science in
particular to their fullest extent (Atek et al. 2024; Cuillandre et al. 2024;
Hunt et al. 2024; Kluge et al. 2024; Marleau et al. 2024; Saifollahi et al.
2024).

The critical factor in assessing a telescope’s ability to investigate ultra-
faint extended emission, or faint contrasts against a noisy background, is the
characterisation of its extended PSF, as discussed in various works by Mihos
et al. (2005), Abraham & van Dokkum (2014), Sandin (2014), Watkins et al.
(2016), Infante-Sainz et al. (2020), and Liu et al. (2022). The extended PSF
quantifies the distribution of energy within the PSF’s wings with respect to
its core, often detectable up to tens of arcminutes away. The relevance to LSB
science is clear: a PSF with significant energy in its extended wings,
manifesting as diffuse light, will inherently compromise the telescope’s
capability to discern genuine signals of this nature. This section is
dedicated to validating the premise that, for LSB science at its limits,
Euclid data require no correction for the extended PSF for VIS and NISP.

Figure 23: HD 1973, a 5th magnitude star in the $H_{\scriptscriptstyle\rm
E}$-band ($I_{\scriptscriptstyle\rm E}=6.3,Y_{\scriptscriptstyle\rm
E}=5.5,J_{\scriptscriptstyle\rm E}=5.3,H_{\scriptscriptstyle\rm E}=4.9)$, is
featured on a deep (3 ROS) ERO stack in the $I_{\scriptscriptstyle\rm E}$-band
(left) and the $H_{\scriptscriptstyle\rm E}$-band (right) within a
$$$\times$$$ field. The extended halo of VIS (left) concludes smoothly,
exhibiting no detectable signal beyond a $None$ radius. Conversely, the NISP
extended halo (right) terminates more abruptly – a characteristic of its
refractive optics – yet also without a detectable signal past a $None$ radius.
The diffraction spikes for VIS extend outward to approximately $None$, whereas
for NISP in $H_{\scriptscriptstyle\rm E}$-band they reach out to about $None$.
The gradient observed in the background of the VIS image is attributed to a
true LSB signal from Galactic cirrus intersecting the line of sight,
demonstrating Euclid’s exceptional ability to discern faint contrasts at high
S/N across a broad field.  Figure 24: Radial profile of HD 1973 on a deep (3
ROS) ERO stack in the $I_{\scriptscriptstyle\rm E}$-band (top) and the
$Y_{\scriptscriptstyle\rm E}$-band (bottom) reveals distinct characteristics
of the VIS and NISP instruments. For VIS, the extended halo concludes at a
radius of $None$, with AutoProf not detecting any signal beyond this point. In
contrast, the NISP extended halo exhibits a notable excess of light at a
radius of $None$, indicative of its refractive optics (this feature is
observable as a distinct arc in Fig. 23), and terminates shortly thereafter at
a radius of $None$. Cyan and red points refer to the colours of isophotes in
an associated AutoProf visual, which help guide the eye when comparing plots.

###  9.2 The observational Euclid extended PSF

####  9.2.1 Encompassed energy of the Euclid extended PSF

In analysing the extended PSF within the ERO data to estimate encircled energy
up to a certain radius, we focused on the brightest star in the ERO fields, HD
1973 (V∗BP Phoenicis, with AB magnitudes of 5.1 and 4.7 in the 2MASS $J$ and
$H$ bands, see Fig. 23) near Abell 2764 (Atek et al. 2024). This star shows a
prominent extended halo and distinct diffraction spikes that extend to large
radii. Utilising AutoProf, a tool originally designed for galaxies, we
conducted isophotal photometry on the PSF halo to obtain radial profiles in
all four bands. By enforcing circular isophotes, we were able to extract a
reliable signal up to $None$ for VIS and $None$ for NISP, ceasing at a surface
brightness of 28.5 mag arcsec-2 for VIS and 30.0 mag arcsec-2 for NISP.
Despite the star’s luminosity and the observation’s depth (three times the
standard Euclid depth), we could not identify any signal beyond these extents
and concluded we did reach the full extent of the extended PSF. HD 1973
approaches a magnitude close to Euclid’s threshold for avoiding such
observations (4 AB mag in each band, see Euclid Collaboration: Scaramella et
al. 2022), an indication that the telescope will have rare encounters with
such stars in the EWS during its mission: the EWS is composed of 27 571
pointings, with only 293 of them (1%) featuring a star
$I_{\scriptscriptstyle\rm E}<5$, and 1350 (5%) with a star
$H_{\scriptscriptstyle\rm E}<5$.

Figure 25: Left panel: We analysed radial profiles of stars of varying
brightness, clipping the radius range to balance their contribution against
the high-quality radial profile of HD 1973 (shown in green, upper right) and
the high-S/N PSFex radial profile at the PSF core based on thousands of bright
unsaturated stars (depicted in red, lower left). This approach ensured that
the aggregate profile leverages both the detailed observation of a singularly
bright star and the precision afforded by PSFex in the PSF’s core regions.
Middle panel: The optimisation step involved aligning all profiles to achieve
coherence across the data set. This optimisation process is critical for
synthesising a unified radial profile from the disparate data points provided
by stars of different magnitudes and the detailed profiles of HD 1973 and the
PSF core. Right panel: The final VIS extended PSF, with the profile normalised
to a base surface brightness of $\mu_{0}=0$ (corresponding in that case to a
$I_{\scriptscriptstyle\rm E}=3.1$ mag star). This standardised profile serves
as a comprehensive model of the VIS PSF’s behaviour across a wide range of
radii.

This star alone would be sufficient to characterise the extended PSF, except
that the detector saturates in the brightest central regions of the stellar
image (top left of the two profiles of Fig. 24). This information is needed to
anchor the energy found in the extended halo to the energy found in the core
of the PSF (Infante-Sainz et al. 2020; Liu et al. 2022). To extend the PSF
brightness profile into the inner regions, as illustrated in Fig. 25, we
extracted from single non-resampled frames a number of intermediate-brightness
saturated stars, and some unsaturated stars, again using AutoProf to determine
the profile of the PSF halo. For each profile (23 in total in each band) we
manually determined the region in which the profile was robust by identifying
clear features of saturation (a flattened profile in the inner regions) and
the noise limit in the outskirts (that is high variance surface-brightness
measurements).

For the key inner few pixels, we produced a pixel map with PSFex at 10$\times$
the native resolution, then converted to a radial profile using AutoProf.
PSFex builds a complex polynomial model of the PSF through the analyses of
thousands of bright unsaturated stars across a single non-resampled frame
here, and captures key features of the Airy disc in all four bands in the ERO
data.

This strategy averages out from the core out to a radius of $None$ possible
second-order effects related to our broad filters versus various spectral
types of stars. All of the profiles for the $I_{\scriptscriptstyle\rm E}$-band
can be seen in the left panel of Fig. 25 where the stars have not yet been
shifted from their original extraction. Using each profile only in the region
where it was most robust, we performed an optimisation to rescale each profile
until it aligned with the profile in star HD 1973. An example of this
alignment for the $I_{\scriptscriptstyle\rm E}$-band can be seen in the middle
panel of Fig. 25 where all the profiles are now aligned. We note that some
profiles have no overlap with star HD 1973, however by simultaneously aligning
all the profiles we could bridge the gap from $None$ down to the sub-pixel
level at the very core of the PSF. As a final step, we produced a collapsed
profile which was the median of all profiles that contribute in a given
region. This can be seen for the $I_{\scriptscriptstyle\rm E}$-band in the
right panel of Fig. 25 which spans over four orders of magnitude in radius;
the profile is normalised to $\mu_{0}=0$ by convention.

With this extended PSF available for all Euclid bands as shown in Fig. 26, we
could then simply integrate the light to any radius and compare with the full
integral. We find exceptional light enclosure for Euclid, with the values
listed in Table 3 exceeding the original design specifications. VIS and NISP
exhibit similar performance with about 90% of the encircled energy within a
$None$ radius, 99% at $None$, and 100% at $None$. In Fig. 27 we compare our
results with our simulations described in Appendix D, extending to the PSF
core and verifying the accuracy of our data-based model. Given the basic
assumptions of our theoretical PSF model, including ideal optics without phase
variations or defects, this outcome underscores the effectiveness of Euclid’s
optical design and fabrication quality.

In Fig. 26 simulations extending to larger radii are represented in blue.
Across all four bands, there is a deviation from the extended wings of the
Bessel-function characteristic of the Airy disc ($r^{-3}$ slope) at large
radius, with our simulation assuming an ideal circular pupil. Nevertheless,
the slope measured from ERO data shows only a minor divergence from this ideal
case of a pure diffraction halo and never reaches an $r^{-2.5}$ slope. Such a
slope would suggest a profile influenced by defects, dust, and various
aberrations at the millimetre scale on the primary mirror, as discussed by
Racine (1996). The observed dominance of optical diffraction over mirror
surface roughness underscores the excellence of the manufacturing process and
suggests that a negligible amount of particulates was deposited on the primary
mirror during launch.

The extended PSF does not exhibit any obvious effects from the thin nanometre-
scale layer of ice that accumulated on the optics near the VIS instrument
after launch due to outgassing (Euclid Collaboration: Schirmer et al. 2023).
Given that the VIS extended PSF contains less power in its halo compared to
NISP, as shown in Fig. 26, we hypothesise that a portion of the PSF flux is
uniformly extracted from the PSF and scattered isotropically, contributing to
the overall background in the instrument’s cavity.

Figure 26: Euclid’s extended PSF across the four bands is depicted with solid lines representing the stacked PSF, as detailed in Fig. 25, derived from ERO data. The $I_{\scriptscriptstyle\rm E}$-band is normalised to $\mu_{0}=0$, while the NISP $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands are visually separated by respective offsets of +5, +10, and +15 vertical units for clarity. The total magnitude of a star corresponding to each of the four profiles anchored at $\mu_{0}=0$ is $I_{\scriptscriptstyle\rm E}=3.1,Y_{\scriptscriptstyle\rm E}=1.6,J_{\scriptscriptstyle\rm E}=1.5$, and $H_{\scriptscriptstyle\rm E}=1.4$ (it takes a brighter star in NISP to reach the same $\mu_{0}=0$ as VIS, which concentrates more energy in the core of the PSF, while the longer the wavelength, the poorer it gets in the NIR). The simulation of the diffraction halo (Appendix D) is presented in pale blue, where the pale area represents the band-specific noisy computation profile and the dashed line indicates a second-order polynomial fit (an $r\,^{-3}$ power law). This fit is aligned with the PSF at $None$ radius. The extended PSF concludes at $None$ radius, and its average slope shows only slight deviation from the theoretical model of a pure diffraction halo. This consistency underscores the exceptional quality of the optics, which appear to be free from particulate contamination. The three NIR extended PSFs are similar (constant offset between the purple, red, and orange profiles), but clearly contain more energy at large radii than the VIS extended PSF (the artificial 5 mag offset between the green and orange lines here quickly diminishes with radius). We represent in grey the median behaviour of all best wide-field LSB observatories reviewed by Liu et al. (2022) with an $r\,^{-2.5}$ power law, shifted up to match our $\mu_{0}=0$, as originally done by Watkins et al. (2016). The specific extended $V$-band PSF of the Burrell Schmidt telescope is reproduced here (W16), as published in Watkins et al. (2016), limited to the range of this plot although it extends to a radius of $None$, ending at a surface brightness of 22.2 mag arcsec-2. This demonstrates that Euclid excels in minimising scattering of light, suppressing the extended wings better than the best ground-based optical telescopes by 8 magnitudes, and 6 magnitudes in the NIR, thereby opening a new observational window on the Universe.  Figure 27: Comparison of the encircled energy in the inner part ($<$$$) of the extended PSF between measured data and a simulation of perfect optics for all four Euclid bands. The near match at the core, based on a PSFex profile from our sky data, indicates our extended PSF accurately reflects expected performance. The slight disagreement between the simple, aberration-free model and the data at a radius below $None$ ($10^{0}$) most likely stems from low-order aberrations introduced by optics. These aberrations tend to slightly broaden the core but have little to no effect on the extended PSF. The observation that the model-to-data discrepancy decreases with increasing wavelength tends to support this hypothesis, as optical aberrations are more pronounced at shorter wavelengths. It should be noted that the disagreement appears more pronounced due to the use of a log-log plot.  Figure 28: Diffraction spikes of the star HD 1973 analysed through photometric extraction profiles at the bottom, juxtaposed with the star’s halo profile in a corresponding lighter shade (as illustrated in Fig. 26). This comparison highlights the pronounced dominance of spike brightness over the halo, becoming evident beyond a radius of a few arcseconds. Additionally, a simulation of the four spikes extending to a $None$ radius (with matching colours, and the $H_{\scriptscriptstyle\rm E}$-band arbitrarily set to $\mu_{0}=10$ for the purposes of this plot) corroborates the relative surface brightness of the spikes as observed across the four Euclid bands. Unlike the halo that adheres more closely to a 1/$r^{3}$ function consistent with the Bessel envelope at high radius, the spike profiles, as anticipated, approximate a 1/$r^{2}$ function.  Table 3: Measured encircled energy of the Euclid extended PSF as a function of radius from $None$ to $None$ (there is no further signal detection beyond), derived from the ERO data set. For context, the theoretical FWHM are $I_{\scriptscriptstyle\rm E}$ =$None$, $Y_{\scriptscriptstyle\rm E}$ =$None$, $J_{\scriptscriptstyle\rm E}$ =$None$, and $H_{\scriptscriptstyle\rm E}$ =$None$.  Radius [arcsec] | $I_{\scriptscriptstyle\rm E}$ | $Y_{\scriptscriptstyle\rm E}$ | $J_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$
---|---|---|---|---
0.1 | 0.36300 | 0.11880 | 0.11067 | 0.09818
0.2 | 0.66571 | 0.39405 | 0.35903 | 0.31939
0.3 | 0.78320 | 0.68071 | 0.61916 | 0.54811
0.4 | 0.85492 | 0.82898 | 0.76611 | 0.68006
0.5 | 0.87174 | 0.88110 | 0.84034 | 0.75903
1.0 | 0.93556 | 0.91891 | 0.89640 | 0.88333
1.5 | 0.95459 | 0.94315 | 0.93054 | 0.91843
2.0 | 0.96443 | 0.95475 | 0.94425 | 0.93760
4.0 | 0.98135 | 0.97364 | 0.96855 | 0.96615
8.0 | 0.99161 | 0.98566 | 0.98242 | 0.98175
16.0 | 0.99545 | 0.99258 | 0.99116 | 0.99091
32.0 | 0.99717 | 0.99601 | 0.99551 | 0.99566
64.0 | 0.99828 | 0.99783 | 0.99785 | 0.99786
120.0 | 0.99911 | 0.99898 | 0.99913 | 0.99905
240.0 | 0.99987 | 0.99983 | 0.99987 | 0.99982
280.0 | 0.99999 | 0.99997 | 0.99997 | 0.99994
310.0 | 1.00000 | 1.00000 | 1.00000 | 1.00000

####  9.2.2 Energy in the diffraction spikes

The PSF halo profiles, established through AutoProf employing median pixel
values along the isophotes,999Except for the PSFex sub-pixel stack for which
the mean was used. resulted in the initial analysis excluding the diffraction
spike profiles from the PSF. However, these spikes represent a significant
aspect of the PSF structure, and thus, the enclosed energy within the six
spikes necessitates estimation in comparison to that derived from our ideal
optical model. This step is crucial for a comprehensive understanding of the
PSF’s energy distribution and for ensuring the accuracy of our extended-PSF
model in reflecting the true performance of the optical system.

For our brightest star, HD 1973, we extracted all six spikes across each band,
subsequently rotating and median-stacking them to produce a single,
uncontaminated spike per band. This process ensured each spike was averaged
across its entire width ($None$ for all bands), culminating in the profiles
depicted in Fig. 28. The plot highlights the diffraction halo in lighter
shades, clearly showing that the spike profiles exceed the halo’s brightness
at large radii. Furthermore, it can be seen that the overall surface
brightness escalates with increasing wavelength. The data align closely with
our straightforward simulation (Appendix D), as illustrated in Fig. 28,
particularly in terms of the relative brightness among the four bands,
offering a vivid representation of the spike profiles’ luminance in comparison
to the halo.

Figure 29: Negligible impact of the extended PSF on physical parameters of
very extended sources. Left panels: On the top, an $I_{\scriptscriptstyle\rm
E}=14$ elliptical galaxy with a full extension less than that of the extended
PSF ($r=$$$), and at the bottom, an $I_{\scriptscriptstyle\rm E}=9$ galaxy
(NGC 1553) larger than the extended PSF – colour intensity is in logarithmic
scale on all four panels (-3.0 indicates a 10-3 ratio, or 0.1%). Right panels:
the relative variation of the flux redistribution after convolution with the
extended PSF is at the sub-percent level and does not impact the derived
physical properties such as their photometry or morphology.

We assessed the total flux present in the diffraction spikes of HD 1973
relative to its overall brightness in the Euclid bands. This evaluation was
facilitated by the extended PSF, which allows for accurate magnitude
estimation of any saturated star by aligning its profile outside the saturated
core. Our findings are in line with the initial simulation estimates: beyond a
$None$ radius, the combined total-light fraction in both the spikes and the
halo amounts to approximately 1.5% – averaging 1% for the halo and 0.5% for
the spikes across all four bands. However, there is a notable distinction in
their spatial distribution; the spikes are distinctly localised, whereas the
halo extends azimuthally, covering a substantially larger area. In fact, at a
$None$ radius, the halo encompasses about two orders of magnitude more light
than the spikes. Consequently, we opted not to incorporate the spike profiles
into our extended PSF model, given our aim for percent-level accuracy in the
results.

####  9.2.3 Consequence for the extended-emission science

Euclid boasts the most refined extended PSF ever achieved by a wide-field,
high-resolution imaging telescope. It sets a new benchmark far beyond past
endeavours aimed at optimising telescopes for LSB science, a leap of 8 mag in
minimising optical scattering of light in the optical while opening a whole
new observational window in the NIR with a comparable leap of 6 mag in
conjunction with the low background experienced at L2. See figure 8 of Liu et
al. (2022) review of the best optical LSB wide-field facilities around the
world for an illustration, and our Fig. 26 for a comparison.

Characterised by an exceptionally high energy concentration in the PSF’s core,
Euclid outperforms its predecessors and maintains this dominance within a
nearly pure diffraction-halo regime extending up to a radius of $None$,
marking the boundary of the extended PSF’s influence. This unparalleled
performance underscores Euclid’s revolutionary potential for astronomical
observations in the realm of LSB science from the optical to the NIR.

Science focused on diffuse emission suffers through two main consequences of
an extended PSF. First, bright stars in the FoV produce an accumulation of
extended and overlapping halos that cause a modulation of the sky brightness,
jeopardising the extraction of the LSB astronomical signal that gets lost in
that non-flatness noise. Second, bright extended objects contaminate their own
extended emission, for example a big elliptical galaxy biasing its radial
profile by pushing light from its core into its stellar halo.

####  9.2.4 Contamination by overlapping stellar halos

The ERO field Abell 2764 – featuring the $H_{\scriptscriptstyle\rm E}=5$ star
HD 1973 – presents a scenario that Euclid will seldom face during its
scientific mission. Despite its brightness, this star influences only about
0.022 deg2 (4%) of the 0.5 deg2 field through its extended diffusion halo. The
predominant background component is the zodiacal light that averages around
22.2 mag arcsec-2, and the influence of the extended halo drops below 1%
(equivalent to a 5 mag difference) at a radius of $None$, as illustrated in
Fig. 24.

To significantly affect the FoV at the 0.01% level at a radius of $None$
(which would be 1/100th of HD 1973’s impact, or 32 mag arcsec-2), one would
need nearly 50 stars of magnitude 9 evenly scattered throughout the FoV.
However, at worst across the entire EWS composed of 27 571 pointings, one
pointing (0.004%) features at most 15 stars of this class (VIS or NISP), while
on average across the EWS, the density of such stars amounts to just 2.8 per
Euclid FoV.

Taking a more realistic perspective, considering the VIS saturation limit at
magnitude 18.5 for long exposures and hypothesising the presence of one such
star per square arcminute, the 1% level of zodiacal-light background (27.2 mag
arcsec-2, a problematic level for LSB science) is attained within a radius of
approximately $None$, affecting merely 2% of a square arcminute. In even this
pessimistic scenario, the overall impact on the detection of extended emission
across scales of arcseconds and above, on average throughout the field,
remains minimal. This analysis underscores Euclid’s robustness in handling the
effects of bright stars on LSB science, facilitated by its advanced design.

Across the 17 ERO fields we encounter a range of stellar densities. Despite
this variability, no field contains a sufficient number of stars to
significantly impact the dominant zodiacal background. The noise in our
images, across all scales, is primarily driven by photon statistics.
Consequently, we deduce that our performance metric for assessing the LSB
capabilities of our data set should concentrate exclusively on the zodiacal
background’s brightness level. This approach remains applicable as long as the
data processing is finely tuned for LSB science, as exemplified by the ERO
pipeline. This optimisation ensures that the primary consideration in
evaluating our LSB performance is the zodiacal light contribution, rather than
the collective influence of stellar contributions and data processing
signatures.

####  9.2.5 Self-contamination of a stellar halo

A potential issue in LSB science involves extended objects potentially
contaminating their own signal (Slater et al. 2009; Karabal et al. 2017). This
concern is particularly relevant when analysing large galaxies within the ERO
science framework. However, due to Euclid’s exceptionally clean extended PSF,
no correction for energy redistribution is necessary. For instance, the
brightest surface-brightness levels ($\mu_{0}$) were measured for NGC 1549 and
NGC 1553 in the ERO Dorado field, reaching approximately 14.3 mag arcsec-2 in
the $I_{\scriptscriptstyle\rm E}$ band. When incorporating the extended PSF
(Fig. 26) at this brightness level, the self-contamination drops to around 30
mag arcsec-2 at a $None$ radius and to approximately 36 mag arcsec-2 at a
$None$ radius. The minor energy redistribution caused by the extended PSF does
not significantly impact ERO science. This is because most galaxies under
study exceed in size the 99.7% encircled energy diameter of $None$ for both
VIS and NISP, as detailed in Table 3. This is demonstrated in Fig. 29, where
the impact of the convolution on two extended galaxies (one smaller and one
larger than the extended PSF), leads to residuals at the sub-percent level.
Consequently, the physical properties of these galaxies remain accurate,
affirming that Euclid’s extended PSF allows for reliable LSB measurements
without the need for adjustments for self-contamination.

####  9.2.6 Contamination by Galactic cirrus

A notable consideration in assessing Euclid’s LSB detection capabilities is
that its actual limitation often stems from the interstellar medium foreground
also known as Galactic cirrus (Sandage 1976). This phenomenon is detectable
across all Galactic latitudes at present with optical wide-field cameras
(Miville-Deschênes et al. 2016; Román et al. 2020; Lim et al. 2023), with
brightness levels ranging between 26 and 28 mag arcsec-2. This factor is
especially pertinent in the context of the ERO Perseus cluster of galaxies,
where LSB performance is constrained by the non-uniformity of the background
attributed to Galactic cirrus, as noted in studies like Cuillandre et al.
(2024); Kluge et al. (2024). The pronounced visibility of such cirrus, even in
observations targeting HD 1973 (Fig. 23, left), underscores Euclid’s
exceptional ability to discern extremely low-contrast LSB features,
highlighting the challenge posed by the Galactic cirrus in accurately
quantifying faint extragalactic astronomical signals. It is noteworthy that
all 17 ERO fields showcased in Fig. 32 easily reveal a faint background of
Galactic cirrus even at high galactic latitudes.

Figure 30: This paper quantifies Euclid’s capacity to measure faint extended
emission in various ways. This capability is dramatically demonstrated through
an extreme case where LSB features on the largest spiral galaxy in the top
right corner are clearly visible, despite its proximity – just $None$ away –
from HD 1973 ($I_{\scriptscriptstyle\rm E}=6.3,Y_{\scriptscriptstyle\rm
E}=5.5,J_{\scriptscriptstyle\rm E}=5.3,H_{\scriptscriptstyle\rm E}=4.9)$. The
field size is $None$ by $None$. Faint galaxies are easily perceived within
tens of arcseconds from this M3II star that is nearly visible to the naked
eye: $R$=6.6 Vega magnitude, Pickles & Depagne (2010). This colour image was
created by combining VIS and NISP data (without subtraction of the extended
PSF model) using the $I_{\scriptscriptstyle\rm E}$-band for the blue,
$Y_{\scriptscriptstyle\rm E}$ for the green, and $H_{\scriptscriptstyle\rm E}$
for the red channel. The colour image at the NISP resolution is cast onto the
VIS channel through a LAB (luminance + colours) combination to showcase the
angular resolution and the sensitivity to LSB features. The oval structure at
the centre is the result of a dichroic ghost in VIS caused by HD 1973 which
appears yellow because the colour image is dominated at that distance from the
star by the NISP extended PSF (green+red = yellow).  Figure 31: Centre of the
Abell 2764 cluster. Extended emission in the form of shells and stellar
streams is traced in the NIR (colour image with $I_{\scriptscriptstyle\rm
E}$-band in blue, $Y_{\scriptscriptstyle\rm E}$ in green, and
$H_{\scriptscriptstyle\rm E}$ in red) down to $27.0$ mag arcsec-2 in the
$H_{\scriptscriptstyle\rm E}$-band for a direct visual detection of physical
features, such as a stellar stream, at 1 $\sigma$ at the single square
arcsecond scale. Structures within these faint features are well defined. The
field size is $None$ by $None$.

###  9.3 LSB performance of the ERO data set

In Table 6 we present the limiting surface brightness for each ERO field
across the four Euclid bands, defining the anticipated depth for LSB science.
This estimation is based on the assumption that the primary component of noise
is pure photon statistics from the zodiacal light background, a justification
rooted in the preceding discussions about the exceptional quality of the
Euclid extended PSF. We determine the LSB depth metric following the
methodology outlined in Euclid Collaboration: Scaramella et al. (2022),
adapting the LSB asinh metric introduced by Mihos et al. (2013) deriving from
the asinh metric for compact sources by Lupton et al. (1999), to more
accurately mirror the real science capabilities in LSB-optimised images. This
strategy aims to predict Euclid’s future performance in conducting LSB science
with the understanding that the noise budget would primarily consist of
photon-noise statistics from the zodiacal light. For a comprehensive
explanation of this 1 $\sigma$ asinh AB magnitude metric applied at the
$$$\times$$$ scale – used chiefly as a representative measure for various LSB
scientific analyses – we refer to section 5.3 of Euclid Collaboration:
Scaramella et al. (2022).

Adopting this metric, the ERO data set achieves depths of
$I_{\scriptscriptstyle\rm E}=29.9$, $Y_{\scriptscriptstyle\rm E}=28.2$,
$J_{\scriptscriptstyle\rm E}=28.4$, and $H_{\scriptscriptstyle\rm E}=28.4$ AB
mag arcsec-2, averaged across the 17 fields, aligning with predictions in
Euclid Collaboration: Scaramella et al. (2022). These depths illustrate the
capability to detect a 100 arcsec2 extended feature at the 1 $\sigma$ level
based solely on photon statistics from the background, given the ultra-low
impact of the extended PSF we have shown. The consistency in depth across our
collection is attributable to the ERO targets being located at ecliptic
latitudes comparable to those surveyed by the EWS, as depicted in Fig. 1. The
photometric catalogues from the first public release of the ERO data do not
feature automated photometry for extended sources (scale above $$$\times$$$).
This functionality is slated for inclusion in the subsequent public data
release, expanding the scope of scientific exploration enabled by Euclid.

As highlighted in the previous subsections, it is important to note that the
LSB performance achieved for each individual ERO field is considerably
influenced by the astronomical characteristics of the observed sky area, such
as the presence of Galactic cirrus, stellar density, and – in certain
instances – the density of large galaxies like in the ERO Perseus field. These
factors can substantially affect the ability to detect and analyse LSB
features. The ERO Perseus cluster serves as a vivid illustration of how depth
depends on the nature, scale, and analysis methods of specific astronomical
entities: (i) the faintest dwarf galaxies in the new ERO Perseus cluster
catalogue (Marleau et al. 2024) present a typical effective radius of $None$
and reach down to an average effective surface brightness of
$\langle\mu_{I_{\scriptscriptstyle\rm E},\rm{e}}\rangle=26.3$ mag arcsec-2,
and a surface brightness at the effective radius of
$\mu_{I_{\scriptscriptstyle\rm E},\rm{e}}=28.7$ mag arcsec-2, at a total S/N
within the effective radius high enough to enable derivation of physical
parameters (SNR$>12$, the performance being purely limited by background
photon statistics at this scale); (ii) intra-cluster light reaches down to
$\mu_{I_{\scriptscriptstyle\rm E}}=29.4$ mag arcsec-2 at an S/N of 1 by
integrating the signal over very large areas (Kluge et al. 2024); and (iii)
radial profiles of galaxies go down to $\mu_{I_{\scriptscriptstyle\rm
E}}=30.1$ mag arcsec-2 (Cuillandre et al. 2024) when integrating light at
increasing radii, by combining over 360 deg the signal of many 100 arcsec-2
areas, each at the S/N$\sim$2 level. The full suite of ERO papers related to
LSB science provides a deeper understanding of the challenges and successes
encountered in capturing and interpreting LSB phenomena within Euclid’s
observations. For comprehensive insights into the actual scientific
performance, we direct the reader to the first results of the ERO programme
(Atek et al. 2024; Hunt et al. 2024; Martín et al. 2024; Massari et al. 2024;
Saifollahi et al. 2024; Cuillandre et al. 2024; Kluge et al. 2024; Marleau et
al. 2024). To encapsulate the main points of this section, Figs. 30 and 31
demonstrate Euclid’s unique capacity to detect and measure LSB features from
the optical to the NIR.

##  10 Summary

We described the ERO programme, aimed at demonstrating Euclid’s capabilities
before its primary mission. It focuses on 17 unique astronomical targets and
employs a range of advanced technical methods to process these observations.
The scientific results obtained for the individual targets are presented in a
set of accompanying papers. Besides the overview of the ERO programme, the
present paper focuses on the specific data processing that prepared the images
for the individual ERO projects, and an evaluation of Euclid’s unique LSB
performance.

The ERO pipeline, crucial for creating data products for initial science
studies, emphasises preserving data quality. The FWHM of the PSF in the
advanced products (stacks) for the four Euclid channels shows a diffraction-
limited telescope with $None$ in the optical $I_{\scriptscriptstyle\rm
E}$-band, and $None$ in the NIR bands $Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ (Table 2).
The point-source and extended-source detection limits with the Euclid survey
nominal observing sequence match the pre-launch expectations of 25.3 and 23.2
AB mag with a S/N of 10 for galaxies, and 27.1 and 24.5 AB mag at an S/N of 5
for point sources for VIS and NISP, respectively.

The pipeline’s main tasks involve removing instrumental signatures,
calibrating astrometry and photometry, stacking images, and producing science-
ready catalogues. Detrending involves several steps specific to each
instrument to enhance image quality. For VIS, this includes using tools like
deepCR to remove cosmic rays and maintain accurate astrometry. Similar steps
are taken for NISP, including additional corrections of, for example, charge
persistence and row-correlated noise. The zodiacal-light background is the key
for both instruments to produce a flat-field enabling LSB science. Astrometric
calibration starts by establishing an initial framework using Astrometry.net
with Gaia-DR3, followed by refining global astrometry with SCAMP to address
geometric distortions. Calibration accuracy is high, with VIS achieving a
median internal precision of 6 mas RMS while NISP remains limited to 15 mas
RMS due to its coarser sampling of the PSF.

External catalogues were used to refine the photometric zero points by making
adjustments based on empirical data and synthetic photometry. VIS calibration
remains highly accurate, while NISP faces challenges due to model-dependent
colour transformations. Detailed per-detector analysis in the VIS mosaic
revealed statistically significant zero-point fluctuations, suggesting
variability within and across detectors. The uncertainty of the VIS absolute
flux calibration after tying it to Gaia averages better than 1%, with residual
colour and brightness trends up to 10%. For NISP, calibration accuracy is
capped at about 10% due to the model-dependent colour transformations and a
limited early calibration data set.

The resampling and stacking process involved merging exposures using SWarp,
producing two types of stacks: a background-removed stack for compact sources
and a stack for studying extended emission, choosing interpolating functions
like the Lanczos3 kernel for VIS and bilinear interpolation for NISP to
preserve data quality. PSF models were created using PSFex, however the
accuracy of these models is limited for NISP data by factors like aliasing.
The rich and detailed catalogues produced using SourceExtractor include
extensive data from both VIS and NISP, designed to support a broad range of
scientific studies.

This ERO effort revealed that Euclid boasts the best extended PSF ever
achieved by a wide-field, high-resolution imaging telescope, setting a new
benchmark that surpasses previous efforts to optimise telescopes for LSB
science. It represents a leap of 8 magnitudes of surface brightness of the
extended PSF halo in the optical range and opens in particular a new
observational window into the NIR LSB Universe, facilitated by the low
background experienced at L2. Such performance indicates that photometry of
extended sources can be measured with high precision across the entire FoV
without needing to deconvolve the image. Also, the background of the Euclid
images is dominated by photon noise across the entire image, confirming pre-
launch expectations, and reaching a surface brightness for the nominal
observing sequence of $I_{\scriptscriptstyle\rm E}=29.9$,
$Y_{\scriptscriptstyle\rm E}=28.2$, $J_{\scriptscriptstyle\rm E}=28.4$,
$H_{\scriptscriptstyle\rm E}=28.4$ AB mag arcsec-2 achieved in the ERO data
set for detecting a 100 arcsec2 extended feature at the 1 $\sigma$ level
(Table 2).

This first ERO data release includes science-ready source catalogues, with a
total of 11 million objects in the VIS, and more than 5 million common
detections in NISP, across the 17 ERO fields. While this paper highlights this
first release of the ERO data (stacks and catalogues) to the global scientific
community, future ERO data releases will address existing challenges, such as
photometry non-uniformity, improved stray-light correction, and introduce new
features like automated LSB photometry, and possibly include a curated
spectroscopy collection. This initial ERO release marks the beginning of a new
era of scientific discoveries as Euclid embarks on its main mission.

###### Acknowledgements.

This work has made use of the Early Release Observations (ERO) data from the
Euclid mission of the European Space Agency (ESA), 2024,
https://doi.org/10.57780/esa-qmocze3. The Euclid Consortium acknowledges the
European Space Agency and a number of agencies and institutes that have
supported the development of Euclid, in particular the Agenzia Spaziale
Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMK,
the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches
Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in
Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a
Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de
Ciencia, Innovación y Universidades, the National Aeronautics and Space
Administration, the National Astronomical Observatory of Japan, the
Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the
Research Council of Finland, the Romanian Space Agency, the State Secretariat
for Education, Research, and Innovation (SERI) at the Swiss Space Office
(SSO), and the United Kingdom Space Agency. A complete and detailed list is
available on the Euclid web site (http://www.euclid-ec.org). This work
presents results from the European Space Agency (ESA) space mission Gaia. Gaia
data are being processed by the Gaia Data Processing and Analysis Consortium
(DPAC). Funding for the DPAC is provided by national institutions, in
particular the institutions participating in the Gaia MultiLateral Agreement
(MLA). The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have
been made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST–1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.
This project used public archival data from the Dark Energy Survey (DES).
Funding for the DES Projects has been provided by the U.S. Department of
Energy, the U.S. National Science Foundation, the Ministry of Science and
Education of Spain, the Science and Technology FacilitiesCouncil of the United
Kingdom, the Higher Education Funding Council for England, the National Center
for Supercomputing Applications at the University of Illinois at Urbana-
Champaign, the Kavli Institute of Cosmological Physics at the University of
Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State
University, the Mitchell Institute for Fundamental Physics and Astronomy at
Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos
Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho
Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da
Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft, and the
Collaborating Institutions in the Dark Energy Survey. CS acknowledges the
support of the Natural Sciences and Engineering Research Council of Canada
(NSERC). Cette recherche a été financée par le Conseil de recherches en
sciences naturelles et en génie du Canada (CRSNG). CS also acknowledges
support from the Canadian Institute for Theoretical Astrophysics (CITA)
National Fellowship program.

## References

  * Abbott et al. (2021) Abbott, T. M. C., Adamów, M., Aguena, M., et al. 2021, ApJS, 255, 20
  * Abraham & van Dokkum (2014) Abraham, R. G. & van Dokkum, P. G. 2014, PASP, 126, 55
  * Antilogus et al. (2014) Antilogus, P., Astier, P., Doherty, P. E., Guyonnet, A., & Regnault, N. 2014, Journal of Instrumentation, 9, C03048
  * Atek et al. (2024) Atek, H., Gavazzi, R., Weaver, J., et al. 2024, A&A, this issue
  * Bertin (2006) Bertin, E. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 112
  * Bertin (2009) Bertin, E. 2009, Mem. Soc. Astron. Italiana, 80, 422
  * Bertin (2011) Bertin, E. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 442, Astronomical Data Analysis Software and Systems XX, ed. I. N. Evans, A. Accomazzi, D. J. Mink, & A. H. Rots, 435
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
  * Bertin et al. (2002) Bertin, E., Mellier, Y., Radovich, M., et al. 2002, in Astronomical Society of the Pacific Conference Series, Vol. 281, Astronomical Data Analysis Software and Systems XI, ed. D. A. Bohlender, D. Durand, & T. H. Handley, 228
  * Bertin et al. (2020) Bertin, E., Schefer, M., Apostolakos, N., et al. 2020, in Astronomical Society of the Pacific Conference Series, Vol. 527, Astronomical Data Analysis Software and Systems XXIX, ed. R. Pizzo, E. R. Deul, J. D. Mol, J. de Plaa, & H. Verkouter, 461
  * Biesiadzinski et al. (2011) Biesiadzinski, T., Lorenzon, W., Newman, R., et al. 2011, PASP, 123, 958
  * Boch et al. (2012) Boch, T., Pineau, F., & Derriere, S. 2012, in Astronomical Society of the Pacific Conference Series, Vol. 461, Astronomical Data Analysis Software and Systems XXI, ed. P. Ballester, D. Egret, & N. P. F. Lorente, 291
  * Born & Wolf (1999) Born, M. & Wolf, E. 1999, Principles of optics : electromagnetic theory of propagation, interference and diffraction of light
  * Bougoin et al. (2018) Bougoin, M., Mallet, F., Lavenac, J., et al. 2018, in SPIE Conference Series, Vol. 11180, International Conference on Space Optics—ICSO 2018, ed. Z. Sodnik, N. Karafolas, & B. Cugny, 111801P–2
  * Bouy et al. (2013) Bouy, H., Bertin, E., Moraux, E., et al. 2013, A&A, 554, A101
  * Carassou (2017) Carassou, S. 2017, PhD thesis, Université Pierre et Marie Curie - Paris VI
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Cuillandre et al. (2024) Cuillandre, J.-C., Bolzonella, M., Boselli, A., et al. 2024, A&A, this issue
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog, II/246
  * Czekaj (2012) Czekaj, M. A. 2012, PhD thesis. University of Barcelona, Spain. Galaxy evolution: A new version of the Besançon galaxy model constrained with Tycho data, https://ui.adsabs.harvard.edu/abs/2012PhDT…….467C
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168
  * Euclid Collaboration: Borlaff et al. (2022) Euclid Collaboration: Borlaff, A. S., Gómez-Alvarez, P., Altieri, B., et al. 2022, A&A, 657, A92
  * Euclid Collaboration: Cropper et al. (2024) Euclid Collaboration: Cropper, M., Al Bahlawan, A., Amiaux, J., et al. 2024, A&A, this issue
  * Euclid Collaboration: Jahnke et al. (2024) Euclid Collaboration: Jahnke, K., Gillard, W., Schirmer, M., et al. 2024, A&A, this issue
  * Euclid Collaboration: Mellier et al. (2024) Euclid Collaboration: Mellier, Y., Abdurro’uf, Acevedo Barroso, J., Achúcarro, A., et al. 2024, A&A, this issue
  * Euclid Collaboration: Scaramella et al. (2022) Euclid Collaboration: Scaramella, R., Amiaux, J., Mellier, Y., et al. 2022, A&A, 662, A112
  * Euclid Collaboration: Schirmer et al. (2022) Euclid Collaboration: Schirmer, M., Jahnke, K., Seidel, G., et al. 2022, A&A, 662, A92
  * Euclid Collaboration: Schirmer et al. (2023) Euclid Collaboration: Schirmer, M., Thürmer, K., Bras, B., et al. 2023, A&A, 675, A142
  * Euclid Collaboration: Serrano et al. (2024) Euclid Collaboration: Serrano, S., Hudelot, P., Seidel, G., et al. 2024, eprint, arXiv:2401.01452
  * Euclid Early Release Observations (2024) Euclid Early Release Observations. 2024, https://doi.org/10.57780/esa-qmocze3
  * Ferrarese et al. (2012) Ferrarese, L., Côté, P., Cuillandre, J.-C., et al. 2012, ApJS, 200, 4
  * Fruchter & Hook (2002) Fruchter, A. S. & Hook, R. N. 2002, PASP, 114, 144
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1
  * Gaspar Venancio et al. (2016) Gaspar Venancio, L. M., Pachot, C., Carminati, L., et al. 2016, in SPIE Conference Series, Vol. 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, ed. H. A. MacEwen, G. G. Fazio, M. Lystrup, N. Batalha, N. Siegler, & E. C. Tong, 99040P
  * Gruen et al. (2014) Gruen, D., Seitz, S., & Bernstein, G. M. 2014, PASP, 126, 158
  * Hunt et al. (2024) Hunt, L., Annibali, F., Cuillandre, J.-C., et al. 2024, A&A, this issue
  * Husser et al. (2013) Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6
  * Infante-Sainz et al. (2020) Infante-Sainz, R., Trujillo, I., & Román, J. 2020, MNRAS, 491, 5317
  * Kalirai et al. (2007) Kalirai, J. S., Anderson, J., Richer, H. B., et al. 2007, ApJ, 657, L93
  * Karabal et al. (2017) Karabal, E., Duc, P. A., Kuntschner, H., et al. 2017, A&A, 601, A86
  * Kluge (2020) Kluge, M. 2020, PhD thesis, Ludwig-Maximilians University of Munich, Germany
  * Kluge et al. (2024) Kluge, M., Hatch, N., Montes, M., et al. 2024, A&A, this issue
  * Korsch (1977) Korsch, D. 1977, Appl. Opt., 16, 2074
  * Lagarde et al. (2021) Lagarde, N., Reylé, C., Chiappini, C., et al. 2021, A&A, 654, A13
  * Lançon et al. (2021) Lançon, A., Gonneau, A., Verro, K., et al. 2021, A&A, 649, A97
  * Lang et al. (2010) Lang, D., Hogg, D. W., Mierle, K., Blanton, M., & Roweis, S. 2010, AJ, 139, 1782
  * Lastennet et al. (2002) Lastennet, E., Lejeune, T., Oblak, E., Westera, P., & Buser, R. 2002, Ap&SS, 280, 83
  * Laureijs et al. (2011) Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, eprint, arXiv:1110.3193
  * Le Graët et al. (2022) Le Graët, J., Secroun, A., Barbier, R., et al. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12191, X-Ray, Optical, and Infrared Detectors for Astronomy X, ed. A. D. Holland & J. Beletic, arXiv:2209.01831
  * Leinert et al. (1998) Leinert, C., Bowyer, S., Haikala, L. K., et al. 1998, A&AS, 127, 1
  * Lim et al. (2023) Lim, S., Hill, R., Scott, D., et al. 2023, MNRAS, 525, 1443
  * Liu et al. (2022) Liu, Q., Abraham, R., Gilhuly, C., et al. 2022, ApJ, 925, 219
  * Lupton et al. (1999) Lupton, R. H., Gunn, J. E., & Szalay, A. S. 1999, AJ, 118, 1406
  * Magnier & Cuillandre (2004) Magnier, E. A. & Cuillandre, J. C. 2004, PASP, 116, 449
  * Marleau et al. (2024) Marleau, F., Cuillandre, J.-C., Cantiello, M., et al. 2024, A&A, this issue
  * Marmo & Bertin (2008) Marmo, C. & Bertin, E. 2008, in Astronomical Society of the Pacific Conference Series, Vol. 394, Astronomical Data Analysis Software and Systems XVII, ed. R. W. Argyle, P. S. Bunclark, & J. R. Lewis, 619
  * Martín et al. (2024) Martín, E., Žerjal, M., Bouy, H., et al. 2024, A&A, this issue
  * Massari et al. (2024) Massari, D., Dalessandro, E., Erkal, D., et al. 2024, A&A, this issue
  * McLeod & Smith (2016) McLeod, B. A. & Smith, R. 2016, in SPIE Conference Series, Vol. 9915, High Energy, Optical, and Infrared Detectors for Astronomy VII, ed. A. D. Holland & J. Beletic, 99150G
  * Mihos et al. (2005) Mihos, J. C., Harding, P., Feldmeier, J., & Morrison, H. 2005, ApJ, 631, L41
  * Mihos et al. (2013) Mihos, J. C., Harding, P., Spengler, C. E., Rudick, C. S., & Feldmeier, J. J. 2013, ApJ, 762, 82
  * Miville-Deschênes et al. (2016) Miville-Deschênes, M. A., Duc, P. A., Marleau, F., et al. 2016, A&A, 593, A4
  * Oke & Gunn (1983) Oke, J. B. & Gunn, J. E. 1983, ApJ, 266, 713
  * Pickles & Depagne (2010) Pickles, A. & Depagne, É. 2010, PASP, 122, 1437
  * Pickles (1998) Pickles, A. J. 1998, PASP, 110, 863
  * Pineau (2020) Pineau, F. X. 2020, in Astronomical Society of the Pacific Conference Series, Vol. 527, Astronomical Data Analysis Software and Systems XXIX, ed. R. Pizzo, E. R. Deul, J. D. Mol, J. de Plaa, & H. Verkouter, 685
  * Pipien et al. (2018) Pipien, S., Basa, S., Cuby, J. G., et al. 2018, A&A, 616, A55
  * Planck Collaboration XI (2014) Planck Collaboration XI. 2014, A&A, 571, A11
  * Powalka et al. (2016) Powalka, M., Lançon, A., Puzia, T. H., et al. 2016, ApJS, 227, 12
  * Racca et al. (2016) Racca, G. D., Laureijs, R., Stagnaro, L., et al. 2016, in SPIE Conference Series, Vol. 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, ed. H. A. MacEwen, G. G. Fazio, M. Lystrup, N. Batalha, N. Siegler, & E. C. Tong, 99040O
  * Racine (1996) Racine, R. 1996, PASP, 108, 699
  * Regnault et al. (2009) Regnault, N., Conley, A., Guy, J., et al. 2009, A&A, 506, 999
  * Robin et al. (2003) Robin, A. C., Reylé, C., Derrière, S., & Picaud, S. 2003, A&A, 409, 523
  * Rodrigo & Solano (2020) Rodrigo, C. & Solano, E. 2020, in XIV.0 Scientific Meeting (virtual) of the Spanish Astronomical Society, 182
  * Rodrigo et al. (2012) Rodrigo, C., Solano, E., & Bayo, A. 2012, SVO Filter Profile Service Version 1.0, IVOA Working Draft 15 October 2012
  * Román et al. (2020) Román, J., Trujillo, I., & Montes, M. 2020, A&A, 644, A42
  * Rothman et al. (2013) Rothman, L., Gordon, I., Babikov, Y., et al. 2013, Journal of Quantitative Spectroscopy and Radiative Transfer, 130, 4, hITRAN2012 special issue
  * Saifollahi et al. (2024) Saifollahi, T., Voggel, K., Lançon, A., et al. 2024, A&A, this issue
  * Sandage (1976) Sandage, A. 1976, AJ, 81, 954
  * Sandin (2014) Sandin, C. 2014, A&A, 567, A97
  * Schlafly et al. (2019) Schlafly, E. F., Meisner, A. M., & Green, G. M. 2019, ApJS, 240, 30
  * Secroun et al. (2018) Secroun, A., Barbier, R., Buton, C., et al. 2018, in SPIE Conference Series, Vol. 10709, High Energy, Optical, and Infrared Detectors for Astronomy VIII, ed. A. D. Holland & J. Beletic, 1070921
  * Serra et al. (2015) Serra, B., Secroun, A., Clémens, J. C., et al. 2015, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9602, Optics for EUV, X-Ray, and Gamma-Ray Astronomy VII, ed. H. A. MacEwen & J. B. Breckinridge, 96020G
  * Slater et al. (2009) Slater, C. T., Harding, P., & Mihos, J. C. 2009, PASP, 121, 1267
  * Szalay et al. (1999) Szalay, A. S., Connolly, A. J., & Szokoly, G. P. 1999, AJ, 117, 68
  * Taylor (2005) Taylor, M. B. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 347, Astronomical Data Analysis Software and Systems XIV, ed. P. Shopbell, M. Britton, & R. Ebert, 29
  * Tody (1986) Tody, D. 1986, in SPIE Conference Series, Vol. 627, Instrumentation in astronomy VI, ed. D. L. Crawford, 733
  * Tulloch (2018) Tulloch, S. 2018, arXiv e-prints, arXiv:1807.05217
  * van Dokkum (2001) van Dokkum, P. G. 2001, PASP, 113, 1420
  * Waczynski et al. (2016) Waczynski, A., Barbier, R., Cagiano, S., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9915, High Energy, Optical, and Infrared Detectors for Astronomy VII, ed. A. D. Holland & J. Beletic, 991511
  * Watkins et al. (2016) Watkins, A. E., Mihos, J. C., & Harding, P. 2016, ApJ, 826, 59
  * Zhang & Bloom (2020) Zhang, K. & Bloom, J. S. 2020, ApJ, 889, 24
  * Zhang & Bloom (2020) Zhang, K. & Bloom, J. S. 2020, ApJ, 889, 24

##  Appendix A Euclid ERO programme summary

Table 4: Euclid ERO observations per proposal sorted by date. The project ID was assigned across all submitted proposals based on distance. ERO ID | ERO project title | Overview paper | Field name | Date | Comments
---|---|---|---|---|---
ERO02 | A first glance at free- | Martín et al. (2024) | NGC 1333 | 09-09-2023 | 1 ROS, bad guiding, few exposures
| floating baby Jupiters |  | Taurus | 09-09-2023 | 1 ROS, bad guiding, no data
| with Euclid |  | NGC 1333 | 16-09-2023 | 1 ROS, bad guiding, few exposures
|  |  | Taurus | 16-09-2023 | 1 ROS, dither rotated
|  |  | Horsehead | 02-10-2023 | 1 ROS
|  |  | Messier 78 | 12-10-2023 | 1 ROS
|  |  | Barnard 30 | 12-10-2023 | 1 ROS
ERO03 |  Euclid view of Milky | Massari et al. (2024) | NGC 6254 | 09-09-2023 | 1 ROS, dither rotated
| Way globular clusters |  | NGC 6397 | 22-09-2023 | 1 ROS
ERO08 | A Euclid Showcase | Hunt et al. (2024) | IC 10 | 03-09-2023 | 1 ROS, dither rotated
| of Nearby Galaxies |  | IC 10 | 06-09-2023 | 1 ROS, dither rotated
|  |  | IC 342 | 02-10-2023 | 1 ROS
|  |  | NGC 6744 | 02-10-2023 | 1 ROS
|  |  | NGC 6822 | 12-10-2023 | 1 ROS
|  |  | NGC 2403 | 12-10-2023 | 1 ROS
|  |  | Holmberg II | 28-11-2023 | 1 ROS, hints of stray light
ERO09 | The Fornax galaxy | Saifollahi et al. (2024) | Fornax | 23-08-2023 | 1 ROS, bad guiding, few exposures
| cluster seen with |  | Fornax | 03-09-2023 | 1 ROS, bad guiding, few exposures
| Euclid |  | Fornax | 06-09-2023 | 1 ROS, bad guiding, few exposures
|  |  | Dorado | 28-11-2023 | 1 ROS
ERO10 | The Perseus cluster | Cuillandre et al. (2024) | Perseus | 09-09-2023 | 2 ROS, dither rotated
| of galaxies |  | Perseus | 16-09-2023 | 2 ROS, dither rotated
ERO11 | A glimpse into Euclid’s | Atek et al. (2024) | Abell 2390 | 28-11-2023 | 3 ROS
| Universe through a |  | Abell 2764 | 28-11-2023 | 3 ROS
| giant magnifying lens |  |  |  |

##  Appendix B Euclid ERO data summary

Table 5: Main characteristics and properties of the 17 ERO fields are consistent across the $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands; therefore, we will report only on the $H_{\scriptscriptstyle\rm E}$ band. The right ascension (RA) and declination (Dec) coordinates represent the centres of the stacks. The average colour excess $E(B-V)$ from Planck Collaboration XI (2014) is calculated across all valid pixels in each image, which cover approximately 0.6 deg2. For a summary of the data set’s general properties, refer to Table 2. ERO fields | RA | Dec | $l$ | $b$ |  $E(B-V)$ | FWHM | Astrometry | Number of
---|---|---|---|---|---|---|---|---
per project | [deg] | [deg] | [deg] | [deg] | [FoV] | [arcsec] | [mas] | objects
|  |  |  |  |  | $I_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$ | $I_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$ | $I_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$
Horsehead | $85.150$ | $-2.613$ | $207.053$ | $-16.931$ | 2.020 | 0.158 | 0.54 | 4.7 | 14.2 | 157 264 | 250 942
Messier 78 | $86.690$ | $-0.015$ | $205.414$ | $-14.356$ | 1.588 | 0.158 | 0.56 | 3.9 | 14.5 | 116 373 | 238 334
Taurus | $64.983$ | $+28.023$ | $169.257$ | $-15.552$ | 0.468 | 0.165 | 0.53 | 3.8 | 13.7 | 123 726 | 223 725
Barnard 30 | $82.880$ | $+12.316$ | $192.500$ | $-11.526$ | 1.001 | 0.158 | 0.54 | 4.4 | 14.4 | 163 063 | 243 012
NGC 6254 | $254.303$ | $-4.100$ | $15.145$ | $+23.062$ | 0.227 | 0.155 | 0.55 | 4.5 | 16.5 | 413 297 | 321 363
NGC 6397 | $265.174$ | $-53.658$ | $338.178$ | $-11.951$ | 0.316 | 0.160 | 0.54 | 2.8 | 15.5 | 782 612 | 493 281
NGC 6822 | $296.236$ | $-14.788$ | $25.352$ | $-18.389$ | 0.203 | 0.156 | 0.55 | 3.5 | 14.5 | 1 694 021 | 488 601
Holmberg II | $124.790$ | $+70.706$ | $144.291$ | $+32.697$ | 0.035 | 0.157 | 0.60 | 5.8 | 15.4 | 466 276 | 245 597
IC 10 | $5.063$ | $+59.288$ | $118.952$ | $-3.342$ | 0.822 | 0.157 | 0.55 | 3.0 | 14.9 | 1 403 807 | 416 300
IC 342 | $56.730$ | $+68.084$ | $138.188$ | $+10.577$ | 0.342 | 0.156 | 0.54 | 5.3 | 14.6 | 2 033 293 | 452 034
NGC 2403 | $114.211$ | $+65.586$ | $150.587$ | $+29.184$ | 0.046 | 0.155 | 0.54 | 6.8 | 15.1 | 1 152 966 | 316 055
NGC 6744 | $287.430$ | $-63.842$ | $332.240$ | $-26.139$ | 0.059 | 0.157 | 0.52 | 6.2 | 14.9 | 924 913 | 336 109
Fornax | $54.017$ | $-35.267$ | $236.425$ | $-54.132$ | 0.018 | 0.162 | 0.63 | 10.3 | 14.4 | 369 315 | 265 091
Dorado | $64.014$ | $-55.780$ | $265.638$ | $-43.706$ | 0.018 | 0.159 | 0.65 | 7.2 | 15.7 | 518 445 | 356 621
Perseus | $49.638$ | $+41.651$ | $150.296$ | $-13.272$ | 0.156 | 0.156 | 0.56 | 8.2 | 15.4 | 546 563 | 335 340
Abell 2390 | $328.397$ | $+17.709$ | $73.967$ | $-27.799$ | 0.106 | 0.157 | 0.56 | 5.1 | 15.2 | 469 056 | 310 617
Abell 2764 | $5.713$ | $-49.249$ | $315.028$ | $-67.201$ | 0.018 | 0.158 | 0.69 | 7.9 | 15.8 | 542 729 | 321 407
Table 6: Sky coverage and depth properties for the 17 ERO fields, pertaining to both compact sources (galaxies and point sources) and extended emission, are detailed below. The limiting magnitude for extended emission (LSB limit) is expressed in terms of the 1 $\sigma$ asinh AB magnitude, utilising the $$$\times$$$ scale metric. For further information on the depth metrics, refer to Sects. 8 and 9. ERO fields | Area | Galaxies, 10 $\sigma$ [AB mag] | Point sources, 5 $\sigma$ [AB mag] |  LSB limit [AB mag arcsec-2]
---|---|---|---|---
per project | [deg2] | $I_{\scriptscriptstyle\rm E}$ | $Y_{\scriptscriptstyle\rm E}$ | $J_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$ | $I_{\scriptscriptstyle\rm E}$ | $Y_{\scriptscriptstyle\rm E}$ | $J_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$ | $I_{\scriptscriptstyle\rm E}$ | $Y_{\scriptscriptstyle\rm E}$ | $J_{\scriptscriptstyle\rm E}$ | $H_{\scriptscriptstyle\rm E}$
Horsehead | 0.58 | 24.83 | 22.63 | 22.80 | 22.77 | 27.05 | 24.32 | 24.46 | 24.34 | 29.53 | 28.04 | 28.25 | 28.22
Messier 78 | 0.60 | 24.90 | 22.61 | 22.71 | 22.82 | 27.10 | 24.34 | 24.47 | 24.41 | 29.66 | 28.08 | 28.24 | 28.26
Taurus | 0.61 | 24.93 | 22.77 | 23.01 | 23.05 | 27.09 | 24.34 | 24.49 | 24.45 | 29.58 | 28.06 | 28.24 | 28.28
Barnard 30 | 0.60 | 24.91 | 22.70 | 22.86 | 22.99 | 27.12 | 24.31 | 24.44 | 24.38 | 29.54 | 28.01 | 28.18 | 28.18
NGC 6254 | 0.60 | 25.11 | 22.97 | 23.22 | 23.26 | 27.23 | 24.37 | 24.51 | 24.46 | 29.66 | 28.05 | 28.22 | 28.26
NGC 6397 | 0.61 | 25.16 | 22.93 | 23.11 | 23.15 | 27.11 | 24.21 | 24.31 | 24.22 | 29.51 | 27.70 | 27.74 | 27.75
NGC 6822 | 0.60 | 25.19 | 22.81 | 23.08 | 23.11 | 26.79 | 24.20 | 24.34 | 24.27 | 29.53 | 27.83 | 27.98 | 27.99
Holmberg II | 0.60 | 25.54 | 23.20 | 23.44 | 23.47 | 27.45 | 24.69 | 24.85 | 24.78 | 29.97 | 28.43 | 28.60 | 28.61
IC 10 | 0.62 | 26.12 | 23.43 | 23.63 | 23.65 | 27.43 | 24.80 | 24.89 | 24.74 | 30.23 | 28.09 | 28.23 | 28.20
IC 342 | 0.59 | 25.41 | 22.87 | 23.23 | 23.31 | 26.70 | 24.45 | 24.60 | 24.52 | 29.81 | 28.04 | 28.18 | 28.18
NGC 2403 | 0.60 | 25.51 | 23.15 | 23.38 | 23.43 | 27.22 | 24.62 | 24.79 | 24.71 | 29.98 | 28.21 | 28.38 | 28.39
NGC 6744 | 0.60 | 25.29 | 22.97 | 23.21 | 23.31 | 27.09 | 24.50 | 24.64 | 24.58 | 29.81 | 28.05 | 28.20 | 28.21
Fornax | 0.57 | 25.07 | 22.97 | 23.38 | 23.37 | 26.89 | 24.56 | 24.87 | 24.81 | 29.66 | 28.29 | 28.56 | 28.56
Dorado | 0.60 | 25.52 | 23.15 | 23.37 | 23.37 | 27.40 | 24.68 | 24.84 | 24.76 | 30.05 | 28.41 | 28.58 | 28.60
Perseus | 0.70 | 26.12 | 23.77 | 24.04 | 24.08 | 28.03 | 25.20 | 25.38 | 25.32 | 30.57 | 28.77 | 28.95 | 28.94
Abell 2390 | 0.75 | 25.88 | 23.60 | 23.85 | 23.87 | 27.83 | 25.08 | 25.23 | 25.17 | 30.42 | 28.70 | 28.86 | 28.88
Abell 2764 | 0.75 | 26.06 | 23.71 | 23.94 | 23.96 | 27.83 | 25.19 | 25.34 | 25.27 | 30.56 | 28.78 | 28.96 | 28.98
Figure 32: The 17 ERO fields (approximately 0.6 deg2 each,
$I_{\scriptscriptstyle\rm E}$ preview). The blue frame encompasses the
entirety of the FITS image for each science stack, guaranteeing that no
quality Euclid data are omitted during projection into the equatorial
coordinate system. Pixels identified as valid are those shared by both the VIS
and NISP instruments. A dithering pattern impacted three fields – Taurus, NGC
6254, and IC 10 – resulting in incomplete sky coverage. The Fornax field is
limited by having only two VIS exposures, leading to prominent gaps. Holmberg
II, Fornax, and Dorado suffer from issues related to stray light, which will
be addressed in the upcoming ERO data release. Any observed variations in the
background of the remaining images stem from the LSB detection of Galactic
nebulae (top row) or the presence of faint Galactic cirrus, illustrating the
Euclid’s capability to easily capture these subtle astronomical features.
Figure 33: Released on 7 November 2023, the first set of five colour images
unveiled Euclid’s capabilities to the global community. The images (cropped
FoV$=0.5$ deg2), starting from the top left, feature the Perseus cluster, IC
342, NGC 6822, NGC 6397, and the Horsehead nebula, along with a cutout on the
lower right ($$$\times$$$) that highlights the image resolution and depth
achieved by Euclid. The pipeline detailed in this paper produced each of the
three channels that contributed to the initial RGB images. These images were
subsequently refined using external tools. The chosen colour palette assigns
assigns the $I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$ bands to the blue, green, and red channels
respectively, displaying the full sensitivity range of the observatory and
offering a new perspective on these astronomical subjects. Credit:
ESA/Euclid/Euclid Consortium/NASA, image processing by J.-C. Cuillandre (CEA
Paris-Saclay), G. Anselmi.

##  Appendix C Selection of relevant stars along a given line of sight

Colour transformations for comparing Euclid photometry with existing
literature are based on synthetic photometry of prevalent stars in the
observation region, demonstrated through the Dorado and Perseus cases. Figure
34 depicts outcomes from querying the Besançon model of the Galaxy (Robin et
al. 2003; Czekaj 2012; Lagarde et al. 2021) for a 1 deg2 area towards NGC
1553, illustrating the process of deriving these transformations for accurate
photometric comparisons. Both the Besançon model and the Planck 2013 dust map
indicate an $A_{V}\simeq 0.04$ in the direction of NGC 1553, suggesting that
extinction effects are minimal and unlikely to be discernible in the figure.
The right panels of the figure illustrate the models employed, with the SSED
models represented by black open squares and the TSED models by black dots. It
is important to note that [$\alpha$/Fe] is explicitly considered only in the
selection process for TSED models. Figure 35 showcases the stellar populations
expected along the line of sight towards Perseus, traversing extensive regions
of the Galaxy’s thin and thick discs.

Figure 34: Relevant stars along the line of sight towards the Dorado field.
This example showcases the selection process conducted prior to deriving
colour transformations. The coloured dots depict the simulated stellar
population along the line of sight, as provided by the Besançon model of the
Galaxy. In the two left panels, the colour coding represents metallicity
[M/H]. In the two right panels, the colour coding corresponds to
[$\alpha$/Fe], with black symbols marking the models available within the
data-containing range of the simulation. Grey lines delineate the approximate
boundaries we established for this selection process, ensuring that the
subsequent colour transformations accurately reflect the characteristics of
the stellar population along the observed line of sight.

Figure 35: Relevant stars along the line of sight towards the Perseus field.
The layout is as in Fig. 34

##  Appendix D Optical model of the telescope

To accurately correlate the flux observed at large radii with the energy
concentrated in the core of the PSF, a model of the Euclid PSF was developed.
This modelling encompassed the broadband Euclid PSF across five distinct
wavelengths, each representing the $I_{\scriptscriptstyle\rm E}$,
$Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$ bands. The approach involved calculating the
modulus squared of the Fourier transform of the pupil function, adhering to
the Fraunhofer far-field diffraction approximation (Born & Wolf 1999). The
pupil function represents the complex amplitude of light within the pupil,
assuming ideal optical conditions without any phase term. Consequently, the
pupil function equates to the real transmission of the pupil, designated as 1
inside the pupil’s boundary and 0 outside. The Euclid pupil was simulated on a
substantial grid ($16\,384\times 16\,384$) using an outer diameter of 1.21 m
for the primary mirror M1, a central obstruction of 0.395 m by the secondary
mirror M2, and the width of 12 mm for the three spider arms. The spiders are
connected tangentially to the structure supporting M2 (see e.g. Racca et al.
2016).

###  D.1 Model of the encompassed energy of the Euclid PSF

To precisely determine the radial profile of the PSF by examining the
cumulative flux fraction as a function of radius, we implemented a sampling
strategy for our model PSF to achieve a resolution finer than $None$. This
necessitates oversampling by a factor of 5 relative to the Nyquist rate,
resulting in a simulated field size of $$$\times$$$ on our $16\,384\times
16\,384$ grid. Subsequently, we calculated the four Euclid broadband PSFs,
adjusting the pupil sampling to ensure a consistent pixel scale across all
wavelengths. This enabled us to calculate the proportion of total flux within
a circular aperture of incrementally increasing radius, aligning these values
with measurements extracted from the ERO data set.

For context, if we consider a perfect Airy disc for Euclid, the FWHM in
radians is determined by the formula $1.025\times\lambda$/D (M1), which yields
the following FWHM values at the central wavelength for each of the four
broadband filters: $I_{\scriptscriptstyle\rm E}=$$$, $Y_{\scriptscriptstyle\rm
E}=$$$, $J_{\scriptscriptstyle\rm E}=$$$, and $H_{\scriptscriptstyle\rm
E}=$$$. This theoretical calculation aligns with the natural FWHM observed in
VIS non-resampled data at the finer $None$ pixel-1 sampling rate. However, the
coarser $None$ pixel-1 sampling rate of NISP degrades the observed FWHM,
averaging approximately $None$ across its three bands.

###  D.2 Energy in the diffraction spikes

Both VIS and NISP images display six pronounced diffraction spikes around
bright stars, a result of the structure created by the three supporting
spiders. In the case of a nearly 5th magnitude star, such as that seen in one
of our ERO fields (Fig. 23), each spike stretches from $None$ in VIS to as
much as $None$ in NISP for the $H_{\scriptscriptstyle\rm E}$-band. The extent
of these spikes is influenced by the wavelength, with longer wavelengths
exhibiting stronger effects and allowing for detection at greater distances.
This phenomenon underscores two crucial points: first, the extended PSF is
likely to have minimal power at large radii, evidenced by our ability to trace
the spikes over substantial distances; second, there is a need to specifically
model and measure the energy contained within the diffraction spikes for each
Euclid band to affirm the methodology employed in determining the extended
PSF.

A preliminary estimate of the total flux present in the diffraction pattern
can be derived geometrically by calculating the area ratio of the spiders to
the transmissive area, resulting in a value of 1.89%. However, due to the
blinding effect of a 5th magnitude star on the ERO images, it is not feasible
to directly measure this total quantity within a radius of $None$ from our
images. Instead, the proportion of energy situated beyond a specific radius,
which is quantifiable based on the ERO data, must initially be predicted
through simulations. To simulate the fraction of flux from the central object
located within the six diffraction spikes, we created the largest feasible
field for our simulation grid, realised when the PSF is critically (Nyquist)
sampled. In this scenario, the pupil diameter is halved in comparison to our
grid size, rendering one pupil pixel equivalent to the diameter of M1 divided
by our grid size: 148 microns on the primary mirror. This adjusted simulation
extends to a radius of $None$, with analyses of the ERO data suggesting that a
significant portion of the energy within the spikes is contained within this
radius. By creating identical pupil models both with and without the presence
of spiders, we computed the corresponding PSFs, subtracted one from the other,
and subsequently quantified the fraction of flux attributable to the spiders.
In this way we ascertain the total fraction of flux from the central star
located within all six diffraction spikes beyond a radius of $None$, yielding
the following percentages for each band: $I_{\scriptscriptstyle\rm E}=0.22\%$,
$Y_{\scriptscriptstyle\rm E}=0.41\%$, $J_{\scriptscriptstyle\rm E}=0.60\%$,
and $H_{\scriptscriptstyle\rm E}=0.80\%$.

Figure 36: Main panels from left to right: The full $None$$\times$$None$ field
simulated PSF in the $I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm
E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands,
in log scale, the core of the PSF in the inset ($None$$\times$$None$), and the
pupil function in the top-left corner of the left panel. The pure diffraction
halo grows larger towards the NIR.

##  Appendix E ERO catalogue parameters by SourceExtractor

Table 7: Input parameters for the SourceExtractor run producing the ERO science validation catalogues are outlined below. Some parameters generate multiple columns in the output catalogue, as exemplified by MAG_APER, which covers 10 different apertures as described in Sect. 8. This is indicated by the jump in column numbers in this table. In total, the ERO catalogues feature 364 columns. The parameter descriptions are from SourceExtractor. Column | Parameter | Description | Unit
---|---|---|---
1 | NUMBER | Running object number |
2 | X_IMAGE | Object position along x | [pixel]
3 | Y_IMAGE | Object position along y | [pixel]
4 | ID_PARENT | Parent ID (before deblending) |
5 | EXT_NUMBER | FITS extension number |
6 | FLUX_ISO | Isophotal flux | [ADU]
7 | FLUXERR_ISO | RMS error for isophotal flux | [ADU]
8 | MAG_ISO | Isophotal magnitude | [mag]
9 | MAGERR_ISO | RMS error for isophotal magnitude | [mag]
10 | FLUX_ISOCOR | Corrected isophotal flux | [ADU]
11 | FLUXERR_ISOCOR | RMS error for corrected isophotal flux | [ADU]
12 | MAG_ISOCOR | Corrected isophotal magnitude | [mag]
13 | MAGERR_ISOCOR | RMS error for corrected isophotal magnitude | [mag]
14 | FLUX_APER | Flux vector within fixed circular aperture(s) | [ADU]
24 | FLUXERR_APER | RMS error vector for aperture flux(es) | [ADU]
34 | MAG_APER | Fixed aperture magnitude vector | [mag]
44 | MAGERR_APER | RMS error vector for fixed aperture mag. | [mag]
54 | FLUX_AUTO | Flux within a Kron-like elliptical aperture | [ADU]
55 | FLUXERR_AUTO | RMS error for AUTO flux | [ADU]
56 | MAG_AUTO | Kron-like elliptical aperture magnitude | [mag]
57 | MAGERR_AUTO | RMS error for AUTO magnitude | [mag]
58 | KRON_RADIUS | Kron apertures in units of A or B |
59 | FLUX_PETRO | Flux within a Petrosian-like elliptical aperture | [ADU]
60 | FLUXERR_PETRO | RMS error for Petrosian flux | [ADU]
61 | MAG_PETRO | Petrosian-like elliptical aperture magnitude | [mag]
62 | MAGERR_PETRO | RMS error for Petrosian magnitude | [mag]
63 | PETRO_RADIUS | Petrosian apertures in units of A or B |
64 | FLUX_GROWTH | Cumulated growth-curve | [ADU]
65 | FLUX_GROWTHSTEP | Step for growth-curves | [pixel]
66 | MAG_GROWTH | Cumulated magnitude growth-curve | [mag]
67 | MAG_GROWTHSTEP | Step for growth-curves | [pixel]
68 | FLUX_RADIUS | Fraction-of-light radii | [pixel]
69 | BACKGROUND | Background at centroid position | [ADU]
70 | MU_MAX | Peak surface brightness above background |  [mag arcsec-2]
71 | X_FOCAL | Barycenter position along focal-plane x axis |
72 | Y_FOCAL | Barycenter position along focal-plane y axis |
73 | X_WORLD | Barycenter position along world x axis | [deg]
74 | Y_WORLD | Barycenter position along world y axis | [deg]
75 | ALPHA_SKY | Right ascension of barycenter (native) | [deg]
76 | DELTA_SKY | Declination of barycenter (native) | [deg]
77 | ALPHA_J2000 | Right ascension of barycenter (J2000) | [deg]
78 | DELTA_J2000 | Declination of barycenter (J2000) | [deg]
79 | ALPHA_B1950 | Right ascension of barycenter (B1950) | [deg]
80 | DELTA_B1950 | Declination of barycenter (B1950) | [deg]
81 | ERRX2_IMAGE | Variance of position along x |  [pixel2]
82 | ERRY2_IMAGE | Variance of position along y |  [pixel2]
83 | ERRXY_IMAGE | Covariance of position between x and y |  [pixel2]
84 | ERRA_IMAGE | RMS position error along major axis | [pixel]
85 | ERRB_IMAGE | RMS position error along minor axis | [pixel]
86 | ERRTHETA_IMAGE | Error ellipse position angle (CCW/x) | [deg]
87 | ERRCXX_IMAGE | Cxx error ellipse parameter |  [pixel-2]
88 | ERRCYY_IMAGE | Cyy error ellipse parameter |  [pixel-2]
89 | ERRCXY_IMAGE | Cxy error ellipse parameter |  [pixel-2]
90 | XPEAK_IMAGE | x-coordinate of the brightest pixel | [pixel]
91 | YPEAK_IMAGE | y-coordinate of the brightest pixel | [pixel]
92 | XPEAK_FOCAL | Focal-plane x coordinate of the brightest pixel |
93 | YPEAK_FOCAL | Focal-plane y coordinate of the brightest pixel |
94 | XPEAK_WORLD | World-x coordinate of the brightest pixel | [deg]
95 | YPEAK_WORLD | World-y coordinate of the brightest pixel | [deg]

Column | Parameter | Description | Unit
---|---|---|---
96 | ALPHAPEAK_SKY | Right ascension of brightest pix (native) | [deg]
97 | DELTAPEAK_SKY | Declination of brightest pix (native) | [deg]
98 | ALPHAPEAK_J2000 | Right ascension of brightest pix (J2000) | [deg]
99 | DELTAPEAK_J2000 | Declination of brightest pix (J2000) | [deg]
100 | ALPHAPEAK_B1950 | Right ascension of brightest pix (B1950) | [deg]
101 | DELTAPEAK_B1950 | Declination of brightest pix (B1950) | [deg]
102 | XMIN_IMAGE | Minimum x-coordinate among detected pixels | [pixel]
103 | YMIN_IMAGE | Minimum y-coordinate among detected pixels | [pixel]
104 | XMAX_IMAGE | Maximum x-coordinate among detected pixels | [pixel]
105 | YMAX_IMAGE | Maximum y-coordinate among detected pixels | [pixel]
106 | XWIN_IMAGE | Windowed position estimate along x | [pixel]
107 | YWIN_IMAGE | Windowed position estimate along y | [pixel]
108 | ERRX2WIN_IMAGE | Variance of windowed position along x |  [pixel2]
109 | ERRY2WIN_IMAGE | Variance of windowed position along y |  [pixel2]
110 | ERRXYWIN_IMAGE | Covariance of windowed position between x and y |  [pixel2]
111 | ERRAWIN_IMAGE | RMS windowed position error along major axis | [pixel]
112 | ERRBWIN_IMAGE | RMS windowed position error along minor axis | [pixel]
113 | ERRTHETAWIN_IMAGE | Windowed error ellipse position angle (CCW/x) | [deg]
114 | ERRCXXWIN_IMAGE | Cxx windowed error ellipse parameter |  [pixel-2]
115 | ERRCYYWIN_IMAGE | Cyy windowed error ellipse parameter |  [pixel-2]
116 | ERRCXYWIN_IMAGE | Cxy windowed error ellipse parameter |  [pixel-2]
117 | X2_IMAGE | Variance along x |  [pixel2]
118 | Y2_IMAGE | Variance along y |  [pixel2]
119 | XY_IMAGE | Covariance between x and y |  [pixel2]
120 | A_IMAGE | Profile RMS along major axis | [pixel]
121 | B_IMAGE | Profile RMS along minor axis | [pixel]
122 | THETA_IMAGE | Position angle (CCW/x) | [deg]
123 | ELONGATION | A_IMAGE/B_IMAGE |
124 | ELLIPTICITY |  1 - B_IMAGE/A_IMAGE |
125 | CXX_IMAGE | Cxx object ellipse parameter |  [pixel-2]
126 | CYY_IMAGE | Cyy object ellipse parameter |  [pixel-2]
127 | CXY_IMAGE | Cxy object ellipse parameter |  [pixel-2]
128 | ISOAREAF_IMAGE | Isophotal area (filtered) above Detection threshold |  [pixel2]
129 | ISOAREA_IMAGE | Isophotal area above analysis threshold |  [pixel2]
130 | X2WIN_IMAGE | Windowed variance along x |  [pixel2]
131 | Y2WIN_IMAGE | Windowed variance along y |  [pixel2]
132 | XYWIN_IMAGE | Windowed covariance between x and y |  [pixel2]
133 | CXXWIN_IMAGE | Windowed Cxx object ellipse parameter |  [pixel-2]
134 | CYYWIN_IMAGE | Windowed Cyy object ellipse parameter |  [pixel-2]
135 | CXYWIN_IMAGE | Windowed Cxy object ellipse parameter |  [pixel-2]
136 | AWIN_IMAGE | Windowed profile RMS along major axis | [pixel]
137 | BWIN_IMAGE | Windowed profile RMS along minor axis | [pixel]
138 | THETAWIN_IMAGE | Windowed position angle (CCW/x) | [deg]
139 | CLASS_STAR | S/G classifier output |
140 | FWHM_IMAGE | FWHM assuming a gaussian core | [pixel]
141 | XPSF_IMAGE | X coordinate from PSF-fitting | [pixel]
142 | YPSF_IMAGE | Y coordinate from PSF-fitting | [pixel]
143 | ALPHAPSF_J2000 | Right ascension of the fitted PSF (J2000) | [deg]
144 | DELTAPSF_J2000 | Declination of the fitted PSF (J2000) | [deg]
145 | FLUX_PSF | Flux from PSF-fitting | [ADU]
146 | FLUXERR_PSF | RMS flux error for PSF-fitting | [ADU]
147 | MAG_PSF | Magnitude from PSF-fitting | [mag]
148 | MAGERR_PSF | RMS magnitude error from PSF-fitting | [mag]
149 | FLUX_POINTSOURCE | Point source flux from fitting | [ADU]
150 | FLUXERR_POINTSOURCE | RMS error on fitted point source total flux | [ADU]
151 | MAG_POINTSOURCE | Point source total magnitude from fitting | [mag]
152 | MAGERR_POINTSOURCE | RMS error on fitted point source total magnitude | [mag]
153 | FLUX_DISK | Disk total flux from fitting | [ADU]
154 | FLUXERR_DISK | RMS error on fitted disk total flux | [ADU]
155 | MAG_DISK | Disk total magnitude from fitting | [mag]
156 | MAGERR_DISK | RMS error on fitted disk total magnitude | [mag]
157 | MU_MAX_DISK | Peak disk surface brightness above background |  [mag arcsec-2]
158 | MU_EFF_DISK | Effective disk surface brightness above background |  [mag arcsec-2]
159 | MU_MEAN_DISK | Mean effective disk surface brightness above background |  [mag arcsec-2]
160 | FLUX_SPHEROID | Spheroid total flux from fitting | [ADU]
161 | FLUXERR_SPHEROID | RMS error on fitted spheroid total flux | [ADU]

Column | Parameter | Description | Unit
---|---|---|---
162 | MAG_SPHEROID | Spheroid total magnitude from fitting | [mag]
163 | MAGERR_SPHEROID | RMS error on fitted spheroid total magnitude | [mag]
164 | MU_MAX_SPHEROID | Peak spheroid surface brightness above background |  [mag arcsec-2]
165 | MU_EFF_SPHEROID | Effective spheroid surface brightness above background |  [mag arcsec-2]
166 | MU_MEAN_SPHEROID | Mean effective spheroid surface brightness above background |  [mag arcsec-2]
167 | DISK_INCLINATION | Disk inclination from fitting | [deg]
168 | DISK_INCLINATIONERR | RMS error on disk inclination from fitting | [deg]
169 | DISK_THETA_IMAGE | Disk position angle (CCW/x) from fitting | [deg]
170 | DISK_THETAERR_IMAGE | RMS error on fitted disk position angle | [deg]
171 | SPHEROID_SERSICN | Spheroid Sersic index from fitting |
172 | SPHEROID_SERSICNERR | RMS error on fitted spheroid Sersic index |
173 | SPHEROID_THETA_IMAGE | Spheroid position angle (CCW/x) from fitting | [deg]
174 | SPHEROID_THETAERR_IMAG | RMS error on spheroid position angle | [deg]
175 | SPHEROID_REFF_IMAGE | Spheroid effective radius from fitting | [pixel]
176 | SPHEROID_REFFERR_IMAGE | RMS error on fitted spheroid effective radius | [pixel]
177 | FLUX_MODEL | Flux from model-fitting | [ADU]
178 | FLUXERR_MODEL | RMS error on model-fitting flux | [ADU]
179 | MAG_MODEL | Magnitude from model-fitting | [mag]
180 | MAGERR_MODEL | RMS error on model-fitting magnitude | [mag]
181 | MU_MAX_MODEL | Peak model surface brightness above background |  [mag arcsec-2]
182 | FLUX_MAX_MODEL | Peak model flux above background | [ADU]
183 | FLUX_EFF_MODEL | Effective model flux above background | [ADU]
184 | FLUX_MEAN_MODEL | Mean effective model flux above background | [ADU]
185 | MU_EFF_MODEL | Effective model surface brightness above background |  [mag arcsec-2]
186 | MU_MEAN_MODEL | Mean effective model surface brightness above background |  [mag arcsec-2]
187 | XMODEL_IMAGE | X coordinate from model-fitting | [pixel]
188 | YMODEL_IMAGE | Y coordinate from model-fitting | [pixel]
189 | CXXMODEL_IMAGE | Cxx ellipse parameter from model-fitting |  [pixel-2]
190 | CYYMODEL_IMAGE | Cyy ellipse parameter from model-fittinh |  [pixel-2]
191 | CXYMODEL_IMAGE | Cxy ellipse parameter from model-fitting |  [pixel-2]
192 | SPREAD_MODEL | Spread parameter from model-fitting |
193 | SPREADERR_MODEL | Spread parameter error from model-fitting |
194 | NOISEAREA_MODEL | Equivalent noise area of the fitted model |  [pixel2]
195 | NITER_MODEL | Number of iterations for model-fitting |
196 | VECTOR_MODEL | Model-fitting coefficients |
208 | VECTOR_MODELERR | Model-fitting coefficient uncertainties |
220 | MATRIX_MODELERR | Model-fitting covariance matrix |
364 | CHI2_MODEL | Reduced Chi2 of the fit |
  *[ERO]: Early Release Observations
  *[PSF]: point spread function
  *[NIR]: near-infrared
  *[S/N]: signal-to-noise ratio
  *[LSB]: low-surface brightness
  *[FoV]: field of view
  *[PV]: performance-verification
  *[H2RG]: HAWAII-2RG
  *[EWS]: Euclid Wide Survey
  *[ROS]: reference observing sequence
  *[RoI]: region of interest
  *[FGS]: fine guidance sensor
  *[WCS]: world coordinate system
  *[CFHT]: Canada-France-Hawaii Telescope
  *[LED]: light-emitting diode
  *[LEDs]: light-emitting diode
  *[SEDs]: spectral energy distribution
  *[CRs]: cosmic ray
  *[CR]: cosmic ray
  *[FWHM]: full width at half maximum
  *[H2RGs]: HAWAII-2RG
  *[ZP]: zero point
  *[ZPs]: zero point
  *[SED]: spectral energy distribution
  *[DES]: Dark Energy Survey
  *[FoVs]: field of view
  *[PSFs]: point spread function