---
title: 'HST2EUCLID: Realistic Euclid Mocks from HST Data'
url: https://www.emergentmind.com/topics/hst2euclid
type: topic
---

# HST2EUCLID: Realistic Euclid Mocks from HST Data

HST2EUCLID is a Python code for generating realistic mock Euclid observations from panchromatic Hubble Space Telescope imaging. In the Euclid preparation literature, it is presented as a tool that produces Euclid-like images in the \(H_{\rm E}\), \(J_{\rm E}\), \(Y_{\rm E}\), and \(I_{\rm E}\) photometric bands by matching Euclid’s filter set, spatial resolution, pixel scale, depths, and noise properties to deep HST data [2508.20860]. The code was used to build a simulated database for the 27 galaxy clusters observed in the Cluster Lensing And Supernova survey with Hubble and the Hubble Frontier Fields program, and it was further applied to blank fields, galaxy-scale lenses, and a Euclid Deep Survey preview field [2508.20860]. Within the broader Euclid-preparation program, HST2EUCLID is one implementation of “Euclidisation,” the transformation of high-resolution HST observations into synthetic Euclid data products suitable for algorithm validation, lens-modelling forecasts, and pre-survey training workflows [2508.20860; 2501.08372].

## 1. Definition, scope, and observational setting

HST2EUCLID was introduced to exploit the fact that HST images are much deeper and higher-resolution than Euclid, and can therefore serve as a practical empirical basis for realistic Euclid mocks [2508.20860]. The intended outputs are Euclid-quality images that retain the structural complexity of real astrophysical scenes, rather than idealized galaxy models. Because the inputs are real observations, the simulated products incorporate, by construction, the observed complexity of galaxy clusters and deep extragalactic fields [2508.20860].

The code is situated in the observational regime of the Euclid survey, for which the relevant design values quoted in the HST2EUCLID description are coverage of \(\simeq 15\,000~{\rm deg}^2\), limiting depths of \(I_{\rm E}\approx 24.5\) for \(10\sigma\) extended sources and \(Y_{\rm E}/J_{\rm E}/H_{\rm E}\approx 24\) for \(5\sigma\) point sources, and a PSF FWHM of \(\simeq 0.13''\) in \(I_{\rm E}\) [2508.20860]. On that basis, realistic Euclid mocks are motivated for several tasks: validation of shape-measurement and photo-\(z\) algorithms, testing of strong- and weak-lensing analyses on cluster fields, forecasting of number counts and size distributions, generation of training sets for deep-learning applications, and planning of spectroscopic follow-up campaigns [2508.20860].

A closely related line of work in the Euclid preparation series examines whether HST images can be used as inputs for weak-lensing image simulations with sufficiently small calibration biases. That study uses a GalSim-based testing environment and directly addresses systematic effects from PSF modelling, interpolation, resampling, and correlated noise [2501.08372]. HST2EUCLID should therefore be understood both as a science-enabling image-synthesis framework and as part of a wider methodological effort to determine when HST-derived Euclid-like data are adequate for precision lensing applications.

## 2. Pipeline architecture and Euclidisation workflow

The HST2EUCLID pipeline is organized into five main steps, denoted \((a)\)–\((e)\), and all operations are controlled by a simple YAML or text parameter file [2508.20860]. The starting point is a set of calibrated HST FITS images in units of counts in \(e^-\,{\rm s}^{-1}\), typically spanning the ACS and WFC3 bands needed to reconstruct Euclid photometric channels.

Step \((a)\) converts each HST input image to surface brightness in AB flux density,
\[
f_\nu \,[{\rm erg\,s^{-1}\,cm^{-2}\,Hz^{-1}}] = F_{e^-/s}\times10^{-0.4(ZP_{\rm HST}+48.6)},
\]
with
\[
ZP_{\rm HST} = -2.5\,\log_{10}({\rm PHOTFLAM}) -5\,\log_{10}({\rm PHOTPLAM}) -2.4079.
\]
After this conversion, all HST bands are reprojected to a common astrometric frame and pixel grid using `reproject_exact` from Astropy/Reproject [2508.20860].

Step \((b)\) performs PSF matching. TinyTim-derived HST PSF models, with FWHM of order \(70\)–\(130\) mas, are transformed to Euclid PSFs with convolution kernels \(K(x,y)\) computed via `Photutils.create_matching_kernel`, such that
\[
{\rm PSF}_{\rm HST} * K \simeq {\rm PSF}_{\rm Euclid}.
\]
Each HST image is then convolved with the appropriate kernel for the target Euclid band [2508.20860].

Step \((c)\) constructs Euclid-band images from linear combinations of HST filters. If \(\{F_{R_j}\}\) are neighbouring HST fluxes and \(F_Q\) is the desired Euclid-band flux, then for a basis of SEDs \(\{f_i\}\),
\[
R_{ij} = \frac{1}{c\,g_\nu^{\rm AB}} \cdot \frac{\int d\lambda\,\lambda\,f_i(\lambda)\,R_j(\lambda)}{\int d\lambda\,R_j(\lambda)/\lambda},
\qquad
q_i  = \frac{1}{c\,g_\nu^{\rm AB}} \cdot \frac{\int d\lambda\,\lambda\,f_i(\lambda)\,Q(\lambda)}{\int d\lambda\,Q(\lambda)/\lambda},
\]
and, writing \(F_R = R\,k\) and \(F_Q = q^T k\),
\[
F_Q = q^T R^{-1} F_R \equiv w^T F_R.
\]
In the implementation described for HST2EUCLID, the adopted relations are the following [2508.20860]:

| Euclid band | HST relation |
|---|---|
| \(Y_{\rm E}\) | \(\simeq {\rm F105W}\) |
| \(H_{\rm E}\) | \(\simeq {\rm F160W}\) |
| \(I_{\rm E}\) | \(0.542\,{\rm F606W}+0.458\,{\rm F814W}\) |
| \(J_{\rm E}\) | \(0.617\,{\rm F125W}+0.383\,{\rm F160W}\) |

Step \((d)\) rebins the convolved, combined images to Euclid pixel scales: \(100\) mas px\(^{-1}\) in \(I_{\rm E}\) and \(300\) mas px\(^{-1}\) in \(Y_{\rm E}/J_{\rm E}/H_{\rm E}\), again using `reproject_exact`. The images are then converted back from surface brightness to \(e^-\,{\rm s}^{-1}\,{\rm px}^{-1}\) with
\[
F_{e^-/s} = 10^{0.4(ZP_{\rm Euclid}-m_{\rm AB})},
\qquad ZP_{\rm Euclid}=23.9~{\rm mag}
\]
for all bands in the code description [2508.20860].

Step \((e)\) adds Euclid-like sky and detector noise. Assuming HST noise is negligible relative to Euclid noise, the background per pixel is chosen so that a source at the limiting magnitude \(m_{\rm lim}\) attains the desired \(S/N_{\rm lim}\) in an aperture of \(N_{\rm px}\) pixels and exposure \(t_{\rm exp}\):
\[
BK_{\rm sky} = \left\{ \frac{F_{\rm lim}^2\,t_{\rm exp}\,(SN_{\rm lim})^{-2} - F_{\rm lim}}{N_{\rm px}} \right\}\,[e^-\,s^{-1}\,px^{-1}],
\]
with
\[
F_{\rm lim} = 10^{0.4(ZP_{\rm Euclid}-m_{\rm lim})}.
\]
The final image is produced as a Poisson realization of \(I_{\rm rebin}+BK_{\rm sky}\) [2508.20860].

## 3. Photometric and PSF foundations

The HST2EUCLID procedure combines empirical image transport with explicit photometric-system assumptions. On the HST side, the input images are converted from instrumental count rates using the header-derived quantities \({\rm PHOTFLAM}\) and \({\rm PHOTPLAM}\); on the Euclid side, the target images are expressed in Euclid-band count rates after PSF matching, filter combination, and pixel-scale conversion [2508.20860].

For the near-infrared bands, the broader Euclid photometric-system description provides the formal context for the \(Y_{\rm E}\), \(J_{\rm E}\), and \(H_{\rm E}\) passbands. In that framework, the total system throughput is
\[
T_X(\lambda)=T_{\rm tel}(\lambda)\cdot T_{\rm NIOA}(\lambda)\cdot T_{{\rm filter},X}(\lambda)\cdot QE(\lambda),
\]
and the quoted AB zero points are \(ZP_{Y_{\rm E}}=25.04~{\rm mag}\pm0.05\), \(ZP_{J_{\rm E}}=25.26~{\rm mag}\pm0.05\), and \(ZP_{H_{\rm E}}=25.21~{\rm mag}\pm0.05\) [2203.01650]. That paper also reports field-dependent cut-on and cut-off shifts of up to \(2.7\)–\(5.8\) nm across the focal plane [2203.01650]. This suggests that the HST2EUCLID configuration, which uses \(ZP_{\rm Euclid}=23.9\) mag in its image-generation recipe, is aimed at internally consistent mock production rather than a full focal-plane-dependent realization of the Euclid NISP photometric system.

PSF treatment is equally central. HST2EUCLID uses TinyTim-derived HST PSF models as the starting point for convolution-kernel construction [2508.20860]. In the parallel weak-lensing validation literature, TinyTim PSFs are also examined directly against HST star fields in F606W and F814W, with focus-recovery scatter \(\sigma_f\approx2.9\,\mu{\rm m}\) and \(\approx2.6\,\mu{\rm m}\) for F606W chip 1 and chip 2, versus \(\approx0.9\,\mu{\rm m}\) and \(\approx0.4\,\mu{\rm m}\) for F814W [2501.08372]. Residual PSF-model errors at the \(10^{-3}\) level in normalized quadrupole and higher moments were found to induce additive biases if not mitigated [2501.08372]. For HST2EUCLID, this establishes a systematic backdrop: PSF transport is operationally straightforward, but PSF fidelity matters whenever the output is intended for calibration-grade lensing use.

## 4. Validation on blank fields and image realism

Validation of HST2EUCLID was performed with six Hubble Frontier Fields parallel blank fields [2508.20860]. In these tests, the measured \(S/N\) as a function of \(m_{\rm AB}\) follows the target limiting-\(S/N\) relations, indicating that the background prescription reproduces the designed depth behaviour in the simulated Euclid bands [2508.20860].

The same validation set was used to measure image-size and number-count statistics. For galaxies brighter than \(24.5\) mag in \(I_{\rm E}\), the median FWHM is \(\simeq0.59''\), and \(96\%\) of the light falls within a radius \(0.65''\) aperture [2508.20860]. The differential galaxy counts per magnitude in \(I_{\rm E}\) agree with HST number counts from Capak (2007) down to \(m=24.5\) at \(10\sigma\), and the cumulative density is \(\simeq28~{\rm arcmin}^{-2}\) [2508.20860]. In the application-oriented summary, the number density is given as \(28\pm1~{\rm arcmin}^{-2}\) at \(I_{\rm E}\le 24.5\), and Euclid is reported to resolve \(93.8\%\) of galaxies to \({\rm FWHM}\le1.3''\) [2508.20860].

These tests establish that the pipeline reproduces survey-level observables rather than merely producing visually degraded HST images. A plausible implication is that HST2EUCLID is most valuable when the target diagnostic is tied to detectable-source statistics, morphology at Euclid resolution, or the fidelity of photometric and lensing workflows under realistic observing conditions.

## 5. Strong-lensing applications and survey forecasting

A principal scientific demonstration of HST2EUCLID is the Euclidisation of the galaxy cluster MACS J0416.1\(-\)2403 for strong-lensing analysis [2508.20860]. The reference model denoted B23 contains 4 halos, gas, and 213 dPIE galaxies, constrained by 237 spectroscopically confirmed images. When Euclidised data are used together with spectroscopic redshifts for 31 detected images of 12 sources, the resulting EM\(_{\rm spec}\) model attains \(\Delta_{\rm RMS}=0.39''\), which is \(9\%\) smaller than the B23 value of \(0.43''\). In the EM\(_{\rm phot}\) configuration, where photometric redshifts are used with \(\sigma_z=0.05(1+z)\), the rms increases to \(\Delta_{\rm RMS}=0.53''\) [2508.20860]. The same study reports that the total projected mass within the critical curves is recovered to \(\lesssim5\%\) [2508.20860].

The code was also used to simulate galaxy-scale strong lenses, specifically SDSS J0946+1006 and HE0435\(-\)1223, in regions representative of the Euclid Wide Survey [2508.20860]. For Euclid Deep Survey preparation, it generated a simulated \(150''\times150''\) view of the Chandra Deep Field South at \(t_{\rm exp}=90\,744\) s and \(m_{\rm lim}=26.5\) at \(10\sigma\) [2508.20860]. In the abstract-level framing, the methodology is presented as suitable for validating legacy science cases and for training deep-learning techniques before Euclid data become available [2508.20860].

For cluster lensing in particular, the mock data were used to assess whether Euclid-quality imaging alone is sufficient for model construction. The stated conclusion is conditional: complementary photometric or spectroscopic follow-up campaigns are required to measure the redshifts of multiple images and cluster member galaxies [2508.20860]. That requirement places HST2EUCLID not only in the category of image simulation software, but also in the planning infrastructure for coordinated survey follow-up.

## 6. Limitations, systematics, and relation to weak-lensing calibration

The limitations explicitly identified for HST2EUCLID are primarily spectrophotometric and instrumental [2508.20860]. The \(H_{\rm E}\) band relies solely on F160W because HST lacks coverage beyond \(1.6~\mu{\rm m}\), which entails the assumption \(f(\nu)={\rm const}\) over the \(H_{\rm E}\) band. Cosmic rays, stray light, and detector cosmetic effects are not modelled, although the code is described as modular and able to ingest custom cosmic-ray masks or a full instrument simulator such as SIXTE. The current PSF modelling uses TinyTim and is identified as a candidate for replacement with end-to-end Euclid PSF simulations such as Mantisale. Additional planned enhancements include lens-light subtraction, sky gradients, and scattered-light features [2508.20860].

The broader weak-lensing Euclidisation study identifies several systematics that are directly relevant whenever HST-derived mocks are used for shear calibration rather than for general image realism [2501.08372]. In that work, the difference between direct Euclid-like simulations and Euclidised HST simulations is quantified by
\[
\Delta m = m_E-m_D, \qquad \Delta c = c_E-c_D,
\]
with Euclid-quality calibration targets \(|\Delta m|<2\times10^{-3}\) and \(|\Delta c|<5\times10^{-5}\) [2501.08372]. Using native pixel scales, the Lanczos–15 interpolation kernel, noise-correlation correction, and consistent galaxy signal-to-noise ratios between branches reduced residual multiplicative biases to sub-percent levels; finer sampling at \(0.04''\) reduced \(\Delta m\) further to \(\lesssim2\times10^{-3}\) at \(S/N\ge20\), while \(\Delta c\) remained \(\lesssim5\times10^{-5}\) [2501.08372]. The same analysis found that a \(10\%\) uncertainty in the extra Gaussian noise \(\sigma_G\) propagates to \(\delta(\Delta m)\sim10^{-3}\), and that PSF-model residuals can drive additive bias unless neutralised via random rotations or post-deconvolution isotropisation [2501.08372].

Taken together, these results delineate the current status of HST-derived Euclid simulation. HST2EUCLID already supports realistic multi-band survey emulation, strong-lensing feasibility studies, and training-data generation [2508.20860]. The companion calibration literature indicates that, for weak-lensing shear calibration, additional care is required in the treatment of correlated noise, interpolation, PSF anisotropy, and galaxy morphology beyond single Sérsic models [2501.08372]. This suggests that HST2EUCLID is mature as a Euclid-preparation framework for realistic image synthesis, while calibration-grade lensing deployment remains coupled to the more stringent systematic controls developed in the wider Euclidisation program.

Source: https://www.emergentmind.com/topics/hst2euclid