Further author information: (Send correspondence to M.S.)
M.S.: E-mail<EMAIL_ADDRESS>
# The MICADO first light imager for the ELT:
off-axis performance of PSF reconstruction

Matteo Simioni  INAF – Osservatorio Astronomico di Padova, Vicolo Osservatorio
5, I-35122, Padova, Italy  Daniel Jodlbauer  Industrial Mathematics Institute,
Johannes Kepler University, Altenberger Straße 69, Linz, 4040, Linz, Austria
Carmelo Arcidiacono  INAF – Osservatorio Astronomico di Padova, Vicolo
Osservatorio 5, I-35122, Padova, Italy  Andrea Grazian  INAF – Osservatorio
Astronomico di Padova, Vicolo Osservatorio 5, I-35122, Padova, Italy  Marco
Gullieuszik  INAF – Osservatorio Astronomico di Padova, Vicolo Osservatorio 5,
I-35122, Padova, Italy  Elisa Portaluri  INAF – Osservatorio Astronomico
d’Abruzzo, Via Mentore Maggini, I-64100, Teramo, Italy  Benedetta Vulcani
INAF – Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, I-35122,
Padova, Italy  Roland Wagner  Johann Radon Institute for Computational and
Applied Mathematics of the Austrian Academy of Sciences (RICAM), Altenberger
Straße 69, 4040, Linz, Austria  Anita Zanella  INAF – Osservatorio Astronomico
di Padova, Vicolo Osservatorio 5, I-35122, Padova, Italy  Johanna Hartke
Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Finland
University of Turku, Turun yliopisto, FI-20014, Turku, Finland  Tapio Helin
LUT University, Yliopistonkatu 34, 53850, Lappeenranta, Finland  Hanindyo
Kuncarayakti  University of Turku, Turun yliopisto, FI-20014, Turku, Finland
Fernando Pedichini  INAF - Osservatorio astronomico di Roma, Via Frascati 33,
I-00078, Monte Porzio Catone, Italy  Roberto Piazzesi  INAF - Osservatorio
astronomico di Roma, Via Frascati 33, I-00078, Monte Porzio Catone, Italy
Piero Vaccari  INAF - Osservatorio astronomico di Roma, Via Frascati 33,
I-00078, Monte Porzio Catone, Italy

###### Abstract

The highest scientific return, for adaptive optics (AO) observations, is
achieved with a reliable reconstruction of the PSF. This is especially true
for MICADO@ELT. In this presentation, we will focus on extending the MICADO
PSF reconstruction (PSF-R) method to the off-axis case. Specifically, a novel
approach based on temporal-based tomography of AO telemetry data has been
recently implemented. Results from the PSF-R of both simulated and real data
show that, at half isoplanatic angle distances, a precision of about $10-15\%$
is achievable in both Strehl ratio and full-width at half maximum, paving the
way to extend the MICADO PSF-R tool also to the multi-conjugated AO case.

###### keywords:

Adaptive optics, Point spread functions, Point spread function reconstruction,
Infrared imaging, Astronomy, MICADO@ELT, MICADO PSF reconstruction, ERIS@VLT
PSF reconstruction

##  1 INTRODUCTION

MICADO[1] will be the first-light adaptive optics (AO) assisted imager of the
ESO extremely large telescope. When integrated, it will operate in single-
conjugated AO (SCAO) mode. Multi-conjugate AO (MCAO) observations will be
subsequently possible with MICADO when MORFEO[2] will start operations. It
will also be the first ESO instrument designed to offer a PSF reconstruction
(PSF-R) service to the final user: the detailed knowledge of the PSF is
crucial for the majority of the planned scientific drivers[3, 4]. In this
context, the core algorithm of the MICADO PSF-R tool[5] follows a telemetry-
only approach and the PSF is reconstructed without using information from the
science images. It will rely instead on the analysis of the AO telemetry,
recorded simultaneously with the scientific observations, on careful
calibrations, and on additional external information (e.g. regarding the
turbulence profile).

The MICADO PSF-R tool was proven to work once applied to real SCAO on-axis
observations (e.g. reconstructing SOUL+LUCI@LBT data[6]), consistently
achieving precision in the reconstruction of the on-axis PSF of the order of
$2-5\%$ in both Strehl Ratio (SR) and full-width at half maximum (FWHM) and
highlighting the versatility of the method.

However, the highest scientific return, especially for SCAO observations, is
achieved with a reliable reconstruction of the off-axis PSF. This capability
has been recently implemented in the MICADO PSF-R algorithm enabling the
derivation of the residual incoming wavefront in any selected off-axis
direction through a temporal-based tomography of AO telemetry data[7].

Our off-axis method was evaluated using both simulated[7, 8] and real SCAO
data. This presentation will focus on validating our PSF-R method using real
data, specifically SCAO observations of off-axis point sources. In addition, a
scientific evaluation has been performed, using the simulated off-axis PSFs to
quantify the impact of our PSF-R, on a selected, idealized scientific case:
the morphology of compact star-forming regions in high-redshift galaxies.

##  2 DATA

The data used consists of ERIS@VLT[9] SCAO observations of a bright asterism,
obtained in the context of a dedicated ESO technical time request (TTR). Three
bright stars are present in the observed field of view (FoV), one of them has
been used as the AO reference star (i.e. has been observed on-axis) while the
other $2$ have a radial distance of $7"$ and $16"$ respectively.

---
Figure 1:  Comparison between observed (left column) and reconstructed (middle
column) ERIS@VLT PSFs; Rows are associated with increasing off-axis distance
from top to bottom: S2 is the AO reference star, S3 is the $7"$ off-axis one
while S1 has an off-axis distance of $16"$. PSFs are shown in logarithmic
color scale, residuals ($|$O-R$|$, right column) in linear color scale. The
box width is $110$px ($1".4$).

The observed PSFs elongation is proportional to off-axis distance and is
mostly radially aligned with the AO reference star. The different elongation
of the observed PSFs can be appreciated in the left panels of Figure 1.
Magnitudes are in the range H$=9-9.5$ VEGAmag and the observations have been
performed in Fe-II narrow-band filter (${\rm\lambda_{c}}=1.644{\rm\mu m}$). We
analyzed $225$s of continuous observations subdivided in frames of $1$s each.
The data is accompanied by the associated AO telemetry, saved simultaneously
to scientific observations[5, 6, 7] with a frequency of $1$KHz.

In addition to ERIS data, a sample of simulated MICADO@ELT SCAO off-axis PSFs
has been considered, the associated reconstructed PSFs have already been
presented in Ref. 8. They are $3$ simulated 30” off-axis SCAO PSFs at
$2.2{\rm\mu m}$ (e.g. K band) with different AO reference brightness regimes.

##  3 DISCUSSION

The tomographic approach of the MICADO PSF-R[7] requires an estimation of the
atmospheric turbulence and the wind vector profiles, in addition to the
information already needed for the on-axis reconstruction[5, 6]. In the
present reconstruction, we integrated MASS-DIMM measurements with accurate
wind model predictions[10], to obtain a sampling of the atmosphere of $3$
layers at the height of $0.1$, $1$, and $10$ km. The resulting reconstructed
PSFs are reported in Figure 1 (middle column).

---
Figure 2:  Comparison between the radial profiles of observed PSFs (black
lines) and of the reconstructed ones (red lines). Off-axis distance is
increasing from left to right, the name convention for the PSFs is the same as
in Figure 1. A logarithmic scale has been used for the luminosity and the
radial distance. All the profiles are normalized in flux on a circular
aperture of radius $100$px ($1".3$, maximum radial distance shown). As a
reference, a signal-to-noise ratio of $5$ for the observed PSFs is also
marked.

From the residuals, rightmost column of Figure 1, the good agreement between
each pair of observed and reconstructed PSFs can be noted. This can be further
quantified from Figure 2 where the radial plots are shown with increasing off-
axis distance from left to right. All the profiles are normalized in flux and
the same scale has been used for the $3$ stars highlighting the decrease of SR
at increasing off-axis distance.

As a consistency check, the obtained SR values as a function of off-axis
distance have been used to derive an isoplanatic angle[11, 12, 13]:

$SR(\theta)\propto\exp{\left(\frac{\theta}{\theta_{0}}\right)^{5/3}}$

where $\theta_{0}$ is the isoplanatic angle and $\theta$ is the off-axis
distance. The isoplanatic angle, in the wavelength of observations, that best
reproduces the observed data, results in $\theta_{0,OBS}=25".41$, while using
the reconstructed PSFs a $\theta_{0,REC}=32".04$ results. For comparison,
MASS-DIMM measurements associated with the observations111the Fried parameter
r0 is proportional to $\lambda^{6/5}$[14]. provide a $\theta_{0,1.65{\rm\mu
m}}=16".00$. The corresponding anisoplanatisms are reported in Figure 3. A
possible cause for the higher value of $\theta_{0,OBS}$ compared to the MASS-
DIMM measurements could be the VLT telescope vibrations: these are fully
isoplanatic and intrinsic of the VLT telescope and not to the DIMM which is on
a separated mounting on the Paranal platform.

---
Figure 3:  Anisoplanatism derived from the distribution of measured SR in the
ERIS observations (black line) is compared with the anisoplanatism obtained
from the reconstructed PSFs (red line). For reference, the same quantity
derived from MASS-DIMM measurements, at the same wavelength, is also reported
(azure line).

The performance of our PSF-R method, in the SCAO off-axis case is reported in
Table 1. For each SCAO off-axis PSF considered, and the associated
reconstructed one, the values of SR, FWHM, and encircled energy of the core
are provided. A precision of the reconstruction of the order of $10\%$ is
reached in each case.

Table 1: Off-axis PSF-R results for real ERIS SCAO data (first 2 columns) and simulated MICADO ones (last 3 columns). For each dataset, values of SR, FWHM, and encircled energy of the core are provided, along with the effective wavelength of the PSF ($\lambda_{\rm eff}$) and the off-axis distance. | REAL | SIMULATED
---|---|---
| ERIS_7” | ERIS_16” | MICADO_bright | MICADO_int. | MICADO_faint
SR${}_{\rm OBS}\,[\%]$ | 60 | 45 | 12 | 12 | 7
SR${}_{\rm REC}\,[\%]$ | 50 | 51 | 13 | 12 | 8
FWHM${}_{\rm OBS}\,[mas]$ | 54 | 56 | 13 | 13 | 14
FWHM${}_{\rm REC}\,[mas]$ | 53 | 54 | 12 | 13 | 13
EEcore,OBS | 0.35 | 0.24 | 0.07 | 0.07 | 0.04
EEcore,REC | 0.33 | 0.30 | 0.07 | 0.07 | 0.04
$\lambda_{\rm eff}\,[{\rm\mu m}]$ | 1.65 | 1.65 | 2.2 | 2.2 | 2.2
off-axis $["]$ | 7 | 16 | 30 | 30 | 30

It can be noted that the reconstruction accuracy is, on average, higher for
MICADO PSFs. This is due, in part, to the total control over the input
atmospheric conditions: something that with real data cannot be easily
achieved. Still, fundamental sources of errors, intrinsic to the temporal
tomography approach, are already included; for example, approximating the
initial conditions with a model atmosphere of just $3$ layers for the
reconstruction.

###  3.1 Scientifc evaluation of MICADO off-axis PSF-R

An important activity of the MICADO PSF-R team, complementing the development
of the MICADO PSF-R tool, is the scientific evaluation of the reconstructed
PSFs[3, 4]. Specifically, we focus on assessing how the PSF-R performances
affect the measurement of scientific quantities in selected science cases. Our
telemetry-only PSF-R approach is particularly convenient in the case of
typical extra-galactic observations, where too few (or none) suitable point
sources are present in the field of view to characterize the PSF directly from
scientific frames[3, 15, 6]. For this reason, we use the MICADO off-axis PSF
associated with the intermediate AO reference brightness regime, as the
template PSF for generating MICADO SCAO simulated observations of a typical
z=2 galaxy hosting a population of star-forming regions. Specifically,
SimCADO[16] has been used to create MICADO observations, using GALFIT[17] for
both generating the input galaxy model and, later, to perform the
morphological and photometric analysis on the obtained images.

The galaxy model used to generate the simulated MICADO observations samples a
large interval of star-forming region sizes (and consequently brightness; see
e.g. Ref. 18), but we are primarily interested in exploring the effect of
PSF-R in the high spatial-resolution regime, where accurately reconstructing
the shape of the PSF, and in particular matching its FWHM, is fundamental.
Specifically, the resolution limit of MICADO, in terms of the radius of
compact sources at redshift $2$ is about $45$pc, which corresponds to $\sim
5.2$mas ($40\%$ of PSF FWHM with a pixel-scale of $4$mas/px).

---
Figure 4:  Scientific evaluation results: characterization of the size (bottom
panel) and luminosity (top panel) of a compact star-forming region in a
typical z$=2$ galaxy. The input size of the star-forming region is $45$ pc;
the MICADO 30” off-axis PSF is used as a template and the effect of using
different PSFs is evaluated. The star-forming region cannot be resolved if no
information on the PSF is available (NONE). Moreover, also the associated on-
axis MICADO PSF is not a good representation of the actual PSF. In this case,
the obtained reconstructed PSF (off-axis) allows the successful recovery of
both the size and the luminosity of the star-forming region.

The results of the analysis are presented in Figure 4. They indicate that the
precision reached by our off-axis PSF-R on MICADO PSFs allows the successful
recovery of both the morphological (with an error around $20\%$ in size) and
photometric properties of the selected star-forming region.

##  4 CONCLUSION

In the context of the MICADO PSF-R, a tomographic method has been recently
implemented in the algorithm to allow the reconstruction of off-axis PSFs in
SCAO observations, without using any information coming from the scientific
images[7]. We used dedicated ERIS@VLT observations (taken in the context of an
ESO TTR) of a bright asterism of $3$ stars, to validate the method with real
SCAO data.

A precision of the order of $10\%$ can be achieved in SR, FWHM, and encircled
energy of the core can be achieved for off-axis distances up to half
isoplanatic angle. The current results are already paving the way to extend
the tool for MCAO observations; still, an extended dataset is needed to
properly assess the consistency and applicability of the MICADO PSF-R method.
For this purpose, the mentioned ESO TTR is aimed at collecting ERIS SCAO data
as diverse as possible in terms of atmospheric and AO conditions. All the
planned observations will be available to the community.

Finally, our off-axis PSF-R method has been applied also to simulated MICADO
PSFs. A 30” off-axis MICADO SCAO PSF has been used to assess the impact of the
PSF-R on the characterization of a compact star-forming region in an idealized
z=2 galaxy. Encouraging results have been obtained using the reconstructed
PSF, both in terms of size of the star-forming region ($\sim 20\%$ error in
effective radius) and of its luminosity (of the order of $0.2$mag in
integrated magnitude), suggesting that an acceptable precision could be
reached with our PSF-R tool.

###### Acknowledgements.

We thank E. Valenti, M. LeLouarn, J. Vernet, and M. Cirasuolo of ESO for their
effort in preparing and coordinating the ERIS technical time requests. We also
thank E. Masciadri for providing wind vector estimates used in the computation
of the reconstructed PSFs of ERIS@VLT data. MS and AG acknowledge partial
support from Bando Ricerca Fondamentale INAF 2023 (Ob. Fu. 1.05.23.04.05, P.I.
Simioni).

## References

  * [1] Davies, R., Schubert, J., Hartl, M., Alves, J., Clénet, Y., Lang-Bardl, F., Nicklas, H., Pott, J. U., Ragazzoni, R., Tolstoy, E., Agocs, T., Anwand-Heerwart, H., Barboza, S., Baudoz, P., Bender, R., Bizenberger, P., Boccaletti, A., Boland, W., Bonifacio, P., Briegel, F., Buey, T., Chapron, F., Cohen, M., Czoske, O., Dreizler, S., Falomo, R., Feautrier, P., Förster Schreiber, N., Gendron, E., Genzel, R., Glück, M., Gratadour, D., Greimel, R., Grupp, F., Häuser, M., Haug, M., Hennawi, J., Hess, H. J., Hörmann, V., Hofferbert, R., Hopp, U., Hubert, Z., Ives, D., Kausch, W., Kerber, F., Kravcar, H., Kuijken, K., Lang-Bardl, F., Leitzinger, M., Leschinski, K., Massari, D., Mei, S., Merlin, F., Mohr, L., Monna, A., Müller, F., Navarro, R., Plattner, M., Przybilla, N., Ramlau, R., Ramsay, S., Ratzka, T., Rhode, P., Richter, J., Rix, H. W., Rodeghiero, G., Rohloff, R. R., Rousset, G., Ruddenklau, R., Schaffenroth, V., Schlichter, J., Sevin, A., Stuik, R., Sturm, E., Thomas, J., Tromp, N., Turatto, M., Verdoes-Kleijn, G., Vidal, F., Wagner, R., Wegner, M., Zeilinger, W., Ziegler, B., and Zins, G., “MICADO: first light imager for the E-ELT,” in [Ground-based and Airborne Instrumentation for Astronomy VI ], Evans, C. J., Simard, L., and Takami, H., eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 9908, 99081Z (Aug. 2016).
  * [2] Ciliegi, P., Agapito, G., Aliverti, M., Annibali, F., Arcidiacono, C., Azzaroli, N., Balestra, A., Baronchelli, I., Baruffolo, A., Bergomi, M., Bianco, A., Bonaglia, M., Briguglio, R., Busoni, L., Cantiello, M., Capasso, G., Carlà, G., Carolo, E., Cascone, E., Chinellato, S., Cianniello, V., Colapietro, M., Correia, J.-J., Cosentino, G., D’Auria, D., De Caprio, V., Devaney, N., Di Antonio, I., Di Cianno, A., Di Dato, A., Di Giammatteo, U., Di Rico, G., Dolci, M., Eredia, C., Esposito, S., Fantinel, D., Farinato, J., Feautrier, P., Foppiani, I., Genoni, M., Giro, E., Gluck, L., Goncharov, A., Grani, P., Greggio, D., Guieu, S., Gullieuszik, M., Haguenauer, P., Hubert, Z., Lapucci, T., Laudisio, F., Le Louarn, M., Magrin, D., Malone, D., Marafatto, L., Munari, M., Oberti, S., Pariani, G., Pettazzi, L., Plantet, C., Portaluri, E., Puglisi, A., Rabou, P., Ragazzoni, R., Redaelli, E., Riva, M., Rochat, S., Rodeghiero, G., Salasnich, B., Savarese, S., Scalera, M., Schipani, P., Sordo, R., Sztefek, M.-H., Valentini, A., and Xompero, M., “MAORY/MORFEO at ELT: general overview up to the preliminary design and a look towards the final design,” in [Adaptive Optics Systems VIII ], Schreiber, L., Schmidt, D., and Vernet, E., eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 12185, 1218514 (Aug. 2022).
  * [3] Simioni, M., Arcidiacono, C., Grazian, A., Clenet, Y., Davies, R., Gullieuszik, M., Verdoes Kleijn, G., Pedichini, F., Wagner, R., Ramlau, R., Zeilinger, W. W., Vidal, F., Vulcani, B., Ragazzoni, R., Sevin, A., Salasnich, B., Baruffolo, A., Busoni, L., Esposito, S., Gendron, É., Piazzesi, R., Portaluri, E., Zanella, A., Helin, T., Kuncarayakti, H., Mattila, S., Falomo, R., and Pinna, E., “MICADO PSF-reconstruction work package description,” in [Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series ], Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 11448, 1144837 (Dec. 2020).
  * [4] Grazian, A., Simioni, M., Arcidiacono, C., Achren, J., Clenet, Y., Cao, Y., Davies, R., Gullieuszik, M., Helin, T., Jodlbauer, D., Kuncarayakti, H., Le Louarn, M., Mattila, S., Pedichini, F., Piazzesi, R., Portaluri, E., Verdoes Kleijn, G., Vulcani, B., Wagner, R., Williams, S., Zanella, A., and Zeilinger, W. W., “Status of the PSF reconstruction work package for MICADO at ELT,” in [Adaptive Optics Systems VIII ], Schreiber, L., Schmidt, D., and Vernet, E., eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 12185, 1218541 (Aug. 2022).
  * [5] Wagner, R., Hofer, C., and Ramlau, R., “Point spread function reconstruction for single-conjugate adaptive optics on extremely large telescopes,” Journal of Astronomical Telescopes, Instruments, and Systems 4, 049003 (Oct. 2018).
  * [6] Simioni, M., Arcidiacono, C., Wagner, R., Grazian, A., Gullieuszik, M., Portaluri, E., Vulcani, B., Zanella, A., Agapito, G., Davies, R., Helin, T., Pedichini, F., Piazzesi, R., Pinna, E., Ramlau, R., Rossi, F., and Salo, A., “Point spread function reconstruction for SOUL + LUCI LBT data,” Journal of Astronomical Telescopes, Instruments, and Systems 8, 038003 (July 2022).
  * [7] Wagner, R., Niebsch, J., and Ramlau, R., “Off-axis point spread function reconstruction for single conjugate adaptive optics,” Journal of the Optical Society of America A 40, 1382 (July 2023).
  * [8] Simioni, M., Arcidiacono, C., Grazian, A., Gullieuszik, M., Portaluri, E., Vulcani, B., Wagner, R., and Zanella, A., “Towards the MICADO@ELT PSF-R with simulated and real data,” in [Adaptive Optics for Extremely Large Telescopes (AO4ELT7) ], 34 (June 2023).
  * [9] Davies, R., Absil, O., Agapito, G., Agudo Berbel, A., Baruffolo, A., Biliotti, V., Black, M., Bonaglia, M., Bonse, M., Briguglio, R., Campana, P., Cao, Y., Carbonaro, L., Cortes, A., Cresci, G., Dallilar, Y., Dannert, F., De Rosa, R. J., Deysenroth, M., Di Antonio, I., Di Cianno, A., Di Rico, G., Doelman, D., Dolci, M., Dorn, R., Eisenhauer, F., Esposito, S., Fantinel, D., Ferruzzi, D., Feuchtgruber, H., Finger, G., Förster Schreiber, N. M., Gao, X., Gemperlein, H., Genzel, R., Gillessen, S., Ginski, C., Glauser, A. M., Glindemann, A., Grani, P., Hartl, M., Hayoz, J., Heida, M., Henry, D., Hofmann, R., Huber, H., Kasper, M., Keller, C., Kenworthy, M., Kravchenko, K., Kuntschner, H., Lacour, S., Lightfoot, J., Lunney, D., Lutz, D., Macintosh, M., Mannucci, F., Marsset, M., Modigliani, A., Neeser, M., Orban de Xivry, G., Ott, T., Pallanca, L., Patapis, P., Pearson, D., Peña, E., Percheron, I., Puglisi, A., Quanz, S. P., Rabien, S., Rau, C., Riccardi, A., Salasnich, B., Schmid, H. M., Schubert, J., Serra, B., Shimizu, T., Snik, F., Sturm, E., Tacconi, L., Taylor, W., Valentini, A., Waring, C., Wiezorrek, E., and Xompero, M., “The Enhanced Resolution Imager and Spectrograph for the VLT,” Astronomy & Astrophysics 674, A207 (June 2023).
  * [10] Masciadri, E., Lascaux, F., and Fini, L., “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites - I. Overview and vertical stratification of atmospheric parameters at 0-20 km,” MNRAS 436, 1968–1985 (Dec. 2013).
  * [11] Fried, D. L., “Anisoplanatism in adaptive optics,” Journal of the Optical Society of America (1917-1983) 72, 52 (Jan. 1982).
  * [12] Beckers, J. M., “Adaptive Optics for Astronomy: Principles, Performance, and Applications,” ARA&A 31, 13–62 (Jan. 1993).
  * [13] Roddier, F., [Adaptive optics in astronomy ], Cambridge University Press (1999).
  * [14] Fried, D. L., “Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures,” Journal of the Optical Society of America (1917-1983) 56, 1372 (Oct. 1966).
  * [15] Simioni, M., Arcidiacono, C., Wagner, R., Grazian, A., Gullieuszik, M., Portaluri, E., Vulcani, B., Zanella, A., Agapito, G., Davies, R., Helin, T., Pedichini, F., Piazzesi, R., Pinna, E., Ramlau, R., Rossi, F., and Salo, A., “LBT SOUL data as a science test bench for MICADO PSF-R tool,” in [Adaptive Optics Systems VIII ], Schreiber, L., Schmidt, D., and Vernet, E., eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 12185, 121850D (Aug. 2022).
  * [16] Leschinski, K., Czoske, O., Köhler, R., Mach, M., Zeilinger, W., Verdoes Kleijn, G., Alves, J., Kausch, W., and Przybilla, N., “SimCADO: an instrument data simulator package for MICADO at the E-ELT,” in [Modeling, Systems Engineering, and Project Management for Astronomy VI ], Angeli, G. Z. and Dierickx, P., eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 9911, 991124 (Aug. 2016).
  * [17] Peng, C. Y., Ho, L. C., Impey, C. D., and Rix, H.-W., “Detailed Decomposition of Galaxy Images. II. Beyond Axisymmetric Models,” Astronomical Journal 139, 2097–2129 (June 2010).
  * [18] Meštrić, U., Vanzella, E., Zanella, A., Castellano, M., Calura, F., Rosati, P., Bergamini, P., Mercurio, A., Meneghetti, M., Grillo, C., Caminha, G. B., Nonino, M., Merlin, E., Cupani, G., and Sani, E., “Exploring the physical properties of lensed star-forming clumps at 2 $\lesssim$ z $\lesssim$ 6,” MNRAS 516, 3532–3555 (Nov. 2022).