Impact of water vapor seeing on mid-infrared high-contrast imaging at ELT scale Olivier Absila Christian Delacroixa Gilles Orban de Xivrya Prashant Pathaka

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Impact of water vapor seeing on mid-infrared high-contrast

imaging at ELT scale

Olivier Absila, Christian Delacroixa, Gilles Orban de Xivrya, Prashant Pathaka,

Matthew Willsona,†, Philippe Beriob, Roy van Boekelc, Alexis Matterb, Denis Defr`ered,

Leo Burtschere, Julien Woillezf, and Bernhard Brandle

aSTAR Institute, Universit´e de Li`ege, All´ee du Six Aoˆut 19c, B-4000 Li`ege, Belgium

bUniversit´e Cˆote d’Azur, Observatoire de la Cˆote d’Azur, CNRS, Laboratoire Lagrange, Parc

Valrose, Bˆat H. Fizeau, 06108 Nice, France

cMax-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, Heidelberg 69117, Germany

dInstitute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium

eLeiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands

fEuropean Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany

ABSTRACT

The high-speed variability of the local water vapor content in the Earth atmosphere is a signiﬁcant contributor to

ground-based wavefront quality throughout the infrared domain. Unlike dry air, water vapor is highly chromatic,

especially in the mid-infrared. This means that adaptive optics correction in the visible or near-infrared domain

does not necessarily ensure a high wavefront quality at longer wavelengths. Here, we use literature measurements

of water vapor seeing, and more recent infrared interferometric data from the Very Large Telescope Interferom-

eter (VLTI), to evaluate the wavefront quality that will be delivered to the METIS mid-infrared camera and

spectrograph for the Extremely Large Telescope (ELT), operating from 3 to 13 µm, after single-conjugate adap-

tive optics correction in the near-infrared. We discuss how the additional wavefront error due to water vapor

seeing is expected to dominate the wavefront quality budget at N band (8–13 µm), and therefore to drive the

performance of mid-infrared high-contrast imaging modes at ELT scale. Then we present how the METIS team

is planning to mitigate the eﬀect of water vapor seeing using focal-plane wavefront sensing techniques, and show

with end-to-end simulations by how much the high-contrast imaging performance can be improved.

Keywords: high-contrast imaging, mid-infrared instrumentation, wavefront control, atmospheric eﬀects, water

vapor seeing

1. INTRODUCTION

In the standard theory of turbulence, atmospheric seeing results from local variations of refractive index that are

transported by the wind. At optical wavelengths, dry air is the dominant source of refractive index variations,

although there is a small refractivity (and hence seeing) contribution that can be attributed to atmospheric

water vapor (WV), and to other minor species (such as CO2) not considered here. Both dry air and water vapor

are slightly dispersive in the visible. At infrared wavelengths, dry air becomes much less dispersive, while WV

become increasingly dispersive. This is illustrated in Fig. 1, where we show the reduced refractive indices ˆn(λ)

for dry air and WV, deﬁned as follows:

ˆn(λ) = n(λ)−1

cρ ,(1)

with n(λ) the refractive index, cthe speed of light, and ρthe molar density in mol/m3. The reduced refractive

index will be expressed in units of femtoseconds per mol/m2throughout this document.

E-mail: olivier.absil@uliege.be

†This work is dedicated to our colleage and friend Matthew Willson, who tragically passed away in January 2022.

Matt made strong contributions to the development of focal-plane wavefront sensing for ELT/METIS.

arXiv:2210.12412v1 [astro-ph.IM] 22 Oct 2022

Figure 1. Reduced refractive indices of dry air (left) and water vapor (right), in units of fs/(mol/m2), based on the model

of Mathar.1The eﬀect of CO2absorption is included in the model of dry air used here, for the sake of illustration.

Figure 2. Reduced refractive index of WDA, for standard conditions at Cerro Paranal (288 K, 743 mbar).

When the wavefront is controlled at optical or near-infrared wavelengths, like for the METIS single-conjugate

adaptive optics (SCAO) operating at H–K bands, this dispersion can lead to strong additional wavefront errors

at mid-infrared wavelengths, which are not seen by the wavefront control system and therefore not corrected.

This eﬀect was extensively studied in the context of mid-infrared interferometers in the early 2000s,2,3and was

ﬁrst investigated in the context of mid-infrared instrumentation for extremely large telescopes in the late 2000s.4

A convenient quantity to describe the contribution of WV to atmospheric seeing is water displacing air (WDA),

introduced in Ref. 2. Holding the pressure (and temperature) constant, a column density ﬂuctuation of WV

induces an opposite variation in the dry air column density. We can thus deﬁne a mole of WDA as one mole of

WV plus one negative mole of dry air. Consequently, WDA has a reduced refraction index ˆnWDA = ˆnWV −ˆnair.

At infrared wavelengths, the reduced refraction index of WDA is negative, as shown in Fig. 2. With the concept

of WDA, a given quantity of air can be modeled as an amount of dry air, given solely by the ambient temperature

and pressure, plus a quantity of WDA representing the humidity.

2. WATER VAPOR SEEING

As can be seen in Fig. 2, a given amount of WV along the line-of-sight creates a strong chromatic dependence

in the mid-infrared refractive index of the atmosphere. The wavefront error seen by the METIS SCAO at H–K

Figure 3. Conceptual illustration of WV seeing, where blue circles represent WV molecules in the air, and the rectangular

shades of blue the local column density of WV.

bands will therefore not be the same as the wavefront error inside the METIS imager and spectrograph, which

cover the L, M and N bands, with an additional delay of about 0.5 fs/(mol/m2) between K and L band, and of

6 fs/(mol/m2) between K and N band. The additional delay (and hence wavefront error) depends on the local

column density of WV above the telescope aperture, as conceptually illustrated in Fig. 3. The non-uniformity

of the WV distribution in the air creates additional spatial variations in the wavefront, which are blown over

the telescope pupil by the wind, like in the frozen ﬂow turbulence model. It is therefore expected that WV

turbulence follows a Kolmogorov – von Karman statistics like dry air turbulence. This hypothesis was veriﬁed

experimentally in Refs. 5and 6.

2.1 Measurements from the literature

In order to predict the eﬀect of WV seeing on wavefront errors at mid-infrared wavelengths, one needs to know

the spatio-temporal variations of the WV column density. Some measurements of this kind are available in the

literature:

•Masson5used two sub-mm dishes separated by 100 m at Mauna Kea to measure the path length ﬂuctuations

due to WV. The measured variance of the column number density is 4 ×1019 cm−2over 15 minutes, which

corresponds to 0.66 mol/m2rms. Based on the same data, Colavita et al.3infer that the median water-

vapor seeing from the visible to the L band should be ∼1/20 of dry air seeing, and ∼1/7 at 10 µm.

•A similar setup at the Owens Valley Radio Observatory (OVRO) used by Lay6suggests a typical level of

ﬂuctuations of 1.5 mol/m2over a 100-m baseline (see also Ref. 2). These authors also suggests that the

outer scale of turbulence might be signiﬁcantly larger for WV turbulence than for dry air turbulence, which

would lead to generally slower ﬂuctuations than dry air.

•Meisner & Le Poole2mention that group delay measurement with VINCI at VLTI have yielded estimates

ranging from 0.5 mol/m2on a 16-m baseline to about 1.8 mol/m2on a 66-m baseline, on a 100-s timescale.

•Another type of experiment was conducted by Kerber et al.,7using all-sky precipitable water vapor (PWV)

measurements with a microwave radiometer at Paranal. These measurements suggest a median variation

of 0.07 mm in PWV over the entire sky, down to 27.5 deg elevation. That corresponds to 3.8 mol/m2rms,

and should probably be regarded as an upper limit of what could be experienced by single-dish observations

along a given line of sight.

Based on the results mentioned above, we should expect for a high-quality astronomical observing site like

Cerro Armazones to have an average WV column density ﬂuctuation of the order of 1 mol/m2rms on a 100 m

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Impactofwatervaporseeingonmid-infraredhigh-contrastimagingatELTscaleOlivierAbsila,ChristianDelacroixa,GillesOrbandeXivrya,PrashantPathaka,MatthewWillsona,,PhilippeBeriob,RoyvanBoekelc,AlexisMatterb,DenisDefrered,LeoBurtschere,JulienWoillezf,andBernhardBrandleaSTARInstitute,UniversitedeLiege,All...

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Impact of water vapor seeing on mid-infrared high-contrast imaging at ELT scale Olivier Absila Christian Delacroixa Gilles Orban de Xivrya Prashant Pathaka

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