# Altering reality to fit our turbulence simulations... A slow descent into madness?

Olivier Lai, Kanoa Withington, Mark Chun

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Olivier Lai, Kanoa Withington, Mark Chun. Altering reality to fit our turbulence simulations... A slow descent into madness?. COAT 2023: Communications and Observations through Atmospheric Turbulence, James Osborne, Mar 2023, Durham (GB), United Kingdom. hal-04605075

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<figure><img src="image_1.png" /></figure>
# Altering reality to fit our turbulence simulations...
## A slow descent into madness?

Olivier Lai*<sup>a</sup>, Kanoa J. Withington<sup>b</sup>, Mark Chun<sup>c</sup>

<sup>a</sup>Université Côte d'Azur, Observatoire de la Côte d'Azur, Laboratoire Lagrange, Batiment Fizeau, Parc Valrose, 06000 Nice, France; <sup>b</sup>Canada France Hawaii Telescope Corporation, 65-1238

Mamalahoa Hwy, Kamuela, HI 96743, <sup>c</sup>Institute for Astronomy, University of Hawaii, 640 North A‘ohōkū Place, Hilo, HI 96720-2700

## ABSTRACT

Self-generated turbulence and dome seeing are strong contributors to the degradation of astronomical image quality; besides the now infamous low wind effect, strange temporal power spectra, low (temporal) frequency turbulence, high (spatial) frequency turbulence and strong ground layer all point to local effects. Accounting for and including all these sources of image degradation in our modeling seems intractable. Measuring dome turbulence in telescopes as varied as CFHT, LBT, UH88 and ASTEP, we have shown that these effects are transient, stochastic, and non-stationary, and that they depend on too many environmental parameters to be causally interpreted, such as wind speed, direction, dome azimuth, heat sources, radiative cooling in the telescope structure and its (differential) thermal inertia, natural air temperature variations and partial venting. It therefore seems useless, and on top of that very difficult, to estimate realistic AO performance from simulations that would try to incorporate all these effects. Instead of trying to align our simulations to reality, we propose that we try to align reality to our simulations. Indeed, we do not have to incorporate all these effects in our simulations; we can attempt to prevent them from occurring in the first place. Fortunately, local effects can be attenuated or averted at the source but improving on passive methods requires rapid and accurate sensing of turbulence inside the telescope and dome. To this end, we have been trying to develop a “turbulence camera” for almost a decade, but it has proved difficult to design a system with a sufficiently wide field and sufficient sensitivity. In the process, we have developed AIRFLOW, a localized turbulence sensor, and recent work on a wide field wavefront sensor based on optical differentiation may open new possibilities.

**Keywords:** Dome seeing, image quality, turbulence, wavefront sensing

## 1. INTRODUCTION

The image degradation generated by dome seeing has been getting more attention in recent years, as instruments become more sensitive and deviations from standard (Kolmogorov or von Karman) models of turbulence become more obvious: the consequences of the Low Wind Effect on SPHERE at ESO were dramatic, lowering the delivered Strehl ratio from >80% to ~30% [1], but more subtle effects have also been found in Ground Layer Adaptive Optics (GLAO) where the halo of corrected PSFs appears larger than expectation [2]. In fact, weird power spectra (with an excess of high spatial or low temporal frequencies) are not uncommon.

In a good astronomical site, local seeing (including dome, telescope and topography induced) can be a substantial fraction of the image quality degradation, on the order of 0.2” ~ 0.4”, but can also be amplified through aliasing in the AO correction (such as with the low wind effect, or through aliasing). But the more delicate problem is that dome seeing is highly variable and most certainly not stationary, as it is generated by thermal sources inside the dome, the cooling of the telescope structure and dome itself and is therefore dependent on a large variety of configurations, each with its own form of turbulence; in fact turbulence itself may be a little bit of a misnomer, since temperature inversions can generate local gradient in the air, which are not turbulent but can still deviate light beams and degrade image quality. Also, mechanical turbulence at homogeneous temperature does not generate optical turbulence and conversely non-turbulent, or not fully developed turbulent flows can degrade image quality but are much more difficult to include in error budgets or simulations. Furthermore local/dome seeing is almost certainly not Kolmogorov since confined spaces do not allow for energy cascades and equipartition of energy at all scales.

<footnote>* Olivier lai: olivier.lai@oca.eu</footnote>
# Altering reality to fit our turbulence simulations...
## A slow descent into madness?

Olivier Lai*<sup>a</sup>, Kanoa J. Withington<sup>b</sup>, Mark Chun<sup>c</sup>

<sup>a</sup>Université Côte d'Azur, Observatoire de la Côte d'Azur, Laboratoire Lagrange, Batiment Fizeau, Parc Valrose, 06000 Nice, France; <sup>b</sup>Canada France Hawaii Telescope Corporation, 65-1238

Mamalahoa Hwy, Kamuela, HI 96743, <sup>c</sup>Institute for Astronomy, University of Hawaii, 640 North A‘ohōkū Place, Hilo, HI 96720-2700

## ABSTRACT

Self-generated turbulence and dome seeing are strong contributors to the degradation of astronomical image quality; besides the now infamous low wind effect, strange temporal power spectra, low (temporal) frequency turbulence, high (spatial) frequency turbulence and strong ground layer all point to local effects. Accounting for and including all these sources of image degradation in our modeling seems intractable. Measuring dome turbulence in telescopes as varied as CFHT, LBT, UH88 and ASTEP, we have shown that these effects are transient, stochastic, and non-stationary, and that they depend on too many environmental parameters to be causally interpreted, such as wind speed, direction, dome azimuth, heat sources, radiative cooling in the telescope structure and its (differential) thermal inertia, natural air temperature variations and partial venting. It therefore seems useless, and on top of that very difficult, to estimate realistic AO performance from simulations that would try to incorporate all these effects. Instead of trying to align our simulations to reality, we propose that we try to align reality to our simulations. Indeed, we do not have to incorporate all these effects in our simulations; we can attempt to prevent them from occurring in the first place. Fortunately, local effects can be attenuated or averted at the source but improving on passive methods requires rapid and accurate sensing of turbulence inside the telescope and dome. To this end, we have been trying to develop a “turbulence camera” for almost a decade, but it has proved difficult to design a system with a sufficiently wide field and sufficient sensitivity. In the process, we have developed AIRFLOW, a localized turbulence sensor, and recent work on a wide field wavefront sensor based on optical differentiation may open new possibilities.

**Keywords:** Dome seeing, image quality, turbulence, wavefront sensing

## 1. INTRODUCTION

The image degradation generated by dome seeing has been getting more attention in recent years, as instruments become more sensitive and deviations from standard (Kolmogorov or von Karman) models of turbulence become more obvious: the consequences of the Low Wind Effect on SPHERE at ESO were dramatic, lowering the delivered Strehl ratio from >80% to ~30% [1], but more subtle effects have also been found in Ground Layer Adaptive Optics (GLAO) where the halo of corrected PSFs appears larger than expectation [2]. In fact, weird power spectra (with an excess of high spatial or low temporal frequencies) are not uncommon.

In a good astronomical site, local seeing (including dome, telescope and topography induced) can be a substantial fraction of the image quality degradation, on the order of 0.2” ~ 0.4”, but can also be amplified through aliasing in the AO correction (such as with the low wind effect, or through aliasing). But the more delicate problem is that dome seeing is highly variable and most certainly not stationary, as it is generated by thermal sources inside the dome, the cooling of the telescope structure and dome itself and is therefore dependent on a large variety of configurations, each with its own form of turbulence; in fact turbulence itself may be a little bit of a misnomer, since temperature inversions can generate local gradient in the air, which are not turbulent but can still deviate light beams and degrade image quality. Also, mechanical turbulence at homogeneous temperature does not generate optical turbulence and conversely non-turbulent, or not fully developed turbulent flows can degrade image quality but are much more difficult to include in error budgets or simulations. Furthermore local/dome seeing is almost certainly not Kolmogorov since confined spaces do not allow for energy cascades and equipartition of energy at all scales.

<footnote>* Olivier lai: olivier.lai@oca.eu</footnote>
## 1.1 Imaka

It is through the Imaka GLAO system at the University of Hawaii 88" telescope [2] that our group first became aware of the importance of dome seeing. Imaka is a GLAO demonstrator using 5 Shack-Hartman wavefront sensors and a single bimorph curvature deformable mirror conjugate to the telescope pupil, developed with the goal of understanding the performance and the limits of GLAO and has been very successful as such, and more, such as for uncovering the prevalence of dome seeing.

The main evidence of dome seeing came from two quite independent measurements. The first one is from focal plane measurements of the PSFs, which reveal much stronger wings than originally anticipated. The issue here is that an improvement of the FWHM at the expense of a strong halo does not improve the Noise Equivalent Area (NEA, which is a measure of the optimal aperture size for photometry of SNR) as much as a simple geometric area ratio. This can be seen in the value of the exponent β of the Moffat PSF profile, which is given by:

$$f(r; \alpha, \beta) = 2 \frac{\beta - 1}{\alpha^2} \left[ 1 + \left( \frac{r^2}{\alpha^2} \right) \right]^{-\beta}$$

When β=1, the Moffat profile follows a Lorentzian (or Cauchy) distribution, and a Gaussian distribution is approximated as β→∞. The canonical value of β for atmospheric turbulence limited imaging is around 4.7, although semi-analytical computations shown that the value depends on the wavelength, D, r₀ and L₀. Imaka commissioning data (shown in Figure 1) show that in open loop (no correction), values of β agree fairly well with the canonical value, although when vibrations are present, β increases to fit a Gaussian distribution. When the loop is closed however, the wings become much stronger, with β well below its canonical value and the PSF often approximating a Lorentzian. A predominant halo is due to an excess of high spatial frequencies (or a very small outer scale), which is characteristic of dome seeing.

<figure><img src="image_1.png" /><figcaption>Figure 1. Values of FWHM and β in the Moffat fitting profile of PSFs from imaka commissioning data. Left, open loop agrees with the canonical value of β; high values of β are due to vibrations which have a Gaussian distribution. Right, in closed loop, β is always smaller than its canonical value, which is due to an excess of high spatial frequencies, characteristic of dome seeing.</figcaption></figure>

Imaka has 5 wavefront sensors to measure the ground layer turbulence; but these sensors can also be used to infer the vertical turbulence profile [3], using SLODAR-like methods (multiple sources allow for a global solution to the profile). This allows to probe turbulence at negative altitude conjugation, after reflection on the primary mirror. We found intermittent turbulence inside the telescope tube on numerous occasions, an example of which is shown on Figure 2.

<figure><img src="image_2.png" /><figcaption>Figure 2: Vertical turbulence profile obtained from imaka wavefront sensors on the night of February 16, 2017. Intermittent turbulence can be seen at negative altitudes, i.e., inside the telescope tube.</figcaption></figure>

## 1.2 Turbulence camera, AIRFLOW

Originally, we wanted to develop a “turbulence camera”, capable of detecting variations of the index of refraction in very wide (and incoherent) scenes. This turns out to be particularly difficult, as most of the known methods (Schlieren photography, shadowgraphy) depend on some form of coherence (of the light, of a pattern) from which to measure a deviation from.
## 1.1 Imaka

It is through the Imaka GLAO system at the University of Hawaii 88” telescope [2] that our group first became aware of the importance of dome seeing. Imaka is a GLAO demonstrator using 5 Shack-Hartman wavefront sensors and a single bimorph curvature deformable mirror conjugate to the telescope pupil, developed with the goal of understanding the performance and the limits of GLAO and has been very successful as such, and more, such as for uncovering the prevalence of dome seeing.

The main evidence of dome seeing came from two quite independent measurements. The first one is from focal plane measurements of the PSFs, which reveal much stronger wings than originally anticipated. The issue here is that an improvement of the FWHM at the expense of a strong halo does not improve the Noise Equivalent Area (NEA, which is a measure of the optimal aperture size for photometry of SNR) as much as a simple geometric area ratio. This can be seen in the value of the exponent β of the Moffat PSF profile, which is given by:

$$f(r; \alpha, \beta) = 2 \frac{\beta - 1}{\alpha^2} \left[ 1 + \left( \frac{r^2}{\alpha^2} \right) \right]^{-\beta}$$

When β=1, the Moffat profile follows a Lorentzian (or Cauchy) distribution, and a Gaussian distribution is approximated as β→∞. The canonical value of β for atmospheric turbulence limited imaging is around 4.7, although semi-analytical computations shown that the value depends on the wavelength, D, r₀ and L₀. Imaka commissioning data (shown in Figure 1) show that in open loop (no correction), values of β agree fairly well with the canonical value, although when vibrations are present, β increases to fit a Gaussian distribution. When the loop is closed however, the wings become much stronger, with β well below its canonical value and the PSF often approximating a Lorentzian. A predominant halo is due to an excess of high spatial frequencies (or a very small outer scale), which is characteristic of dome seeing.

<figure><img src="image_2.png" /><figcaption>Figure 1. Values of FWHM and β in the Moffat fitting profile of PSFs from imaka commissioning data. Left, open loop agrees with the canonical value of β; high values of β are due to vibrations which have a Gaussian distribution. Right, in closed loop, β is always smaller than its canonical value, which is due to an excess of high spatial frequencies, characteristic of dome seeing.</figcaption></figure>

Imaka has 5 wavefront sensors to measure the ground layer turbulence; but these sensors can also be used to infer the vertical turbulence profile [3], using SLODAR-like methods (multiple sources allow for a global solution to the profile). This allows to probe turbulence at negative altitude conjugation, after reflection on the primary mirror. We found intermittent turbulence inside the telescope tube on numerous occasions, an example of which is shown on Figure 2.

<figure><img src="image_3.png" /><figcaption>Figure 2: Vertical turbulence profile obtained from imaka wavefront sensors on the night of February 16, 2017. Intermittent turbulence can be seen at negative altitudes, i.e., inside the telescope tube.</figcaption></figure>

## 1.2 Turbulence camera, AIRFLOW

Originally, we wanted to develop a “turbulence camera”, capable of detecting variations of the index of refraction in very wide (and incoherent) scenes. This turns out to be particularly difficult, as most of the known methods (Schlieren photography, shadowgraphy) depend on some form of coherence (of the light, of a pattern) from which to measure a deviation from.
To make some progress, we decided to build a localized optical turbulence sensor, capable of measuring Cn² within a measurement cell. The name AIRFLOW is an acronym for Airborne Interferometric Recombiner – Fluctuations of Light at Optical Wavelengths, and as is implied by “airborne” the concept was to measure the fluctuation of refractive index locally and scan the given volume to reconstruct a 3D map of the turbulence, as shown on Figure 3.

<figure><img src="image_3.png" /><figcaption>Figure 3: Original design for AIRFLOW, an airborne interferometer designed to measure the local turbulence and scan the volume to build a 3D map. This of course had to be done without affecting the measurement so the instrument could have been borne aloft by a kite or a drone.</figcaption></figure>

Thus, we set about building an AIRFLOW prototype that would measure the phase structure function of the turbulence within a measurement cell [4]. The principle is based on propagating a monochromatic, parallel beam through a non-redundant mask in a pupil plane and a measurement cell, then refocusing the light and measuring the resulting PSF on a fast camera. The argument of the Fourier transform of the PSF gives the instantaneous phase for different baselines and separations, which allows to infer the phase structure function. This is an important parameter, since it allows to determine the type of turbulence (Kolmogorov, diffusive, von Karman, etc.) as well as its temporal properties.

<figure><img src="image_4.png" /><figcaption>Figure 4: Left, principle of AIRFLOW. A parallel beam propagates through a measurement cell and is filtered by a non-redundant mask, producing the PSF in the center top panel. The amplitude of the Fourier transform of the PSF is shown in the center bottom panel, and the variance of its argument allows to obtain the Phase Structure Function. Right, a photograph of the first prototype.</figcaption></figure>

## 2. FIELD EXPERIMENTS

### 2.1 CFHT, UH88, LBT

In November 2018, AIRFLOW was deployed at CFHT and at the UH88 telescope, for preliminary tests [4]. At CFHT, daytime tests showed a pronounced increase of Cn² when the windward vents were open, whether the downwind vents were open or not (although the worse turbulence was observed when all the vents were open), and a slight improvement when the downwind vents were open, but the upwind vents closed (Figure 5, left). At the UH88 telescope, AIRFLOW was lowered into the telescope tube to observe whether there was any stratification of the turbulence, and although the Cn² was constant inside the tube (lower at the tube entrance), it was at a relatively high level. Temporal analysis showed that the index of refraction variations had a steep power spectrum with most of the power at low frequencies (f⁻⁴), an unmistakable departure from Kolmogorov behavior (Figure 5, center).

<figure><img src="image_5.png" /><figcaption>Figure 5. Left, the effect of opening dome vents in the CFHT dome increased the turbulence by orders of magnitude but could be mitigated by selectively closing upwind vents. Middle, the temporal behavior of turbulence inside the UH88 telescope tube was heavily biased at low frequencies. Right, on the LBT, after a dome rotation of a few tens of degrees, the turbulence of one of the sensors increased and remained at a high level compared to the other one.</figcaption></figure>
To make some progress, we decided to build a localized optical turbulence sensor, capable of measuring $C_n^2$ within a measurement cell. The name AIRFLOW is an acronym for Airborne Interferometric Recombiner – Fluctuations of Light at Optical Wavelengths, and as is implied by “airborne” the concept was to measure the fluctuation of refractive index locally and scan the given volume to reconstruct a 3D map of the turbulence, as shown on Figure 3.

<figure><img src="image_4.png" /><figcaption>Figure 3: Original design for AIRFLOW, an airborne interferometer designed to measure the local turbulence and scan the volume to build a 3D map. This of course had to be done without affecting the measurement so the instrument could have been borne aloft by a kite or a drone.</figcaption></figure>

Thus, we set about building an AIRFLOW prototype that would measure the phase structure function of the turbulence within a measurement cell [4]. The principle is based on propagating a monochromatic, parallel beam through a non-redundant mask in a pupil plane and a measurement cell, then refocusing the light and measuring the resulting PSF on a fast camera. The argument of the Fourier transform of the PSF gives the instantaneous phase for different baselines and separations, which allows to infer the phase structure function. This is an important parameter, since it allows to determine the type of turbulence (Kolmogorov, diffusive, von Karman, etc.) as well as its temporal properties.

<figure><img src="image_5.png" /><figcaption>Figure 4: Left, principle of AIRFLOW. A parallel beam propagates through a measurement cell and is filtered by a non-redundant mask, producing the PSF in the center top panel. The amplitude of the Fourier transform of the PSF is shown in the center bottom panel, and the variance of its argument allows to obtain the Phase Structure Function. Right, a photograph of the first prototype.</figcaption></figure>

## 2. FIELD EXPERIMENTS

### 2.1 CFHT, UH88, LBT

In November 2018, AIRFLOW was deployed at CFHT and at the UH88 telescope, for preliminary tests [4]. At CFHT, daytime tests showed a pronounced increase of $C_n^2$ when the windward vents were open, whether the downwind vents were open or not (although the worse turbulence was observed when all the vents were open), and a slight improvement when the downwind vents were open, but the upwind vents closed (Figure 5, left). At the UH88 telescope, AIRFLOW was lowered into the telescope tube to observe whether there was any stratification of the turbulence, and although the $C_n^2$ was constant inside the tube (lower at the tube entrance), it was at a relatively high level. Temporal analysis showed that the index of refraction variations had a steep power spectrum with most of the power at low frequencies ($f^{-4}$), an unmistakable departure from Kolmogorov behavior (Figure 5, center).

<figure><img src="image_6.png" /><figcaption>Figure 5. Left, the effect of opening dome vents in the CFHT dome increased the turbulence by orders of magnitude but could be mitigated by selectively closing upwind vents. Middle, the temporal behavior of turbulence inside the UH88 telescope tube was heavily biased at low frequencies. Right, on the LBT, after a dome rotation of a few tens of degrees, the turbulence of one of the sensors increased and remained at a high level compared to the other one.</figcaption></figure>
In June 2019, we were invited to LBT on Mount Graham and installed two sensors, one fixed at the edge of the primary, the other mobile to explore the volume, for three nights. One of the most striking events was a measurement of differential turbulence between both sides of the primary mirror after a telescope repointing [5]. The reason why this event was notable was twofold: First it showed the sudden onset of turbulence in the outer edge sensor, showing that the turbulent behavior is not linear at all, especially with respect to continuous variable such as the dome azimuth (or more precisely its difference to the wind azimuth). Second, a measurement of inhomogeneous $C_n^2$ confirmed that integrating $C_n^2$ along the optical path to obtain a phase variance which could be related to image parameters would prove to be complex and challenging.

## 2.2 ASTEP telescope

ASTEP (Antarctic Search for Transiting ExoPlanets) is a 40cm Newtonian telescope at Dome C in Antarctica [6]. The telescope is dedicated to transit photometry and makes use of the long continuous night to sample transits difficult to obtain elsewhere. However, Dome C is a hostile environment, with winter temperatures which can reach -80°C, so optics (the primary and secondary mirrors, as well as the camera box) must be heated to prevent frost (Figure 6). However, heating optics is never recommended, but this allowed for quantitative measurements in situ for the first time.

<figure><img src="image_6.png" /><figcaption>Figure 6: ASTEP telescope at Dome C, Antarctica. The picture on the left shows the summer team 2021-22, from top-left clockwise: Djamel Mekarnia, Olivier Lai, Georgina Dransfield, Karim Agabi. The picture on the right shows the telescope almost at Solstice, June 20, 2022, illustrating the need to heat optics to prevent frost.</figcaption></figure>

A difficulty arose as we were carrying out these tests in daytime, and we wanted to prevent thermal driving of turbulence from sunlight hitting the structure and introducing temperature gradients. We carried out some tests with the dome closed, which revealed a good log-linear relationship between $C_n^2$ and $\Delta T$ but did not include any of the effects of flushing and venting afforded by the open dome design and the gap between the primary mirror and the tube (Figure 7). We carried out more measurements with the dome partially open (to prevent sunlight from hitting the telescope), and these results, taking into account a thermal lag of ~10 minutes, show a region of $\Delta T$ (>2~3°C) where there is sufficient flushing to prevent $C_n^2$ from increasing (Figure 8). More tests were carried out which showed severely non-Kolmogorov turbulence around the camera box, where the turbulence did not have space to develop.

<figure><img src="image_7.png" /><figcaption>Figure 7: Measuring the dependence of $C_n^2$ vs. $\Delta T$ with the dome closed. Left: the turbulence cell was at the edge of the primary mirror. Right: a $\Delta T$ of 4°C increases $C_n^2$ by an order of magnitude.</figcaption></figure>
In June 2019, we were invited to LBT on Mount Graham and installed two sensors, one fixed at the edge of the primary, the other mobile to explore the volume, for three nights. One of the most striking events was a measurement of differential turbulence between both sides of the primary mirror after a telescope repointing [5]. The reason why this event was notable was twofold: First it showed the sudden onset of turbulence in the outer edge sensor, showing that the turbulent behavior is not linear at all, especially with respect to continuous variable such as the dome azimuth (or more precisely its difference to the wind azimuth). Second, a measurement of inhomogeneous $C_n^2$ confirmed that integrating $C_n^2$ along the optical path to obtain a phase variance which could be related to image parameters would prove to be complex and challenging.

## 2.2 ASTEP telescope

ASTEP (Antarctic Search for Transiting ExoPlanets) is a 40cm Newtonian telescope at Dome C in Antarctica [6]. The telescope is dedicated to transit photometry and makes use of the long continuous night to sample transits difficult to obtain elsewhere. However, Dome C is a hostile environment, with winter temperatures which can reach -80°C, so optics (the primary and secondary mirrors, as well as the camera box) must be heated to prevent frost (Figure 6). However, heating optics is never recommended, but this allowed for quantitative measurements in situ for the first time.

<figure><img src="image_7.png" /><figcaption>Figure 6: ASTEP telescope at Dome C, Antarctica. The picture on the left shows the summer team 2021-22, from top-left clockwise: Djamel Mekarnia, Olivier Lai, Georgina Dransfield, Karim Agabi. The picture on the right shows the telescope almost at Solstice, June 20, 2022, illustrating the need to heat optics to prevent frost.</figcaption></figure>

A difficulty arose as we were carrying out these tests in daytime, and we wanted to prevent thermal driving of turbulence from sunlight hitting the structure and introducing temperature gradients. We carried out some tests with the dome closed, which revealed a good log-linear relationship between $C_n^2$ and $\Delta T$ but did not include any of the effects of flushing and venting afforded by the open dome design and the gap between the primary mirror and the tube (Figure 7). We carried out more measurements with the dome partially open (to prevent sunlight from hitting the telescope), and these results, taking into account a thermal lag of ~10 minutes, show a region of $\Delta T$ (>2~3°C) where there is sufficient flushing to prevent $C_n^2$ from increasing (Figure 8). More tests were carried out which showed severely non-Kolmogorov turbulence around the camera box, where the turbulence did not have space to develop.

<figure><img src="image_8.png" /><figcaption>Figure 7: Measuring the dependence of $C_n^2$ vs. $\Delta T$ with the dome closed. Left: the turbulence cell was at the edge of the primary mirror. Right: a $\Delta T$ of 4°C increases $C_n^2$ by an order of magnitude.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 8: Measuring the dependence of $C_n^2$ vs. $\Delta T$ with the dome open. Left: the turbulence cell was in the middle of the primary mirror. Right: Flushing by natural wind allowed a $\Delta T$ of 2°C before $C_n^2$ starts increasing rapidly to reach the same order of magnitude by 4°C.</figcaption></figure>

## 2.3 General comments on Dome Seeing

We have conclusively shown, if it still needed demonstrating, that indoor turbulence is highly variable, both spatially and temporally, driven by numerous environmental factors, such as: wind speed and direction, dome azimuth (and design), presence of heat sources (electronics or other instruments), radiative cooling of the telescope structure (and dome itself), variations of ambient air temperatures, and primary mirror temperature, partial venting, (differential) telescope thermal inertia, etc.

It is worth noting that it is also not linear with these parameters, with sudden onsets and settling times. After all, turbulence is inherently stochastic, and we are literally chasing wisps of hot air. Overall, it seems like a highly intractable problem using traditional approaches (Principal Component Analysis, linear regressions). First pass machine learning studies suggest that dome seeing can be predicted [7] and have demonstrated some potential for unraveling the variable and non-linear relationships. Linking those predictions to direct in-situ measurements (such as AIRFLOW) has proved difficult due in parts to the lack of homogeneous data sets, even within one single observatory, containing all the required parameters, such as image quality at the focal plane, environmental sensors as well as local turbulence sensors.

This lack of linear dependence makes it especially difficult to define a median performance for our simulations, or to align simulations with a fluctuating environment.

<figure><img src="image_9.png" /><figcaption>Figure 9: measuring “ambient” daytime turbulence 2m above the ground in Antarctica led to absurd situations, such as a ladder in the middle of the ice desert. So absurd that it was reminiscent of the French joke: “Accroche toi au pinceau, j’enlève l’échelle” (*hang on to the paintbrush while I remove the ladder*), prompting to modify Gotlib’s famous cartoon “Accroche toi à AIRFLOW, j’enlève la turbulence”!</figcaption></figure>

## 2.4 Altering reality

But in fact, we do not need to include all these effects into our simulations; instead, we should try to prevent them from occurring in the first place, so we do not have to simulate them. In other words, we must alter reality to fit our
<figure><img src="image_9.png" /><figcaption>Figure 8: Measuring the dependence of $C_n^2$ vs. $\Delta T$ with the dome open. Left: the turbulence cell was in the middle of the primary mirror. Right: Flushing by natural wind allowed a $\Delta T$ of 2°C before $C_n^2$ starts increasing rapidly to reach the same order of magnitude by 4°C.</figcaption></figure>

## 2.3 General comments on Dome Seeing

We have conclusively shown, if it still needed demonstrating, that indoor turbulence is highly variable, both spatially and temporally, driven by numerous environmental factors, such as: wind speed and direction, dome azimuth (and design), presence of heat sources (electronics or other instruments), radiative cooling of the telescope structure (and dome itself), variations of ambient air temperatures, and primary mirror temperature, partial venting, (differential) telescope thermal inertia, etc.

It is worth noting that it is also not linear with these parameters, with sudden onsets and settling times. After all, turbulence is inherently stochastic, and we are literally chasing wisps of hot air. Overall, it seems like a highly intractable problem using traditional approaches (Principal Component Analysis, linear regressions). First pass machine learning studies suggest that dome seeing can be predicted [7] and have demonstrated some potential for unraveling the variable and non-linear relationships. Linking those predictions to direct in-situ measurements (such as AIRFLOW) has proved difficult due in parts to the lack of homogeneous data sets, even within one single observatory, containing all the required parameters, such as image quality at the focal plane, environmental sensors as well as local turbulence sensors.

This lack of linear dependence makes it especially difficult to define a median performance for our simulations, or to align simulations with a fluctuating environment.

<figure><img src="image_10.png" /><figcaption>Figure 9: measuring “ambient” daytime turbulence 2m above the ground in Antarctica led to absurd situations, such as a ladder in the middle of the ice desert. So absurd that it was reminiscent of the French joke: “Accroche toi au pinceau, j’enlève l’échelle” (*hang on to the paintbrush while I remove the ladder*), prompting to modify Gotlib’s famous cartoon “Accroche toi à AIRFLOW, j’enlève la turbulence”!</figcaption></figure>

## 2.4 Altering reality

But in fact, we do not need to include all these effects into our simulations; instead, we should try to prevent them from occurring in the first place, so we do not have to simulate them. In other words, we must alter reality to fit our
(simplistic) simulations. Because dome turbulence is really the only source of image degradation that can be attenuated or averted right at the source, using intelligent dome design, cleverly positioned fans or precise real time thermal control including active telescope structure heating. None of the solutions are technologically challenging but they do depend on a sensitive, active, and real time control. This requires an accurate sensing and mapping of the turbulence inside the telescope and the dome.

## 2.5 Multiple AIRFLOWs at UH88

Since August 2022, we have installed 5 AIRFLOW units around the UH88 telescope and dome: two sensors are on the mezzanine at right angle to each other to sample the “ambient” turbulence; one sensor is at the bottom left of the slit, another sensor is at the top of the slit and the fifth sensor is above the secondary mirror spider, hidden from the telescope beam, as shown in Figure 9.

<figure><img src="image_10.png" /><figcaption>Figure 9: 5 AIRFLOWs deployed at UH88: top left, two units sample the “ambient” turbulence above the mezzanine. Top right, AIRFLOW sensor at the bottom of the slit. Bottom left, sensor at the top of the slit. Bottom middle and right: AIRFLOW above the secondary mirror spider.</figcaption></figure>

The sensors have been running for almost 8 months, but results are inconclusive. Specifically, we looked at the measurements of the sensor during an Imaka observing run and were looking for any correlation between the Imaka WFS negative altitude conjugation signal and any (or any linear combination) of our sensors, to no avail. But this was a first attempt, we placed the sensors in locations that were accessible and seemed relevant but knowing where to put them based on something else than our “intuition” could make all the difference. Therefore, what we really need is a “point&click” turbulence camera.

# 3. TURBULENCE CAMERA

All methods used to image turbulence (Schlieren photography, shadowgraphy) require some form of coherence against which deviations can be measured. This coherence can be in the light itself (as in a Foucault test, or the uniform illumination required for shadowgraphy) or it can be a pattern. The question as to whether such fluctuations can be measured on a wide field incoherent scene is a difficult one. One solution would be to put many point sources inside the dome, as well as cameras with sufficient resolution to measure any spot motion induced by turbulence. It would then be possible to perform a true tomographic inversion to reconstruct the turbulence volume inside the dome; however, astronomy domes are not usually welcoming of Christmas garlands. Also, the camera design requires some thought, as it needs to be both wide angle (to capture as many sources as possible) and high resolution (to measure spot motion).

Solar wavefront sensing using optical differentiation provides a possible solution: the focal plane is reimaged on a binary transmissive mask which selects for regions of greatest contrast on solar granulation [8]. Beams that are deviated from nominal make it past (or are blocked) by the transmissive mask, introducing intensity fluctuations in the pupil plane, which are related to the turbulence pattern in the beam. This may also work with a greyscale transmissive mask of the inverse of the intensity of the scene. Again, any deviated beam will hit a different part of the mask, not matched to its intensity, which will show up in the pupil plane. We are currently developing a Very Wide Field WavFront Sensor, $V(\text{WF})^2\text{S}$ based on a similar idea.

### 3.1 $V(\text{WF})^2\text{S}$

The motivation to develop a very wide field wavefront sensor is mainly 1-2m class semi-professional telescopes dedicated to education, imaging, and astrophotography [9]. For such applications, traditional SCAO is very limited: subapertures must be small and the system temporal cadence must be high, such that the limiting magnitude is usually
(simplistic) simulations. Because dome turbulence is really the only source of image degradation that can be attenuated or averted right at the source, using intelligent dome design, cleverly positioned fans or precise real time thermal control including active telescope structure heating. None of the solutions are technologically challenging but they do depend on a sensitive, active, and real time control. This requires an accurate sensing and mapping of the turbulence inside the telescope and the dome.

## 2.5 Multiple AIRFLOWs at UH88

Since August 2022, we have installed 5 AIRFLOW units around the UH88 telescope and dome: two sensors are on the mezzanine at right angle to each other to sample the “ambient” turbulence; one sensor is at the bottom left of the slit, another sensor is at the top of the slit and the fifth sensor is above the secondary mirror spider, hidden from the telescope beam, as shown in Figure 9.

<figure><img src="image_11.png" /><figcaption>Figure 9: 5 AIRFLOWs deployed at UH88: top left, two units sample the “ambient” turbulence above the mezzanine. Top right, AIRFLOW sensor at the bottom of the slit. Bottom left, sensor at the top of the slit. Bottom middle and right: AIRFLOW above the secondary mirror spider.</figcaption></figure>

The sensors have been running for almost 8 months, but results are inconclusive. Specifically, we looked at the measurements of the sensor during an Imaka observing run and were looking for any correlation between the Imaka WFS negative altitude conjugation signal and any (or any linear combination) of our sensors, to no avail. But this was a first attempt, we placed the sensors in locations that were accessible and seemed relevant but knowing where to put them based on something else than our “intuition” could make all the difference. Therefore, what we really need is a “point&click” turbulence camera.

# 3. TURBULENCE CAMERA

All methods used to image turbulence (Schlieren photography, shadowgraphy) require some form of coherence against which deviations can be measured. This coherence can be in the light itself (as in a Foucault test, or the uniform illumination required for shadowgraphy) or it can be a pattern. The question as to whether such fluctuations can be measured on a wide field incoherent scene is a difficult one. One solution would be to put many point sources inside the dome, as well as cameras with sufficient resolution to measure any spot motion induced by turbulence. It would then be possible to perform a true tomographic inversion to reconstruct the turbulence volume inside the dome; however, astronomy domes are not usually welcoming of Christmas garlands. Also, the camera design requires some thought, as it needs to be both wide angle (to capture as many sources as possible) and high resolution (to measure spot motion).

Solar wavefront sensing using optical differentiation provides a possible solution: the focal plane is reimaged on a binary transmissive mask which selects for regions of greatest contrast on solar granulation [8]. Beams that are deviated from nominal make it past (or are blocked) by the transmissive mask, introducing intensity fluctuations in the pupil plane, which are related to the turbulence pattern in the beam. This may also work with a greyscale transmissive mask of the inverse of the intensity of the scene. Again, any deviated beam will hit a different part of the mask, not matched to its intensity, which will show up in the pupil plane. We are currently developing a Very Wide Field WavFront Sensor, $V(\text{WF})^2$S based on a similar idea.

### 3.1 $V(\text{WF})^2$S

The motivation to develop a very wide field wavefront sensor is mainly 1-2m class semi-professional telescopes dedicated to education, imaging, and astrophotography [9]. For such applications, traditional SCAO is very limited: subapertures must be small and the system temporal cadence must be high, such that the limiting magnitude is usually
relatively low, around 5 or 6; anisoplanatism is also stronger at optical wavelengths so only a few tens of arcsecond around a few thousand stars visible to the naked eye can benefit from AO correction. Our position is that for such applications, sky coverage is critical, at the expense of superb correction; this is exactly the goal of Ground Layer Adaptive Optics (GLAO), which aims at correcting the turbulence common to the entire field, i.e., at or near the telescope's pupil. A very wide field wavefront sensor would aim to provide the matching measurement, by optically averaging the phase from all sources in the field onto a single pupil image. The trick is to find an optical operator in the focal plane, which can be applied to every source in the field [10] and which provides the correct mathematical operation on the intensity in the pupil plane (for reference, the mathematical property that the Fourier transform of the derivative of a signal is the Fourier transform of the signal multiplied by a linear operator applies to the Fourier Transform relationship between focal and pupil planes: multiplying the focal plane by a linear operator produces a signal proportional to the first derivative of the phase in the pupil plane). For example, the multi-pyramid layer-oriented MCAO system Lync-NIRVANA at LBT uses an array of deployable pyramids in the focal plane to produce four individual pupil images, each containing light from all the pyramids.

<figure><img src="image_11.png" /><figcaption>Figure 10, principle of the V(WF)²S: A rotating Foucault knife edge test is programmed onto an addressable transmissive mask such as a SLM, LCD or DLP. The light from all the stars in the field is collected by a single lens to reimage the pupil on a single camera. In the bottom panel, the two images on the left would be used to measure the horizontal derivative and the two image on the right for the vertical. The rest of the transmissive mask is dark.</figcaption></figure>

The biggest issue of using all the light in the field of interest is the sky background which can be as high as 22/arcsec² for excellent astronomical sites, but as low as 18/arcsec² in semi-urban sites, which can add hundreds of thousands of photons in the pupil which only contain noise. It is therefore much more efficient to mask this sky background, and this led to the idea [11] of an addressable transmissive mask (such as an LCD screen or a DLP), on which we project a rotational Foucault test on each star in the field, while masking the rest of the background (Figure 10).

Simulations have shown that there is sufficiently flux for 100% sky coverage at the North Galactic Pole with a 2.2m telescope and a 40' field of view. For 1-m class telescope, the field of view could be reduced (to say a more reasonable 10' or 20') to reduce the cost, at the expense of sky coverage. Simulations have also shown (Figure 11) that a gain of a factor 2 are possible both on the resolution (FWHM) and the contrast (Strehl) in GLAO mode over such field.

<figure><img src="image_12.png" /><figcaption>Figure 11: Left, R-band image quality (FWHM and Strehl) uncorrected (white) and with AO correction (red) for bad (r₀=7cm) and good (r₀=20cm) seeing. Right, example of GLAO correction on M22m comparing seeing limited (bottom left), GLAO correction (bottom middle) and ground truth (or should it be space-truth) HST.</figcaption></figure>

Finally an optical design for such a system becomes very elegant if using Dynamic Optics deformable lenses (https://www(dynamic-optics.it/deformable-lenses/) or new technology actuators (such as the TNO approach, using magnetic reluctance) enabling potentially more affordable adaptive secondary mirrors. This concept will be further developed in a forthcoming publication in AO4ELT7 [11].
relatively low, around 5 or 6; anisoplanatism is also stronger at optical wavelengths so only a few tens of arcsecond around a few thousand stars visible to the naked eye can benefit from AO correction. Our position is that for such applications, sky coverage is critical, at the expense of superb correction; this is exactly the goal of Ground Layer Adaptive Optics (GLAO), which aims at correcting the turbulence common to the entire field, i.e., at or near the telescope's pupil. A very wide field wavefront sensor would aim to provide the matching measurement, by optically averaging the phase from all sources in the field onto a single pupil image. The trick is to find an optical operator in the focal plane, which can be applied to every source in the field [10] and which provides the correct mathematical operation on the intensity in the pupil plane (for reference, the mathematical property that the Fourier transform of the derivative of a signal is the Fourier transform of the signal multiplied by a linear operator applies to the Fourier Transform relationship between focal and pupil planes: multiplying the focal plane by a linear operator produces a signal proportional to the first derivative of the phase in the pupil plane). For example, the multi-pyramid layer-oriented MCAO system Lync-NIRVANA at LBT uses an array of deployable pyramids in the focal plane to produce four individual pupil images, each containing light from all the pyramids.

<figure><img src="image_12.png" /><figcaption>Figure 10, principle of the V(WF)²S: A rotating Foucault knife edge test is programmed onto an addressable transmissive mask such as a SLM, LCD or DLP. The light from all the stars in the field is collected by a single lens to reimage the pupil on a single camera. In the bottom panel, the two images on the left would be used to measure the horizontal derivative and the two image on the right for the vertical. The rest of the transmissive mask is dark.</figcaption></figure>

The biggest issue of using all the light in the field of interest is the sky background which can be as high as 22/arcsec² for excellent astronomical sites, but as low as 18/arcsec² in semi-urban sites, which can add hundreds of thousands of photons in the pupil which only contain noise. It is therefore much more efficient to mask this sky background, and this led to the idea [11] of an addressable transmissive mask (such as an LCD screen or a DLP), on which we project a rotational Foucault test on each star in the field, while masking the rest of the background (Figure 10).

Simulations have shown that there is sufficiently flux for 100% sky coverage at the North Galactic Pole with a 2.2m telescope and a 40' field of view. For 1-m class telescope, the field of view could be reduced (to say a more reasonable 10' or 20') to reduce the cost, at the expense of sky coverage. Simulations have also shown (Figure 11) that a gain of a factor 2 are possible both on the resolution (FWHM) and the contrast (Strehl) in GLAO mode over such field.

<figure><img src="image_13.png" /><figcaption>Figure 11: Left, R-band image quality (FWHM and Strehl) uncorrected (white) and with AO correction (red) for bad (r₀=7cm) and good (r₀=20cm) seeing. Right, example of GLAO correction on M22m comparing seeing limited (bottom left), GLAO correction (bottom middle) and ground truth (or should it be space-truth) HST.</figcaption></figure>

Finally an optical design for such a system becomes very elegant if using Dynamic Optics deformable lenses (https://www(dynamic-optics.it/deformable-lenses/) or new technology actuators (such as the TNO approach, using magnetic reluctance) enabling potentially more affordable adaptive secondary mirrors. This concept will be further developed in a forthcoming publication in AO4ELT7 [11].
<figure><img src="image_13.png" /><figcaption>Figure 12: simple optical layout using adaptive lenses or adaptive secondary mirrors for the V(WF)²S: an adaptive lens is placed at the telescope pupil conjugate plane and a DLP is placed at the focal plane; in between a beam splitter produces the corrected focal plane where the science camera is placed.</figcaption></figure>

## 3.2 Incoherent scene phase contrast imaging

Following the approach of the V(WF)²S concept, we can envision putting a greyscale transmissive mask with the inverse of the intensity in the focal plane and reimage the pupil plane to try to obtain the phase of the beam. Figure 13 shows such an example on an extended source such as Jupiter. The inverse intensity needs to be scaled by some factor, since it cannot amplify the flux in dark regions, so such a mask will never produce a perfect grey level after filtering in the focal plane. Furthermore, due to the ambiguity between pupil plane phase and Fourier phase (since the intensity is squared absolute value of the amplitude in the focal plane), such a wavefront sensor will be insensitive to even aberrations, although using an asymmetric pupil mask can help with this. Nonetheless it is worth noting that measuring a phase variance in a turbulence camera is not as stringent as measuring the exact phase, required in a wavefront sensor. The main limitation of this approach lies in the fact that the measured phase is the GLAO phase, i.e., the optical averaging of the phase in all directions of the beam. Therefore, on an extended scene with a small aperture, this is the phase at the pupil, and such a measurement will contain no information on the distant turbulence affecting only a small part of the beam. To get around this, one could envision a parallel beam (such that the average phase is the total phase), but this then requires a scanning mechanism of the scene, which adds complexity and doesn't allow for an instantaneous, or at least synchronous measurement of the turbulence within the scene.

<figure><img src="image_14.png" /><figcaption>Figure 13: the input phase is shown in the top left panel and the associated PSF in the lower left panel. The next column shows the ideal (top) and degraded (bottom) intensity of Jupiter. The middle column shows the transmissive mask (top) and filtered focal plane intensity (bottom). The next column shows the Fourier phase of the mask (top) and the Fourier phase of the filtered image. The rightmost column shows their difference (top) and the same difference but smoothed, which does reveal a phase pattern similar to the input.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 14: same as Figure 13 but with a stronger amplitude (as can be seen in the PSF panel), leading to wrap-around on the reconstructed phase.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 12: simple optical layout using adaptive lenses or adaptive secondary mirrors for the V(WF)²S: an adaptive lens is placed at the telescope pupil conjugate plane and a DLP is placed at the focal plane; in between a beam splitter produces the corrected focal plane where the science camera is placed.</figcaption></figure>

## 3.2 Incoherent scene phase contrast imaging

Following the approach of the V(WF)²S concept, we can envision putting a greyscale transmissive mask with the inverse of the intensity in the focal plane and reimage the pupil plane to try to obtain the phase of the beam. Figure 13 shows such an example on an extended source such as Jupiter. The inverse intensity needs to be scaled by some factor, since it cannot amplify the flux in dark regions, so such a mask will never produce a perfect grey level after filtering in the focal plane. Furthermore, due to the ambiguity between pupil plane phase and Fourier phase (since the intensity is squared absolute value of the amplitude in the focal plane), such a wavefront sensor will be insensitive to even aberrations, although using an asymmetric pupil mask can help with this. Nonetheless it is worth noting that measuring a phase variance in a turbulence camera is not as stringent as measuring the exact phase, required in a wavefront sensor. The main limitation of this approach lies in the fact that the measured phase is the GLAO phase, i.e., the optical averaging of the phase in all directions of the beam. Therefore, on an extended scene with a small aperture, this is the phase at the pupil, and such a measurement will contain no information on the distant turbulence affecting only a small part of the beam. To get around this, one could envision a parallel beam (such that the average phase is the total phase), but this then requires a scanning mechanism of the scene, which adds complexity and doesn't allow for an instantaneous, or at least synchronous measurement of the turbulence within the scene.

<figure><img src="image_15.png" /><figcaption>Figure 13: the input phase is shown in the top left panel and the associated PSF in the lower left panel. The next column shows the ideal (top) and degraded (bottom) intensity of Jupiter. The middle column shows the transmissive mask (top) and filtered focal plane intensity (bottom). The next column shows the Fourier phase of the mask (top) and the Fourier phase of the filtered image. The rightmost column shows their difference (top) and the same difference but smoothed, which does reveal a phase pattern similar to the input.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 14: same as Figure 13 but with a stronger amplitude (as can be seen in the PSF panel), leading to wrap-around on the reconstructed phase.</figcaption></figure>
To avoid the GLAO averaging and necessity to scan the scene, one could interchange pupil plane and focal plane, so that the optical filtering takes place in the pupil plane and the scene is re-imaged on the detector; for example a high-pass filter could remove all the large intensity variations present in the scene, only leaving fine details on the image, and these would be most affected by local turbulence, and could be detected by measuring flux variance in each pixel. However, the simultaneous requirements for fine sampling over a wide scene at high frame rate and (relatively) low flux levels put stringent demands on the camera. Also, it is not obvious how one would build an effective high pass optical filter for an extended scene (e.g. [12]). This is still work in progress.

## 4. CONCLUSIONS

In this paper, we have presented results from imaka that led us to consider dome and telescope seeing as a serious contributor to image degradation, especially due to the high spatial frequency content of this turbulence, which amplifies the halo of the PSF and can be amplified in an AO loop through aliasing. This is particularly detrimental to the noise equivalent area (NEA), which is a much more useful quantitative measure of image quality (e.g., the SNR on photometry or astrometry is inversely proportional to the NEA) than the usually quoted FWHM. This led to the development of a localized turbulence sensor, AIRFLOW, which we successfully tested at CFHT, UH88, LBT and at the ASTEP telescope in Antarctica. If it revealed anything, it was that dome turbulence is intermittent, not stationary, not Kolmogorov, and not linear with respect to environmental parameters! Facing such an intractable situation, our position is that it is not even possible to define a “median” dome seeing, and that it is pointless to try to include it in our AO simulations. We are better off trying to prevent this turbulence from occurring in the first place, so that it doesn’t degrade the image quality in such a difficult way to model, which implies altering reality so that it matches our simplified simulations.

Preventing dome turbulence is probably not very technologically challenging, using fans, thermal control of the dome or active heating of the telescope structure but it does require a real time, active and sensitive measurement of the turbulence. To this end we have been trying to develop a “turbulence camera”, which would be able to measure wavefront variations on a incoherent scene. We have been developing a wide field wavefront sensor V(WF)²S, based on Horace Babcock’s original rotating Foucault knife edge [13], Roberto Ragazzoni’s layer oriented MCAO and pupil plane wavefront sensing concepts [14] as well as Rigaut and Tokovinin’s GLAO concept [15]. This wavefront sensor will be described more fully in an upcoming paper in AO4ELT7 [11].

But our goal is to develop a turbulence camera such as the Schlieren photograph shown in Figure 15: a device that would allow us to measure turbulence while reading the newspaper (euphemism for easy to use!) [16].

<figure><img src="image_16.png" /><figcaption>Figure 15: famous Schlieren photography using a large spherical mirror behind the scene of interest. The photograph is a montage of the phase from the Foucault knife edge and the intensity of the foreground subjects.</figcaption></figure>
To avoid the GLAO averaging and necessity to scan the scene, one could interchange pupil plane and focal plane, so that the optical filtering takes place in the pupil plane and the scene is re-imaged on the detector; for example a high-pass filter could remove all the large intensity variations present in the scene, only leaving fine details on the image, and these would be most affected by local turbulence, and could be detected by measuring flux variance in each pixel. However, the simultaneous requirements for fine sampling over a wide scene at high frame rate and (relatively) low flux levels put stringent demands on the camera. Also, it is not obvious how one would build an effective high pass optical filter for an extended scene (e.g, [12]). This is still work in progress.

## 4. CONCLUSIONS

In this paper, we have presented results from imaka that led us to consider dome and telescope seeing as a serious contributor to image degradation, especially due to the high spatial frequency content of this turbulence, which amplifies the halo of the PSF and can be amplified in an AO loop through aliasing. This is particularly detrimental to the noise equivalent area (NEA), which is a much more useful quantitative measure of image quality (e.g., the SNR on photometry or astrometry is inversely proportional to the NEA) than the usually quoted FWHM. This led to the development of a localized turbulence sensor, AIRFLOW, which we successfully tested at CFHT, UH88, LBT and at the ASTEP telescope in Antarctica. If it revealed anything, it was that dome turbulence is intermittent, not stationary, not Kolmogorov, and not linear with respect to environmental parameters! Facing such an intractable situation, our position is that it is not even possible to define a “median” dome seeing, and that it is pointless to try to include it in our AO simulations. We are better off trying to prevent this turbulence from occurring in the first place, so that it doesn’t degrade the image quality in such a difficult way to model, which implies altering reality so that it matches our simplified simulations.

Preventing dome turbulence is probably not very technologically challenging, using fans, thermal control of the dome or active heating of the telescope structure but it does require a real time, active and sensitive measurement of the turbulence. To this end we have been trying to develop a “turbulence camera”, which would be able to measure wavefront variations on a incoherent scene. We have been developing a wide field wavefront sensor $V(\text{WF})^2$S, based on Horace Babcock’s original rotating Foucault knife edge [13], Roberto Ragazzoni’s layer oriented MCAO and pupil plane wavefront sensing concepts [14] as well as Rigaut and Tokovinin’s GLAO concept [15]. This wavefront sensor will be described more fully in an upcoming paper in AO4ELT7 [11].

But our goal is to develop a turbulence camera such as the Schlieren photograph shown in Figure 15: a device that would allow us to measure turbulence while reading the newspaper (euphemism for easy to use!) [16].

<figure><img src="image_17.png" /><figcaption>Figure 15: famous Schlieren photography using a large spherical mirror behind the scene of interest. The photograph is a montage of the phase from the Foucault knife edge and the intensity of the foreground subjects.</figcaption></figure>
REFERENCES

[1] Sauvage, J.-F., Fusco, T., Guesalaga, A., et al., "Low Wind Effect, the main limitation of the SPHERE instrument", in *Adaptive Optics for Extremely Large Telescopes IV (AO4ELT4)*, (2015).

[2] Abdurrahman, F.N., Lu, J.R., Chun, M., et al., "Improved Image Quality over 10 Fields with the Imaka Ground-layer Adaptive Optics Experiment", *Astronomical Journal*, **156**, (2018). doi:10.3847/1538-3881/aad1f2

[3] Lai, O., Chun, M., Abdurrahman, F., et al., "Deconstructing turbulence and optimizing GLAO using imaka telemetry", *Proc. SPIE: Adaptive Optics Systems VI*, **10703**, 107036D, (2018). doi:10.1117/12.2313356

[4] Lai, O., Withington, J. K., Laugier, R., and Chun, M., "Direct measure of dome seeing with a localized optical turbulence sensor", *Monthly Notices of the Royal Astronomical Society*, **484**, pp. 5568–5577, (2019). doi:10.1093/mnras/stz396.

[5] Lai, O., Withington, K., Laugier, R., and Chun, M., "Local Turbulence: Effects and causes", in *Adaptive Optics for Extremely Large Telescopes VI (AO4ELT6)* arXiv e-prints, (2019). doi:10.48550/arXiv.1912.02680

[6] Schmider, F.-X., Abe, L., Agabi, A., et al., "Observing exoplanets from Antarctica in two colours: set-up and operation of ASTEP+", *Proc. SPIE: Ground-based and Airborne Telescopes IX*, **12182**, (2022). doi:10.1117/12.2628952.

[7] Gilda, S., Draper, S.~C., Fabbro, S., et al. "Uncertainty-aware learning for improvements in image quality of the Canada-France-Hawaii Telescope", *Monthly Notices of the Royal Astronomical Society*, **510**, pp. 870–902, (2022). doi:10.1093/mnras/stab3243.

[8] Schmidt, D., von der Lühe, O., "Optical wavefront differentiation: wavefront sensing for solar adaptive optics based on a LCD", in *Proc. SPIE: Adaptive Optics for Laser Systems and Other Applications*, **6584**, (2007). doi:10.1117/12.722640.

[9] Lai, O., Kuiper, S., Doelman, N., et al., "Making adaptive optics available to all: a concept for 1m-class telescopes.", *SF2A-2021: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics*, pp. 300–301, (2021).

[10] Lai, O., Kuiper, S., Doelman, N.J., et al., "Making adaptive optics available to all: a concept for 1m class telescopes", *Proc. SPIE: Adaptive Optics Systems VIII*, **12185**, 1218576, (2022). doi:10.1117/12.2626074.

[11] Lai, O. et al, "V(WF)²S: Very Wide Field WaveFront Sensor for GLAO", in preparation, *Adaptive Optics for Extremely Large Telescopes 7 (AO4ELT7)*, (2023).

[12] Ali P. Vafa, Parisa Karimi, Amin Khavasi, "Analog optical edge detection by spatial high-pass filtering using lithography-free structures", *Optics Communications*, **495**, 127084, (2021). https://doi.org/10.1016/j.optcom.2021.127084.

[13] Babcock, H. W., "The Possibility of Compensating Astronomical Seeing", *Publications of the Astronomical Society of the Pacific*, **65**, p. 229, (1953). doi:10.1086/126606.

[14] Diolaiti, E., Ragazzoni, R., and Tordi, M., "Closed loop performance of a layer-oriented multi-conjugate adaptive optics system", *Astron. & Astrophys.*, **372**, pp. 710–718, (2001). doi:10.1051/0004-6361:20010514.

[15] Tokovinin, A., "Seeing Improvement with Ground-Layer Adaptive Optics", *Pub. Astron. Soc. Pacific*, **116**, pp. 941–951, (2004). doi:10.1086/424805.

[16] Settles, Gary, "Visualizing full scale ventilation airflows", ASHRAE journal, (1997). https://pawsoflife.org.k9handleracademy.com/Library/Scent/Settles%201997%20Full-ScaleVentilation.pdf
REFERENCES

[1] Sauvage, J.-F., Fusco, T., Guesalaga, A., et al., "Low Wind Effect, the main limitation of the SPHERE instrument", in *Adaptive Optics for Extremely Large Telescopes IV (AO4ELT4)*, (2015).

[2] Abdurrahman, F.N., Lu, J.R., Chun, M., et al., "Improved Image Quality over 10° Fields with the 'Imaka Ground-layer Adaptive Optics Experiment", *Astronomical Journal*, **156**, (2018). doi:10.3847/1538-3881/aad1f2

[3] Lai, O., Chun, M., Abdurrahman, F., et al., "Deconstructing turbulence and optimizing GLAO using imaka telemetry", *Proc. SPIE: Adaptive Optics Systems VI*, **10703**, 107036D, (2018). doi:10.1117/12.2313356

[4] Lai, O., Withington, J. K., Laugier, R., and Chun, M., "Direct measure of dome seeing with a localized optical turbulence sensor", *Monthly Notices of the Royal Astronomical Society*, **484**, pp. 5568–5577, (2019). doi:10.1093/mnras/stz396.

[5] Lai, O., Withington, K., Laugier, R., and Chun, M., "Local Turbulence: Effects and causes", in *Adaptive Optics for Extremely Large Telescopes VI (AO4ELT6) arXiv e-prints*, (2019). doi:10.48550/arXiv.1912.02680

[6] Schmider, F.-X., Abe, L., Agabi, A., et al., "Observing exoplanets from Antarctica in two colours: set-up and operation of ASTEP+", *Proc. SPIE: Ground-based and Airborne Telescopes IX*, **12182**, (2022). doi:10.1117/12.2628952.

[7] Gilda, S., Draper, S.~C., Fabbro, S., et al. "Uncertainty-aware learning for improvements in image quality of the Canada-France-Hawaii Telescope", *Monthly Notices of the Royal Astronomical Society*, **510**, pp. 870–902, (2022). doi:10.1093/mnras/stab3243.

[8] Schmidt, D., von der Lühe, O., "Optical wavefront differentiation: wavefront sensing for solar adaptive optics based on a LCD", in *Proc. SPIE: Adaptive Optics for Laser Systems and Other Applications*, **6584**, (2007). doi:10.1117/12.722640.

[9] Lai, O., Kuiper, S., Doelman, N., et al., "Making adaptive optics available to all: a concept for 1m-class telescopes.", *SF2A-2021: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics*, pp. 300–301, (2021).

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