Estimating Dome Seeing for LSST Jacques Sebag a and Konstantinos Vogiatzis

Estimating Dome Seeing for LSST Jacques Sebag a and Konstantinos Vogiatzis a LSST Project, National Optical Astronomy Observatory, 950 N. Cherry Ave., Tucson, AZ, 85719 USA ABSTRACT Begin Dome seeing is a critical effect influencing the optical performance of ground based telescopes. A previously reported combination of Computational Fluid Dynamics (CFD) and optical simulations to model dome seeing was implemented for the latest LSST enclosure geometry. To this end, high spatial resolution thermal unsteady CFD simulations were performed for three different telescope zenith angles and four azimuth angles. These simulations generate time records of refractive index values along the optical path, which are post-processed to estimate the image degradation due to dome seeing. This method allows us to derive the distribution of seeing contribution along the different optical path segments that composed the overall light path between the entrance of the dome up to the LSST science camera. These results are used to recognize potential problems and to guide the observatory design. In this paper, the modeling estimates are reviewed and assessed relative to the corresponding performance allocation, and combined with other simulator outputs to model the dome seeing impact during LSST operations. Keywords: LSST, Dome Seeing, CFD 1. INTRODUCTION Over the years of design development, LSST has used Computational Fluid Dynamics (CFD) modeling to guide the design and to establish requirements [1,2,3]. Optimization of the building and dome design was guided using CFD modeling combined with thermal analyses for modeling the effects of passive ventilation, enclosure-building configuration and topography on the optical performance. Results of this analysis demonstrated the value of several features integrated into the final design of the summit facility [4]. In addition, LSST has developed a schedule operations simulator called OpSim which executes automatic scheduling and produces a database with time-sequence of visits over the duration of the LSST 10-year survey [5]. The OpSim database includes a detailed history of observations, sequences, observing conditions and telescope motions. In this paper, a combination of CFD and OpSim results is used to estimate the dome seeing distribution. In the following sections, the CFD model and thermal modeling are presented including the effects of turbulence and thermal variations within the airflow around the buildings and inside the telescope-enclosure configuration. The optical performance due to the thermal seeing along the optical path is summarized. The LSST telescope pointing statistics determined from OpSim are detailed and combined with the CFD results to build a dome seeing model. 2. COMPUTATIONAL FLUID DYNAMICS MODEL The CFD model includes the local topography of the telescope site on Cerro Pachón, the building and the dome with a mass model of the telescope inside. The enclosure geometry, including the support building, is shown in Figure 1. Features less than 0.1m in size have been omitted to allow the grid of the CFD STAR-CCM+ modeling software to approximate the form. This grid was generated over a 3-D SolidWorks model of the observatory that depicted the baseline design. The thermal boundary conditions set in the CFD model are summarized in Table 1. The nominal value for the ambient temperature Tamb is 277 K (zero vertical gradient). The enclosure was then placed on a Digital Elevation Model (DEM) of the selected LSST site at Cerro Pachón to account for the impact of the local topography. The horizontal computational domain was a square area 500m x 500m, which was aligned with the prevailing wind direction, 20 o NNE. The outside wind velocity was set at 5m/sec, the average wind speed for the site. The ceiling was set at an elevation of 3000m. Reference air properties for pressure and Modeling, Systems Engineering, and Project Management for Astronomy VI, edited by George Z. Angeli, Philippe Dierickx, Proc. of SPIE Vol. 9150, 91500R 2014 SPIE CCC code: 0277-786X/14/$18 doi: 10.1117/12.2054436 Proc. of SPIE Vol. 9150 91500R-1

density were set to 70 kpa and 0.88 kg/m3 respectively. The spatial resolution varied from 10m in the outer region of the volume, to 0.1-0.5m inside and around the enclosure/telescope surfaces and <0.1m normal to the structure. Table 1 LSST CFD Thermal Boundary Conditions Component/surface T-T amb (K) Topography -1 NNE (inlet) 0 SSW (outlet) 0 Top end +4 Camera, M2 (glass) +1 M1/M3 (glass) +0.5 Drives (telescope & dome) 0 Dome floor 0 Exterior surfaces -3 (most of dome & building) Others -1 (-0.5) Figure 1 Current LSST CFD model 3. THERMAL SEEING MODELING CFD was used as a tool for thermal seeing modeling. The purpose of this analysis is to evaluate the seeing contribution of the dome design adopted in the LSST baseline and to identify possible design changes to improve it. CFD simulations offer a validated and cost-effective method which provides seeing estimates that can be calculated for different configurations of the telescope. The current model [6] is using as input unsteady state analysis (instantaneous) CFD simulation results, and it has been validated against existing Observatory measurements [7]. Instantaneous temperature and velocity fields are saved every 5 second over a period of 60 seconds. Four different enclosure azimuth angles were used for the simulations and three telescope zenith angles were selected for each of the enclosure direction for a total of 12 cases. The four azimuth directions are 0 o where the enclosure slit is pointing into the wind, 90 o where the optical axis is perpendicular to the wind (pointing both towards East and West) and 180 o where the slit is pointing away from the wind. Proc. of SPIE Vol. 9150 91500R-2

The three selected zenith angles are 20 o, 40 o and 75 o. These three angles correspond to a very different position of the enclosure light baffle/wind screen wheree the screen is completely raised at 20 o, is in an intermediate position at 40 o (nominal case) and is completely deployed at 75 o. This screen is used as a light baffle to reduce the amount of stray light inside the enclosure. In addition, the enclosure flushing vents are also designed with light baffles (Figure 2) to minimize light scattering and these baffles are included in the CFD grid. The vents are also equipped with louvers to control the wind speed inside the dome during observing and to provide light tightness during the day. This new model allows integration along the specific LSST optical light path. Using 3 large mirrors, the contribution of each optical path is not negligible relative to the contribution of the main entrance beam. The optical path was divided into four segments from outside of the dome to the camera following the multiple reflections on the three mirrors (Figure 3). k Figure 2 Enclosure light baffles in main entrance opening (at 45 o zenith angle) and inside the flushing vents The presencee of the light baffles inside the vents affects the air flow through the dome and the enclosure attenuation factor appears to be around 0.1 to 0.2 regardless of the orientation. Specific flow patterns are created for facing/ /opposite wind direction but these do not seem to appear in the optical path. In the (40 o zenith, 0 o Azimuth) orientation, the dome clear aperture is facing the wind direction. The telescope mount appears well protected from wind, with wind speed around the mount around 0.5m/sec. Outside the optical path, a higher velocity flow appears to travel around the mount at a higher velocity around 2m/sec. In the (40 o zenith, 90 o Azimuth) orientation (Figure 4) ), the dome clear aperture is perpendicular to the wind direction. The wind speed is around 1m/sec inside the dome. In the (40 o zenith, 180 o Azimuth) orientation, the dome clear aperture is opposite to the wind direction. In this case, the flushing inside the dome appears to be less efficient with a wind speed less than 1m/sec inside the dome. In the (20 o Zenith, 90 o Azimuth) orientation, the wind speed inside the dome appears similar to the (40 o Zenith,90 o Azimuth) case. The wind speed distribution inside the dome appears to not be too sensitive to the zenith angle change. In the (75 o Zenith,90 o Azimuth) orientation, the wind speed inside the dome appears similar to the (40 o Zenith,90 o Azimuth) case. Similarly, the wind speed distribution inside the dome does not appear to be too sensitive to the zenith angle change. Proc. of SPIE Vol. 9150 91500R-3

Light Path Predominant Wind Direction (NNE) M2 M1M3 Camera Vertical Section Through Telescope Figure 3: Temperature distribution for a telescope pointing at 40 o zenith angle and at 0 o azimuth angle (facing into the wind direction) Average wind speed ~1m/s inside the dome Flow is affected by the stray light baffle shape Predominant Wind Direction (NNE) Figure 4: Wind speed distribution for a telescope pointing at 40 o zenith angle and at 90 o azimuth angle (perpendicular to the wind direction) Proc. of SPIE Vol. 9150 91500R-4

The integration was first performed along the optical path starting some distance from the telescope elevation axis (outwards) all the way to the camera to estimate the overall contribution from the inside and outside of the enclosure. The starting point of the integration varies with orientation, referenced as Dome Layer (DL) in the table. It corresponds to the distance where dome induced turbulence becomes insignificant. The general methodology of using CFD to estimate optical turbulence and image quality degradation due to dome seeing goes as follows: Run simulation for two flow-through times (2FT) to flush initial conditions Start saving the instantaneous temperatures/velocities at given sampling rate on the corresponding optical path grids for sufficient duration Calculate turbulence statistics For every time-step, calculate the Optical Path Length (OPL), collapse it to a 2D OPD, and then remove piston Nominal OPD grid is 2048 2. Since the initial OPD has comparable resolution to the CFD resolution (0.25m- 0.5m) we may choose to add high frequency component based on a given spectral distribution. For every time-step, calculate the Optical Transfer Function (OTF), and the average for the observation time Multiply it with the atmospheric Modulation Transfer Function (MTF, calculated from the Kolmogorov atmospheric structure function for a given r0, nominally 0.2m @ 0.5micron) Calculate PSF & FWHM From Dome Beam 1 M1 Y M2 Beam 2 Beam 3 M3 Z Beam 4 Camera Figure 5: Dome Layer (DL) to Camera Path used to compute the seeing contribution The total integration is divided into different components to separately identify the contributions from the enclosure and telescope surfaces. The results are presented in Table 2. In the third column, the contribution from the outside of the enclosure is integrated between DL and 15m, (the entrance of the enclosure is located at ~15m measured from the telescope elevation axis). This integration path allows for an estimate of the local contribution around the enclosure. As can be seen, this contribution is very small and is basically constant for most of the different cases. Proc. of SPIE Vol. 9150 91500R-5

Table 2: Seeing contribution (in mas) at three different telescope zenith angles for four different enclosure azimuth angles CASE Total DL-15 15-M1 M1-M2 M2-M3 M3-cam M1-cam 15-cam z20a0 83 <~10 22 35 55 23 76 81 z20a90e 68 <~10 13 34 41 21 63 66 z20a90w 85 <~10 37 40 46 17 69 83 z20a180 92 <~10 28 49 57 12 82 90 z40a0 96 <~10 32 46 62 15 85 95 z40a90e 89 <~10 33 41 54 18 77 87 z40a90w 93 <~10 34 44 53 24 80 91 z40a180 92 20 29 37 59 21 79 88 z75a0 62 <~10 28 30 24 22 49 60 z75a90e 71 <~10 26 37 36 19 61 69 z75a90w 58 <~10 21 25 25 27 50 56 z75a180 63 <~10 27 28 34 14 51 61 In the fourth column, the integration is only along the main optical beam between the entrance of the enclosure and the primary mirror (M1) in order to give an estimate of the relative contribution of that segment. The contributions between the main optical components (M1 to M2 secondary mirror, M2 to M3 tertiary mirror and M3 to camera) are given in the next three columns. In the last two columns, the contribution of the inside of the enclosure was calculated by integrating between M1 and the camera and 15m and the camera following the path of the light rays and including all the multiple reflections between the mirrors. Table 3: Averaged total enclosure seeing contribution (mas) per azimuth angle 0 o azimuth 90 o East azimuth 90 o West azimuth 180 o azimuth 80 76 79 82 The averaged total enclosure seeing contribution varies between 76mas for the 90 o East azimuth orientation and 82mas for the 180 o East azimuth orientation indicating that the 90 o East azimuth orientation has on average a better configuration for wind flushing inside the dome (Table 3). This is confirmed in Table 4 for the inside enclosure seeing contribution with the exception of the 75 degree zenith angle. It should be noted that the 75 degree zenith angle is better on average than the other zenith angle cases. Because the telescope is low enough, direct venting occurs through the aperture. Table 4: Inside Enclosure Seeing Contribution (mas) Telescope Zenith Angle (degrees) 0 o azimuth z=15m to Camera 90 o E azimuth z=15m to Camera 180 o azimuth z=15m to Camera 90 o W azimuth z=15m to Camera Averaged azimuth z=15m to Camera 20 81 66 90 83 80 40 95 87 88 91 90 75 60 69 61 56 62 4. TELESCOPE POINTING HISTOGRAMS FROM OPSIM LSST has developed an operation simulator (OpSim) with a modular and object-oriented design. The main components include a telescope model, a sky model, a weather database, a scheduler and multiple observing proposals. The telescope model computes the slew time delay from the current position to any given target position, using a complete kinematic model for the mount, dome and rotator, as well as optics alignment corrections. The telescope model was designed to keep track of the position of the most important telescope components during the simulation and to Proc. of SPIE Vol. 9150 91500R-6

calculate delay time during slews. It basically works by simulating the tracking of a target during an observation. The scheduler module combines the information received from the proposals and the telescope model for selecting the best target at each moment, promoting targets that fulfill multiple surveys and storing all the simulator activities in a MySQL database for further analysis of the run. The telescope azimuth and zenith angles distributions presented here (figure 4 and 5) were determined from the 10-year operations simulation run used as reference (known as run 361). The histograms are far from a uniform distribution. For example, the telescope azimuth angle distribution is mainly towards the west. In table 5 below, the number of occurrences in the histogram is binned by 90 degree increments around the azimuth directions used in the CFD cases. The results are normalized to calculate the percentage per case. We find that more than 50% of the telescope pointings have an azimuth angle pointed west. In the zenith angle cumulative histogram (figure 6), more than 85% of the telescope pointings have a zenith angle below 50 degrees. Additionally, in table 6, 69% of the zenith angle pointings are between 30 degrees and 55 degrees zenith angle. This range is centered on the 40 degree zenith angle direction used in the CFD analysis. 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 Telescope Azimuth Angle Histogram (opsim361-10-year) 0 0 50 100 150 200 250 300 350 400 Azimuth (Degrees) Figure 6: Telescope Azimuth Angle Histogram (0deg is North and 90deg is East) 9 x 104 Telescope Zenith Angle Histogram (opsim361-10-year) 8 7 6 5 4 3 2 1 Figure 7: Telescope Zenith Angle Histogram 0 0 10 20 30 40 50 60 70 80 Zenith Angle (Degrees) Proc. of SPIE Vol. 9150 91500R-7

Table 5: CFD Azimuth Angle Bin Percentages CFD Azimuth Angle case Azimuth Angle Bin Size (degree) % 0 North 315 to 45 16.7 90 East 45 to 135 8.3 180 - South 135 to 225 18.9 90 West (270) 225 to 315 56.1 1 Telescope Zenith Angle Cumulative Histogram (opsim361-10-year) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 Zenith Angle (Degrees) Figure 8: Telescope Zenith Angle Cumulative Histogram Table 6: CFD Zenith Angle Bin Percentages CFD Zenith Angle case (degree) Zenith Angle Bin Size (degree) % 20 0 to 30deg Zenith 25.1 40 30 to 55deg 69.1 75 Above 55deg 5.8 5. DOME SEEING CONTRIBUTION From all the different cases, a total dome seeing contribution model was established to be used in conjunction with the telescope pointing histograms for Monte Carlo simulations. This model is summarized in table 7 below. Table 7: Dome Seeing Model versus Azimuth and Zenith Angles Telescope Zenith Angle (degrees) 0 o azimuth (315-45) 90 o E azimuth (45-135) Azimuth Angle 180 o azimuth (135-225) 90 o W azimuth (225-315) 20 (0-30) 83 68 92 85 40 (30-55) 96 89 92 93 75 (55-75) 62 71 63 58 Proc. of SPIE Vol. 9150 91500R-8

The Monte Carlo analysis was done with the Crystal Ball software from Oracle. Custom distributions can be defined as assumptions for the analysis and the telescope azimuth and zenith angle distributions from OpSim were entered using that function (figure 7). Telescope Zenith Cumulative Histogram 1.00-0.90-0.80 - - 10,000 9,000 8,000 C j 0.50 co 0.40 - E d 0.30-0.20 - i 0.10-0.00 10.00 20.00 30.00 40.00 50.00 60100 7000 Zenith Angle (degrees) Figure 9: Telescope Zenith Angle Cumulative Histogram - 7,000 c iv 6,000.z m - 5,000 TI - 4,000 c m - 3,000 = - 2,000.2 From the results of the Monte Carlo Analysis (table 8), we obtained a dome seeing of around 86mas for the 30% value of the dome seeing distribution and of around 92mas for the 50% value of the dome seeing distribution. It appears also that more than 90% of the dome seeing distribution is in the range of 82 to 93mas (figure 8). Table 8: Dome Seeing Distribution from Monte Carlo Analysis Monte Carlo Simulation Dome Seeing Percentiles (mas) 30% 86 50% 92 90% 94 The LSST image quality error budget includes three main contributors related to the dome: - Dome seeing due to the dome air flow and dome temperature. - Wind shake of the telescope mount due to the wind load inside the enclosure necessary to flush the dome - Dome shake due to vibration transfer between the enclosure and the telescope pier 1,000 0 Dome Seeing Cumulative Distrbulion 1.00 0.90 0.80 ä 0.70 m _o a ó 0.60 j 0.50 2 0.40 U0.30 0.20 0.10 TT TTTT II i rtai = 93.34% 0.00 68 70 72 74 76 78 80 82 84 86 Dome Seeing (mas) Figure 10: Dome Seeing Cumulative Distribution from the Monte Carlo Analysis 88 90 92 94 96 10,000 9,000 8,000 O 7,000 3 6,000 m 5,000 1 'ma 4,000 m 3,000 ` 2,000 1,000 o Proc. of SPIE Vol. 9150 91500R-9

The dome seeing allocation in the LSST image quality error budget is of the order of 85mas and the combined allocation for dome seeing and wind shake is of the order of 96 mas. The combined allocation can be compared with the outcome of the Monte Carlo analysis because as result of its high natural frequency, the LSST telescope has low susceptibility to wind induced vibrations [8]. Wind pressure loading applied to the FEA model has shown that the wind induced image motions are negligible at wind speed inside the dome below 1m/sec. Dome seeing estimation is within the combined error budget allocation for the average outside wind speed on Cerro Pachón. For the nights with higher wind speed, the balance between wind shake and dome flushing will be maintained by actively controlling the dome louvers designed with the air vents. In summary, using the current dome seeing model and the OpSim database, the dome seeing contribution to the image quality error budget is estimated to be below 94mas in 90% of the time for the average wind speed and predominant wind direction on site. In the future, we are planning to run some additional CFD cases at different outside wind speed to complete the dome seeing model. REFERENCES [1] Vogiatzis, K., Angeli, Z. G., Sebag, J., Chandrasekharan, S., Thermal Seeing Modeling as a Design and Performance Analysis Tool, Mauna Kea Weather Center First Symposium on Seeing, Kona, HI, March 20-22, (2007). [2] Sebag, J., Vogiatzis, K., LSST camera heat requirements using CFD and thermal seeing modeling, Proc. SPIE 7738, (2010) [3] Cho, M., Vogiatzis, K., Sebag, J., Neill, D., Wind responses of the LSST secondary mirror, Proc. SPIE 8449, (2012) [4] Sebag, J., Vogiatzis, K., Barr, J., Neill, D., LSST Summit Enclosure-Facility Design Optimization using aerothermal modeling, Proc. SPIE 8449 (2012) [5] Delgado F., et al. LSST Operation Simulator Implementation, Proc. SPIE 6270, (2006) [6] Vogiatzis, K., Aero-thermal modeling framework for TMT, Proc. SPIE 8336, (2011) [7] Vogiatzis, K., Otarola, A., Skidmore, W., Travouillon, T., Angeli, G. Z., Thermal seeing modeling validation through observatory measurements, Proc. SPIE 8449 (2012) [8] Neill, D., Sebag, J., Warner, M., Krabbendam, V., Wind Induced Image Degradation (jitter) of the LSST Telescope, SPIE 7012, (2008) Proc. of SPIE Vol. 9150 91500R-10