Quantitative evaluation on internal seeing induced by heat-stop of solar telescope

Yangyi Liu; Naiting Gu; Changhui Rao

doi:10.1364/OE.23.019980

1. Introduction

With the progress of solar observations and researches, higher temporal and spatial resolutions at solar atmosphere surface are required. Therefore, the aperture of the solar telescope continuously increases. Larger aperture improves the resolutions but also brings excessive heat input, which may result in thermal deformation of optical elements. To protect optical elements from severe thermal deformation, a field stop, also called heat-stop, is installed at the prime focus of the telescope [1]. By limiting the field-of-view, the excessive sunlight is blocked by heat-stop. However, for exposure to the concentrated sunlight at prime focus, some of the sunlight is transformed to heat absorbed by heat-stop, leading to its temperature rise. Different from traditional vacuum structure of sub-meter-size solar telescope, open structure is widely used in the telescopes of meter-size or above for difficulties in sealing for large vacuum telescope. For open solar telescope, the temperature rise of heat-stop will heat the ambient air and lead to internal seeing caused by temperature inhomogeneity inside the telescope. The internal seeing will cause wavefront aberration and finally degrade the high resolution imaging quality of open solar telescope.

The research on internal seeing for primary mirror of night astronomical telescope was first proposed in 1982 [2,3]. From then on, the researches continued [4,5]. However, most of these researches were empirical or experimental ones based on the experimental data of a specific telescope. There were no reports about direct quantitative evaluation on internal seeing. As the newly developed instrument, large solar telescope with open structure was developed in recent years. For internal seeing controlling, the requirement of high effective thermal control for heat-stop was firstly proposed for the GREGOR in 2001 [6]. However, in practical applications, it was impossible and unnecessary to totally eliminate the temperature rise of heat-stop. To obtain a reasonable one, which was acceptable for both system realization and imaging quality, the determination of thermal control objective was the first consideration in thermal control system design for heat-stop. In 2003, it was proposed by the GREGOR that the temperature rise of heat-stop was up to 5 Kelvins above the ambient air to avoid obvious internal seeing [7]. In 2008, thermal control objective of 6 Kelvins for the heat-stop was proposed by the DKIST [8]. In 2010, according to qualitative criterion that no obvious thermal plume generation, thermal control objective of 8 Kelvins was proposed for heat-stop of the EST based on computational fluid dynamics (CFD) calculations [9].

So far, the proposals of thermal control objective of heat-stop mostly depend on engineering experience or indirect CFD calculations. The lack of effective and quantitative evaluation method makes the correlation between internal seeing and temperature rise still not clear. Therefore, it is necessary to quantitatively evaluate the internal seeing.

For quantitative evaluation on internal seeing of solar telescope heat-stop, an integrated analysis method for internal seeing calculation based on CFD and geometric optics is proposed in this paper. By using this method, the temperature rise of heat-stop is transformed to the corresponding wavefront aberration, which is used to evaluate the internal seeing. Based on the quantitative correlation between temperature rise and internal seeing, the thermal control objective is decided based on the system optical error budget.

In this paper, the integrated method for internal seeing evaluation is described in details. Based on the heat-stop of the Chinese Large Solar Telescope [10] (CLST), this method is utilized to evaluate the internal seeing induced by its temperature rise quantitatively. The maximum acceptable temperature rise for heat-stop of the CLST and the correlation between internal seeing and other factors are also shown in the following sections.

2. Integrated analysis method for internal seeing

The generation of internal seeing consists of two phases. First, the heated heat-stop under concentrated solar irradiance spatially and nonuniformly heats the ambient air, leading to the inhomogeneity of the air on the optical path inside the telescope. Second, the air of nonuniform temperature becomes variable refractive index medium, leading to additional wavefront aberration for the rays passing through it. Here, this additional aberration caused by the nonuniform air on the optical path is used to evaluate the internal seeing directly.

As shown in Fig. 1, the proposed integrated analysis method for the internal seeing has three steps.

Fig. 1 Integrated analysis method for internal seeing.

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Firstly, based on the CFD calculation, the temperature field of heat-affected zone induced by heat-stop temperature rise is obtained. Secondly, the corresponding equations are used to transform the temperature field to refractive index field. Thirdly, by the method of optical integration, the wavefront aberration of the rays passing through the heat-affected zone is obtained.

2.1 CFD calculation for heat-stop heat-affected zone

Firstly, the heated heat-stop will heat the ambient air, which always causes thermal plume. With the proposed method, the air model around the heated heat-stop is built in the Ansys-CFX software based on the CFD theory.

The CFD model of air contains equations of mass, momentum and energy. These equations can be expressed in Eqs. (1) [11], which corresponds to different fluid standard equations for different characteristic variables.

\frac{\partial (ρ φ)}{\partial t} + d i v (ρ φ u) = d i v (Γ g r a d φ) + S_{φ}

In Eqs. (1), the four terms represent time, convection, proliferation, and source respectively. $φ$ is the characteristic variable, which represents the velocity component in momentum equations and temperature in energy equations. $ρ$ , $u$ and $Γ$ are density, velocity vector and diffusion coefficient of fluid respectively.

The generation of internal seeing is due to natural convection between high temperature object and low temperature air. Hence the air buoyancy is the main drive of natural convection. For air buoyancy calculation, a source term should be added to the momentum equations as Eqs. (2).

S_{M} = (ρ - ρ_{r e f}) g

In Eqs. (2), $ρ - ρ_{r e f}$ , $g$ are density difference and gravity acceleration respectively.

The stable temperature field is obtained after CFD calculation based on the Ansys-CFX software.

2.2 Transformation from temperature field to refractivity field

As a physical characteristic, the refractive index of the air depends on temperature, pressure and humidity, According to equations proposed by Rueger [12,13], for visible and infrared band, the refractivity $n$ is expressed in Eqs. (3).

n = 1 + (\frac{273.15}{101325} \frac{P}{T} \cdot (287.6155 + \frac{1.62887}{λ^{2}} + \frac{0.0136}{λ^{4}}) - 0.1127 \frac{e}{T}) \times 10^{- 6}

In Eqs. (3), $P$ , $T$ , $λ$ , $e$ are local pressure (unit: Pa), local temperature (unit: K), wavelength (unit: μm) and local vapour pressure (unit: Pa) respectively. When the temperature ranges from −40 to 100 degrees and the pressure ranges from 80 to 120 kPa and the wavelength ranges from 300 to 1690nm, the computational accuracy of Eqs. (3) achieves 10⁻⁷.

The vapour pressure is neglected for its influence on refractivity is less than 1% [14]. The Eqs. (3) is rewritten as Eqs. (4).

n = 1 + \frac{273.15}{101325} \frac{P}{T} \cdot (287.6155 + \frac{1.62887}{λ^{2}} + \frac{0.0136}{λ^{4}}) \times 10^{- 6}

Taking derivatives of Eqs. (4), Eqs. (5)-(6) are obtained.

d n = \frac{273.15}{101325} N_{s p} \cdot \frac{1}{T} \times 10^{- 6} d P - \frac{273.15}{101325} N_{s p} \cdot \frac{P}{T^{2}} \times 10^{- 6} d T

N_{s p} = (287.6155 + \frac{1.62887}{λ^{2}} + \frac{0.0136}{λ^{4}})

In Eqs. (5), $d P$ and $d T$ are pressure and temperature difference to the standard pressure and temperature respectively. $d n$ is the relative refractive index.

Set the normal atmosphere ( $P_{s t d} = 1.01325 \times 10^{5}$ Pa) and 25°C( $T_{s t d} = 298.15 K$ ) at the standard point where the relative refractive index is zero. The refractive reflective index at other points is decided by the pressure difference and temperature difference to the standard point.

For the air flow at low speed (velocity < 90m/s), the total pressure variation is less than 10 Pa [15]. According to the Eqs. (5), the corresponding relative refractive index variation is about 10⁻⁸. Meanwhile, the relative refractive index variation for temperature variation is about 10⁻⁶ per Kelvin. Therefore, the variation of pressure is neglected. For numerical calculation, Eqs. (5) is rewritten as Eqs. (7).

Δ n_{i} = \int_{T_{s t d}}^{T_{i}} - 7.853 (1 + \frac{5.666 \times 10^{- 3}}{λ^{2}} + \frac{4.731 \times 10^{- 5}}{λ^{4}}) \cdot \frac{1}{T^{2}} \times 10^{- 4} d T

$Δ n_{i}$ is the relative refractive index at ith point. $T_{i}$ and $T_{s t d}$ are the temperature at ith point and standard point respectively.

Using Eqs. (7), the discrete temperature field obtained in section 2.1 is transformed to discrete relative refractivity index field.

2.3 Wavefront calculation based on optical path integration

Based on the relative refractivity index field obtained in section 2.2, optical path integration is used along the optical path. When the heat-stop heats the ambient air, the temperature field becomes non-uniform. The non-uniform temperature field transforms to non-uniform refractive index field. The refractive index field obtained in Eqs. (7) generates the optical path difference (OPD). The OPD is the direct and quantitative evaluation on internal seeing.

O P D_{k} = \int_{L} Δ n (x, y, z) d s

In Eqs. (8), $Δ n (x, y, z)$ is the relative refractive index. L is the path of integration. For numerical calculation, Eqs. (8) is written as Eqs. (9). $d z$ is the length of integrating range.

Δ l_{i} (x, y, z) = Δ n_{i} (x, y, z) \cdot d z

O P D_{k} = \sum_{i = 1}^{N} Δ l_{i} (x, y, z)

In Eqs. (9), the constant $Δ n_{i} (x, y, z)$ is the local relative refractivity index at the start point of ith integrating range. However, the points where relative refractivity index required doesn’t always correspond to the nodes of CFD grid. Therefore, an inverse distance weighted interpolation algorithm is imported in Eqs. (11).

Δ n_{i} (x, y, z) = \sum_{j = 1}^{N} \frac{Δ n_{j} (x, y, z)}{d_{j} (x, y)} / (\sum_{j = 1}^{N} \frac{1}{d_{j} (x, y)})

The idea of the algorithm is to use the surrounding points with refractive index value to obtain the refractive index value at the start point. In Eqs. (11), $Δ n_{j} (x, y, z)$ is the relative refractive index value at jth point. $d_{j} (x, y)$ is the distance from jth point to the start point. N is the number of surrounding nearest N points with relative refractive index value. In the calculation, N equals 20.

Repeating the optical path integration for one ray after another ray, the OPD of large amounts of rays is obtained. The OPD is the quantitative evaluation on the wavefront aberration induced by the internal seeing of heat-stop.

It is notable that the development of thermal plume is a transient process. When the timescale of thermal plume evolution is shorter than that of imaging, such as the long exposure, the steady analysis on temperature field should be replaced by the transient analysis. In this paper, it is concentrated on the correlation between the heat-stop at a certain temperature rise and the corresponding internal seeing. Therefore, the wavefront piston and tilt will not degrade the imaging quality obviously in the steady state analysis. Certainly, it should be ensured that the timescale of thermal plume evolution is longer than that of imaging, if the proposed method in this paper is used in practical.

For the wavefront obtained, the Zernike Polynomial decomposition [16] is used to remove the first three modes, which represents piston, tilt in x direction and tilt in y direction respectively. Finally, the wavefront without piston and tilt is obtained. That is the direct evaluation on the wavefront aberration induced by the heat-stop temperature rise.

3. CLST and its reflective heat-stop

3.1 Chinese Large Solar Telescope (CLST)

We are constructing the large ground-based solar telescope CLST in China [17]. The CLST is a classical on-axis Gregorian configuration telescope with open structure and alt-azimuth mount. The clear aperture of primary mirror of the CLST is 1.76m. When it is equipped with the Adaptive Optics systems, the diffraction limit angular resolution of the CLST is about 0.052 arc sec at G-band wavelength, which is able to reveal the fundamental astrophysical processes at smaller spatial scale. The relevant parameters and 3D sketch of the CLST are shown in Table 1 and Fig. 2 respectively

Table 1. Parameters of the CLST

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Fig. 2 3D sketch of mechanical design for the CLST.

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3.2 heat-stop of the CLST

To avoid light blocking, the heat-stop of on-axis solar telescope should be restricted in the central obstruction of the secondary mirror. For space limitation, the heat-stop is designed in the form of reflecting type for its relatively smaller volume [18]. As shown in Fig. 3(a), the heat-stop is located at the prime focus, which is also in the central obstruction.

Fig. 3 Reflecting heat-stop of CLST (a). 3-D sketch (b). engineering drawing.

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As shown in Fig. 3(b), the heat-stop is a cylinder truncated by a 45 degrees inclined plane with a conical channel. For compact structure of the CLST, its heat-stop is near the optical path. The heat-affected zone induced by heat-stop temperature rise may overlap with the optical path. That will lead to wavefront aberration.

4. Parameter setting for integration method

4.1 Domain and boundary condition for CFD calculation

Possible overlap area of the heat-affected zone and the optical path inside the telescope is shown in the Fig. 4. At any telescope pointing direction, the selected domain contains the possible overlap area of thermal plume and optical path. In the CFD calculation, the heat-affected zone is selected as fluid domain of the cylinder area with 1820mm diameter and 1240mm height.

Fig. 4 Selection of air fluid domain.

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The material of fluid domain is selected as the air at 25 degrees ( $T_{s t d} = 298.15$ K) and normal atmosphere ( $P_{s t d} = 1.01325 \times 10^{5}$ Pa). The inner boundary (green surface in Fig. 5) is the interface of heat-stop and ambient air. To simulate different temperature rises of heat-stop, the inner boundary is set to constant temperature boundary. Corresponding to the heat-stop temperature rises of 1, 2, 5, 10, 15, 20, 25, 30, 35, 40 Kelvins, the temperature of inner boundary are set to 26, 28, 30, 35, 40, 45, 50, 55, 60 and 65 degrees in the different simulations respectively. The outer boundary of fluid domain is set to open boundary. For simplification, the analysis type of CFD calculation is assumed as steady state. The relevant settings in the CFD are shown in Table 2.

Fig. 5 Boundary condition of air domain.

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Table 2. Model Selection and Boundary Setting of CFD

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In the simulation, except for different temperature rises of heat-stop, the telescope pointing direction is also taken into consideration. $α$ is the elevation angle. When $α$ equals 0 or 90 degrees, it respectively represents the telescope pointing to the horizontal direction or zenith. Corresponding to $α$ varying from 0 to 90 degrees (from horizontal direction to zenith), the directions of gravity acceleration successively sets to 90, 75, 60, 45, 30, 15 and 0 degrees to the horizontal direction respectively.

4.2 Parameter setting for relative refractivity index transformation

In the simulation, assume the wavelength is 0.5μm ( $λ$ = 0.5μm). For numerical calculation, Eqs. (7) is rewritten as Eqs. (12).

Δ n_{i} = \int_{T_{s t d}}^{T_{i}} \frac{- 0.0804}{T_{i}^{2}} d T

4.3 Parameter setting for optical integration

Considering the overlap of heat-affected zone and the optical path, the optical path which may be overlapped by the heat-affected zone contains three phases. The three phases for optical integration are incoming rays of M1 [Fig. 4(a)], reflected rays from M1 to M2 [Fig. 4(b)] and reflected rays from M2 to M3 [Fig. 4(c)] respectively [shown in Fig. 6].

Fig. 6 Optical paths for optical integration (a). rays transmission process of M1, (b). rays transmission process from M1 to M2, (c). rays transmission process from M2 to M3.

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In the simulation, the determination of integrating range $d z$ and number of ray M relates to the accuracy of results. Too large $d z$ and small M is time-saving but not quite accurate. On the opposite, it is accurate but time-consuming. To make a compromise between accuracy and calculation time, we make a criterion that with decrement of $d z$ or M, the calculation difference of two calculations is smaller than 1%. At that moment, the selected $d z$ and M are the optimal numbers. After repeated calculations, the optimal $d z$ and M respectively equal 8mm and 1096.

Meanwhile, to ensure the irrelevance between calculated wavefront and grid density of CFD, the repeated calculations are made with different density of grid. A criterion of irrelevance is made that with the increase of grid density, the calculation difference of wavefront root-mean-square (RMS) of two calculations is smaller than 1%. After repeated calculations, the selected numbers of nodes and elements of CFD grid are 139790 and 790651 respectively.

4.4 Evaluation on the wavefront quality

In the simulation, the RMS is used to evaluate the magnitude of the wavefront aberration induced by internal seeing. The definition of the RMS is shown in Eqs. (13).

R M S = \sqrt{\frac{1}{m n} \sum_{x = 1}^{m} \sum_{y = 1}^{n} {[φ_{e} (x, y) - \bar{φ_{e} (x, y)}]}^{2}}

In Eqs. (13), $φ_{e} (x, y)$ and $\bar{φ_{e} (x, y)}$ are the wavefront aberration and its average value. $m$ and $n$ are the sampling number of row and column respectively.

According to the system optical error budget for the CLST, the wavefront aberration without piston and tilt induced by the heat-stop internal seeing is required to be within 25nm.

5. Quantitative Results for CLST

Based on the analysis in section 4.3, the optical path affected by the internal seeing contains three phases. In the following sections, we’ll quantitatively analyze the influence of internal seeing on each transmission process at first, and then obtain the total influence by the method of superposition.

5.1 Transmission process of M1

For the transmission process of M1, the wavefront RMS and peak-to-valley (PV) without piston and tilt with different heat-stop temperature rises and telescope pointing directions variation are shown in Fig. 7.

Fig. 7 Wavefront (without piston and tilt) of M1with different telescope pointing directions and temperature rises variation (a). RMS (b). PV.

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Fig. 7(a) and (b) show that with the telescope pointing varying from the horizontal to the vertical directions ( $α$ varies from 0 to 90 degrees), the wavefront RMS and PV of M1 gradually decrease. When the telescope points to the vertical direction, the wavefront RMS of M1 approaches zero. Meanwhile, it is found that the RMS value of wavefront aberration increases with the increase of heat-stop temperature rise.

To figure out the correlation between wavefront RMS and telescope pointing direction, the temperature field of ambient air at different telescope pointing directions and corresponding wavefront diagrams are respectively shown in Fig. 8 and 9.

Fig. 8 Temperature field of ambient air when the heat-stop temperature rise is 25 Kelvins at different telescope pointing directions (a). $α = 0^{\circ}$ , (b). $α = 30^{\circ}$ , (c). $α = 60^{\circ}$ , (d). $α = 90^{\circ}$ .

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Fig. 9 Wavefront diagrams of M1 at different telescope pointing directions.

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Fig. 8 shows that the thermal plume forms along the buoyancy direction. Therefore, drastic temperature change of the thermal plume causes wavefront aberration. When $α$ equals 0 degree (horizontal pointing), the thermal plume forms along the vertical direction [Fig. 8 (a)]. The vertical thermal plume produces the transverse OPD on the wavefront diagram, which is shown in Fig. 9 (a). With the increase of $α$ , the position of the thermal plume changes and leads to corresponding change on wavefront diagrams [Fig. 9 (b), (c)]. When $α$ equals 90 degrees (vertical pointing), the thermal plume is in the central obstruction. That nearly never generates any wavefront aberrations [Fig. 9 (d)].

For the correlation between heat-stop temperature rise and wavefront aberration, the wavefront diagrams of different heat-stop temperature rises are shown in Fig. 10. It is easy to find that when the telescope pointing remains, the magnitude of wavefront aberration increases with the increase of heat-stop temperature rise.

Fig. 10 Wavefront diagrams of different heat-stop temperature rises.

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Therefore, for the transmission process of M1, with the variation of telescope pointing varying from the horizon to the vertical direction, the magnitude of wavefront aberration gradually decreases. Meanwhile, the magnitude of wavefront aberration increases with the increase of heat-stop temperature rise.

5.2 Transmission process from Primary Mirror (M1) to Secondary Mirror (M2)

For the transmission process from M1 to M2, the wavefront RMS without piston and tilt with different heat-stop temperature rises and telescope pointing directions variation are shown in Fig. 11.

Fig. 11 Wavefront RMS (without piston and tilt) of M1→M2 with different telescope pointing directions and temperature rises variation.

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Fig. 11 shows that with the telescope pointing varying from the horizontal to the vertical direction, the wavefront RMS decreases at first and then increases. Meanwhile, as the heat-stop temperature increases, the wavefront RMS increases.

For the same heat-stop temperature rise at different telescope pointing direction, the buoyancy direction is in the inverse direction of gravity acceleration [shown in Fig. 12]. The temperature fields of air at different telescope pointing directions are shown in Fig. 13.

Fig. 12 Velocity field of ambient air when the heat-stop temperature rise is 25 Kelvins at different telescope pointing directions (a). $α = 0^{\circ}$ , (b). $α = 30^{\circ}$ , (c). $α = 60^{\circ}$ , (d). $α = 90^{\circ}$ .

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Fig. 13 Temperature field of ambient air when the heat-stop temperature rise is 25 Kelvins at different telescope pointing directions (a). $α = 0^{\circ}$ , (b). $α = 30^{\circ}$ , (c). $α = 60^{\circ}$ , (d). $α = 90^{\circ}$ .

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Fig. 12 shows that when the elevation angle $α$ is 0 degree [Fig. 12 (a), horizontal pointing], the buoyancy direction is parallel to the back side of heat-stop. Therefore, the development of thermal plume at the back side of heat-stop is eliminated by the air flow effectively (Fig. 13 (a)). With the increase of $α$ [Fig. 12 (b), (c), and (d)], the buoyancy direction changes from the horizontal to the vertical. The air flow velocity component parallel to the back side of heat-stop gradually decreases for blocking. Therefore, the internal seeing at the back side of heat-stop gradually reinforces with the increase of $α$ [Fig. 13 (b), (c), and (d)].

As $α$ increases from 0 degree to 45 degrees, the air flow velocity component parallel to the front side of heat-stop becomes larger [Fig. 12 (a), and (b)]. With the increase of velocity component parallel to the front side of heat-stop, the development of thermal plume is gradually reduced and the wavefront RMS gradually decreases [Fig. 13 (a), and (b)]. When $α$ exceeds about 45 degrees, the air flow can always flow the front side of heat-stop [Fig. 12 (c), and (d)]. Therefore, the internal seeing at font side of heat-stop is always kept small enough [Fig. 13 (c), and (d)].

As a summary, with the increase of $α$ varying from 0 degree to 90 degrees, the wavefront RMS induced by internal seeing at back side of heat-stop gradually increases. With the increase of $α$ varying from 0 degree to 45 degrees, the wavefront RMS induced by internal seeing at front side of heat-stop gradually decreases. When $α$ exceeds 45 degrees, the internal seeing at the front side of heat-stop is kept small enough. Based on the superposition of the effects on both sides of heat-stop, it is found that with the increase of $α$ , the wavefront aberration decreases at first and then increases from about 45 degrees [shown in Fig. 11].

For the correlation between heat-stop temperature rise and wavefront aberration, the wavefront diagrams of different heat-stop temperature rises are shown in Fig. 14.

Fig. 14 Wavefront diagrams of M1-M2 at different heat-stop temperature rises.

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Fig. 14 shows that when the telescope pointing remains, the wavefront RMS increases with the increase of heat-stop temperature rise.

Therefore, for the transmission process of M1 to M2, with the variation of telescope pointing varying from the horizontal to the vertical direction, the magnitude of wavefront aberration decreases at first and then increases. Meanwhile, the magnitude of wavefront aberration increases with the increase of heat-stop temperature rise.

5.3 Transmission process from Secondary Mirror (M2) to Tertiary Mirror (M3)

For the transmission process from M2 to M3, the wavefront RMS without piston and tilt with different heat-stop temperature rises and telescope pointing directions variation are shown in Fig. 15.

Fig. 15 Wavefront RMS (without piston and tilt) of M2→M3 with different telescope pointing directions and temperature rises variation.

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Fig. 15 shows that with the telescope pointing varying from the horizontal to the vertical direction, the wavefront RMS decreases at first and then increases. For a certain heat-stop temperature rise, the wavefront RMS increases with the increase of heat-stop temperature rise.

To figure out the correlation between wavefront aberration and telescope pointing direction, the wavefront diagrams with different telescope pointing directions at same heat-stop temperature rise are shown in Fig. 16. For further explanation, the diagram of position of rays and heat-affected zone is shown in Fig. 17.

Fig. 16 Wavefront diagrams of M2-M3 at different telescope pointing directions.

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Fig. 17 Position of ray and heat-affected zone.

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When $α$ equals 0 degree (horizontal pointing), the heat-affected zone is in the position 3 as shown in Fig. 17. There is an overlap of heat-affected zone and ray in the transverse direction. Corresponding to the Fig. 16(a), a transvers OPD is generated on the wavefront diagram. With the increase of $α$ , the transvers OPD is gradually reduced. However, when $α$ equals 90 degrees (vertical pointing), the heat-affected zone is in the position 1 of Fig. 17. There is an overlap of heat-affected zone and ray at the inner ring of the ray. Corresponding to Fig. 16(d), a circumferential OPD is produced on the wavefront diagram. Contrary to the transverse OPD, the circumferential OPD gradually increases with the increase of $α$ .

Both the transverse OPD and the circumferential OPD generate wavefront aberration of high spatial frequency. However, their variation trends with telescope pointing directions are opposite. Therefore, the wavefront RMS from M2 to M3 is the superposition of above two kinds of OPDs. The result of superposition decreases at first and then increases with the increase of $α$ .

As for the correlation between wavefront RMS and heat-stop temperature rise, the wavefront diagrams with different heat-stop temperature rises are shown in Fig. 18.

Fig. 18 Wavefront diagrams of M2-M3 at different heat-stop temperature rises.

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Fig. 18 shows that when the telescope pointing remains, the wavefront aberration increases with the increase of heat-stop temperature rise.

Therefore, for the transmission process of M2 to M3, with the variation of telescope pointing varying from the horizontal to the vertical direction, the magnitude of wavefront aberration decreases at first and then increases. Meanwhile, the magnitude of wavefront aberration increases with the increase of heat-stop temperature rise.

5.4 Total Transmission process

The total OPD of whole transmission process is the superposition of previous three transmission processes. Therefore, the total wavefront RMS without piston and tilt is the superposition of previous three transmission processes. The total wavefront RMS with different telescope pointing directions and heat-stop temperature rises variation are shown in Fig. 19.

Fig. 19 Total wavefront RMS (without piston and tilt) with different telescope pointing directions and temperature rises variation.

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Fig. 19 shows that with the telescope pointing varying from the horizontal to the vertical direction, the wavefront RMS decrease at first and then increases. Meanwhile, with the increase of heat-stop temperature rise, the wavefront RMS continually increases.

The wavefront RMS in Fig. 19 is the direct and quantitative evaluation on internal seeing induced by heat-stop temperature rise. Based on the optical error budget of the CLST, the RMS of wavefront aberration without piston and tilt induced by heat-stop internal seeing is required to be within 25nm. That is, the RMS value of wavefront aberration should be within 25nm (CR) at any telescope pointing direction. Therefore, as shown in Fig. 19, the maximum acceptable temperature rise for the heat-stop of the CLST is up to 5 Kelvins above the ambient air at any pointing direction.

6. Summary and conclusions

In this paper, an integrated method for the quantitative evaluation on internal seeing induced by heat-stop of solar telescope is proposed and the results for the CLST are presented.

The analytical results show that the maximum acceptable temperature rise for the heat-stop of the CLST is up to 5 Kelvins above the ambient air when the wavefront aberration without piston and tilt induced by the heat-stop internal seeing should be within 25nm. Moreover, the analytical results show that with the increase of heat-stop temperature rise, the magnitude of wavefront aberration gradually increases for the same telescope pointing direction. Meanwhile, with the telescope pointing varying from the horizontal to the vertical direction, the magnitude of wavefront aberration decreases at first and then increases at a certain heat-stop temperature rise.

This method is general for the analysis on the internal seeing induced by the heat-stop of solar telescopes.

Acknowledgments

This work is funded by the Hi-Tech Project of China, the National Natural Science Foundation of China (No. 11178004) and Science and Technology Innovation Talent Project of Sichuan Province (No. 2015105). A special acknowledgment should be shown to Prof. Wenhan Jiang from the Institute of Optics and Electronics, Chinese Academy of Sciences, for his revision we benefited greatly. Meanwhile, we are very grateful to the reviewers for their valuable advice. We also would like to express our gratitude to Mrs. Hui Zhang, Mrs. Cheng Li, Dr. Lei Zhu, Dr. Lanqiang Zhang, Mr. Jinlong Huang, Mr. Yuntao Chen, Mr. Benxi Yao and Mr. Zhiyong Wang from Institute of Optics and Electronics, Chinese Academy of Sciences, for their help.

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Parameter	value
Aperture size of M1	Φ1800mm
Field of View (FOV)	≥Φ3′
Wavelength cover	380nm~2500nm
Image space F#	F/54.5
Focal Length	~96m
Aperture size of M2	Φ490mm
Aperture size of M3	Φ390mm

Model	Setting
Analysis Type	Steady sate
Turbulence model	k-Epsilon
Buoyancy model	Boussinesq approximation
Inner boundary (Heat-Stop surface)	Wall at fixed temperature
Outer boundary	Open boundary

Parameter	value
Aperture size of M1	Φ1800mm
Field of View (FOV)	≥Φ3′
Wavelength cover	380nm~2500nm
Image space F#	F/54.5
Focal Length	~96m
Aperture size of M2	Φ490mm
Aperture size of M3	Φ390mm

Model	Setting
Analysis Type	Steady sate
Turbulence model	k-Epsilon
Buoyancy model	Boussinesq approximation
Inner boundary (Heat-Stop surface)	Wall at fixed temperature
Outer boundary	Open boundary

Quantitative evaluation on internal seeing induced by heat-stop of solar telescope

Abstract

1. Introduction

2. Integrated analysis method for internal seeing

2.1 CFD calculation for heat-stop heat-affected zone

2.2 Transformation from temperature field to refractivity field

2.3 Wavefront calculation based on optical path integration

3. CLST and its reflective heat-stop

3.1 Chinese Large Solar Telescope (CLST)

3.2 heat-stop of the CLST

4. Parameter setting for integration method

4.1 Domain and boundary condition for CFD calculation

4.2 Parameter setting for relative refractivity index transformation

4.3 Parameter setting for optical integration

4.4 Evaluation on the wavefront quality

5. Quantitative Results for CLST

5.1 Transmission process of M1

5.2 Transmission process from Primary Mirror (M1) to Secondary Mirror (M2)

5.3 Transmission process from Secondary Mirror (M2) to Tertiary Mirror (M3)

5.4 Total Transmission process

6. Summary and conclusions

Acknowledgments

References and links

Cited By

Figures (19)

Tables (2)

Equations (13)

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