Optical system overview of the MUST
Based on the above optical system model and iteration criteria, the conceptual design and optimization of the optical system of MUST are obtained as shown in Fig. 4, Tables. 3 and 4. The results include the design of a compact R-C system with Cassegrain focus along with all of its mirror components (i.e., the primary mirror, the secondary mirror, and the WFC). As shown in Fig. 4(a), a concave hyperboloid primary mirror (6.5m diameter, M1) with a central hole (1.8m diameter) and a convex hyperboloid secondary mirror (2.45m diameter, M2) with 5500mm apart (d1 ) form the basic R-C optical system with a focal ratio of F/3.6 and a total focal length of 23323mm. Considering the material availability and fabrication feasibility, the WFC (i.e., L1-L5) will be manufactured entirely using fused silica. Only four surfaces of the WFC are designed as aspheric surfaces with relatively low asphericity [see Fig. 4(b) and Table. 4]. A counter-rotating type atmospheric dispersion corrector (ADC) consisting of lenses L3 and L4 is used to compensate for the atmospheric dispersion when the telescope scans the sky at different zenith angles. The mechanical diameters of each lens of the WFC are set as 1.8m, 1.5m, 1.49m, 1.5m, and 1.45m. And the intervals between two adjacent lenses (i.e., dc1-dc4) are 1200mm, 350mm, 40mm, and 1120mm, respectively. In practice, as the diameter of lens L1 is almost the same as that of the central hole of the primary mirror, lens L2-L5 will be assembled into a single structure and installed in the mirror cell [Fig. 5(a)] as the first step. Lens L1 will then be subsequently installed from above. Using the designed optical system, MUST will achieve an excellent image quality with an EE80 size of image spots less than 0.6 arcsec in diameter for the entire 3° FOV and over a 50° zenith angle range. Figure 4 illustrates where the image spots will enter the optical fibers positioned at the focal plane [700mm (i.e., dc5) away from lens L5]. The fibers will be connected to multi-object spectrographs that will collect spectra ranging from 0.365µm to 1.1µm.
Table 3
Optical parameters of the primary mirror, secondary mirror, WFC, and focal plane
Surface | Radius (mm) | Thickness (mm) | Material | Mech Semi-Dia (mm) | Conic |
M1 | −16256.000 | −5500 | MIRROR (Ohara E6 Borosilicate) | 3251.2 | −1.219518 |
M2 | −8302.487 | 3350 | MIRROR (Zerodur glass) | 1225.0 | −7.585198 |
L1-F | 5224.476 | 125 | SILICA | 900.0 | - |
L1-B | 15259.604 | 1200 | | 900.0 | - |
L2-F | 4332.628 | 80 | SILICA | 750.0 | - |
L2-B | 1748.227 | 350 | | 750.0 | - |
L3-F | −2535.230 | 70 | SILICA | 745.0 | - |
L3-B | 8465.709 | 40 | | 745.0 | - |
L4-F | 3860.132 | 180 | SILICA | 750.0 | - |
L4-B | −4903.155 | 1120 | | 750.0 | - |
L5-F | 1510.265 | 140 | SILICA | 725.0 | - |
L5-B | 2514.536 | 700 | | 725.0 | - |
FP | −9216.780 | - | IMAGE | 615.3 | - |
Table 4
Aspheric surfaces of the WFC and focal plane
Surface | 4th | 6th | 8th | 10th | Maximum depth to remove (mm) |
L1-B | 3.400E − 12 | −2.230E − 18 | 5.985E − 25 | −4.647E − 32 | 0.21 |
L2-F | −1.058E − 13 | −9.539E − 18 | −3.779E − 24 | 1.916E − 29 | 0.30 |
L3-F | 7.675E − 2 | 3.148E − 18 | −2.215E − 24 | −2.337E − 29 | 0.40 |
L5-B | 1.388E − 11 | −1.409E − 17 | −1.576E − 23 | −1.450E − 30 | 0.51 |
FP | −1.254E − 11 | 6.264E − 17 | −1.899E − 22 | 1.801E − 28 | - |
By utilizing the compact R-C configuration, the full height of the telescope could be limited to < 7230mm to achieve better dome seeing. During operation, the wavefront aberration caused by mirror gravity, mirror deviation, structural stress, and temperature difference will be compensated by the primary mirror's deformed surface shape and the secondary mirror's adjustment. MUST can focus the high-quality spots into the densely packed 20000 optical fibers on the focal plane. Compared with other existing and future spectroscopic survey telescopes, MUST has the unique advantage of the critical performance of survey capability, which could be expressed in Eq. (5) [29].
$$\eta =A\varOmega N{f}_{use}{\theta }^{-2} ,$$
5
where A represents the area of the primary mirror, Ω represents the area of the FOV, N represents the number of optical fibers in the focal plane, fuse represents the proportion of time used for the survey, and θ means the natural seeing at the telescope site. As shown in Table. 5, MUST has a survey efficiency 19 times that of the DESI. It will become one of the largest and most advanced spectroscopic survey telescopes and make essential contributions to astrophysics and cosmology.
Table 5
Survey performance of current and future typical spectroscopic survey telescopes using the measure of Eq. (5) proposed by [26]
Telescope | Area of primary mirror (A/m2) | Area of FOV (Ω/ deg2) | Number of optical fibers (N) | Proportion of time for survey (fuse) | Seeing (θ/arcsec) | Index of survey capability (\(\eta\)/\(\eta\)DESI) |
2dF* | 11.95 | 3.1 | 392 | 50% | 1.50 | 0.012 |
SDSS | 4.91 | 7.1 | 1400 | 50% | 1.40 | 0.044 |
WEAVE* | 13.85 | 3.1 | 1000 | 70% | 0.76 | 0.184 |
4MOST* | 13.20 | 4.0 | 2436 | 70% | 0.80 | 0.497 |
DESI | 12.57 | 7.5 | 5000 | 60% | 1.00 | 1.000 |
MOONS* | 52.81 | 0.14 | 1000 | 30% | 0.80 | 0.012 |
Subaru | 52.81 | 1.1 | 2400 | 25% | 0.75 | 0.219 |
MUST | 30.64 | 7.1 | 20000 | 70% | 0.75 | 19.144 |
*2dF: Two-degree-Field Galaxy Redshift Survey; WEAVE: WHT Enhanced Area Velocity Explorer, 4MOST: 4-meter Multi-Object Spectroscopic, MOONS: Multi-object Optical and Near-IR spectrograph. |
Primary Mirror
In the optical system of MUST, the primary mirror is designed as a honeycomb-shaped lightweight single mirror instead of a segmented mirror to improve image quality and reduce control complexity. As shown in Table.3 and Fig. 5, the 6.5m primary mirror with a circular hole in the center is a hyperbolic concave-flat Ohara E6 borosilicate mirror with a curvature radius of − 16256mm, the conic constant of − 1.22 and it weights 8 tons. Figure 5(a) is the machining drawing of the primary mirror, which presents the detailed geometric dimensions of the diameters of the front and back surface (6512.6mm and 6471.9mm), the front and back diameters of the central hole (1800mm and 1815.2mm) and the thicknesses of the edge and the central hole (711.2mm and 385.1mm), respectively. During operation, various factors (e.g., gravity, temperature variation, and wind) will introduce deformations to the surface shape of the primary mirror and thereby affect the image quality. To compensate for the aberration and maintain the surface quality, the primary mirror will be installed in the cell [Fig. 5(b)], an active support system is equipped to adjust the surface shape at each zenith angle dynamically. Figure 5(c) shows the 100 load spreaders arranged at the back of the primary mirror, which are connected to the active support in the mirror cell. Moreover, a thermal control system installed inside the mirror cell will adjust and maintain the temperature of the primary mirror so that it is consistent with the ambient temperature to avoid any thermal-induced distortion or mirror seeing.
As shown in Fig. 5(d), a finite element analysis model is built to simulate this large-scale primary mirror's surface shape and correction ability. The mirror will be polished and tested on the same pattern of load spreaders as in the telescope, the astigmatism in zenith-pointing support is subtracted off zenith-pointing support in the actual processing. What is analyzed here is the situation under the ideal mirror support without considering the actual polishing. Figures. 5(e) and (f) show the surface deformations caused by the gravity in the zenithal and horizontal pointing, respectively. In the zenith direction, the surface shape is mainly characterized as astigmatism and defocus with the peak-to-valley (PV) value of 0.2268µm and root-mean-square (RMS) value of 0.041µm, while the surface shape at the horizontal direction is mainly coma aberration with a PV value of 0.6865µm and an RMS value of 0.096µm. These gravity-induced aberrations could be well compensated by controlling the surface shape through the active support system. As shown in Figs. 5(g) and 5(h), 85.8% of the distortion in the zenith direction is depressed, and the PV and RMS values of the correction residual are 0.086µm and 0.0058µm. At the same time, 84.4% of the distortion in the horizontal direction is decreased, and the PV and RMS values of the residual are 0.1476µm and 0.015µm.
According to the detailed design, the primary mirror and the mirror cell are manufactured at the Mirror Lab of the Steward Observatory, University of Arizona. The primary mirror and cell integration will be precisely adjusted when manufactured and assembled to ensure excellent performance under different zenith angles and working temperatures. It is worth noting that, in the optical system of MUST, the primary mirror will be the reference to the assembly of the secondary mirror and the WFC.
Secondary Mirror
The secondary mirror is combined with the primary mirror to form the R-C telescope with Cassegrain focus to achieve high image resolution in a compact structure. As shown in Fig. 6(a), the secondary mirror is designed as a hyperbolic flat-convex mirror (2.45m diameter, 300mm thickness at the edge) with a curvature radius of − 8302.487mm and a conic constant of − 7.585. To decrease the thermal effect under a wide range of environmental temperatures, the Zerodur with zero thermal expansion coefficient is chosen as the material of the secondary mirror. To effectively reduce the total weight to under 1 ton, the secondary mirror adopts a light-weighted structure with a ~ 75% light-weighting ratio [Fig. 6(a)]. Like the primary mirror, the secondary mirror is coated with the aluminum film with a reflectivity of > 98% from 0.365µm to 1.1µm to improve the optical efficiency.
As shown in Figs. 6(b) and (c), there is a 36-point whiffle-tree for axial support and a 6-tangent-bar for lateral support designed and mounted on a hexapod along with the secondary mirror in current preliminary scheme. This design will reduce the component's overall complexity and ensure the functions for rigid motion adjustment in five dimensions (i.e., piston or focus, tip/tilt, and decenter). Besides the hexapod, there are other ways to achieve high-precision adjustment by deploying 5 actuators to constrain 5 degrees of freedom. Figures 6(d)-(g) present the preliminary finite element analysis results of the secondary mirror on the 36-point passive support under the gravity effect in the zenith direction. The surface deformations of the secondary mirror affected by the passive support are as small as 46 nm RMS, and the maximum support force in the mirror is only 0.05MPa. We should point out that, in the optical system of MUST, when the ADC rotates to eliminate the atmospheric dispersion, the secondary mirror will simultaneously shift along and deflect around the axis to compensate for the aberration caused by the rotation of the ADC and the deviation of the WFC.
Multiple-element Widefield Corrector
Based on the R-C configuration consisting of a 6.5m primary mirror and a 2.45m secondary mirror, the WFC is designed to achieve excellent imaging quality within the entire 3° FOV covering a 50° zenith angle range by compensating the atmospheric dispersion and wavefront aberration. As shown in Fig. 7(a), five pieces of lenses (L1 ~ L5) in total make use of the WFC. All the lenses in the WFC will use the same material (i.e., fused silica) to improve the image quality and match the manufacturing feasibility of the lens blanks. Table. 4 shows the detailed aspheric coefficients of the four aspheric surfaces, including the back surface of lens L1 (L1-B), the front surface of lens L2 (L2-F), the front surface of lens L3 (L3-F), and the back surface of lens L5 (L5-B). We need to emphasize that lens L1, with a diameter of 1.8m (the largest lens in the WFC), is currently the largest transmissive corrector element in the world. To improve the optical efficiency and suppress the ghost images, all the corrector elements are coated with the single-layer magnesium fluoride film in high transmissivity (> 95%@0.365µm-1.1µm).
In the WFC, lenses L3 and L4 form the ADC system to correct the atmospheric dispersion for high image quality. As shown in Fig. 7(b), the back surface of lens L3 and front surface of lens L4 are tilted by 0.1148° and 0.1178°, respectively, and thus L3 and L4 form a pair of wedge lenses, which act as the prism that disperses the input light by wavelength. Drive motors control the rotation of lenses L3 and L4 in the opposite directions to generate the dispersion required to correct the atmospheric dispersion during survey observation, as shown in Fig. 7(c). As the atmospheric dispersion varies across the sky, the rotating angle of the ADC will also change according to the zenith angle of the telescope. In practice, the driving motors of the ADC and the secondary mirror are jointly operated by the telescope control system to maintain image quality and stability.
In the WFC, a flexible circumferential structure supports these 5 pieces of lenses to decrease the mirror deformations and maintain the surface shapes. As an example, Figs. 7(d)-(k) show the surface deformations of lens L1 in the axial and radial directions, which are introduced by gravity at the 0° and 90° zenith angles. When the telescope points at the zenith, the aberration caused by the surface deformation mainly defocuses in the axial direction and coma in the radial direction. Meanwhile, when pointed horizontally, the aberration is mainly coma in the axial direction and defocusing in the radial direction. It should be noted that the influence of surface deformation on the image quality will be further analyzed in Zemax Optic Studio. If necessary, the secondary mirror will shift along and deflect around the axis to compensate for the aberration. During the construction of MUST, the WFC will first be assembled off-site and then installed through the central hole of the primary mirror.
Along with the primary and secondary mirrors, the WFC will improve the image quality of MUST by suppressing atmospheric dispersion and wavefront aberration. However, as the largest corrector element in the world, the lens L1 with a 1.8m diameter still faces enormous challenges in both material availability and fabrication. The uniformity and homogeneity of the large mirror blank are challenging issues. Currently, the MUST team is discussing with Corning to identify a feasible technical solution that suits the manufacturing progress of the WFC.
Focal Plane
After passing through the compact R-C optical system, the target light beams are focused into high-quality image spots with an EE80 diameter smaller than ~ 0.6 arcsec. They will then enter the 20000 fibers positioned on the focal plane. The focal plane is connected to multi-object spectrographs to collect the spectra. As shown in Figs. 8(a) and (b), the focal plane is designed as a high-order aspheric surface (the aspheric coefficients are listed in Table 4) with the curvature of − 9216.8mm and the diameter of 1230.6mm to reduce the FRD over the 3° FOV and 50° zenith angle range. Figures. 8(c) and (d) show the variation of the incidence angles across the FOV and with the zenith angle. We optimize these angles in the model to ensure the quality of the spectra. As the zenith angle varies, the angle of the incident light also varies within a less than ± 0.1° range over the entire FOV. When the zenith angle is 50°, the light beam at the edge of the FOV reaches the maximum angle of incidence value at 0.65° [Figs. 8(e) and (f)]. Even under this worst case, it still has a negligible impact on the vertical incidence for the optical fiber.
Considering the F/3.6 focal ratio of the R-C system and the angle of incidence, the core diameter and numerical aperture of each fiber are designed to be 1.3 arcsec (i.e., a 150µm diameter) and 0.22 (i.e., 25.4° aperture angle) to ensure high coupling efficiency and high spectral resolution. The 20000 optical fibers will be installed onto a high-density fiber positioning device in the focal plane. Each fiber could target any location within the patrol radius of its positioner. Additionally, the focal plane is mounted on a de-rotation platform. The platform will control the focal plane to rotate in the opposite direction to eliminate the image shift caused by the Earth's rotation during exposure.
Image Quality
As mentioned earlier, the light from the target is focused by the 6.5m primary mirror and the 2.45m secondary mirror, then corrected by the WFC to form a high-quality image spot on the focal plane. Figure. 9 shows the performance of the focused image spot for the whole optical system. This includes the spot patterns, the variation curve of the RMS spot radius, the distribution of the RMS spot radius across the entire FOV, and the enclosed energy across the FOV and at different zenith angles. It is worth mentioning that, considering the image quality in the edge of FOV and the size of the lens blanks, we artificially introduced an average vignetting of ± 1.275° [Fig. 9(q)], a central obscuration of 16.12%, and an additional 1.5% vignetting at the edge when modeling the optical system to improve the fidelity of the simulation.
For the 0° zenith angle [Fig. 9(a)], as shown in Figs. 9(d) and (g), the maximum RMS radius of the image spot within the wavelength range between 0.365µm and 1.1µm could be as small as 21.1µm. This indicates that the atmospheric dispersion and wavefront aberration are effectively controlled. In particular, the RMS radii of all the polychromatic spots are smaller than 19µm within the central 1.8° (i.e., ± 0.9°) of the FOV. The minimum RMS value can be restricted to as small as 16.4µm. When the zenith angles are 30° [Fig. 9(b)] and 50° [Fig. 9(c)], the atmospheric dispersion and wavefront aberration are also well compensated and corrected by the counter-rotation of the ADC and the WFC. According to the spot diagrams for the 30° zenith angle illustrated in Figs. 9(e) and (h), the RMS radii of all the polychromatic spots are smaller than 25µm, although it increases quickly toward the edge of the FOV. The RMS radii are still smaller than 20µm within the central 1.2° (i.e., ± 0.6°) of the FOV. At the maximum zenith angle of 50° for MUST, the RMS radii of the polychromatic spots can also be well controlled within 22.3µm with a minimum size of 16.6µm at the center of the FOV [Figs. 9(f) and (i)]. The distributions of the RMS spot radius for the three zenith angles are shown in Figs. 9(j), (k), and (l). These figures suggest that the image spots are reasonably uniform across the 3° FOV and within the allowed zenith angle range. Furthermore, we calculated the characteristics of the EE80 of the focused image spot, which is an important indicator in evaluating the concentration of the image. Figures 9(m) - (o) show the variations of enclosed energy across the FOV when the zenith angle is 0°, 30°, and 50°. Figure 9(p) shows the variation of the EE80 diameter versus the position of the FOV. Over the entire FOV and the 50° zenith angle range, the EE80 diameters are smaller than 0.512 arcsec, and the minimum value can reach as low as 0.362 arcsec. The image spot perfectly matches the fiber with a 150µm core diameter (equal to 1.3 arcsec @0.0088 arcsec/µm) and ensures the spectra from adjacent fibers will not interfere with each other.
These results confirm that the WFC with an ADC can compensate for the atmospheric dispersion and image aberration. While the primary mirror of MUST is 1.5 times larger than DESI, it can still collect data with an even better image uniformity over the entire FOV. The excellent optical performance allows MUST to survey the entire northern sky with uniform spectral quality efficiently. This reference design can enable exciting science and guide the future development of spectroscopic survey telescopes.
Thermal Effect
As mentioned above, MUST will be sited on the Saishiteng Mountain in Northwest China, where the temperature range is as wide as 55℃ ranging from − 30°C to 25°C. A thermal effect analysis covering such a wide range of temperatures is critical. It can help us assess the stability of image quality and guide the subsequent improvement of the telescope. In the thermal model of the optical system, the variation of the environmental temperature is considered after ignoring its inhomogeneous spatial distribution. The changes in the shape of optical elements and the intervals of optical elements caused by the thermal expansions of the optical materials are the major issues that can degrade the image quality.
To ensure the thermal stability of the image quality of the optical system, all the WFC lenses will be made of fused silica with the desirable uniformity. According to the spot diagrams demonstrated in Fig. 10, the minimum RMS radius of the polychromatic spot is 16.0µm (16.2µm), and the maximum value is 21.4µm (21.5µm) at − 30°C (25). The image quality analysis in the previous section is based on the optical system model at 2°C, which is the average temperature of the observing site. The spot radius and shape at − 30°C and 25°C are similar to those at the average temperature of 2°C. And under these extreme temperatures, the behaviors of the image spots are also as expected: the spots close to the center of the FOV are smaller, and those close to the edge of the FOV become slightly larger. Therefore, the environmental temperature variation has little effect on the image quality. Under the allowed temperature range, MUST will have consistently high image quality. It is also worth mentioning that the small thermal impact on the shape and relative positions of the lenses can be further compensated by shifting and deflecting the secondary mirror to achieve even better image quality.