The Wide-field Spectroscopic Telescope: optical designs for the low-resolution multi-object spectrographs

Abstract: In MOS Low-Resolution mode, WST has a 'spectral etendue' per fiber (etendue x spectral resolution elements) twice as large as any existing MOS instrument, and a total spectral etendue ~20 times larger. Combined, these present enormous challenges for the spectrograph design. Initial designs were based on (a) a novel F/0.775 Folded Solid Schmidt camera with 6cm detectors, (b) an F/1.15 dioptric camera with 6cm detectors, and (c) an F/1.31 dioptric camera with 9cm detectors, all with YAG field-flatteners. However, the imperative of fast camera speed has greatly diminished, as the projected cost and read-noise of large format CMOS detectors is projected to decrease greatly. The adopted baseline solution has 4 dioptric F/1.64 cameras, each with two doublets, a YAG field lens and 9cm x 9cm detector. Theoretical image quality is 8 microns rms radius. The design seems readily athermalised, potentially allowing passive temperature control. Each spectrograph accepts 500+ fibers. Expected RoM costs (scaled from earlier designs) suggest a total cost <4M Euro per spectrograph.

• The paper introduces a 4×9Y, F/1.64 optical design that optimizes throughput and image quality for a ~30,000 fiber MOS system.
• Methodologies include innovative athermal design, modular alignment, and the use of low-noise CMOS detectors to balance cost and performance.
• Implications extend to enhanced survey speed and improved cross-talk control, setting new benchmarks for large-etendue spectroscopy.

Optical Design Strategies for the WST MOS-LR Spectrographs

Introduction

The Wide-field Spectroscopic Telescope (WST) aims to advance the capabilities of multi-object spectroscopy (MOS) by accommodating approximately 30,000 fibers with high spectral resolution ($R > 3000$) over a broad wavelength range (370–930 nm). The unique requirements—an order-of-magnitude increase in multiplexing and spectral etendue relative to extant systems—impose stringent constraints on spectrograph design, compelling innovative solutions that balance optical performance, manufacturability, cost, and operational complexity.

Design Drivers and Constraints

WST's low-resolution MOS mode necessitates a per-fiber spectral etendue nearly twice that of any existing fiber-based MOS facility, and a total etendue $\sim$20 times larger. Major design drivers include the need for compact, affordable, and maintainable spectrographs that can be modularly deployed and efficiently aligned. The detector landscape has shifted due to projected reductions in the cost and read-noise of large-format CMOS sensors, altering the optimal configuration space for camera focal ratios (F/#), beam sizes, and detector dimensions.

Key system-level requirements are:

• Wavelength coverage: 370–930 nm
• Spectral resolution: $R > 3000$ everywhere; $R > 5000$ desirable in the far red
• Multiplex: $\sim$30,000 fibers distributed across $\sim$55 units, each handling $>500$ fibers
• Detector formats: 61 mm × 61 mm (6 cm) and 92 mm × 92 mm (9 cm), pixel sizes $\sim$15 $\mu$m

Design Alternatives Explored

Four main optical architectures were evaluated, distinguished primarily by detector size, number of spectral arms, and camera speed. Early designs were driven by the need for rapid cameras to offset read-noise limitations and maximize throughput, leading to aggressive F/# choices (down to $F/0.775$). The emergence of cost-effective, low-noise 9 cm CMOS sensors led to a paradigm shift, favoring a slower ($\sim$0) more conservative design that eases manufacturing constraints, improves athermalization possibilities, and maintains high performance.

Folded Solid Schmidt (FSS) Camera

The FSS camera achieves $\sim$1 with three arms and 6 cm detectors. Astutely, it leverages the $\sim$2 improvement afforded by an all-glass camera body, with beam folding to facilitate detector placement and minimize obstruction. Chromatic aberration correction is delegated to the disperser, packaged as a grism bonded to a flint/crown doublet. Performance benchmarks are strong (rms radius $\sim$3m across the field; $\sim$4 everywhere, $\sim$5 at $\sim$6 nm), but the manufacturing complexity, unique aspheric surfaces, and challenging alignment and thermal aspects led to its de-prioritization. Industrial feedback expressed reservations regarding realizability within risk and cost constraints.

Fast Dioptric Designs (4×6, 3×9)

These designs utilize transmissive ($\sim$7 and $\sim$8, respectively) dioptric cameras with minimal optical groups for high efficiency. The 4×6 (4 arms, 6 cm detectors) and 3×9 (3 arms, 9 cm detectors) variants both incorporated YAG field flatteners as integrated dewar windows, facilitated by the availability of large YAG blanks. Both variants achieve diffraction-limited spots ($\sim$9 of projected fiber diameter), but the 3×9 design was judged higher risk (compound lens blanks, volume/mass, throughput) and more expensive. These configurations, while optically attractive, became less compelling given advances in available detector technology and anticipated economies of scale.

Baseline Adopted Design: 4×9Y (F/1.64, 9 cm Detectors)

The selected architecture comprises four identical arms with transmissive $R > 3000$0 cameras, each employing two doublets and a YAG field-flattener, supporting 9 cm CMOS detectors. Advantages include:

• Theoretical image quality better than 8 $R > 3000$1m rms everywhere (spatial rms $R > 3000$2 fiber diameter at all wavelengths/positions)
• Significantly improved athermalization potential due to matched CTEs (S-FSL5Y/PBL35Y lenses, YAG window, and stainless steel structures) and high thermal conductivity of YAG
• Modular alignment architecture (offsets and tilts for cameras and detectors) simplifies integration and servicing
• Expected per-unit cost $R > 3000$3M €, aligned with cost-estimates for similar high-performance MOS instruments

Disperser and Grating Considerations

All discussed designs utilize VPH gratings for dispersion, predominantly in non-Littrow configuration to eliminate ghosts and maximize optical utilization. System throughput is relatively insensitive to the number of arms, camera speed, or detector size due to flat VPH efficiency and angular bandwidth characteristics across the design parameter space.

Notably, beam size remains a critical parameter, with larger beams slightly enhancing VPH efficiency (via reduced grating angle), partially offsetting the unavoidable losses (e.g., from beam obstruction in catadioptric systems).

Thermal and Mechanical Performance

The 4×9Y design is intrinsically insensitive to temperature variations over the anticipated operating range at the telescope site (Paranal). Direct integration and FEA modeling of the YAG window predict a negligible risk of window frosting under worst-case humidity and ambient conditions. The athermal design reduces maintenance and eliminates the need for active temperature control, facilitating deployment on a rotating telescope platform.

Fiber Spread Function and Systematics

Stringent requirements on the knowledge and stability of the fiber spread function (FSF) are necessitated by WST’s science goals—precision sky subtraction, radial velocity, and cross-talk minimization in ultra-high multiplex environments. Simulations demonstrate that obtaining $R > 3000$4 calibration accuracy in FSF mandates exceptional optical quality and careful pupil illumination mimicry during calibrations. The analysis confirms that the selected design’s IQ enables this, though ultimate on-sky performance will depend on meticulous calibration hardware and procedures.

Cross-Talk, Scattered Light, and Fiber Density

The limiting factor for fibers per spectrograph is cross-talk, set to match (or outperform) the benchmark of 4MOST LRS. The analysis uses spatial models derived from direct instrument data, factoring in aberrations, detector characteristics, and measured scattered light profiles. The adopted pitch/fiber-diameter ratio achieves cross-talk performance that is at least as good as, and often superior to, reference implementations, with 525 fibers per 4×9Y spectrograph and $R > 3000$528,000–30,000 total fibers for MOS-LR.

Future improvements in disperser technology—particularly the adoption of surface relief gratings—could further suppress scattered light and enable both higher fiber counts per channel and larger science yields.

Implications and Future Developments

These optical designs are positioned to set new benchmarks for large-etendue, massively multiplexed fiber spectroscopy on extremely large telescopes. The 4×9Y transmissive camera design represents a pragmatic balance between performance, manufacturability, cost, and modularity, leveraging current trends in large-area detector technology and advanced optical materials (YAG). The alignment, baffling, and calibration philosophies anticipate unsupervised or remote operation in challenging environments. The rigorous FSF/cross-talk/cost modeling informs an optimal system architecture that is extensible as underlying technologies (detectors, gratings, calibration sources) advance.

Potential future developments include:

• Integration of surface relief gratings or advanced anti-scatter designs to further reduce stray light
• Exploration of curved detectors should manufacturing and integration hurdles be overcome, enabling even faster and more compact cameras
• Continued optimization of athermalization and passive thermal design for space-based or remote/tethered facilities

Conclusion

The optical engineering study for the WST MOS-LR demonstrates that a 4-arm, $R > 3000$6, 9 cm detector, dioptric camera design (4×9Y) delivers superior image quality, throughput, and operational robustness under tightly constrained budgetary and technical requirements. The design process, systematically exploring innovative and aggressive camera architectures before converging on a solution enabled by the latest detector and optical material technology, exemplifies best practice for ELT-class MOS instrumentation. The resultant system enables a transformative leap in survey speed and multiplexing, directly impacting empirical constraints on cosmology, galactic structure, and stellar populations for the coming decade and beyond (2607.05601).