AI 中文总结
研究多目标光谱仪质量、成本与通道数、分辨率的缩放关系，通过分析数据集得出相关函数和指数。介绍基于光子集成电路的方法优势，应用于宽视场光谱望远镜可大幅降低质量和成本，凸显基于阵列波导光栅光子学的重要性。
AI 中文摘要
传统多目标光谱仪（MOS）的质量和成本随通道数\(N_\mathrm{ch}\)和分辨率\(\mathcal{R}\)增长不利。编译并分析了1995 - 2024年的8个光纤馈送MOS - VIS仪器数据集。通过普通最小二乘法拟合得到质量函数\(M \propto N_\mathrm{ch}^{0.78\pm0.28}\)，分辨率指数经实证与零一致（\(\gamma = 0.20\pm0.37\)），但理论预测在\(\mathcal{R}^{0.8 - 2.0}\)。留一法交叉验证确认通道数呈次线性缩放（\(\beta\in[0.59,1.13]\)，均值0.79），成本随\(N_\mathrm{ch}^{-0.22到 - 0.53}\)降低。光子集成电路（PIC）方法使色散元件尺寸与\(N_\mathrm{ch}\)和\(\mathcal{R}\)解耦，芯片面积缩放为\(\mathcal{R}^{1 - 1.5}\)而非\(\mathcal{R}^{3}\)。应用于宽视场光谱望远镜（WST），传统近红外光谱仪系统约140吨，而CAWSMOS等效系统约200千克，成本大幅降低，基于阵列波导光栅（AWG）的光子学对WST至关重要。
英文摘要
Conventional multi-object spectrographs (MOS) incur masses and costs that scale unfavourably with channel count~$N_\mathrm{ch}$ and resolving power~$\mathcal{R}$. A dataset of eight fibre-fed MOS-VIS instruments (1995--2024) is compiled and analysed. Ordinary least-squares fitting yields a mass function $M \propto N_\mathrm{ch}^{0.78\pm0.28}$; the resolving-power exponent is empirically consistent with zero ($γ= 0.20\pm0.37$) but is predicted analytically to lie in $\mathcal{R}^{0.8\text{--}2.0}$. Leave-one-out cross-validation confirms sub-linear channel-count scaling ($β\in[0.59,1.13]$, mean 0.79), with HERMES and AAOmega -- sharing the same telescope and $N_\mathrm{ch}=392$ across a factor of~7 in $\mathcal{R}$ at essentially equal estimated mass -- providing a direct empirical confirmation that $γ\approx 0$. Cost per channel decreases as $N_\mathrm{ch}^{-0.22\text{ to }-0.53}$ for all assumed cost--mass exponents $k\in[0.6,1.0]$, demonstrating a genuine economy of scale. The photonic integrated-circuit (PIC) approach embodied by the arrayed waveguide grating (AWG)-based PAWS demonstrator and the proposed CAWSMOS instrument decouples dispersive element size from $N_\mathrm{ch}$ and $\mathcal{R}$, with chip-area scaling as $\mathcal{R}^{1\text{--}1.5}$ instead of $\mathcal{R}^{3}$. Applied to the Wide-field Spectroscopic Telescope (WST), the model predicts $\sim$140 tonnes for a conventional NIR spectrograph system against $\sim$200 kg for a CAWSMOS equivalent, with projected costs of EUR 300--700M conventional versus EUR 40--120M photonic ($6$--$15\times$ reduction). AWG-based photonics are identified as a strategially important enabling technology for WST.
Comments20 pages, 2 figures, Submitted to the Journal of Astronomical Telescopes, Instruments, and Systems (JATIS)
