本研究為400~1100 nm凹面光柵高光譜儀光學系統之設計與驗證。以二維曲面光柵為主進行凹面光柵高光譜儀光學系統之設計，考慮五種不同光柵的設計參數，其中有出入射臂長與夾角、光源發散角、反射鏡安裝位置考量、影像偵測器尺寸規格、光柵元件尺寸。經過分析後，僅有一種符合空間上配置的需求。
實驗平台出圖加工完成後，首先進行高光譜儀光學系統的光軸校準。本研究以紅光(635 nm)及綠光(532 nm)雷射架設於五軸位移平台上進行光軸校準，將兩道不同波長之雷射併光進入分光鏡中心、狹縫中心以及光柵中心，確認實驗平台與模擬為同一光軸。接著以四道不同波長的單模光纖雷射(520 nm、635 nm、660 nm、673.5 nm)進行繞射效率、半高全寬斑點大小及光譜解析度之量測。由鋁合金5083直接加工出光柵溝槽。經實驗量測後，光柵鍍膜前一階繞射效率為60%。光柵鍍上50 nm的鋁以及170 nm的二氧化矽後，一階繞射效率提升至70%，鍍膜前後整體繞射效率提升了10%。
本研究使用Sony α99單眼相機作為記錄成像斑點大小的影像偵測器，將拍攝擷取的數據，利用光譜分析軟體(Tracker)，分析在不同波長及狹縫高度的條件下，水平及垂直之成像分布。經本研究實驗後，水平半高全寬斑點大小(FWHM)約為 230~340 µm。將理論像差(約50 µm)、單模光纖直徑、雷射光源頻寬以及繞射極限等列入計算後，得出斑點大小約100 µm。比較量測值與理論值發現主要差異來自於加工誤差。若將製成誤差因素一併計算，其量測結果與理論值誤差值小於1像素內。垂直半高全寬斑點大小約為30~150 µm，垂直半高全寬斑點大小則落在±60 µm之加工誤差容許範圍內。通過數據分析計算，光譜解析度範圍為4~7 nm，與計算的結果一致。
本研究已完成四波長繞射效率與斑點大小之量測，並且建立完整的設計開發、光軸校準、效率量測、記錄影像斑點以及光譜解析度分析方法之流程。

A hyperspectral imaging (HSI) optical system is designed and constructed based on an aberration-corrected concave grating. The designed spectral range is from 400 nm to 1100 nm. Five design layouts are generated based on different spatial parameters. It includes the incident and exit arm lengths and angles, divergence of the incident beam, size of the detector module, reflection mirror (in-between entrance slit and the grating) and size of the grating block. After the analysis on the mechanical interferences, only one design fulfills the requirement.
The optical axis alignment system consists of one red laser (635 nm), one green laser (532 nm) and a beam combiner (beam splitter). Each component is mounted on a 5-axis positioning stage (2θ-XYZ) to ensure co-linearity with the HSI optical axis. The alignment system aligns the entrance slit, the reflection mirror, the grating and the detector. Single mode fiber lasers (core diameter of 9 um) of four wavelengths, 520 nm, 635 nm, 660 nm and 673.5 nm, are coupled using optical fiber coupler as a single input of the HSI optical system. Based on this arrangement, the diffraction efficiencies of different orders are measured. The grating is directly machined from an aluminum alloy block (5083). The 1st order efficiency is about 60% before the coating of high reflective material. The efficiency reaches about 70% after the coating, which consists of a 50nm thickness of aluminum and a 170 nm thickness of SiO2.
A Sony α99 camera is used as the image recording module to acquire the spot size of the images. The image data is analyzed using a profile analyzing software Tracker. The vertical and horizontal profiles are obtained for different input conditions, i.e., wavelengths and slit heights. The measurement shows that the horizontal Full-Width-at-Half-Maximal (FWHM) spot size is about 230 µm to 340 µm. The calculated aberration-related spot size is about 50 µm. If the core diameter of the fiber, laser spectral band width, diffraction-limited spot size are taken into account, the total theoretical spot size is about 100 µm. The difference between these two values comes from the setting error of the machining system. In horizontal, if setting error is considered, the differences between the calculated and the measured spot sizes are within one pixel, which is 6 µm. The measured spot size in the vertical is about 30 µm to 150 µm. This is consistent with the results if the machining setting error is taken into account. By analyzing the data, the spectral resolution of the system is about 4 nm to 7 nm, which is consistent with the results of the calculation.
In this study, we establish (1) a design flow of a concave-grating HSI optical system; (2) an optical axis alignment procedure; (3) the efficiency and spot size measurement methodology; and (4) spectral resolution analysis model.

[1]“Airborne Hyperspectral Remote Sensing Systems,” http://uregina.ca/piwowarj/Satellites/Hyperspectral.html
[2]G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” Journal of Biomedical Optics, Vol. 19(1), 010901 (2014).
[3]“Tracker (video analysis and modeling tool, Open Source Physics),” https://www.cabrillo.edu/~dbrown/tracker/
[4]“Product data sheet Aluminium 5083 Aluminium alloy,” http://www.docstoc.com/docs/32838434/PRODUCT-DATA-SHEET-Aluminium-5083-Aluminium-Alloys
[5]E. Hecht, Optics 4th Ed, Addison Wesley, San Francisco, p. 478 (2002).
[6]M. Bertolo, SCHOOL ON SYNCHROTRON RADIATION AND APPLICATIONS, the abdus salam international centre for theoretical physics, Italy, p. 52 (2004).
[7]E. Hecht, Optics 4th Ed, Addison Wesley, San Francisco, pp. 469-472 (2002).
[8]P. Getreuer, “A Survey of Gaussian Convolution Algorithms,” Image Processing On Line, pp. 286-310 (2013).
[9]K. Nakamoto, K. Sugiyama, Y. Takeuchi, “Tool setting of error compensation for multi-axis control ultra-precision machining,” Proceedings of the 14th euspen International Conference, Dubrovnik, pp. 44-46 (2014).