本研究欲設計波段400－1000 nm Offner形式的可見光波段微型光譜影像儀，將光譜儀的體積大幅縮小，使光譜儀增加攜帶的方便性，亦降低光譜儀的製作成本。並利用市售的光學機構、元件組裝進行初步的系統設計與成像斑點分析。
首先利用光學/成像系統設計分析軟體 CODE V 進行初步的系統模型設計，為了要降低製造成本，藉由光柵刻度間距的調變以符合市售光學元件，並利用 550 nm 作為優化波長使成像斑點逼近繞射極限。最終所確定的凹球面鏡曲率半徑為 50 mm，光柵間距為3.95 μm，整體Offner系統大小為 50 mm × 70 mm × 50 mm。
接著利用光線追跡軟體 TracePro進行真實情況的模擬，並驗證 CODE V 設計之結果的一致性。結果顯示，CODE V 所設計之系統結果與TracePro 點光源搭配底片規格之結果近似，最佳總光譜解析度約為 0.35－1.3 nm，最佳總影像解析度約為 1.33 μm；模擬真實成像情形，利用狹縫光源搭配偵測器規格之結果，最佳總光譜解析度約為 2.84－3.24 nm，最佳總影像解析度約為 18.78－19.25 μm，與加上前級光學系統的CODE V光譜總解析度近乎相同。
為考慮光柵分光之反射效率，因此利用PCGrate進行可見光至近紅外波段每個波長的分析，結果顯示在波長 550 nm 時，具有最高的反射效率約為83%，因此挑選550 nm作為光柵閃耀角的設計參數。
後續利用 SolidWorks模擬各元件之間組裝以判別干涉與系統的可行性，並進行各光學元件之間容差分析、評估閃耀光柵公差造成的繞射效率模擬。以調置偵測器擺放位置為前提，該光學系統垂直方向容許誤差為2 mm，水平方向容許誤差為1 mm；以固定偵測器擺放位置為前提，垂直方向位移容差Mirror A、光柵、Mirror B分別可達 0.15 mm、0.3 mm、0.2 mm，水平方向位移容差Mirror A、光柵、Mirror B分別可達 0.06 mm、0.08 mm、0.01 mm。

The propose of this study is to design a Offner miniature spectral imager which band is 400-1000 nm. This will miniature spectrometer’s volume and increase portability. Also, decrease manufacturing cost of spectrometer. And use optics component on sales to simulate system design and imaging analysis.
First, use Optics and imaging system design analysis software CODE V to design system model. In order to decrease manufacturing cost, adjust spacing of grating to match optics component on sales. And let the imaging spot approach to diffraction limit by using wavelength 550 nm as optimization band. Finally, radius of the concave mirror is 50 mm, spacing of the grating is 3.95 μm, the Offner system size is 50 mm × 70 mm × 50 mm.
TracePro is used to simulate realistic imaging situation, and verify preliminary system design result of CODE V. The result show preliminary design is almost the same as point source with film specification in TracePro. The total spectral resolution of 0.5-1.8 nm and an image resolution of 5-7 μm. The realistic imaging situation, the result which using slit source with detector specification in TracePro show total spectral resolution of 3.1-13.5 nm and an image resolution of 22-45 μm.
In order to consider reflectance efficiency of the grating, PCGrate is used to simulate band of VNIR, the result show have most reflectance efficiency at 550 nm. Hence, select 550 nm as design parameter of grating blaze angle.
Finally, using Solidworks simulate the assembly between components to determine the feasibility of interference and system. The optical components have tolerances of 2 mm and 1 mm in the longitudinal and transverse directions respectively. And the position of the detector can be adjusted to reach the DoF range.

[1]徐百輝，「大地的辨識密碼－高光譜影像」，科學發展，第四百一十六期，第13-19頁 (2007)。
[2]李龍正，「高光譜影像儀發展及影像市場前景」，科儀新知，第二十六卷，第二期，第50-57頁 (2004)。
[3]Bekefi, George; Barrett, Alan. Electromagnetic vibrations, waves, and radiation 2nd, illustrated. MIT Press. 1977.
[4]Airy, G. B., "On the Diffraction of an Object-glass with Circular Aperture", Transactions of the Cambridge Philosophical Society, Vol. 5, p. 287
[5]M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1965)
[6]歐陽洋蔥. (2019). 為什麼說像素越高，拍照就越好. Retrieved from
[7]曾奕晴 (2019). 孔徑 | 科學Online. Retrieved from
[8]徐郁茹，「可見光至近紅外波段微型高光譜影像儀之設計與成像分析」，碩士論文，國立台灣科技大學，台北(2018)。
[9]Xesús Prieto-Blanco, Carlos Montero-Orille, Héctor González-Núñez, et al., “Imaging with classical spherical diffraction grating: the quadrature configuration,” Journal of the Optical Society of America, Vol. 26, pp. 2400-2409 (2009).
[10]H. Yinlei, Y. Jianyi, J. Xiaoqing, Z. Wei, Z. Jianying, Z. Haifeng, et al., “Analysis on Curved Waveguide Grating (CWG) with Rowland circle construction,” Optical Fiber Communication and Optoelectronics Conference, Asia, pp. 339-341 (2007).
[11]LIU Wei. Design and analysis of structure of compact Offner spectral imaging system[J]. Chinese Journal of Optics, 2010, 3(2): 157-163.
[12]Mertz L, “Concentric spectrographs,” Applied Optics, Vol. 16, pp.3122-3124 (1977).
[13]Seo Hyun Kim, Hong Jin Kong, Hana Ku; Jun Ho Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” SPIE (2012).
[14]X. Prieto-Blanco, C. Montero-Orille, B. Couce, and R.de la Fuente, “Analytical design of an Offner imaging spectrometer,” Optics Express, Vol. 14, No. 20, pp. 9156-9168 (2006).
[15]M. Borengasser, W. S. Hungate and R. Watkins, Hyperspectral Remote Sensing: Principles and Applications, CRC Press, Boca Raton, pp. 18-23 (2002).
[16]P. Getreuer, “A Survey of Gaussian Convolution Algorithms,” Image Processing On Line, Vol. 3, pp. 286-310 (2013)