本研究為設計波段400 – 1000 nm的Offner光譜儀與成像分析，本研究提供一套Offner光譜儀的設計流程，並利用Code V建模且進行初步分析，觀察此系統是否達到設計者的需求，確定設計合理後，在進入TracePro做光跡追蹤模擬，進行較貼近真實情況的分析，最後，藉由聚焦縱深的分析考量偵測器的擺放位置並分析整套系統的解像品質。
本研究設計出一套Offner光譜儀系統，應用波段於400 – 1000 nm， f/#為2.6，光柵的條紋間距為6.7 μm，在成像端展開的光譜長度為6.6 mm，中心波長700 nm的斑點的RMS為8.8 μm，而考量最差情況的波長400 nm及1000 nm斑點的RMS為9.6 μm及11.6 μm，系統的大小約為15cm。系統的分光方向為垂直方向，在波段範圍內，垂直方向斑點的半高全寬在15 μm至25 μm之間、光譜解析度在1.3 - 2.2 nm之間、繞射極限解析度在0.1 -0.3 nm之間，垂直方向繞射極限斑點的半高全寬在0.3 - 1.5 μm之間。
利用TracePro中進行光跡追蹤模擬，將20 μm狹縫及偵測器的影響一併加入考量系統的總解析度的大小，各個波長結果均不會超過2.5 nm，總斑點的半高全寬均小於27.5 μm。本研究提供了聚焦縱深的分析流程，此系統各個波長垂直方向的聚焦縱深約為140 – 170 μm，水平方向的聚焦縱深約為102 μm。針對解像品質的分析，本研究提供了分析偵測面上MTF的分析流程，此MTF圖可表現最後偵測面上看到的真實數據。

We present the design of an Offner spectrometer and analyze its imaging property. Code V, an optical design software, is used to build the model and operate the preliminary analysis. A design flow for the Offner spectrometer is established. The performance of an Offner spectrometer is simulated using an optical ray tracing software – TracePro. By analyzing the depth-of-focus of the focal points for various wavelengths, the location of the image sensor can be determined.
The designed spectral range is from 400 nm to 1000 nm. The f-number is 2.6. The grating pitch is 6.7 μm. The distance range on the image sensor from 400 nm to 1000 nm is 6.6 mm. The root-mean-square spot sizes are 9.6 μm, 8.8 μm and 11.6 μm for wavelengths of 400 nm, 700 nm and 1000 nm, respectively.
The size of this system is approximately 15 cm. For the 400-1000 nm spectral range, the FWHM spot size is from 15 μm to 25 μm. The aberration-related spectral resolution is between 1.3 nm to 2.2 nm. The diffraction-limited resolution is between 0.1 nm to 0.3 nm. The diffraction-limited spot size is between 0.3 μm to 1.5 μm.
Using a 20-μm -wide slit and an image detector with a pixel size of 3.9 μm, the simulated spot size is smaller than 27.5 μm and the total spectral resolution of the system is better than 2.5 nm. A procedure to obtain the depth-of-focus for the entire designed wavelength range is developed. The result shows that the vertical depth-of-focus within the spectral range is from 140 μm to 170 μm and the horizontal depth-of-focus is around 102 μm. Using the focal point distribution on the detector (point spread function), we also calculate the modulation transfer function for further image quality evaluation.

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