頻率調制(FM)光譜技術相較於直接吸收光譜(DAS)和波長調制(WM)光譜所擁有更高的探測光靈敏度，且可以同時探測待測氣體的吸收與色散項，因此被廣泛應用於原子分子光譜、微量氣體檢測等應用，另一方面也應用於探測靈敏度極高的噪音免疫腔增強光外差分子光譜(NICE-OHMS)中，由此可見，FM光譜技術因為架設簡單與高靈敏度，慢慢成為重要的量測技術之一。FM光譜是一項調制頻率極高的技術，藉由數十MHz以上的調制頻率，使邊帶遠離雷射光中心頻率，降低雷射光所產生的雜訊影響，因此才有極高的靈敏度，目前也應用於分子的吸收與雷射光穩頻相關技術等。
本論文首先對FM的原理做詳盡的公式推導，並將公式以泰勒級數展開式化簡，利用得到吸收與色散的關係式，使用MATLAB以勞倫茲輪廓去模擬FM的吸收訊號與色散訊號，並將其歸一化在不同的調制頻率下作圖，最後為了配合實驗室正在進行的飽和吸收頻率調制光譜量測H3+實驗，我們提出以飽和吸收為模型，去模擬FM的吸收訊號，較符合真實情形，並與先前所量的甲烷數據做比較，H3+有大約600 MHz的都普勒線寬，而其均勻線寬也有大約是20 MHz到100 MHz左右，為了幫助實驗了解，我們以H3+為假想氣體，去改變不同參數，如:均勻線寬、調制頻率、調制深度，觀察光譜的變化。

Compared to direct absorption spectroscopy and wavelength modulation spectroscopy, frequency modulation (FM) spectroscopy employs a higher sensitivity of probe beam and it can simultaneously detect the absorption and the dispersion of the interest gas. Therefore, FM spectroscopy is widely used in atomic and molecular spectroscopy and trace gas detection. On the other hand, FM spectroscopy also is the key technology in the high sensitivity noise immune cavity-enhanced optical heterodyne molecular spectroscopy. Consequently, due to the simple scheme and high sensitivity of FM spectroscopy, it gradually becomes one of popular measurement technology. In order to reduce the noise from the laser light, FM spectroscopy has a very high modulation frequency, which can let the sidebands move away from the center frequency of laser light by more than tens of MHz modulation frequency. It is also used in the molecular spectroscopy and the optical frequency stabilization.
In this thesis, I derive the detailed derivation of the FM principle and use the Taylor series expansion to simplify the equation. Then I use MATLAB to simulate the absorption and the dispersion of FM signal by Lorentizan profile, and normalize the profile at different modulation frequency. Finally, in order to match our experiment for FM saturated spectroscopy. I propose a FM saturation absorption model to compare the experimental data of methane and simulate the case of H3+ by changing different parameters, such as homogenous linewidth, modulation frequency and modulation index.

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