光頻率的精密量測有助於基礎物理的發展，在物理常數的定義、原子分子結構的研究和物理定律的檢驗中扮演著極為重要的角色。光頻梳(optical frequency comb; OFC)將光頻標準直接連結至射頻標準，除了能夠精確量測光的絕對頻率外，同時也在光鐘的研究或是天文上的應用帶來許多嶄新的發展。

　　我們實驗室的鈦藍寶石(Ti:sapphire)光頻梳系統的脈衝重複率及偏差頻率是鎖相至一全球定位系統(GPS)調控的銣原子鐘，可以用來量測波長500 nm-1100 nm可見光到紅外光的絕對頻率，在1000秒積分時間，其準確度高達10-12。我們的光頻梳鎖頻後，在計數器的gate time 為1秒的狀況下，量測脈衝重複率及偏差頻率的標準差分別為3 mHz及10 mHz。

　　本論文利用實驗室的鈦藍寶石光頻梳系統，量測兩個碘分子飽和吸收光譜實驗，這兩個實驗皆是將雷射頻率鎖在躍遷譜線的中心，並使用光頻梳系統量測絕對頻率。其一為碘分子在535 nm P(28) 30-0絕對頻率量測，量測其中的三條超精細結構(a_1, a_10, a_15)的躍遷頻率，並利用不同壓力的量測值得到零壓力的絕對頻率，準確度為11 kHz。

　　其二為緲子偶素(muonium)、氫原子(hydrogen)、氘原子(deuterium)之1S-2S雙光子躍遷的碘分子參考頻率量測，為碘分子在730 nm附近的R(26) 5-13 a_15、P(258) 7-11 a_15以及 R(137) 5-12 a_(19-21)，量測其超精細結構躍遷頻率。我們的初步結果較過去測量值準確，且有500 kHz到1.2 MHz的差異。

　　Precision measurements of optical frequency play important roles in defining physical constants, investigating atomic and molecular structures, and testing physical principles. Optical frequency comb (OFC) directly links the radio frequency standards to optical frequency regime. In addition to optical frequency metrology, OFC grows the research of optical clocks and applications in astronomy.
　　The repetition rate and offset frequency of our Ti:sapphire-based OFC are phase-locked a global positioning system (GPS) disciplined Rb clock. It can use to measuring the absolute frequency of wavelength from 500 to 1100 nm. The accuracy of our OFC is better than 1×〖10〗^(-12) at a 1000 s integration time. After phase locking, the standard deviation of the repetition rate and offset frequency are 3 mHz and 10 mHz respectively at 1 s gate time of the frequency counter.
　　In this thesis, we perform two frequency measurements of molecular iodine hyperfine transitions, and in both experiments the laser frequency is stabilized to the center of hyperfine transitions. One is the absolute frequency measurements of the a_1, a_10, a_15 hyperfine components of molecular iodine P(28) 30-0 line at 535 nm. We obtain the zero-pressure absolute frequencies and the accuracy is 11 kHz.
　　The other is the absolute frequency measurements of molecular iodine reference frequencies for 1S-2S spectroscopy in muonium, hydrogen, and deuterium. We measure the absolute frequencies of R(26) 5-13 a_15, P(258) 7-11 a_15 and R(137) 5-12 a_(19-21) hyperfine components of iodine near 730 nm. Our preliminary results are more precise than previous measurements, but our results show a difference of 500 kHz to 1.2 MHz from the previous results.

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