Abstract
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.