Theoretical Analysis of Length Measurement Using Interference of Multiple Pulse Trains of a Femtosecond Optical Frequency Comb

As an alternative to the conventional method of measuring length as a function of the wavelength of a monochromatic laser source, we investigated the possibility of arbitrary distance estimation using the repetition interval of a femtosecond optical frequency comb (FOFC). The investigation is based on an analysis of the formation of the interference fringes of multiple pulse trains. It is found that distance can be measured as a function of the repetition interval between pulses by determining two values from the interference fringes of multiple pulse trains. One is the distance between temporal coherence peaks, and the other is the phase relation between the multiple interference fringes. Theoretical analysis and numerical investigations pave the way for the development of a new length traceability system directly linked to a stable FOFC for both scientific and industrial uses.

Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency

A heterodyne interference system is developed for baseline measurement by using an acoustic optical modulator and an optical frequency comb stabilized by a rubidium atomic clock. Temporal coherence interference occurs at discrete spatial positions, when two pulse trains overlap. An optical delay of the interferometer with a piezoelectric transducer is created to determine the peak positions of the interference fringe patterns, and the absolute distance is obtained at a high resolution of several tens of nanometers. The experimental results at baseline distances up to 403.2 m show a high reproducibility of about 6 m. # 2012 The Japan Society of Applied Physics L ong-distance absolute measurements with high accuracy are required when constructing huge industrial and scientific facilities. In particular, the quality and safety of such facilities must be evaluated through measurements of hundreds of meters with accuracy better than 10 m. Recently; an optical frequency comb has been considered a useful tool for realizing such measurement systems, because of its precise pulse-repetition frequency, which is an accuracy of 10 À11 . Therefore, an optical frequency comb can be directly used for absolute measurement not only of frequency levels 1-3) but also of various distances. We have developed a new heterodyne temporal-coherence interferometer in order to reduce the effects of air turbulence and mechanical vibration. The interference fringes along optical paths between the zero and target positions are generated by changing the optical delay of the interferometer to be within 250 m. Experimental results show a high accuracy of several tens of nanometers for relatively short distance measurements. Furthermore, in situ measurements of distances up to 403.2 m under typical conditions have high accuracies of about 6 m. All modes within an optical frequency comb can be expressed using two parameters -the carrier envelope-offset frequency ( f ceo ) and the pulse-repetition frequency ( f r ). For integer N, the frequency of the Nth mode is described as f ¼ Nf r þ f ceo . For in situ long-distance measurements, conventional interferometers are affected by air turbulence and mechanical vibration, and therefore, are not easy to apply. In such cases, heterodyne interferometry is highly valuable, since this method is less influenced by the surrounding conditions. Optical frequency combs have a strong potential for use in heterodyne interferometry, because they are characterized by pulse-repetition frequencies that are traceable to the definition of second with a high accuracy of 10 À11 . For example, the frequency of an optical frequency comb is easily stabilized to the standard frequencies of a rubidium (Rb) optical atomic clock or a global positioning system

Accuracy improvement in diameter measurement of micro-sphere based on whispering gallery mode

We have been proposed the new method to measure a dimeter of a micro-sphere on a basis of whispering gallery mode resonance. Resonant wavelengths and mode numbers are necessary quantities to calculate the diameter. In this paper, we proposed and discussed the method to determine the radial mode number of WGMs. Experiments showed the well agreed diameters from various resonant wavelengths, which implies that the radial mode numbers can be successfully estimated by means of the proposed method