Comparison of two-color methods based on wavelength and adjacent pulse repetition interval length

Abstract

This paper describes the characteristics of a two-color method based on the adjacent pulse repetition interval length (APRIL), which functions as a length unit for femtosecond optical frequency combs (FOFCs), and compares the results to the wavelength-based two-color method. The wavelength-based two-color method can eliminate the inhomogeneous disturbance of effects caused by the phase refractive index; therefore, the APRIL-based two-color method can eliminate the air turbulence of errors induced by the group refractive index. Our numerical analysis of the APRIL-based two-color method will contribute to the pulse-laser-based two-color method, which secures traceability to the definition of the meter via APRIL.

Numerical study on uncertainty of two-color method

“…Before discussing the numerical simulations, we note the difference between the above expressions and the previously proposed two-color methods [1], [6]- [12]. The latter are related to either the wavelength or the APRIL.…”

“…For example, the uncertainty of the Edlén empirical equations [2,3] is on the order of 30-50 nm/m [5]. Although the two-color method has been studied by a number of researchers [6]- [12], the uncertainty of the length in vacuum obtained with this technique is not known. We do not know how the order of the uncertainty varies with the measurement environment.…”

Correction of refraction index based on adjacent pulse repetition interval lengths

“…Based on the analogy between the wavelength and the APRIL, we proposed the APRIL-based two-color method, which can eliminate the air turbulence of errors induced by the group refractive index [18,19].…”

Two-color heterodyne laser interferometry for long-distance stage measurement with correction of uncertainties in measured optical distances

“…Atmospheric parameters such as the temperature, pressure, humidity, and possibly the CO 2 content are measured to calculate the refractive index using the Edlén equation 6 , 7 , However, it is difficult to get an accurate distribution of these parameters along the optical path, especially at long distances and with a moving stage 8 . Nevertheless, the influence of the turbulence of the atmosphere can be corrected using the two-color method proposed by Bender and Owens 9 , 10 , which is widely used in optical frequency combs 11 – 14 and laser interferometers 15 – 18 . This method measures a geometric distance, L , with both wavelength λ 1 and λ 2 , to obtain two optical distances, L λ 1 and L λ 2 , and gives the geometric distance L = L λ 1 − A ( L λ 2 − L λ 1 ), where A is the so-called A-coefficient in two-color method that represents the dispersion relation for air refractive indices at two wavelengths.The conventional two-color method eliminated the influence of the atmosphere, yet simultaneously enlarged the uncertainties in measured optical distances, Δ L λ 1 and Δ L λ 2 , because of the stability of the laser wavelength, thermal expansion and the optical thermal drift 19 .…”