Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy

Abstract

In this paper we describe the progress we have made in our simultaneous length measurement and the femtosecond comb interferometric spectroscopy in a conventional arrangement with a moving mirror. Scanning and detection over an interval longer than the distance between two consecutive pulses of the frequency comb allow for a spectral resolution of the individual frequency modes of the comb. Precise knowledge of comb mode frequency leads to a precise estimation of the spectral characteristics of inspected phenomena. Using the pulse train of the frequency comb allows for measurement with highly unbalanced lengths of interferometer arms, i.e. an absolute long distance measurement. Further, we present a non-contact (double sided) method of measurement of the length/thickness of plane-parallel objects (gauge blocks, glass samples) by combining the fs comb (white light) with single frequency laser interferometry. The position of a fringe packet is evaluated by estimating the stationary phase position for any wavelength in the spectral band used. The repeatability of this position estimation is a few nanometres regardless of whether dispersion of the arms is compensated (transform limited fringe packet ∼10 fringes FWHM) or highly different (fringe packet stretched to >200 fringes FWHM). The measurement of steel gauge block by this method was compared with the standard method, and deviation (+13 ± 12) nm for gauge blocks (2 to 100) mm was found. The measurement of low reflecting ceramic gauges or clear glass samples was also tested. In the case of glass, it becomes possible to measure simultaneously both the thickness and the refractive index (and dispersion) of flat samples.

Optical frequency comb Fourier transform spectroscopy with sub-nominal resolution and precision beyond the Voigt profile

“…The spectral comb structure starts to be visible when an interferogram containing several bursts is acquired [5]. However, unless the interferogram is sampled correctly, the spectral resolution is limited to the nominal resolution of the FTS and retrieving the power of comb modes requires interpolation between the FTS sampling points [6]. Recently, we have shown that the power of the comb modes can be precisely measured using single-burst interferograms with the length matched to c/frep [7].…”

Some Basics of Measurement

“…Also, direct application in gauge block measurement has been explored (see Chapter 4), as well as simultaneous measurement of the thickness and refractive index (and dispersion) of flat samples [51].…”

Length Traceability Using Interferometry

“…When using a frequency comb [16,17] (see also Section 2.9.6), the uncertainty in the vacuum wavelength will be negligible compared to other factors. Formally, it sounds very good that the calibration is directly traceable to a primary standard, but for the uncertainty, the other factors mentioned are more important.…”

“…Using a frequency comb (see Section 2.9.6) opens up some interesting new possibilities [16,17], where a beam full of well-defined frequencies can be used both as a white light source that defines an absolute position in space, and as an accurate distance and/or displacement measurement that can be combined to an absolute gauge block length in single-and double-sided set-ups. Double-sided gauge block interferometer [28].…”