Absolute gauge block calibration using ultra-precise optical frequency synthesizer locked to a femtosecond comb

Hatem Hussein; Niveen Farid; Osama Terra

doi:10.1364/AO.54.000622

Applied Optics
Vol. 54,
Issue 4,
pp. 622-626
(2015)
•https://doi.org/10.1364/AO.54.000622

Absolute gauge block calibration using ultra-precise optical frequency synthesizer locked to a femtosecond comb

Hatem Hussein, Niveen Farid, and Osama Terra

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Hatem Hussein, Niveen Farid, and Osama Terra, "Absolute gauge block calibration using ultra-precise optical frequency synthesizer locked to a femtosecond comb," Appl. Opt. 54, 622-626 (2015)

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Abstract

In this paper, we report a gauge block (GB) calibration that is traceable to the SI unit of time, the second. Four ultra-stable optical telecommunication wavelengths near 1556 nm are obtained by locking a narrow-tuning-range fiber laser to a fiber-based femtosecond frequency comb. Since the GB calibration system does not operate at this region of spectrum, the superior frequency stability of the laser is transferred to the 778 nm region by using a waveguide periodically poled lithium niobate crystal. After applying the locking scheme, the stability and accuracy of the laser become better than $8 \times 10^{- 12}$ . The frequency-doubled light is sent through 30 m optical fiber to a GB interferometer, which is installed at a different laboratory in the same building. Using this calibration scheme, a GB with a nominal length of 100 mm is calibrated with an uncertainty of $\pm 52 nm$ . This uncertainty value is still comparable to or even better than other metrology laboratories for a similar block length.

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Source of Uncertainty	$u (x_{i})$	$u (y_{i})$ (μm)
GB interferometer
– Excess fraction	0.01 fringe	0.002
– Wavelengths in use	$8 \times 10^{- 12}$	$4 \times 10^{- 6} L$
– Repetition rate	$5 \times 10^{- 9}$	0.005
Refractive index of air
– Temperature	8 mK	$0.1 L$
– Pressure	20 Pa	$0.05 L$
– Relative humidity	0.5%	$0.1 L$
– Edlen’s formula	$1 \times 10^{- 8}$	$0.01 L$
GB thermal expansion
– TEC	$0.065 \times 10^{- 6} / K$	$0.06 L$
– GB surface temp.	8 mK	$0.1 L$
Wave-front error of the optical components	0.008 μm	0.008
GB wringing	0.005 μm	0.005
GB flatness/parallelism	0.005 μm	0.005
Obliquity	0.08 mm	$0.12 L$
Aperture	5 μm	$0.008 L$
Phase change	0.005 μm	0.005

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Applied Optics