No abstract

A two-dimensional high-speed, long-range tomography and profilometry based on a low-coherence optical interferometry has been developed. A liquid-crystal Fabry-Perot resonator is fabricated to be a low-coherence optical frequency comb generator for expanding the measurement depth of the tomography and profilometry. The line-shape interference fringes with the individual fringe orders are obtained by a CCD camera in real time. The relative optical length, corresponding to the sample depth information, can be derived from the positions of the interference fringes on the CCD camera and their corresponding fringe orders. The fringe orders can be rapidly calculated using the effectiveness of the changeable extraordinary refractive index of the liquid-crystal material of the resonator. The finesse of the liquid-crystal resonator is approximate 9, giving an expansion of the measurement range of up to 9-fold (∼8  mm depth) with a resolution of profilometry and tomography of 3.7 μm and 11 μm, respectively.

Air refractive index fluctuation (Δn(air)) is one of the largest uncertainty sources in precision interferometry systems that require a resolution of nanometer order or less. We introduce a method for the active suppression of Δn(air) inside a normal air-environment chamber using a Fabry-Perot cavity and a piezoelectric volume actuator. The temporal air refractive index (n(air)) at a local point is maintained constant with an expanded uncertainty of ~4.2 × 10(-9) (k = 2), a sufficiently low uncertainty for precise measurements unaffected by Δn(air) to be made inside a chamber.

In this paper, we propose a novel method to measure the free spectral range (FSR) of a Fabry-Perot cavity (FPC) using single-frequency modulation (FM) with one electric optical modulator (EOM) and the null method. A laser beam modulated by the EOM, to which a cosine-wave signal is supplied from a radio frequency (RF) oscillator, is incident on the FPC. The transmission light from the FPC is observed and converted to an RF signal by a highspeed photodetector, and the RF signal is synchronously demodulated with a lock-in amplifier (LIA) by referring to the oscillator. We theoretically and experimentally demonstrate that the LIA signal become null with a steep slope, when the modulation frequency equals the FSR under the condition that the carrier frequency is slightly detuned from the resonance of the FPC. The experimental results show that the proposed method has the capability to determine the FSR by the null method with a small measurement uncertainty.

In this paper, we discuss a method to measure the free spectral range (FSR) of a Fabry–Perot cavity (FP-cavity) using frequency modulation with one electric optical modulator (EOM) and the null method. A laser beam modulated by the EOM, to which a sine wave signal is supplied from a radio frequency (RF) oscillator, is incident on the FP-cavity. The transmitted or reflected light from the FP-cavity is observed and converted to an RF signal by a high-speed photodetector, and the RF signal is synchronously demodulated with a lock-in amplifier by referring to a cosine wave signal from the oscillator. We theoretically and experimentally demonstrate that the lock-in amplifier signal for the transmitted or reflected light becomes null with a steep slope when the modulation frequency is equal to the FSR under the condition that the carrier frequency of the laser is slightly detuned from the resonance of the FP-cavity. To reduce the measurement uncertainty for the FSR, we also discuss a selection method for laser power, a modulation index and the detuning shift of the carrier frequency, respectively.