Accurate displacement-measuring interferometer with wide range using an I₂frequency-stabilized laser diode based on sinusoidal frequency modulation

Abstract

We propose the use of the sinusoidal frequency modulation technique to improve both the frequency stability of an external cavity laser diode (ECLD) and the measurement accuracy and range of a displacement-measuring interferometer. The frequency of the ECLD was modulated at 300 kHz by modulating the injection current, and it was locked to the b 21 hyperfine component of the transition 6-3, P(33), 127 I 2 (633 nm) by the null method. A relative frequency stability of 6.5 × 10 −11 was achieved at 100 s sampling time. The stabilized ECLD was then utilized as a light source for an unbalanced Michelson interferometer. In the interferometer, the displacement and direction of the target mirror can be determined using a Lissajous diagram based on two consecutive and quadrant-phase harmonics of the interference signal. Generally, the measurement range of the interferometer by the proposed method is limited by the modulation index and the signal-to-noise ratio of the harmonics. To overcome this drawback, suitable consecutive harmonic pairs were selected for the specific measurement ranges to measure the displacement. The displacements determined in the specific ranges by the proposed method were compared with those observed by a commercial capacitive sensor. From the comparison, the proposed method has high precision to determine the displacement. The measurement range was also extended up to 10 m by selecting a suitable modulation index and suitable consecutive pairs of harmonics.

A Displacement Measuring Interferometer Based on a Frequency-Locked Laser Diode with High Modulation Frequency

“…The PID controller generated a feedback signal and sent it to the laser controller to lock the frequency of the LD to the I2 hyperfine component. The interference signal collected by PD2 was determined as follows [14]:…”

“…Another drawback of the FM is that the harmonic intensities depend on the modulation index of the LD via the presence of the Bessel functions. The modulation index is a function of the modulation excursion [13,14].…”

Suppression of residual amplitude modulation appeared in commercial electro-optic modulator to improve iodine-frequency-stabilized laser diode using frequency modulation spectroscopy

“…(6) to (10), higher derivative orders such as the third-derivative signal can also be determined. Theoretically, the third-derivative signal is better for eliminating the Doppler background [6]; however, the RAM error, which originates from the products of RAM with the second and fourth-harmonic terms, also affects the third-derivative signal of the absorption lines. Finally, for the high-frequency stabilization of LDs, a compensation technique to eliminate the RAM is necessary.…”

“…To stabilize the LD frequency, the linear or saturated absorption of some atomic-molecular species, such as iodine molecules, rubidium atoms, and Cs atoms [1][2][3], can be utilized. Sinusoidal phase/frequency modulations (SPM/SFM) and demodulation by a lock-in amplifier (LIA) are effective techniques applied to detect the atomic or molecular absorption lines for LD frequency stabilization [4][5][6].…”

“…Many researchers have developed methods of stabilizing the LD frequency to some atomic-molecular absorption lines. Vu et al performed LD frequency stabilization using both a regular LD with linear absorption [5] and an ECLD with saturated absorption [6] of iodine molecules. Some of the authors of this paper also used SPM with a fixed modulation index of 3.768 rad to detect iodine-saturated absorption and stabilize the ECLD frequency for a Mach-Zehnder displacement measuring interferometer [4].…”