Distortion-corrected phase demodulation using phase-generated carrier with multitone mixing

Abstract

We present a novel phase generated carrier (PGC) demodulation technique for homodyne interferometers which is robust to modulation depth variations and source intensity fluctuations. By digitally mixing the waveform with a multitone synthetic function (a linear combination of harmonics of the modulating signal), distortion can become negligible even in presence of large variations of the modulation depth. The technique only requires two mixers and can also provide the DC component of the phase in real time, without needing any previously recorded data or ellipse-fitting algorithms. We validate the technique with simulated waveforms and with experimental data from a wavelength metering experiment using an integrated unbalanced interferometer on-chip, showing that the technique corrects distortion without increasing the noise with respect to the standard PGC technique.

FPGA-Based High-Speed Optical Fiber Sensor Based on Multitone-Mixing Interferometry

“…To solve this problem, instead of mixing with pure sinusoidal waves at frequencies ω and 2ω, in [12] it was proposed to mix with synthetic signals F1 and F2 defined as:…”

“…= 𝑎𝑟𝑐𝑡𝑎𝑛 (7) where I  F1 and I  F2 are results of the mixing and low-pass filtering the light intensity function I(t) with functions F1 and F2, respectively. For the specific case which excludes 4ω (which is recommended when C < π, as it minimizes noise [12]), and for the nominal modulation depth of Cnom = 0.84π, the coefficients that minimize distortion are a1=1, a2 = 2.5806, a3 = -3.03391, and a4=0. This is because by using the appropriate coefficients, the functions in the numerator and denominator in ( 7) can be tailored in such a way that distortion is minimized when C ≠ 0.84π [12].…”

“…For the specific case which excludes 4ω (which is recommended when C < π, as it minimizes noise [12]), and for the nominal modulation depth of Cnom = 0.84π, the coefficients that minimize distortion are a1=1, a2 = 2.5806, a3 = -3.03391, and a4=0. This is because by using the appropriate coefficients, the functions in the numerator and denominator in ( 7) can be tailored in such a way that distortion is minimized when C ≠ 0.84π [12]. The advantage of the MTM scheme with respect to other techniques proposed in the past to reduce distortion, is the fact that its implementation requires a minimal modification of the system, as it only requires the modification of the pure tone waves with synthetic signals for the mixing.…”

“…13. The Y and X components, which are necessary to compute the phase as shown in (7), when they are plotted against each other for different phase shifts from 0 to 2π, they should form a circle if there is no distortion, otherwise they form an ellipse [12].…”

“…To solve that issue, many methods have been proposed in the past [7,8,9,10,11], but these methods have some disadvantages such as increasing noise around certain phase regions, requiring signal variations to work, or requiring complex ellipse-fitting algorithms. In [12], a method called multitone mixing (MTM) was proposed which consists of the substitution of the sinusoidal functions for the mixing with synthetic functions that include up to the 3 rd or 4 th harmonic, in such a way that the first and second-order dependencies on the modulation depth are suppressed. That method, which is FPGA-based high-speed optical fiber sensor based on multitone-mixing interferometry Javier Elaskar, Marcelo Luda, Lorenzo Tozzetti, Jorge Codnia, Claudio J. Oton O very easy to implement in a digital signal processing system, demonstrated to correct distortion in real time with no noise penalties.…”