The fringe visibility measurements on the complex s-plane: A novel method for the fringe visibility measurement

• Published in: Results in physics 2022-07, Vol.38, p.105586, Article 105586
• Main Authors: Trinidad Guillen Bonilla, José, Guillen Bonilla, Alex, Casillas Zamora, Antonio, Guillen Bonilla, Héctor, María Rodríguez Betancourtt, Verónica, Gildo Ortiz, Lorenzo
• Format: Article
• Language: English
• Subjects: Dynamic System Analysis; Fringe Visibility Measurement; Laplace Transform; Low-coherence Interference Pattern; Low-coherence Interferometer
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2022.105586

•A novel method called Fringe Visibility on s-Plane (FVM-SP), is proposed.•Using pole and zero locations and a pole-zero map, the fringe visibility is measured.•Low-coherence interference pattern is analyzed on the s-plane.•The FVM-SP method only uses the modulated function of an interference pattern. In this work, a novel theoretical technique to measure the fringe visibility ν of a low-coherence interference pattern is proposed. The new technique is called Fringe Visibility Measurement on the S-Plane (FVM-SP) because it is developed on the s-plane. The FVM-SP technique only requires to know the pole and zero location of the modulated function, which is filtered from the interference pattern. Since the optical parameter ν can take the necessary values into the interval 0 to 1, some limits are determined for the FVM-SP. The limits are specified on the complex plane and obtained analyzing the pole-zero map of a modulated function. In the numerical experiments, our proposal FVM-SP and the traditional technique are compared performing two series of experiments. In the one, a low-frequency interference pattern is considered, ωo=12rads and the fringe visibility ν is between 0 and 1 with a step of 0.1. While, in the second series, a high-frequency interference pattern is used, ωo=62831.853rads and the fringe visibility ν had the same values. Based on our numerical results, both methods produce close results. When the interference pattern has a low frequency, the mean errors were 7 × 10−4 and 17.5 × 10−4. However, if the pattern has a high frequency, the average errors were 3×10-4 and 7×10-4, respectively. The traditional technique is based on the intensity of the interference pattern while the FVM-SP is based on its frequency. The Fringe Visibility Measurement on the S-Plane technique is applied for the case 1D and it has potential application on signal demodulation and low-coherence system analysis.