Interferometry sensors are frequently analyzed by applying the Fourier transform because the transformation separates all frequency components of its signal, making its study on a complex plane feasible. In this work, we study the relation between the optical path difference (OPD) and poles location theoretically and experimentally, using the Laplace transform and a pole-zero map. Theory and experiments are in concordance. For our study, only the cosine function was considered, which is filtered from the interference pattern. In experimental work, two unperturbed low-finesse Fabry–Pérot interferometers were used. First, a Fabry–Pérot interferometer that has a cavity length of $~$ 1.6 mm was used. Its optical path difference was 2.33 mm and the poles were localized at points $\pm i12$ . rad/nm. Secondly, a Fabry–Pérot interferometer with a cavity length of $~$ 5.2 mm was used, and its optical path difference was 7.59 mm and the poles were localized at points $\pm i40.4$ rad/nm. Experimental results confirmed the theoretical analysis. Our proposal finds practical application for interferometer analysis, signal processing of optical fiber sensors, communication system analysis, and multiplexing systems based on interferometers.

Nickel antimonate (NiSb₂O₆) powders were synthesized using a wet chemistry process assisted by microwave radiation and calcination from 600 to 700 °C to evaluate their photocatalytic and gas-sensing properties. The crystalline phase obtained at 800 °C of trirutile-type nickel antimonate was confirmed with powder X-ray diffraction. The morphology and size of the nanostructures were analyzed employing electron microscopy (SEM and TEM), identifying irregular particles and microrods (~277 nm, made up of polyhedral shapes of size ~65 nm), nanorods with an average length of ~77 nm, and nanostructures of polyhedral type of different sizes. UV-vis analysis determined that the bandgap of the powders obtained at 800 °C was ~3.2 eV. The gas sensing tests obtained a maximum response of ~5 for CO (300 ppm) at 300 °C and ~10 for C₃H₈ (500 ppm) at 300 °C. According to these results, we consider that NiSb₂O₆ can be applied as a gas sensor. On the other hand, the photocatalytic properties of the antimonate were examined by monitoring the discoloration of malachite green (MG) at five ppm. MG concentration monitoring was carried out using UV-visible spectroscopy, and 85% discoloration was achieved after 200 min of photocatalytic reaction.

In this paper, a Michelson interferometer was employed to generate interference patterns, the modulated function was extracted by digital filtering and the Laplace transform was subsequently applied to obtain the complex function $F\left(s\right)=F(\sigma +\omega i)$, which changes its zero structure in response to physical perturbations. This study presents a novel method for detecting millimetric displacements based on analyzing the movement of zeros in the complex s-plane. The proposed technique demonstrates that an unperturbed system displays two zeros on the imaginary axis, whereas the introduction of a displacement $∆x$ generates a third zero with a real component. The position of this third zero in the s-plane directly correlates with the magnitude of the perturbation. Finally, the measurement vector $s_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}$, calculated as the vector difference between reference and perturbed zeros, quantifies the displacement with high precision. Experimentally, displacements ranging from 0.8 mm to 8.8 mm were introduced into one of the interferometer arms, allowing for the systematic observation of the zero migration within the complex plane. The obtained results demonstrate that this methodology transforms the displacement measurement problem into a singularity localization task in the complex domain, offering enhanced robustness against intensity fluctuations compared to conventional techniques based on Fourier analysis or fringe counting.