Maximum Fringe Contrast Research Articles

Frequency response of the non-polarization-maintaining depolarized sagnac interferometer based on maximum fringe contrast

The Sagnac Interferometer offers a promising solution to the speckle problem in interferometric detection due to its insensitivity to environmental low-frequency interference, making it well-suited for applications such as laser ultrasonic detection. Control of the polarization state of light is imperative for achieving high sensitivity in optical fiber interferometer and ensuring optimal quiescent operating conditions. This study employed the coherence matrix method to analyze the theory of optimal polarization control in a non-polarization-maintaining depolarized Sagnac Interferometer, encompassing the deduction of the stable π/2 initial phase bias and the maximum fringe contrast of 50% in theory. In experimental observations during PZT simulated large amplitude ultrasound experiments, the fringe contrast reached 48.4%. Furthermore, the system's amplitude-frequency response was evaluated using an electro-optics phase modulator, demonstrating its capability to detect high-frequency signals within 100 MHz These findings provide essential insights into optimizing the Sagnac Interferometer's performance for laser ultrasonic detection and its potential applications in high-frequency signal detection and ultrasonic amplitude measurement.

Polarization control in single mode optical fibers

Satisfactory operation of a dual beam laser Doppler anemometer system requires that the maximum fringe contrast is achieved. This implies, in turn, that the two intersecting beams should have the same intensity and the same state of polarization. This requirement is achieved in many systems by careful adjustment of the polarization state, often at the time when the laser Doppler anemometer system is first aligned. The present paper describes a compact and relatively cheap device that enables the polarization of the light transmitted through a step index mono-mode optical fiber to be controlled. Design methods for this device are discussed and a prototype opto-mechanical system is described. Finally, some experimental data are presented from which the performance of the device in adjusting the polarization of a laser beam can be assessed.

HCPCF-based in-line fiber Fabry-Perot refractometer and high sensitivity signal processing method

An in-line fiber Fabry-Perot interferometer (FPI) based on the hollow-core photonic crystal fiber (HCPCF) for refractive index (RI) measurement is proposed in this paper. The FPI is formed by splicing both ends of a short section of the HCPCF to single mode fibers (SMFs) and cleaving the SMF pigtail to a proper length. The RI response of the sensor is analyzed theoretically and demonstrated experimentally. The results show that the FPI sensor has linear response to external RI and good repeatability. The sensitivity calculated from the maximum fringe contrast is –136 dB/RIU. A new spectrum differential integration (SDI) method for signal processing is also presented in this study. In this method, the RI is obtained from the integrated intensity of the absolute difference between the interference spectrum and its smoothed spectrum. The results show that the sensitivity obtained from the integrated intensity is about –1.34×105 dB/RIU. Compared with the maximum fringe contrast method, the new SDI method can provide the higher sensitivity, better linearity, improved reliability, and accuracy, and it’s also convenient for automatic and fast signal processing in real-time monitoring of RI.

Experimental study of the effects of the ratio of intensities of the reference and object waves on the performance of off-axis digital holography

In this paper we present an experimental study of the effects of the ratio of the intensities of the reference and object waves on the performance off-axis digital holography operating in tight diffraction-limited regimen. The analysis is focused on the comparison of the information contained in the hologram before and after performing the spatial filtering of the zero diffraction order and the twin image. We show that in the Fourier transform of the recorded hologram the information of the object is preserved regardless the ratio of intensities of the object and reference waves. This fact allows the right spatial filtering of the +1 or −1 diffraction order leading to similar reconstructed images for holograms recorded with very different ratios of the intensities of the reference and object waves. The results show that the usual rule of thumb of 1:1 ratio for seeking maximum fringe contrast is not really required. Experimental results of a regular die are utilized for validating the claims.

Temperature-independent optical fiber Fabry–Perot refractive-index sensor based on hollow-core photonic crystal fiber

A novel optical fiber refractive index (RI) sensor, which is based on an intrinsic Fabry–Perot interferometer (IFPI) formed by a section of hollow-core photonic crystal fiber (HCPCF) and standard single mode fibers (SMF), is proposed. The external refractive index is determined according to the maximum fringe contrast of the interference fringes in the reflective spectrum of the sensor. The RI response performance is demonstrated for the measurement of the different RI solutions. The experimental data agree well with the theoretical results. Also the RI resolution and repeatability of ∼1.5×10−5 and ±0.5% in the linear measurement region, are achieved. In addition, the temperature response is tested from 20°C to 120°C, which exhibits excellent thermal stability. Therefore, such an HCPCF-based F–P sensor provides a practical way to measure RI with non-temperature compensation.

Automated determination of best focus and minimization of optical path difference in Linnik white light interferometry

It is difficult to search for interference fringes in Linnik white light interferometry with an extremely short coherence length because of the optical path mismatch of two interference arms and the defocus of the reference mirror and the test surface. We present an automated method to tackle this problem in this paper. The determination of best foci of the reference mirror and the test surface is implemented by the astigmatic method based on a modified commercial DVD pickup head embedded in the interference system. The astigmatic method is improved by setting a threshold value in the sum signal to truncate the normalized focus error signal (NFES). The truncated NFES has a monotonic relationship with the displacement of the test surface, which removes the position ambiguity of the test surface during the autofocus process. The developed autofocus system is confirmed experimentally with a dynamic range of 190 μm, average sensitivity of 70 mV/μm, average standard deviation of 0.041 μm, displayed resolution of 4.4 nm, and accuracy of 55 nm. The minimization of the optical path difference of two interference arms is carried out by finding the maximum fringe contrast of the image captured by a CCD camera with the root mean square fringe contrast (RMSFC) function. The RMSFC function, combined with a 4×4 pixel binning of the CCD camera, is recommended to improve the computational efficiency. Experimental tests show that the automated method can be effectively utilized to search for interference fringes in Linnik white light interferometry.

Fiber-Optic Fabry-Pérot Sensor Based on Periodic Focusing Effect of Graded-Index Multimode Fibers

In this letter, the periodic focusing effect of graded-index multimode fibers is used to improve the performance of fiberoptic Fabry-Perot (FFP) sensors. The maximum fringe contrast of the reflective spectrum of the FFP sensor in air is >32 dB. By detecting the fringe contrast variation and wavelength shift of the reflective spectrum, such an FFP sensor is used to measure the refractive index and temperature with sensitivities of ~45.05 dB/RIU and 11.5 pm/°C , respectively. It is also verified by the experiment that the simultaneous measurement of refractive index and temperature can be realized.

A ray-transfer-matrix model for hybrid fiber Fabry-Perot sensor based on graded-index multimode fiber

A theoretical model based on the ray-transfer-matrix method is developed for explaining the principle of a graded-index multimode fiber (GI-MMF) based hybrid fiber Fabry-Perot (GI-FFP) sensor. It is verified by the numerical simulations and experimental results that the high fringe contrast of the reflective spectrum of the sensor is due to the periodic self-focusing effect of the GI-MMF. The influence of the GI-MMF length on the shape of reflective spectrum and corresponding maximum fringe contrast are investigated. Experimental results are in good agreement with the theory. A typical GI-FFP sensor is fabricated and its response to the external refractive index is measured with a maximum sensitivity of approximately 160 dB/RIU (Refractive Index Unit).

Micro Extrinsic Fiber-Optic Fabry-Perot Interferometric Sensor Based on Erbium- and Boron-Doped Fibers

Micro extrinsic Fabry–Perot interferometers (MEFPIs), with cavity lengths of up to ∼ 9 μm and maximum fringe contrast of ∼ 19 dB, are fabricated by chemically etching Er- and B-doped optical fibers and then splicing the etched fiber to a single-mode fiber, for the first time to the best of our knowledge. The strain and temperature responses of the MEFPI sensors are investigated experimentally. Good linearity and high sensitivity are achieved. Such a type of MEFPI sensor is cost-effective and suitable for mass production, indicating its great potential for a wide range of applications.

Laser-micromachined Fabry-Perot optical fiber tip sensor for high-resolution temperature-independent measurement of refractive index

We propose and demonstrate a Fabry-Perot (F-P) optical fiber tip sensor for high-resolution refractive-index measurement fabricated by using 157-nm laser micromachining, for the first time to our knowledge. The sensor head consists of a short air F-P cavity near the tip of a single-mode fiber and the fiber tip. The external refractive index is determined according to the maximum fringe contrast of the interference fringes in the reflective spectrum of the sensor. Such a sensor can provide temperature-independent measurement of practically any refractive index larger than that of air and offers a refractive-index resolution of ~4 x 10(-5) in its linear operating range. The experimental data agree well with the theoretical results.

Deformation and Vibration Measurements Using Digital Speckle Pattern Interferometers

Speckle interferometers using digital image processing techniques are described. The systems consist of interferometric optical setups and a digital TV-image processing facility with a large frame memory. The digital facility allows us to perform precise and flexible operations such as subtraction, summation, and Level slicing of TV-images. The interferometers make it easy to measure in quasi-real-time surface deformations and modal vibration amplitude of objects. Digital image processing techniques easily generate high contrast fringes. Some experimental results are presented.A statistical theory is applied to analyze the fringe formations due to 3-D displacements of objects for various types of speckle interferometers. Interpretation of the results leads to conditions of maximum fringe contrast and the limitation of the measurements.

Digital speckle-pattern shearing interferometry

An application of digital image processing techniques to speckle-shearing interferometry is described. A present system consists of an image-shearing camera using a Fresnel biprism of small angles and a digital TV-image processing facility. This interferometer makes it easy to measure in quasi-real-time spatial derivatives of surface displacement and modal vibration amplitude of objects. A statistical theory is applied to analyze the formations of these fringes due to 3-D displacement. Interpretation of the result leads to conditions of maximum fringe contrast and the limitation of this technique. Experimental results in the three cases of slope of normal displacement, surface strain, and slope of vibration amplitude measurements are presented.

Correlation Functions for Coherent Fields

A factorization condition which must be satisfied by the first $n$ correlation functions for the electromagnetic field operators has been used to define nth-order coherence. The first-order coherence condition has been shown to imply maximum fringe contrast in interference patterns. In the present paper we investigate the mathematical consequences of assuming the condition for maximum fringe contrast. By considering the correlation functions as scalar products and formulating rigorous inequalities for them we are able to show that the assumed condition in turn implies factorization of the first-order correlation function. By extending the same methods we are able to show that all of the higher order correlation functions factorize into forms similar to those required for full coherence, but differing from them through the inclusion of a sequence of constant numerical factors. These coefficients are shown to furnish a convenient description of the higher-order coherence properties of the field. Their values are presented for some typical examples. We derive a number of inequalities satisfied by the coefficients for the case of fields which possess positive-definite weight functions in the $P$ representation. Some inequalities obeyed by the correlation functions for such fields are derived as well.

A constant gap moir fringe reading head

This note describes a method of maintaining a constant grating gap in a moire fringe measuring system. The design of the reading head is such that the index grating rides against the scale grating on air-bearing pads. In this way, the design clearance is more easily set and is maintained more accurately than it is with the conventional type of fixed index; maximum fringe contrast and signal modulation can thus be attained at all positions along the scale grating.