Fringe Contrast Research Articles

Femtosecond laser-inscribed in-fiber Mach-Zehnder interferometer for ultra-sensitive small-angle torsion measurement

We propose and demonstrate a novel in-fiber Mach-Zehnder interferometer (MZI), using a femtosecond (FS) laser to inscribe two parallel straight waveguides along both sides of the core-cladding boundary of an optical fiber. Both simulations and experiments demonstrated that constructing a second straight waveguide (WG2) on the opposite side of the fiber core significantly enhances the mode coupling efficiency in fiber, resulting in ultra-sensitive small twist-angle torsion measurement by intensity interrogation. By finely adjusting the waveguide spacing between the WG2 and the fiber core during the FS fabrication process, a large tuning range of ∼ 200 nm for the designable interference wavelength with maximal fringe contrast has been achieved. Through comparative experiments, the proposed in-fiber MZI performs ultra-sensitivity with 17417.92 dB/(rad/mm) over small twist angles from −10° to 0° for the sample “WG1-4/WG2-4” and 19480.57 dB/(rad/mm) over small twist angles from 0° to 10° for the sample “WG1-4/WG2-6”. Besides, the device is insensitive to temperature and strain. The exhibited advantages of high sensitivity, high reproducibility, and low crosstalks promote the proposed in-fiber MZI to be applied in future industrial engineering monitoring and intelligent health monitoring.

Computational vibration mitigation using phase interpolation in digital holographic microscopy for overlay metrology

Digital holographic microscopy retrieves amplitude and phase information of an image which allows us to computationally correct for imperfections in the imaging optics. However, digital holographic microscopy is an interferometric technique that is inherently sensitive to undesired phase variations between object and reference beam. These phase variations lower the fringe contrast if they are integrated over a finite exposure time which leads to a reduced amplitude of the retrieved image. This results in significant errors in applications that rely on a stable and accurate amplitude measurement, such as optical overlay metrology in the semiconductor industry. We present experimental results on a computational vibration mitigation method for the application of overlay metrology using phase interpolation between a sequence of measured holograms and demonstrate its capability to improve metrology precision in an overlay metrology application that uses digital holographic microscopy.

Zeeman decoherence effect of trapped 199Hg+ ion Ramsey spectra

Abstract In the 199Hg+ ion microwave clock, the Zeeman decoherence effect caused by the overlapping of Zeeman sidebands and the radial secular motion sidebands will decrease the contrast of the Ramsey fringe, thus reducing the signal-to-noise ratio of the spectra. In this paper, the Zeeman decoherence effect is analyzed theoretically and investigated experimentally. A simplified model is built to describe the Ramsey spectral probability, in which the transverse relaxation time T 2 is introduced to characterize the influence of the Zeeman decoherence effect phenomenologically. The experiments were carried out on a linear quadrupole trap 199Hg+ ion clock. The results show that the probability model matches well with the experimental data, and the magnetic field value should be more than 150 mGs (1 Gs = 10−4 T) to avoid the Zeeman decoherence effect.

Highly sensitive fiber-optic inclinometer utilizing a polymer waveguide-embedded interferometric sensor

A highly sensitive fiber-optic inclination sensor using a modal interferometer was proposed in the present study, which has a photopolymer embedded in a single-mode-few-mode-single-mode fiber (SMF-FMF-SMF) interferometric structure. The sensing component for inclination measurement consists of a cured ellipsoidal photopolymerized-waveguide (EPW) connecting the ends of the FMF and SMF. The effect of EPW on the transmission spectrum and sensitivity of the sensor is specifically investigated using simulation and experiment. In addition, during the preparation of the sensor, it was found that EPW affects the cladding pattern where the FMF is at a low frequency, and a more stable interference pattern can be obtained by modulating the FMF length. The results demonstrate a notable tilt sensitivity of 4.43 dB per degree within the range of 4.4° to 11.4°. Moreover, a change in inclination angle causes misalignment of the FMF and SMF cores, which results in a variation in fringe contrast (FC), allowing a one-to-one correspondence between fringe contrast and θ to be established over a wider range of 0° to 11.4° with an error of less than 3%. The proposed sensor has low temperature crosstalk and is able to cope with disturbances in complex environments. It is expected to be used for microdeformation monitoring of engineered structures.

Quantitative analysis of the contrast modulation for multilateral shearing interferometers

Multilateral shearing interferometers (multi-LSIs) utilize the phase difference information of multiple shear directions with high accuracy and strong noise resistance. However, the interferogram fringe contrast of multi-LSIs can reverse due to the effect of contrast modulation, leading to incorrect measurement result. This issue has lacked comprehensive quantitative research to effectively guide the elimination of its effects. In this work, a quantitative analysis of the contrast modulation is proposed. This paper rigorously derives contrast modulation function, analyzing the effect of aberration and shear ratio on it. It is the first time that a quantitative theoretical model of aberration measurement range and shear ratio has been established, offering guidance in practical application for precise shear ratio adjustment to eliminate modulation effect and extend measurement range. By eliminating modulation effects, phase difference information from multiple directions can be effectively utilized, maximizing the benefits of multi-LSIs. In simulation and experiment, the distribution of fringe contrast reversal bands and the variation of aberration measurement range with shear ratio are consistent with theoretical analysis, which verifies the validity of the proposed approach. This approach aims to address the issue of interferogram fringe contrast inversion caused by modulation in multi-LSIs, providing a theoretical basis and practical guidance for precise measurement.

Liquid drop interferometry on reflective surfaces.

We resolve the main bottleneck of achieving optimal fringe contrast on highly reflective surfaces through the innovative application of rear surface mirrors, unveiling a pioneering approach to precision measurements exemplified by the modified liquid drop interferometry (LDI) technique. By utilizing a liquid drop on a highly reflective surface, the need for a reference lens with a specific coating is eliminated, showcasing the technique's versatility. Furthermore, we first validate a novel, to our knowledge, expression for p-polarization-dependent radiation pressure, addressing a century-old problem reported in the literature. Beyond advancing measurement techniques, this study broadens the scope of applications requiring high precision, particularly in nanotechnology and surface characterization of metallic-coated surfaces.

Neutron-absorption gratings fabricated by ultrasound-assisted filling method based on gadolinium particles

Neutron differential phase-contrast imaging (DPCI) plays a pivotal role in analyzing magnetic domain structures and field gradients in materials, necessitating high-quality neutron absorption gratings for enhanced fringe contrast. Traditional fabrication techniques, typically filling gadolinium (Gd) or Gd-containing materials into the corresponding grating structures, face challenges in achieving optimal Gd filling ratios and thickness, limiting the neutron DPCI system’s performance. This paper introduces an approach utilizing ultrasound-assisted filling method to introduce Gd particles into grating trenches with dense deposition, achieving an absorption grating period of 42 μm. This method achieves an equivalent Gd thickness of 80.3 μm, corresponding to the filling ratio of 53.53%, as confirmed by scanning electron microscopy and x-ray micro-imaging. The utilization of an ultrasound not only improves the Gd filling ratio, but also suggests potential scalability for large-area grating production, marking a significant advancement in neutron DPCI technology by providing high-quality components.

Phase calculation of smooth surface with multi-reflectivity based on phase measurement deflectometry

With the continuous advancement of precision machining technology and the growing demand for products, increasingly complex objects with high reflectivity are becoming more prevalent in production and daily life. phase measurement deflectometry (PMD) is a technique that utilizes a surface light source to project structured light for comprehensive detection of highly reflective surfaces. It offers advantages such as high accuracy, fast speed, low cost, and non-contact operation. However, when the surface of the object being measured has varying levels of reflectivity, this method may produce errors due to significant differences in fringe contrast between different reflective areas. In order to enable the fringe deflection system to simultaneously detect multiple reflective objects without sacrificing accuracy, this paper proposes an adaptive method for fringe generation detection. This method can adaptively adjust the intensity based on the reflectivity of the measured surface and compensate for the light at the reflectivity boundary, ultimately achieving phase calculation for multiple reflective surfaces.

Internal phase control of fiber laser array based on photodetector array

Abstract Coherent beam combining (CBC) of fiber laser array is a promising technique to realize high output power while maintaining near diffraction-limited beam quality. To implement CBC, an appropriate phase control feedback structure should be established to realize phase-locking. In this paper, an innovative internal active phase control CBC fiber laser array based on photodetector array is proposed. The dynamic phase noises of the laser amplifiers are compensated before being emitted into free space. And the static phase difference compensation of emitting laser array is realized by interference measurement based on photodetector array. The principle of the technique is illustrated and corresponding simulations are carried out, and a CBC system with four laser channels is built to verify the technique. When the phase controllers are turned on, the phase deviation of the laser array is less than λ/20, and ∼ 95% fringe contrast of the irradiation distribution is obtained. The technique proposed in this paper could provide a reference for the system design of a massive high-power CBC system.

Generalized neutral axes in nondepolarizing optical systems.

The polarizing properties of optical systems are often characterized by their action on specific polarization states. For example, half-wave plates are used to rotate linear polarizations and quarter-wave plates to turn a linear polarization into an elliptical polarization and into a circular polarization if the linear polarization makes a 45° angle with the slow and fast axes of the quarter-wave plate. Phase shifts introduced by the optical train of an interferometer may lead to coherence losses and the existence of neutral axes-in the sense of linear polarizations whose polarization state is not modified by the optical system-is then of importance to maximize the fringe contrast. Neutral axes do not systematically exist. The purpose of this paper is to investigate how this notion can be generalized to define generalized neutral axes for optical systems. Generalized neutral axes are defined as linear polarizations whose polarization state is not modified by the optical system except for their orientation. It is shown that such generalized neutral axes exist for some classes of optical systems. The scheme proposed in this paper has quasi-unitary Jones matrices to give an approximate description of optical systems when generalized neutral axes do not exist. To the best of my knowledge, this formalism is a new scheme to describe the polarizing properties of nondepolarizing optical systems.

Analysis and simulation of the effect of large optical range difference of common path coherent-dispersion spectrometer on the detection of exoplanet radial velocities

The Exoplanet Explorer common-path coherent-dispersion spectrometer (CODES) utilizes a unique combination of an asymmetric common path Sagnac interferometer and a low to medium resolution spectrometer. The ideal optical range difference (OPD) interval for CODES is OPD ∈ {15.06 mm, 19.45 mm}; however, the OPD of CODES is 64.3 mm to achieve better detection accuracy. Though they will increase the accuracy of detection, large OPDs outside of the ideal interval will also reduce the contrast of the interference fringes, making phase changes more hazy. This may also significantly affect the radial velocity inversion and reduce CODES's instrumental accuracy. This study creates an inverse tone mapping operator based on the photographic model and designs an inverse tone mapping algorithm called CODESCE. The outcomes of the experiments demonstrate that the tone mapping algorithm CODESCE in this work is appropriate for enhancing the contrast of interference fringe images with high OPD, and it can enhance the contrast of interference fringes by three orders of magnitude when OPD = 64.3 mm; the processed interference fringes are located in the range of interference fringe curves of the optimal OPD. By comparison with other current approaches, the suggested algorithm yields superior processing outcomes.

Analysis of Polarization Angle on Holographic Recording Based on PQ/PMMA.

The polarization state of light waves significantly affects the quality of holographic recordings. This paper quantitatively analyzes the impact of different polarization states of signal and reference beams on the quality of holographic recordings in PQ/PMMA photopolymer systems during the holography process. By deriving the light field distribution of the interference between two light waves of different polarization states and introducing the interference fringe contrast and the modulation of the refractive index of the photopolymer, we established the relationship between the diffraction efficiency of PQ/PMMA photopolymer holographic gratings and the angle between polarization directions. Based on this relationship, simulations and experiments were conducted. The experimental results demonstrated that as the angle between the polarization directions increased, the diffraction efficiency of the material decreased, with the efficiency dropping to 24.69% of its original value when the angle increased from 0° to 50°. When the angle increased to 60°, the influence of polarization characteristics became gradually significant, and at 90°, it was entirely dominated by polarization characteristics. The photoinduced birefringence properties of the PQ/PMMA prepared in the measurement experiment were studied, and the polarization characteristics of the reconstructed light under polarization direction angles of 0°, 60°, and 90° were investigated. The results indicated that at a polarization direction angle of 60 degrees, the material exhibited a significant response to the polarization information of the signal light. Finally, holographic recordings of objects at different polarization direction angles were conducted, and the reconstructed images were used to visually reflect the impact of the polarization direction angle on the quality of holographic recordings.

Experiment and analysis of state preparation for atom interferometry

The state preparation is a crucial procedure in atom interferometry; however, there is a shortage of detailed experimental studies on determining the optimal method for achieving this. This paper investigates and compares two methods for state preparation: the combined use of microwave and Raman light (M-R) and the combined use of optical pumping, microwave, and Raman light (O-M-W). The experimental results demonstrate that the M-R method improves the efficiency of Raman transitions for atom interference, which is helpful in enhancing the contrast of the interference fringes. The O-M-R method increases the quantity of prepared atoms, thereby enhancing the signal-to-noise ratio of the detected signals. This work helps provide a useful experimental basis and reference for researchers to design a suitable state preparation scheme.

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.

Framework to optimize fixed-length micro-CT systems for propagation-based phase-contrast imaging.

A laboratory X-ray imaging system with a setup that closely resembles commercial micro-CT systems with a fixed source-to-detector distance of ∼90 cm is investigated for single distance propagation-based phase-contrast imaging and computed tomography (CT). The system had a constant source-to-detector distance, and the sample positions were optimized. Initially, a PTFE wire was imaged, both in 2D and 3D, to characterize fringe contrast and spatial resolution for different X-ray source settings and source-to-sample distances. The results were compared to calculated values based on theoretical models and to simulated (wave-optics based) results, with good agreement being found. The optimization of the imaging system is discussed. CT scans of two biological samples, a tissue-engineered esophageal scaffold and a rat heart, were then acquired at the optimum parameters, demonstrating that significant image quality improvements can be obtained with widely available components placed inside fixed-length cabinets through proper optimization of propagation-based phase-contrast.

Shear-interference assisted deep-learning for enhancing spatially multiplexing capacity of free-space communication

The information capacity is a critical measure in free-space optical (FSO) communication. Traditional mode-multiplexing techniques employed in optical communication utilizing Laguerre-Gaussian beams (LGBs) necessitate proper topological charge interval to prevent mode-crosstalk. In this paper, we propose a novel approach that integrates deep learning (DL) into the LGB-based optical communication model, incorporating shearing interference techniques. This combination enables the FSO system to achieve the theoretical limit of capacity, resulting in a remarkable 300 % increase in information capacity compared to traditional techniques. Experimental results demonstrate that the constructed neural network attains a flawless pattern recognition accuracy of 100 %. Additionally, we evaluate various partially coherent light scenarios under the influence of beam decoherence. The results reveal that accurate discrimination of multiplexing patterns is maintained when the fringe contrast exceeds 0.43. Even at a degraded contrast level of 0.18, the recognition accuracy remains impressively high at 91.16 %. To demonstrate practicality, we successfully encode and transmit a cyan-magenta-yellow-black (CMYK) color image using the proposed system, achieving a low bit error rate of 7.5 × 10-5. These findings highlight the potential of DL-assisted mode-division multiplexing for future optical communication applications.

Demonstrating optical-path compensation in a Michelson interferometer

In this paper we present a simple experiment using a fully compensated Michelson interferometer and a white-light source to demonstrate the importance and the effects of the optical-path compensation. Polyester sheets are introduced in one of the arms of the interferometer to partially decompensate the system. The change in mirror position required to see the fringes in these two cases is related to the refractive index and the thickness of the polyester sheets, and the degradation in the contrast of the white-light fringes due to the partial compensation can easily be demonstrated.

Single-mode waveguides for GRAVITY

The second generation Very Large Telescope Interferometer (VLTI) instrument GRAVITY is a two-field infrared interferometer operating in the K band between 1.97 and 2.43 µm with either the four 8 m or the four 1.8 m telescopes of the Very Large Telescope (VLT). Beams collected by the telescopes are corrected with adaptive optics systems and the fringes are stabilized with a fringe-tracking system. A metrology system allows the measurement of internal path lengths in order to achieve high-accuracy astrometry. High sensitivity and high interferometric accuracy are achieved thanks to (i) correction of the turbulent phase, (ii) the use of low-noise detectors, and (iii) the optimization of photometric and coherence throughput. Beam combination and most of the beam transport are performed with single-mode waveguides in vacuum and at low temperature. In this paper, we present the functions and performance achieved with weakly birefringent standard single-mode fiber systems in GRAVITY. Fibered differential delay lines (FDDLs) are used to dynamically compensate for up to 6 mm of delay between the science and reference targets. Fibered polarization rotators allow us to align polarizations in the instrument and make the single-mode beam combiner close to polarization neutral. The single-mode fiber system exhibits very low birefringence (less than 23°), very low attenuation (3.6–7 dB km−1 across the K band), and optimized differential dispersion (less than 2.04 µrad cm2 at zero extension of the FDDLs). As a consequence, the typical fringe contrast losses due to the single-mode fibers are 6% to 10% in the lowest-resolution mode and 5% in the medium- and high-resolution modes of the instrument for a photometric throughput of the fiber chain of the order of 90%. There is no equivalent of this fiber system to route and modally filter beams with delay and polarization control in any other K-band beamcombiner.

Contrast of Ramsey-CPT Fringes in Quenching and Depolarizing Gases

Molecular nitrogen is often used as a buffer gas in cells with alkali metals due to its known ability to quench resonant fluorescence. It is widely believed that the suppression of spontaneous emission decreases the width of coherent population trapping resonance. However, our recent results have not confirmed this positive action of molecular nitrogen within the typical range of 87Rb concentrations and buffer gas pressures. On the opposite, we have observed the negative influence of quenching, the decrease in contrast of the coherent population trapping resonance in $${{\sigma }^{ + }}$$–$${{\sigma }^{ + }}$$ configuration. In this work, we further confirm these results implementing the Ramsey spectroscopy, and compare the characteristics of the central fringe in nitrogen and neon, and show that the latter provides a significantly better contrast-to-width ratio.

Electrically tunable lens assisted absolute phase unwrapping for large depth-of-field 3D microscopic structured-light imaging

This paper presents an absolute phase unwrapping method for large depth-of-field (DOF) microscopic structured-light 3D imaging. We calculate the wrapped phase maps and the fringe contrast maps from fringe images captured under various focus settings realized by an electrically tunable lens. From the fringe contrast maps, we extract each in-focus pixel and determine its approximate depth value from the focus settings. The approximate depth map is then used to create an artificial phase map. The geometric-constraint-based phase unwrapping method is adopted to unwrap the phase of all in-focus pixels using the artificial phase map. The unwrapped in-focus phase map is then used to reconstruct 3D coordinates for the entire DOF with the multi-focus pin-hole model. Experimental results demonstrate that our proposed method only requires three phase-shifted fringe patterns to achieve large DOF 3D imaging.