Single Interference Fringe Research Articles

Optical trapping in air on a single interference fringe

Stable and reproducible trapping in air of 1μm and 500 nm dielectric particles has been realized using a dual beam optical fiber tweezers with cleaved commercial single mode fibers. The influence of the interference fringes of the two coherent and counter-propagating trapping beam is investigated by controlling the fringe visibility. Optical trapping on a series of up to 10 fringes or trapping on only one to two fringes has been observed in distinct experiments. High axial trapping efficiencies of up to 1 nN μm−1W−1 is observed. The experimental results are supported by numerical simulations.

Under-Sampled Phase Retrieval of Single Interference Fringe Based on Hilbert Transform

Phase retrieval from single interference fringe is important and effective method in obtaining the real phase distribution. The original phase can be retrieved by the line integral of its gradient expressed as sine and cosine components, which were gained by the Hilbert transform twice from a single interference fringe pattern. However, this method fails when the phase transformation of the interference fringe is too fast. In this paper, a novel method to recover the continuous phase of the whole field is proposed to solve the above problems. The shear interference technique is introduced into the phase retrieval method to build an exponential 2-D complex light field of natural base for the phase slope obtained by the Hilbert transform. Then, the expressions of phase slopes in x- and y-directions are constructed as a discrete Poisson equation. Therefore, the calculation of phase retrieval is equivalent to solve the discrete Poisson equation mathematically. Finally, the real phase is gotten by the weighted discrete cosine transform (WDCT) of the discrete Poisson equation. The simulation results verify the validity of this method and show that the proposed method can achieve the phase retrieval of the phase discontinuity in x- and y-directions, which leads to the under-sampled problem. It can restore the whole field phase distribution rapidly and accurately. Moreover, this method is applied to phase retrieval of interferometric synthetic aperture radar (InSAR) with the under-sampled problem in this paper. The experimental results show that this method can recover the phase of InSAR with the under-sampled problems caused by terrain abrupt change and so on. Compared with other commonly used methods, it achieved satisfactory results. This method provides a new idea for solving the under-sampled problem in the phase retrieval from a single-frame interference fringe.

ワンショット位相シフトデジタルホログラフィによる三次元計測装置の開発

In these years, demand for 3D measurement technology is increasing. However, in many of the conventional 3D measurement methods, such as phase-shift patterns projection method, it is difficult to measure shape of specular reflective and transparent objects. This is because power of reflected light is too high from specular reflective objects or too low from transparent objects, so that reflected light cannot be captured accurately by digital camera. Digital Holography has been used for resolving this problem. In digital holography, interference fringe of object wave and reference wave is recorded by digital camera. Phase of object wave can be calculated using Fresnel diffraction, and shape of object can be calculated using interferometry. Although shape of specular reflective and transparent objects can be measured using digital holography, DC and virtual term exist in single interference fringe as noises, decreases measurement accuracy. For higher accuracy measurement, phase-shift digital holography has been developed. However, for generating four phase-shift interference fringes, measurement system is expensive and complex. Moreover, phase-shift interference fringes are instable due to vibration of measurement environment. For these reasons, conventional phase-shift digital holography is difficult to apply. We propose a new method of generating phase-shift interference fringes using wave detection principle, and developed a low price measurement system using the proposal method to solve the problem. This paper uses a measuring method of phase-shift digital holography using single interference fringe. The experimental result shows how the stable 3D measurement system using single-shot phase-shift digital holography can achieve with low-cost and high accuracy.

Optimal multi-photon phase sensing with a single interference fringe

Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. However, the N-photon parity measurements required to achieve this optimal sensitivity are extremely difficult to realize with current photon detection technologies, requiring high-fidelity resolution of N + 1 different photon distributions between the output ports. Recent experimental demonstrations of precision beyond the SNL have therefore used only one or two photon-number detection patterns instead of parity measurements. Here we investigate the achievable phase sensitivity of the simple and efficient single interference fringe detection technique. We show that the maximally-entangled “NOON” state does not achieve optimal phase sensitivity when N > 4, rather, we show that the Holland-Burnett state is optimal. We experimentally demonstrate this enhanced sensitivity using a single photon-counted fringe of the six-photon Holland-Burnett state. Specifically, our single-fringe six-photon measurement achieves a phase variance three times below the SNL.

Interference fringe pattern analysis using inverse cosine function

AbstractThe analysis of interference fringe patterns is a technique which is indispensable in estimating the shape of an object or the refractive index field of a solution from the interference fringe pattern image. In the methods proposed to date, however, satisfactory analysis has been difficult in situations where the image contains only a few fringes, the object shape is not smooth, or the target of measurement is continuously changing with time. This paper proposes the following method of analysis. The inverse cosine function (arccos function) is applied to the interference fringe pattern image after normalizing the intensity. Then the phase inversion is estimated by assuming a monotonically increasing phase. The method is a combination of simple ideas derived from the principles of interference fringe patterns, but can be used to calculate the phase for each pixel from a single interference fringe pattern image. Depending on the conditions, analysis with higher temporal and spatial resolutions than in the Fourier transform method can be achieved. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(1): 61–73, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20325

Continuous Laser Interference Thermometry of Transparent Plates

A method for quasi-continuous measurements of the nonstationary temperature of plane–parallel plates by using optical Fabry–Perot resonators is discussed. The temperature was earlier determined from interferograms only for time intervals corresponding to the extrema of the reflected or transmitted light intensities, because the deviations of the shapes of plates (polished single crystals and glasses) from the perfect plane-parallel shape distort the geometry of the resonators. It is shown that, for plates with a small surface reflectivity (R > 1 within a single interference fringe is implementable. Measurements with 20 temperature readings within each fringe were performed for K-8 glass in a gas-discharge plasma.

A general form for calculating residual stresses detected by using the holographic blind-hole method

A general form used for analyzing residual stresses measured using the holographic blind-hole method is introduced in this paper. Adopting the general form presented, the residual stresses can be obtained using three relative displacements measured from a single interference fringe pattern. Even for the case in which phase-shifting holographic interferometry is not employed, interpolating calculations for determining the fringe orders are not needed, since the choice of data points becomes more flexible when using this general form. Two experiments, the first one carried out by the authors and the second one published previously, are used to illustrate the applicability and usefulness of this general form. Suggestions for the applications of this general form are also established via the upper bound error estimations.