Fringe pattern analysis based on the two-dimensional synchrosqueezing transform.

Windowed Fourier transform (WFT) is used to analyze fringe patterns observed from optical measurements. The space-frequency resolution of the WFT is limited, which affects the analyzing performance. In this Letter, we propose to apply the two-dimensional synchrosqueezing transform (SST) for analyzing fringe patterns. The SST is a technique used to overcome the limitation of the space-frequency resolution of the WFT, which sharpens the WFT representation using the derivative of the WFT phase. Numerical experiments confirm the effectiveness of the SST in denoising the fringe pattern and estimating the local frequency from the observed fringe pattern.

Determination of microphone acoustic center from sound field projection measured by optical interferometry.

This article presents a method for determining the acoustic center of a microphone from a sound field measured by optical interferometry. The acoustic center defines the equivalent point source position of a microphone serving as a sound source where the spherical waveform starts to diverge. The value is used to determine the effective distance between microphones for free-field reciprocity calibration. Conventionally, it is determined from the inverse distance law properties of a point source using the transfer function method. In this study, the acoustic center was determined from the projection of the sound field of the microphone. Parallel phase-shifting interferometry was used to measure the line integration of the sound pressure from a microphone. The acoustic center is determined as the position where the squared error between the measured data and the projection model of a point source is minimized. Experiments with the B&K 4180 (Brüel & Kjær, Nærum, Denmark) microphone were performed for frequencies from 10 to 50 kHz. The best acoustic center estimation was obtained at a microphone distance of 0 mm, with a difference of 0.17 mm to the IEC 61094-3 value and 0.36 mm to the Barrera-Figueroa et al. [J. Acoust. Soc. Am. 120(5), 2668-2675 (2006)] result at a measurement frequency of 20 kHz.

Speckle holographic imaging of a sound field using Fresnel lenses.

In this Letter, we propose to use Fresnel lenses for holographic sound-field imaging. Although a Fresnel lens has never been used for sound-field imaging mainly due to its low imaging quality, it has several desired properties, including thinness, lightweight, low cost, and ease of making a large aperture. We constructed an optical holographic imaging system composed of two Fresnel lenses used for magnification and demagnification of the illuminating beam. A proof-of-concept experiment verified that the sound-field imaging with Fresnel lenses is possible by using the spatiotemporally harmonic nature of sound.

Seeing the sound of castanets: Acoustic resonances between shells captured by high-speed optical visualization with 1-mm resolution.

Sound fields radiated from the castanet, a Spanish percussive instrument comprising two shells, were optically visualized. A measurement system, which used parallel phase-shifting interferometry and a high-speed polarization camera, enabled the capture of instantaneous sound fields around the castanets, while the castanets were played, with the spatial resolution of 1.1 mm and frame rate of 100 000 fps. By carefully aligning the tilt of the castanets, the sound fields within the 1-mm gaps between both the shells were captured. From the visualization results, two acoustic resonances between the shells were identified. The first mode appeared between 1000 and 2000 Hz and exhibited a frequency chirp of several hundred hertz for several milliseconds after the impact. This can be explained by the Helmholtz resonance with a time-varying resonator shape, which is caused by the movement of the shells after impact. The second mode showed a resonance pattern with a single nodal diameter at the center of the shells, i.e., the standing wave mode caused by the interior volume. These physical phenomena involved in the sound radiation were identified owing to the unique features of the optical imaging method, such as contactless nature and millimeter-resolution imaging of instantaneous pressure fields.

Source directivity approximation for finite-difference time-domain simulation by estimating initial value.

In order to incorporate a directive sound source into acoustic simulation using the finite-difference time-domain method (FDTD), this paper proposes an optimization-based method to estimate the initial value which approximates a desired directional pattern after propagation. The proposed method explicitly considers a discretized FDTD scheme and optimizes the initial value directly in the time domain so that every effect of the discretization error of FDTD, including numerical dispersion, is taken into account. It is also able to consider a frequency-wise directivity by integrating the Fourier transform into the optimization procedure, even though the estimated result is defined in the time domain. After the optimization, the obtained result can be utilized in any acoustic simulation based on the same FDTD scheme without modification because the result is represented as the initial value to be propagated and no additional procedure is required.

Optical visualization of a fluid flow via the temperature controlling method.

In this Letter, a visualization method of a fluid flow through temperature control is proposed. The proposed method enables us to visualize an invisible fluid flow by controlling the temperature so that its visibility can be easily adjusted. Such ability of adjusting appearance is effective for visualizing the phenomena consisting of multiple physical processes. In order to verify the validity of the proposed method, the measurement experiment of visualization of both flow and sound in air using parallel phase-shifting interferometry, which is a similar condition to the previous research [Opt. Lett.43, 991 (2018)OPLEDP0146-959210.1364/OL.43.000991], was conducted.

Time-directional filtering of wrapped phase for observing transient phenomena with parallel phase-shifting interferometry.

Recent development of parallel phase-shifting interferometry (PPSI) enables accurate measurement of time-varying phase maps. By combining a high-speed camera with PPSI, it became possible to observe not only time-varying but also fast phenomena including fluid flow and sound in air. In such observation, one has to remove static phase (time-invariant or slowly-varying phase unrelated to the phenomena of interest) from the observed phase maps. Ordinarily, a signal processing method for eliminating the static phase is utilized after phase unwrapping to avoid the 2π discontinuity which can be a source of error. In this paper, it is shown that such phase unwrapping is not necessary for the high-speed observation, and a time-directional filtering method is proposed for removing the static phase directly from the wrapped phase without performing phase unwrapping. In addition, experimental results of simultaneously visualizing flow and sound with 42 000 fps are shown to illustrate how the time-directional filtering changes the appearance. A MATLAB code is included within the paper (also in https://goo.gl/N4wzdp) for aiding the understanding of the proposed method.

Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry.

In this Letter, simultaneous imaging of flow and sound by using parallel phase-shifting interferometry and a high-speed polarization camera is proposed. The proposed method enables the visualization of flow and sound simultaneously by using the following two factors: (i) injection of the gas, whose density is different from the surrounding air, makes the flow visible to interferometry, and (ii) time-directional processing is applied for extracting the small-amplitude sound wave from the high-speed flow video. An experiment with a frame rate of 42,000 frames per second for visualizing the flow and sound emitted from a whistle was conducted. By applying time-directional processing to the obtained video, both flow emitted from the slit of the whistle and a spherical sound wave of 8.7 kHz were successively captured.

Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry.

This paper presents a non-iterative phase retrieval method from randomly phase-shifted fringe images. By combining the hyperaccurate least squares ellipse fitting method with the subspace method (usually called the principal component analysis), a fast and accurate phase retrieval algorithm is realized. The proposed method is simple, flexible, and accurate. It can be easily coded without iteration, initial guess, or tuning parameter. Its flexibility comes from the fact that totally random phase-shifting steps and any number of fringe images greater than two are acceptable without any specific treatment. Finally, it is accurate because the hyperaccurate least squares method and the modified subspace method enable phase retrieval with a small error as shown by the simulations. A MATLAB code, which is used in the experimental section, is provided within the paper to demonstrate its simplicity and easiness.

Improving principal component analysis based phase extraction method for phase-shifting interferometry by integrating spatial information.

Phase extraction methods based on the principal component analysis (PCA) can extract objective phase from phase-shifted fringes without any prior knowledge about their shift steps. Although it is fast and easy to implement, many fringe images are needed for extracting the phase accurately from noisy fringes. In this paper, a simple extension of the PCA method for reducing extraction error is proposed. It can effectively reduce influence from random noise, while most of the advantages of the PCA method is inherited because it only modifies the construction process of the data matrix from fringes. Although it takes more time because size of the data matrix to be decomposed is larger, computational time of the proposed method is shown to be reasonably fast by using the iterative singular value decomposition algorithm. Numerical experiments confirmed that the proposed method can reduce extraction error even when the number of interferograms is small.

Compensation of fringe distortion for phase-shifting three-dimensional shape measurement by inverse map estimation.

For three-dimensional shape measurement, phase-shifting techniques are widely used to recover the objective phase containing height information from images of projected fringes. Although such techniques can provide an accurate result in theory, there might be considerable error in practice. One main cause of such an error is distortion of fringes due to nonlinear responses of a measurement system. In this paper, a postprocessing method for compensating distortion is proposed. Compared to other compensation methods, the proposed method is flexible in two senses: (1) no specific model of nonlinearity (such as the gamma model) is needed, and (2) no special calibration data are needed (only the observed image of the fringe is required). Experiments using simulated and real data confirmed that the proposed method can compensate multiple types of nonlinearity without being concerned about the model.

Convex optimization-based windowed Fourier filtering with multiple windows for wrapped-phase denoising.

The windowed Fourier filtering (WFF), defined as a thresholding operation in the windowed Fourier transform (WFT) domain, is a successful method for denoising a phase map and analyzing a fringe pattern. However, it has some shortcomings, such as extremely high redundancy, which results in high computational cost, and difficulty in selecting an appropriate window size. In this paper, an extension of WFF for denoising a wrapped-phase map is proposed. It is formulated as a convex optimization problem using Gabor frames instead of WFT. Two Gabor frames with differently sized windows are used simultaneously so that the above-mentioned issues are resolved. In addition, a differential operator is combined with a Gabor frame in order to preserve discontinuity of the underlying phase map better. Some numerical experiments demonstrate that the proposed method is able to reconstruct a wrapped-phase map, even for a severely contaminated situation.

High-speed imaging of sound using parallel phase-shifting interferometry.

Sound-field imaging, the visualization of spatial and temporal distribution of acoustical properties such as sound pressure, is useful for understanding acoustical phenomena. This study investigated the use of parallel phase-shifting interferometry (PPSI) with a high-speed polarization camera for imaging a sound field, particularly high-speed imaging of propagating sound waves. The experimental results showed that the instantaneous sound field, which was generated by ultrasonic transducers driven by a pure tone of 40 kHz, was quantitatively imaged. Hence, PPSI can be used in acoustical applications requiring spatial information of sound pressure.