Fringe Scanning Method Research Articles

Feasibility study of interferometric phase-contrast X-ray imaging using the hard-X-ray free-electron laser of the SPring-8 Angstrom Compact Free-Electron Laser.

Aiming for the fine observation of fast physical phenomena such as phonon propagation and laser ablation, phase-contrast X-ray imaging combined with acrystal X-ray interferometer and the X-ray free-electron laser (XFEL) of theSPring-8 Angstrom Compact Free-Electron Laser has been developed. An interference pattern with 70% visibility was obtained by single-shot exposure with a 15 keV monochromated XFEL. In addition, a phase map of an acrylic wedge was successfully obtained using the fringe scanning method.

Millisecond-order X-ray phase tomography with a fringe-scanning method

We successfully realized millisecond-order X-ray phase tomography using a fringe-scanning method in grating-based X-ray interferometry. We obtained phase tomograms with a measurement time of 4.43 ms using a white synchrotron X-ray beam. The use of a fringe-scanning method enables us to achieve not only a higher spatial resolution but also a higher signal-to-noise ratio than that attained by the Fourier transform method. In addition, our approach can be applied to realize four-dimensional or high-throughput X-ray tomography for samples that can be rotated at a high speed.

Comparison of the sensitivities for atom interferometers in two different operation methods**Project supported by the National Natural Science Foundation of China (Grant Nos. 41127002, 11574099, 41504034, and 11474115) and the National Basic Research Program of China (Grant No. 2010CB832806).

We investigated the sensitivities of atom interferometers in the usual fringe-scanning method (FSM) versus the fringe-locking method (FLM). The theoretical analysis shows that for typical noises in atom interferometers, the FSM will degrade the sensitivity while the FLM does not. The sensitivity-improvement factor of the FLM over the FSM depends on the type of noises, which is validated by numerical simulations. The detailed quantitative analysis on this fundamental issue is presented, and our analysis is readily extendable to other kinds of noises as well as other fringe shapes in addition to a cosine one.

Space position measurement using long-path heterodyne interferometer with optical frequency comb

A heterodyne interference system was developed for position measurement. A stabilized optical-frequency comb is used as the laser source. The preliminary experiment to measure a distance of 22.478 m shows a drift of 1.6 μm in 20 minutes after the temperature compensation. Comparison and frequency shift experiments have been done for a distance of about 7.493 m. The experimental results show that the drift is mainly caused by environmental condition changes and the vibration of the table and floor also has some effects. It was verified that the absolute distance measurement can be realized by fringe scanning and frequency-shifting methods.

X-ray phase tomography with a Talbot interferometer in combination with an X-ray imaging microscope

An X-ray Talbot interferometer was combined with an X-ray imaging microscope to generate differential phase contrast. X-ray phase tomography was attained based on the measurement of the differential phase shift using the fringe scanning method. Polymer blend samples were observed and phase separation structures were depicted. The spatial resolution was 1.3 μm in this test experiment, which will be easily improved by increasing the magnification.

X-ray phase micro-tomography using an interference microscope with zone plates

Using an x-ray common-path interference microscope with two zone plates at SPring-8 BL20XU, quantitative phase imaging was investigated by the fringe-scanning method. The phase sensitivity was estimated to be λ/62. Tomographic three dimensional phase image of diamond particles and polystyrene beads of 2.8 μm in diameter could be clearly reconstructed.

X-ray phase imaging of biological soft tissue using a direct-sensing x-ray HARP tube camera

A HDTV camera having a direct-sensing x-ray high-gain avalanche rushing amorphous photoconductor (HARP) tube was used, for the first time, to acquire x-ray phase maps. The tube can achieve a high sensitivity as a result of the avalanche multiplication process in the HARP target. A beryllium plate, rather than a glass plate, was used as the face plate of the tube to minimize the loss of x-rays due to absorption, and a 15 µm thick HARP target was directly formed on it. In the experiment, the x-ray phase shifts produced by a rat liver were measured using synchrotron x-rays (λ = 0.0766 nm) and a triple Laue-case (LLL) x-ray interferometer. Interference patterns produced by the sample were observed with the direct-sensing x-ray HARP tube camera. A voltage of 1300 V was applied to the HARP target to give an output signal gain of two. The camera was operated in 1125 scanning-line mode, and real-time images were stored on a workstation at a rate of 30 images/s with an image format of 960 (H) × 1100 (V) pixels. A phase-map image of the sample was successfully obtained using the fringe scanning method and phase unwrapping. The observed phase shifts ranged from 50° to 200°. Trees of blood vessels in the rat liver were clearly depicted without using a contrast agent. The spatial resolution of the x-ray camera was estimated to be better than 35 µm in the vertical direction and 100 µm in the horizontal direction.

Micro-three dimensional shape measurement method based on shadow Moiré using scanning electron microscopy

A novel, precise, three-dimensional shape measurement method using scanning electron microscopy (SEM) and Moiré topography has been proposed. The possibility for measurement of wavelength order using this method is discussed based on results of experiments to confirm the principle. In these experiments, a high-resolution method based on the new measurement method is proposed, employing fringe scanning technology for the shadow Moiré. The optical system is constructed with a SEM using backscattering electrons, a grating holder that can shift the position of the grating, and a grating having a pitch of 120 µm. Measured results using a bearing ball as a sample show that high resolution measurements of around one micrometre can be performed using the fringe scanning method and the new measurement arrangement. An error analysis of the method is performed to enable improvement of the measuring accuracy.

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.

Phase retrieval with two-beam off-axis x-ray holography

A wave front dividing x-ray interferometer with a prism was applied to two-beam off-axis holography. Complex amplitudes at the detector plane, which were derived from the hologram using the fringe scanning method, were inversely transformed to those at the exit surface of the specimen. The x-ray phase shift due to the amorphous carbon particles was quantitatively determined with the background of the phase image being as small as approximately λ∕100 at 12.4keV.

Digital moiré fringe-scanning method for centering a circular fringe image.

A digital moiré fringe-scanning method for centering a circular fringe image is proposed. The image of a nondiffracting beam, whose cross section is a circular fringe, is first downloaded onto a computer. The image is then superposed with a digital circular grating, whose center is close to the center of the image, to generate circular moiré fringes. Changing the phase of a digital grating can cause moiré fringe scanning. The global center of the image can be calculated by use of sets of the scanned picture. Because all the image data are used for the calculation, the effect of random noise on centering is greatly reduced and the center position resolution can reach the order of a subelement of a CCD. The measurement of spatial straightness is discussed.

Integration Method Using Three Nodes Spaced at Heterogeneous Intervals and Application to Highly Precise Measurement of Mirror Surface Aberrations

The Hartmann test for measuring mirror surface aberrations accumulates integration errors when calculating the aberration on the basis of gradient data. For this reason, highly precise integration is desired. Here, we present a grating projection method modified from the Hartmann test. It involves using ray tracing and fringe scanning methods, in which sampling points can be set at arbitrary intervals. The authors propose a highly precise integration method appropriate for the grating projection method. In this integration method, three nodes are used, and Simpson's rule and the Gauss quadrature can be described in a unified manner. Furthermore, the relationship between the integration error and the coefficient that determines the interval between nodes is shown. We provide the coefficient conditions for rendering the integration error smaller than that of Simpson's 3/8 rule; this is a typical integration method. In addition, the advantage of this method is demonstrated by simulation experiments. The proposed integration method can be applied to any general precise numerical integration problem.

Shearing X-ray interferometer with an X-ray prism and its improvement

A wave-front dividing interferometer was devised in which half of a highly spatially coherent beam deflected by an x-ray prism is overlapped with another half. By placing the samples in the two beams and the x-ray imaging detector closely downstream of the sample, the differential phase of the sample is recorded on the imaging detector. The separation of the two paths at the sample plane, the amount of shear, was approximately 2 pm in the present experiment. This is easily controllable by changing the distance between the sample and the imaging detector. Phase retrieval using the fringe scanning method was successfully demonstrated for various kinds of weakly absorbing samples.

Shearing x-ray interferometer with an x-ray prism

A wave front dividing interferometer was devised in which half of a highly spatially coherent beam deflected by an x-ray prism is overlapped with another half. By placing the samples in the two beams and the x-ray imaging detector closely downstream of the sample, the differential phase of the sample is recorded on the imaging detector. The separation of the two paths at the sample plane, the amount of shear, was 2.2 μm in the present experiment. This is easily controllable by changing the distance between the sample and the imaging detector. Phase retrieval using the fringe scanning method was successfully demonstrated for various kinds of weakly absorbing samples.

Shape error measurement using ray-tracing and fringe scanning methods: projection of grating displayed on a liquid crystal panel

We present an improved Hartmann test, which has high spatial resolution with respect to the measuring points, for measuring projection mirrors. In the method, grid lines with a sinusoidal transmittance distribution are displayed on a liquid crystal panel and illuminated with a collimated laser beam. The beam transmitted through the liquid crystal panel reflects off the mirror surface being tested and reaches a screen. A charge-coupled device camera detects the projected images, which contain information about the inclination of the surface being tested. Any error in the shape of the mirror surface is identified by integrating the inclination. To increase the spatial resolution, the fringe scanning method is performed by shifting the grid lines on the liquid crystal panel. The grid lines are optimized for the shape of the mirror being tested. Because the grid lines are displayed by an electrical method, the shifting operation is easy and rapid, and furthermore, the displacement can be done precisely. The shape error of an off-axis parabolic mirror made of plastic is measured by the proposed method.

Shape measurements of mirror surfaces with a lateral-shearing interferometer during machine running

A common path lateral-shearing interferometer with a minimum number of optical components has been developed. Because the interferometer is little affected by mechanical vibrations and air turbulence, it can be mounted on an ultraprecision lathe and can be used to measure the shapes of workpieces. A plane parallel glass plate is used to shear the wavefront under test in the interferometer. To analyze the interference fringes obtained by the interferometer precisely, a fringe-scanning method using a slight tilt of the glass plate is used. Zone plates that are computer-generated holograms are used to measure spherical and aspherical surfaces with the interferometer. A spherical and a parabolic concave mirror were measured with the interferometer. The spherical mirror was also measured by a Fizeau interferometer to compare the error with that measured by the lateral-shearing interferometer. The experimental results agreed well with those measured by the lateral-shearing interferometer.

Vibration Measurement of Ultrasonic Motor Using Stroboscopic Interferometry.

In this paper, we propose a stroboscopic interferometric method to measure small vibrations of an ultrasonic motor. The Fizeau interferometer in the optical microscope is used to obtain stroboscopic interference images of a vibrating surface. The measured interferograms are analyzed by the fringe scanning method. The stator of an ultrasonic motor is excited at a resonant frequency of 30 kHz. As the laser irradiation time is sufficiently short compared with the vibration period of the sample, interferometric images with a high contrast are obtained. By changing the delay time of the laser irradiation, vibrations of the surface at different phases are obtained. The distribution of the vibration is visualized sequentially. The stator is vibrated at an amplitude of 3. 7μm peak to peak, so the measurement error is evaluated to be 1/20 of the laser wavelength approximately. This method is useful for designing an optimal ultrasonic motor.

Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer

Phase-contrast X-ray computed tomography (PCX-CT) using an X-ray interferometer is introduced for observing a density distribution inside an organic material. PCX-CT images are compared with an absorption-contrast X-ray CT image and shown to be highly sensitive. To convert an interference pattern into an image of phase-shift distribution, which is put into a CT algorithm, the author applied subfringe analysis techniques, such as the Fourier-transform method and the fringe scanning method. In the case presented here, a plastic sphere is used as a test sample, and the resulting spatial resolution of the PCX-CT image is less than 40 μm. The signal-to-noise ratio (S/N) for the PCX-CT image is increased to ten times that for an absorption-contrast CT image. The S/N can be further increased by suppressing the movement of the interference pattern caused by air flow around the interferometer.

しわの非接触３‐Ｄ測定システムの開発とその応用

The skin surface is characterized by small ridges, prominences and furrows that change with aging and degree of sun expose. Quantifying such geometric characteristics as the ridges and furrows on the skin surface can provide cosmetic researchers with a means of assessing changes in wrinkles and understanding the wrinkling process.Many attempts have been tried to analyze the features of wrinkles in order to evaluate the efficacy of anti-wrinkles preparations. However, measurement systems proposed up to now have been unable to provide 3-D information about wrinkle shapes. The authors have developed a new non-contact 3-D measurement system to profile wrinkles based on a fringe scanning method using a sinusoidal grating pattern instead of interference fringes generated by laser. The grating projection system makes it possible to capture the three-dimensional nature of the objective. Another feature of the new device is that fringe scanning is introduced to the grating projection system. The system provides a greater density of measurement points and eliminates the influence of skin surface anomalies such as spots, freckles, moles, etc. Using this system, the depth of wrinkles can be obtained within 1.0 second with a depth accuracy of less than ±14μm over an area of 12.5mm×15mm.3-D measurements of wrinkles were taken on the external corners of the eyes of 599 Japanese women ranging in age from 20 to 67. A mathematical model is proposed which aims to assist in understanding the effects of aging and the efficacy of cosmetic products.

Measurement of a transparent object by using an automated Talbot interferometer

It is reported that the first partial derivative of the phase distribution for a transparent object can be measured automatically by a personal computer with an image processor. The moire pattern is formed by superimposing the Fourier image distorted by the transparent object on the master grating. But if only the moire patterns are observed, it is not shown if the fringe order numbers increase or decrease. The fringe scanning method is presented to overcome the fringe order numbers. The four-step method is used to calculate the first partial derivative. By a simple experiment, the first partial derivative can be shown in the three dimensional graphics.