Double-grating Interferometer Research Articles

Least-squares calibration method for double-grating interferometers used in measurement of long-focal-length lenses.

In this paper, we propose a new calibration method for long-focal-length measurement using a double-grating interferometer. A numerical analysis of the relative error in measurement proves that the main factor affecting accuracy is the angle of inclination between grating grids. Hence, we present a least-squares calibration method using a series of lenses to correct this error. Experiments conducted to demonstrate high precision in wide-range focal length measurement (5-85 m) exhibited an error lower than 0.1% and a repeatability better than 0.03%.

Infinite-mode double-grating interferometer for investigating thermal-lens-acting fluid dynamics

In this paper, we introduce the use of an infinite-mode double-grating interferometer in investigating the fluid dynamics induced by a thermal lens when an intense laser beam—which we call the pump beam—passes through a liquid sample containing strongly absorbing nanoparticles. As the pump beam passes through the sample in normal conditions, since absorption occurs over the beam’s trace, temperature increases and density decreases. The density and temperature changes in the sample can be translated to a phase shift in the passing of a plane probe beam through the sample. By causing two parts of the probe beam to interfere, one part passing from the thermal lens area and the other from another area of the sample spatially separate from the first, it is possible to determine the phase shift value. When the propagation directions of the interfering beams are parallel, infinite-mode double-grating interference fringes are formed. In the infinite mode, the formation and evolution of interference fringes directly reflects any change of density or temperature in the sample. The thermal convection is detected visually and quantitatively determined by chasing the first infinite-mode interference fringe produced. In this work, the measurement of the thermal convection velocity is reported in detail. The measured value is comparable with values obtained with other methods under the same conditions. The proposed method is reliable and very simple; further, the convection process can be visualized in real-time.

Implementation of a double-grating interferometer for phase-contrast computed tomography in a conventional system nanotom® m.

Visualizing the internal architecture of large soft tissue specimens within the laboratory environment in a label-free manner is challenging, as the conventional absorption-contrast tomography yields a poor contrast. In this communication, we present the integration of an X-ray double-grating interferometer (XDGI) into an advanced, commercially available micro computed tomography system nanotom® m with a transmission X-ray source and a micrometer-sized focal spot. The performance of the interferometer is demonstrated by comparing the registered three-dimensional images of a human knee joint sample in phase- and conventional absorption-contrast modes. XDGI provides enough contrast (1.094 ± 0.152) to identify the cartilage layer, which is not recognized in the conventional mode (0.287 ± 0.003). Consequently, the two modes are complementary, as the present XDGI set-up only reaches a spatial resolution of (73 ± 6) μm, whereas the true micrometer resolution in the absorption-contrast mode has been proven. By providing complimentary information, XDGI is especially a supportive quantitative method for imaging soft tissues and visualizing weak X-ray absorbing species in the direct neighborhood of stronger absorbing components at the microscopic level.

Thermal nonlinear optical response of meso-tetraphenylporphyrin under aggregation conditions versus that in the absence of aggregation

In this work, measurement of thermally induced nonlinear refractive index of meso-tetraphenylporphyrin (H2TPP) at different concentrations in 1,2-dicoloroethane using a double-grating interferometer set-up in a pump–probe configuration is reported. The formation of aggregates of H2TPP at concentrations greater than ca. 5 × 10−5 M was evident by deviation from Beer’s law. An almost focused pump beam passes through the solution. A part of the pump beam energy is absorbed by the sample and therefore a thermal lens is generated in the sample. An expanded probe beam propagates through the sample and indicates the sample refractive index changes. Just after the sample a band-pass filter cuts off the pump beam from the path but the distorted probe beam passes through a double-grating interferometer consisting of two similar diffraction gratings with a few centimetres distance. A CCD camera is installed after the interferometer in which on its sensitive area two diffraction orders of the gratings are overlying and producing interference pattern. The refractive index changes of the sample are obtained from the phase distribution of the successive interference patterns recorded at different times after turning on of the pump beam using Fourier transform method. In this study, for different concentrations of H2TPP in 1,2-dichloroethane solution the thermal nonlinear refractive index is determined. Also, we present the measurement of the temperature changes induced by the pump beam in the solution. We found that value of nonlinear refractive index increased by increasing the concentration up to a concentration of 5 × 10−4 M and then decreased at higher concentrations. In addition, we have investigated the stability of the observed thermal nonlinearity after a period of two weeks from the sample preparation.

Grating interferometer for light-efficient spatial coherence measurement of arbitrary sources.

We present a theoretical analysis and experimental verification of a z-scanning double-grating interferometer for spatial coherence measurements in space-frequency and space-time domains. This interferometer permits the measurement of spatial coherence between an arbitrary pair of points along a one-dimensional line, and in favorable conditions, it has a high light efficiency compared to the classical Young's two-pinhole experiment. The scheme is applicable to both quasi-monochromatic and broadband sources that need not obey the Schell model. We first provide experimental results with several narrowband primary and secondary sources, and then apply the technique to broadband sources with discrete and continuous spectra. In the latter case, the complex degree of (time-domain) spatial coherence is retrieved from spectrally resolved measurements using the Friberg-Wolf theorem [Opt. Lett.20, 623 (1995)OPLEDP0146-959210.1364/OL.20.000623]. We compare all results to those obtained with Young's interferometer realized using a digital micromirror device.

Single and double grating-based X-ray microtomography using synchrotron radiation

Hard X-ray phase contrast imaging techniques have become most suitable for the non-destructive three-dimensional visualization of soft tissues at the microscopic level. Among the hard X-ray grating interferometry methods, a single-grating approach (XSGI) has been implemented by simplifying the established double-grating interferometer (XDGI). We quantitatively compare the XSGI and XDGI tomograms of a human nerve and demonstrate that both techniques provide sufficient contrast to allow for the distinction of tissue types. The two-fold binned data show spatial resolution of (5.2 ± 0.6) μm and (10.7 ± 0.6) μm, respectively, underlying the performance of XSGI in soft tissue imaging.

Measurement of long focal lengths with a double-grating interferometer

A method for measuring long focal lengths using a double-grating interferometer is proposed. The intensity distribution of a double-grating interferometer illuminated by a spherical beam is derived with diffraction theory. A tiny rotation angle is set between the two gratings, and a high-contrast interference pattern is produced by the adjacent diffracted orders. The angular change in the fringes after insertion of a test lens is a measure of the focal length. The uncertainty due to aberration of the collimated beam was analyzed by measuring a series of lenses. The relative deviations are less than 0.1%.

Nonlinear refractive index measuring using a double-grating interferometer in pump–probe configuration and Fourier transform analysis

In this paper, we have presented a simple, stable, highly sensitive and timesaving method based on a double-grating interferometer in conjunction with a pump–probe technique for measuring the nonlinear refractive index. A pump laser beam is aligned collinearly with an expanded plane parallel probe beam by a dichroic mirror. These beams pass through the sample, while right behind the sample using a suitable bandpass filter the pump beam is intercepted. The distorted probe beam then passes through a double-grating interferometer. One of the lateral shearing interference patterns is recorded by use of a CCD camera and, after digitization, has been stored in a computer. The interference pattern is analyzed by means of a Fourier transform algorithm. The refractive index changes have been obtained from phase distribution of the recorded fringe patterns. The implementation of the technique is straightforward and the arrangement is very simple and stable yet its sensitivity is comparable with other interferometry methods. It is also not a time consuming method. The method is applied for measuring the thermal nonlinear refractive index n2 of colloidal gold nanoparticles in water solution.

Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry

A study of the coherence and wavefront properties of a pseudo-channel-cut monochromator in comparison with a double-crystal monochromator is presented. Using a double-grating interferometer designed for the hard X-ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel-cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.

Double-grating interferometer for measurement of cylinder diameters.

We describe a double-grating interferometer for the measurement of cylinder diameters. The unique characteristic of this interferometer is that one can freely change the period of the interference fringes by turning the grating, which permits the measurement range of the interferometer also to be changed freely according to the cylinder diameter to be measured. A clear image of the cylinder can be obtained because the aperture diaphragm blocks the beams diffracted from the edge of the cylinder. The outside and inside diameters of the M4 x 0.7 mm hand tap are measured with this double-grating interferometer.

Double-grating interferometer with a one-to-one correspondence with a Michelson interferometer.

We describe a double-grating interferometer that has a one-to-one correspondence with a Michelson interferometer. The half spatial periods of the gratings are equivalent to the wavelengths of the interferometer. The widths of the interference fringes can be changed easily. The intensity distribution of the interference pattern is independent of the wavelength of the light source used. The surface profile of an object can be measured because two interference beams can coincide precisely on the image plane of the object. The measuring range is much larger than that of a Michelson interferometer.

Multiple-beam Interferometers: Analogy with Aberrated Optical Systems and Adjustment Tolerances Estimation

Abstract In this paper we study multiple interference produced by an interferometer when illuminated by an extended quasimonochromatic source. We define a relative modulation factor, which arises from grouping the interference terms for the same frequency. This relative modulation factor measures the departure from ideal behaviour of the interferometer. We also show that for some cases it is possible to associate a single aberrated optical system to each frequency, just as can be done for the single interference case, as was shown in a previous work; this allows an extension of the formalism presented therein. As an example, we calculate, for the case of a double-grating interferometer, the tolerance for the spatial extension of the source, where the modulation factor is close to unity.