Phase Of Interference Fringes Research Articles

Extensive-dynamic-range and high-resolution surface profiling with phase-sensitive spectral-domain white-light interferometry.

We demonstrate a Fourier-transform-based method for extensive-dynamic-range and high-resolution surface profiling using phase-sensitive spectral-domain white-light interferometry. By combining the frequency and phase of interference fringes, this method is capable of displacement measurement with nanometer-scale resolution and a dynamic range up to several millimeters. The performance of the method is demonstrated by surface profiling of a coin, gauge blocks, and a cell-phone circuit board.

The gravity estimation with square-root unscented Kalman filter in the cold atom gravimeter

In the atomic gravimeter, the interference fringe is obtained by scanning the chirp rate of the Raman lasers to compensate for the gravity induced Doppler frequency shift and then the gravitational acceleration can be obtained by extracting the phase of the atomic interference fringe. The phase of the interference fringe is proportional to the chirp rate, therefore the accurate estimation of the chirp rate is the key issue to obtain accurate gravitational acceleration. In practice, the model for estimating the chirp rate is not perfect, and there is system state error. In this paper, we propose a square root unscented Kalman filter (SR-UKF) approach for estimating gravitational acceleration, which can take the system state error into account. The experiments on simulated and real data are performed to demonstrate the feasibility and effectiveness of the SR-UKF method, which can provide an alternative approach for the gravity estimation. In addition, it can be combined with the tidal model for gravity estimation, and can also be used for real-time gravity measurement.

Information criterion of quality of image formation and analysis in the noncontact monitoring of objects

The results of the investigation of the information criterion of quality in terms of image formation and processing in the noncontact monitoring of object systems are presented taking into account the statistical properties of the signals representing the images. An example of the application of the information criterion to interferometric systems is examined, and the information criterion and traditional criteria—signal-to-noise ratio and interference fringe phase error—are compared. The information criterion of quality has a versatile character when applied to various problems of the noncontact monitoring of objects.

Surface Plasmon Resonance-Based Sensing Utilizing Spatial Phase Modulation in an Imaging Interferometer.

Spatial phase modulation in an imaging interferometer is utilized in surface plasmon resonance (SPR) based sensing of liquid analytes. In the interferometer, a collimated light beam from a laser diode irradiating at 637.1 nm is passing through a polarizer and is reflected from a plasmonic structure of SF10/Cr/Au attached to a prism in the Kretschmann configuration. The beam passes through a combination of a Wollaston prism, a polarizer and a lens, and forms an interference pattern on a CCD sensor of a color camera. Interference patterns obtained for different liquid analytes are acquired and transferred to the computer for data processing. The sensing concept is based on the detection of a refractive index change, which is transformed via the SPR phenomenon into an interference fringe phase shift. By calculating the phase shift for the plasmonic structure of SF10/Cr/Au of known parameters we demonstrate that this technique can detect different weight concentrations of ethanol diluted in water, or equivalently, different changes in the refractive index. The sensitivity to the refractive index and the detection limit obtained are −278 rad/refractive-index-unit (RIU) and 3.6 RIU, respectively. The technique is demonstrated in experiments with the same liquid analytes as in the theory. Applying an original approach in retrieving the fringe phase shift, we revealed good agreement between experiment and theory, and the measured sensitivity to the refractive index and the detection limit reached −226 rad/RIU and 4.4 RIU, respectively. These results suggest that the SPR interferometer with the detection of a fringe phase shift is particularly useful in applications that require measuring refractive index changes with high sensitivity.

干涉条纹相位锁定系统

干涉条纹相位锁定系统

Novel method of detecting movement of the interference fringes using one-dimensional PSD.

In this paper, a method of using a one-dimensional position-sensitive detector (PSD) by replacing charge-coupled device (CCD) to measure the movement of the interference fringes is presented first, and its feasibility is demonstrated through an experimental setup based on the principle of centroid detection. Firstly, the centroid position of the interference fringes in a fiber Mach-Zehnder (M-Z) interferometer is solved in theory, showing it has a higher resolution and sensitivity. According to the physical characteristics and principles of PSD, a simulation of the interference fringe’s phase difference in fiber M-Z interferometers and PSD output is carried out. Comparing the simulation results with the relationship between phase differences and centroid positions in fiber M-Z interferometers, the conclusion that the output of interference fringes by PSD is still the centroid position is obtained. Based on massive measurements, the best resolution of the system is achieved with 5.15, 625 μm. Finally, the detection system is evaluated through setup error analysis and an ultra-narrow-band filter structure. The filter structure is configured with a one-dimensional photonic crystal containing positive and negative refraction material, which can eliminate background light in the PSD detection experiment. This detection system has a simple structure, good stability, high precision and easily performs remote measurements, which makes it potentially useful in material small deformation tests, refractivity measurements of optical media and optical wave front detection.

Photothermal Imaging for Single Nanoparticle Using Single Element Interferometer

This article describes a method to detect an apparently magnified image of nanoparticles by the photothermal effect and using a single element interferometer for single biomolecule detection in the field of molecular biology. Nanoparticles can be detected by the photothermal effect which is converting light energy to thermal energy. The photothermal effect makes it possible to magnify an image of nanoparticles. Its image can be detected using a single element interferometer for robust detection and performing phase analysis based on the Fourier transform method for real-time detection. This article reports that the phase of interference fringe changed by the photothermal effect was obtained using the Fourier transform method to detect positions of carbon microparticles in video rate.

A surface plasmon resonance interferometer based on spatial phase modulation for protein array detection

Thousands of kinds of proteins exist in a single cell. Proteomics research aims to characterize these proteins and simultaneously analyse modifications and interactions on a large scale. Here we present a label-free surface plasmon resonance (SPR) imaging interferometer based on spatial phase modulation, which can be useful in this field. It consists of a light source, a SPR sensing unit, a special phase modulator, a photoelectric conversion unit and a computer. Collimated light is projected into a prism and reflected at the gold–glass interface. The p- and s-polarized components of the reflected light pass through a one-dimensional beam expander and a Wollaston prism, and form an interference pattern on a CCD. Interference images are acquired and transferred to the computer for data processing. Protein interaction on the gold surface leads to a local refractive index change and results in interference fringe phase shift. By calculating the phase shift, interaction information can be obtained. It is demonstrated that this technique can detect different concentrations of NaCl solutions, and the phase change generated by a 0.9% NaCl solution is about 10°. In protein–protein interaction experiments, a model system of rabbit IgG and goat–anti-rabbit IgG is tested. The maximum phase change is up to 12°. The phase resolution of the system is 0.2°, equivalent to the refractive index resolution of 3 × 10−5 RIU, and this value can be improved to 2 × 10−6 RIU just by increasing the gold thickness of the sensing chip. It is concluded that the sensitivity of the interferometer is enough to achieve larger capacity than that detected by the present protein micro-array products. These results suggest that the SPR interferometer based on spatial phase modulation provides a potential facility to meet the requirements in proteomics research.

Measurement of air turbulence for on-machine interferometry.

There is increasing demand for in situ shape measurements performed on ultraprecision processing machines. One major source of error during interferometric measurements performed on machines is fringe displacement due to external disturbances. We have developed an interferometer equipped with an electro-optic phase modulator that measures the phase of interference fringes before they are displaced by air turbulence. The frequency characteristics of air turbulence induced by a heat source are derived from successive measurements of a test surface. Experimental results show that the phase of the interference fringes can be accurately measured in the presence of air turbulence when the intensity of the fringes is sampled at a speed of several hundred hertz.

Interferometric-spatial-phase imaging for six-axis mask control

We describe a unified approach to measuring alignment and gap with nanometer detectivity between two planar objects (e.g., a mask and a substrate) in close proximity. The method encodes lateral position in the phase of interference fringes, formed by diffraction from grating and checkerboard alignment marks, designed to enable a wide acquisition range. For gapping, the method incorporates, in the same mark, coarse-gap detection (30–300 μm) and absolute-gap detection at sub-30 μm using a chromatic Fabry–Pérot scheme. Fine detection of sub-30 μm gaps is inferred from the frequency and phase of fringes, calibrated using the chromatic Fabry–Pérot. Illumination with a variable-bandwidth source enables either “achromatic” aligning or “chromatic” gapping. Sub-nanometer detection and feedback control of mask position is demonstrated in X, Y, and θ. Overlay of exposed patterns is demonstrated to be <3 nm.

Stellar polarimetry with SPIN (Spectro-Polarimetric INterferometry)

We propose to take benefit of optical aperture synthesis arrays to resolve local magnetic structures and patchy stellar surfaces. This requires to be able to polarimetrically resolve magnetic lines and thus to add a spectro-polarimetric device at the combined focus of an interferometric array. Within this instrumental context, it becomes possible to map magnetic fields thanks to fringe visibility and phase measurements in circularly polarized light and to map abundance inhomogeneities thanks to classical interferometric measurements ( i.e. without the polarimeter). This appears to be of great interest to better understand the key role of magnetism in atmosphere structuration, in ion migration across the stellar surface, in chemical stratification... In this talk we show how the interference fringe phase is the suitable observable for polarimetric measurements and for mapping patchy surfaces. We illustrate that on various typical cases of magnetic topology and abundance distribution of Chemically Peculiar (CP) stars. Finally we give some instrumental perspectives within the context of the optical interferometric arrays such as the VLTI.

The accuracy of the phase difference formula in holographic interferometry

According to the wave optical description of holographic interferometry, the visibility and the phase of interference fringes are strongly influenced by the aperture of the observing optical instrument. An extra term appears in the phase difference formula compared to the usual one calculated by the method of corresponding points of the undeformed and the deformed object surfaces. Neglecting this extra term could cause (especially at large deformations) a significant error in fringe pattern analysis — even as much as half a period of fringes. In this paper the existence of the extra phase term and its dependence on the aperture of the observing system has been proven experimentally. We have demonstrated that the extra phase term is a periodic function of the ratio of the object displacement to the focal depth of the viewing system. Further on, it has been shown that the visibility is periodic too, although with decreasing maxima. It has the same period as the extra phase term.

Joint transform correlator performing pure phase correlation for optical pattern recognition

Abstract A joint transform correlator, performing pure phase correlation by a phase spatial light modulator in the input to the second stage optical setup, is proposed. It can deliver excellent correlation performance in the presence of non-overlapping noise or additive noise. The proposed method extracts the interference fringe phase information from the joint power spectrum by simple subtraction and division operations; the extracted phase is then encoded onto a phase spatial light modulator to obtain the correlation results. To extract the fringe phasors, the proposed scheme uses an 50/50 beamsplitter and an λ/4 plate in the optical setup, and two CCDs to capture the joint power spectrum and the phase shifted joint power spectrum respectively. This system is found to be equivalent to correlation between only the Fourier phases of the reference and input images; however, there are practical difficulties in implementing this type of pure phase correlation using the VanderLugt architecture. Computer simulations show that the proposed joint transform correlator out-performs binary joint transform correlation, using the binarization methods of multilevel threshold function and adaptive windowing threshold, when the targets are embedded in either non-overlapping noise or scenes with additive noise; performance is maintained even when the target has a very low light contrast ratio in a severely noise corrupted input scene.

Joint transform correlator performing pure phase correlation for optical pattern recognition

Abstract A joint transform correlator, performing pure phase correlation by a phase spatial light modulator in the input to the second stage optical setup, is proposed. It can deliver excellent correlation performance in the presence of non-overlapping noise or additive noise. The proposed method extracts the interference fringe phase information from the joint power spectrum by simple subtraction and division operations; the extracted phase is then encoded onto a phase spatial light modulator to obtain the correlation results. To extract the fringe phasors, the proposed scheme uses an 50/50 beamsplitter and an λ/4 plate in the optical setup, and two CCDs to capture the joint power spectrum and the phase shifted joint power spectrum respectively. This system is found to be equivalent to correlation between only the Fourier phases of the reference and input images; however, there are practical difficulties in implementing this type of pure phase correlation using the VanderLugt architecture. Computer simul...

Immunity to signal degradation by overlayers using a novel spatial-phase-matching alignment system

We describe improvements to the interferometric broad-band imaging alignment scheme introduced in 1993. Alignment is signified by matching, across the midline of a charge-coupled device, the spatial phase of interference fringes formed by diffraction from complementary marks on mask and substrate. Image contrast is enhanced by back diffraction from hatched alignment marks on the substrate. Overlayers of resist, polysilicon, and aluminum have negligible effect on interferometric broad-band imaging alignment; they alter image contrast but not spatial phase. Novel alignment marks that incorporate four gratings increase the capture range to several tens of micrometers. By spatial filtering in the back focal plane of the alignment microscope, mask-sample gap may be determined from the resulting spatial phase shift. An alignment system for x-ray nanolithography (XLS-4) that incorporates the interferometric broad-band imaging scheme has been constructed.