Low-coherent light-source angular interferometer using a square prism and the angular-scanning technique

An interferometer based on using low-coherent light source, a square prism, and the angular-scanning technique is proposed for absolute angular-displacement determinations. An angular displacement of the square prism shifts the correlogram, which is modulated by an envelope function, of the interference signal of the beams passing through the prism. This angle can thus be discovered by detecting the shifting of the envelope peak. A setup constructed to validate the interferometer is used. The results of using this setup are then presented.     

Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach-Zehnder interferometer and amplitude gratings

An experimental system consisting of a Dove prism embedded Mach-Zehnder (M-Z) interferometer and two gratings was built to sort and detect orbital angular momentum (OAM) states of light beams. The helical beams with different OAM states were generated by propagating the fundamental-mode Gaussian beam through a spatial light modulator. The Dove prism embedded M-Z interferometer was used to sort helical beams with odd or even OAM number and two binary amplitude gratings were used to measure the OAM states. Sorting of coaxially-superposed coherent and incoherent helical beams with odd and even OAM states was realized in the experiment.     

Heterodyne interferometer scheme using a double pass in an acousto-optic modulator

We introduce a heterodyne interferometer scheme utilizing the double-pass arrangement of the deflected beams of an acousto-optic modulator. To prove our new idea, the interferometer has been applied for measuring small amplitude vibrations. The output intermediate frequency signal from the interferometer is processed by using an I/Q demodulator. In theory, it can provide the quantum noise limited sensitivity, whereas, in our present Letter, the sensitivity of the phase measurement is limited by the resolution of the 16?bit A/D converter used for processing the I/Q signals. Details of our interferometer scheme are discussed.     

Angular interferometer using calcite prism and rotating analyzer

An interferometer using a calcite prism and rotating analyzer is proposed for angular displacement determinations. The calcite prism senses the angular displacements and the rotating analyzer transfers the interference signals from dc-type into ac-type. Compact optical setup and using low-cost devices are thus the advantages of the interferometer. The theory of the interferometer is first demonstrated. A setup constructed to realize the interferometer and the results of using this setup are then presented.     

Shearing interferometer using low-coherent light source and calcite prism

A shearing interferometer using a low-coherent light source and calcite prism is proposed in this paper. The calcite prism is the shear plate that generates sheared wavefronts with optical-path difference induced only by the contour of the specimen. Low-coherent light source is thus available while the interferometer is adopted for contour derivative determinations. The design of this interferometer is introduced, a setup constructed to realize the interferometer is described, and the experimental results from the uses of the setup are finally presented.     

利用棱镜减小自衍射信号光角色散的研究

自衍射效应在飞秒激光领域有非常重要的应用,如提高飞秒脉冲的时域对比度、作为自参考光谱干涉脉冲测量法的参考光、作为频率分辨光学开关法的信号光等.然而,具有较宽光谱带宽的飞秒激光在自衍射效应过程中产生的信号光存在明显的角色散,这给自衍射效应的应用带来不利影响.本文研究发现通过在自衍射效应的一个光路中加入等腰直角棱镜,当到棱镜的入射角为23fi时可以明显地减小飞秒激光脉冲自衍射信号的角色散.这就为以后将自衍射效应更好的应用到飞秒激光脉冲的研究提供了有用的参考.     

Sub-50 nm patterning by immersion interference lithography using a Littrow prism as a Lloyd's interferometer

We present a simple setup that combines immersion lithography with a Lloyd's mirror interferometer. Aiming for smaller structure sizes, we have replaced the usual Lloyd's interferometer by a triangular Littrow prism with one metal-coated side, which acts as a mirror. Because of the higher refractive index of the prism, the wavelength and, thus, the attainable structure sizes, are decreased significantly. Using a laser with a wavelength of 244nm, we could produce line patterns with a period of less than 100nm and a width of 45nm. The introduced setup retains all the advantages of a Lloyd's mirror interferometer, in particular the flexibility in periodicity.     

Heterodyne interferometer with two spatial-separated polarization beams for nanometrology

An interferometer having accuracy in displacement measurement of <1 nm is necessary in nanometrology. To meet the requirement, the periodic nonlinearity mainly caused by polarization and frequency mixings should be less than deep sub-nanometer. In this paper, two spatial-separated polarization beams are used to avoid mixings and then the periodic nonlinearity. The developed interferometer demonstrates a periodic nonlinearity of about 25 pm and a 2 pm/Hz in displacement noise level.     

Optics design of a top-cut prism interferometer for holographic photonic quasicrystals

Optical interference holography has been proved to be a useful technique in fabricating periodic photonic crystals in which electromagnetic waves are forbidden in certain frequency band-gaps. Compared to periodic crystals, quasicrystals have higher point group symmetry and are more favorable in achieving complete band-gaps. In this report, a top-cut prism interferometer is designed and optimized for photonic quasicrystals. By changing the prism parameters and characteristics of different beams, different quasicrystalline structures can be obtained. At the same time, the diffraction patterns of the designed structures are also provided and reveal the ten-fold symmetry of the structures more clearly. Furthermore, the effect of the intensity threshold on the quasicrystalline structures is also investigated. This will provide guidance for the large-area and fast production of ten-fold quasicrystalline structures with high quality.     

Broadband light source shearing interferometer using Savart plate and angular scanning technique

A shearing interferometer based on using broadband light source, Savart plate, and angular scanning technique is proposed for slope contour measurements in this Letter. Of which, the Savart plate divides the wavefront reflected from the detected surface into two laterally displaced ones, the interference pattern generated by the interference of the divided wavefronts is modulated by an envelope function, and the slope contour of the detected surface is determined by examining the shifting of the darkest fringe as the shear plate is angularly scanned. A setup for realizing the interferometer is constructed. The experimental results of using this setup agree the validity and feasibility of the proposed interferometer.     

Heterodyne interferometer for submicroscopic vibration measurements in the inner ear

Conditions in the inner ear for interferometric measurements are quite different from those encountered in other mechanical systems: (i) The inner ear is not mechanically stable, due to blood pulsations and breathing artifacts; (ii) access to the inner ear is limited by anatomical constraints that make it difficult to visualize the structures of interest; (iii) vibration amplitudes to be measured in the inner ear are very low; (iv) the structures in the inner ear are nearly transparent; therefore, the reflectivity is low and attempts to change this reflectivity artificially usually alter the response characteristics; (v) cells are subject to light damage if the incident light intensity is too high, which limits the laser power that can be utilized in the interferometer. A heterodyne interferometer specially designed to measure vibrations in the living inner ear is described. Theoretical and experimental characteristics of this instrument are discussed in detail. In contrast to the homodyne system, the measurement accuracy of this interferometer is not affected by the low-frequency animal movements. This system does not require attachment of a reference mirror to the animal, thereby providing an unobstructed view of the structure to be measured. It has a high linearity and dynamic range. Its vibration sensitivity is high (2.8 X 10(-13) m for 1-Hz bandwidth) even under the condition of low light reflectivity (0.02%), with 0.5-mW incident laser power.     

Multi-directional lateral shearing interferometer based on rotatable prism pairs

The common camera lens usually includes the spherical glass/plastic lens and aspheric glass/plastic lens. However, spherical/aspheric shape measurement is still a key problem in the process of optical lens fabrication. At present, the in-process measurement of spherical/aspheric shape is conducted mainly by the probe-contacting method. But after a long time, its probe could be scratched severely and cause some big errors. Laser shearing interferometry is a good substitute to some degree. Nevertheless, it is not convenient for general shearing interferometer to carry out the in-process measurement because it is only suitable for certain kind of spherical/aspheric with respect to aperture or asperity. Here a new lateral shearing interferometer is proposed to solve the described problems. It is based on two Jamin plates and rotatable prism pairs which are used not only for shearing displacement and direction, but also for fringe period and tilt degree, in order to meet requirements of various spherical/aspheric shapes or asperities. The new interferometer features a simple optical structure and two symmetric light paths, which makes its system with minimal error. The relation between shearing displacement, fringe period and prism angle of rotation is given in this paper. And the error source is primarily from the manufacture errors of prisms and plates. The final experiments show that one can achieve good-quality fringe patterns according to the requirement of measurement, concerning the shearing direction, shearing displacement, fringe period, tilt degree, etc.     

Heterodyne interferometer for displacement measurement with amplitude quadrature and noise suppression

The high precision displacement measurement in nanoscale is crucial to many applications. We present a heterodyne interferometry with differential phase to amplitude conversion scheme for displacement measurement in nanoscale. In this approach, the differential phase introduced by the displacement is converted into the amplitudes of heterodyne signals in quadrature. Meanwhile, the heterodyne signals in phase quadrature are also achieved so that the displacement can be determined from the amplitude ratio of the quadrature signals, and the direction of displacement can be determined from the phase quadrature. Since the differential phase to quadrature amplitude conversion is achieved through the optical addition and subtraction by polarization tuning, which are based on differential detection concept. Thus the proposed method benefits from the features of differential detection with common phase noise and correlated amplitude noise rejection and that of quadrature detection with real time and wide dynamic range of phase measurement. To demonstrate the capability of proposed method in differential phase measurement, we measure the displacement drove by a commercially available PZT pusher and found close agreement between the experiment and the theory. The experimental evidence of noise suppression is also found with spectral measurements, which demonstrates the resolution of displacement measurement at 60 pm and minimum detectable differential phase of 5.6 × 10⁻⁶ rad/ over 50 kHz.     

Visualization of flow past a square prism with cut-corners at the front-edge

Flow past a square prism with cut-corners at the front-edge is numerically and experimentally visualized to investigate a mechanism of drag reduction. An adaptive numerical scheme based on the vortex method is implemented for two values of the Reynolds number between 200 and 1,250, and the results are compared with experiments. Experimental visualization techniques include the hydrogen-bubble technique atRe=4,000 and the oil-flow technique atRe=10,000 for a global wake formation, and the aluminum-flake technique for transient flow at the early stage of motion atRe=1,250. A similar reattachment flow pattern is shown in a wide range of the Reynolds number between 200 and 10,000, which implies a possibility of the drag reduction in the Reynolds number being approximately lower than 8,000 unlike the previous findings.     

X-ray spectrum determination from the angular dispersion of radiation in a diamond prism

The X-ray spectrum of hard polychromatic radiation with energies of up to 40 keV was obtained from the angular dispersion of the radiation beam in a diamond prism. In contrast to the classical optical scheme, the beam to be analyzed is passed through the entrance face of the prism without refraction and is directed onto the exit face at a glancing angle ～(2δ)^1/2, where δ is the real part of the decrement of the refractive index for the short-wavelength edge of the spectrum. The spectrum distortions caused by the intersection of the reciprocal lattice points by the Ewald sphere at a fixed number of wavelengths λ are minimized by the use of the angular divergence of the beam of ～10′ in the plane perpendicular to the refraction plane. In the energy range of 8–9 keV, an energy resolution of less than 100 eV was obtained, which exceeds the corresponding parameter for cooled semiconductor detectors. The measuring scheme suggested makes it possible to solve the problem of the analysis of spectra of directional X-ray beams when studying fast nonstationary generation processes.     

Phase-difference amplification using a Sagnac interferometer

In this paper, we describe a new method for achieving phase-difference amplification, which is quick and convenient, operates in real time, and requires no photographic steps. Magnification factors of 2, 4 or 6 are achieved easily in one step. Because the system operates in real time, phase stepping may be applied to extract the amplified phase distributions. Our method is a variation on longitudinally reversed shearing interferometry, using first- or higher-order diffraction from a grating (hologram) which is in fact the interferogram of the wavefront under test. The grating is derived from a standard two-beam interferometer which is phase-stepped, and displayed in real time on a spatial light modulator in the phase-difference amplification setup. It is illuminated by the two output beams from a Sagnac interferometer, similar to the set up used by (Barnes et al. Barnes TH, Eiju T, Matsuda K. Appl Opt 1986; 25:1864). for spectral resolution enhancement, and a phase-amplified fringe pattern is obtained by spatial filtering using a Fourier transform lens. We demonstrate operation of the phase amplifier and show amplified phase maps retrieved by phase-stepping. We believe this is the first time that real-time phase amplification without photographic steps and with phase stepping has been demonstrated.     

Lensmeter using a lateral shearing interferometer

The use of a laser shear interferometer for checking the collimation condition within a lensmeter is proposed. The interferometer consist of a wedged glass plate which produces a shear along the orthogonal direction to the wedge; when the fringes at the center of the pattern are parallel to the shear, the collimation condition is attained. The feasibility of the proposal for measuring the vertex power is experimentally shown and the accuracy of the method is under 5% of the measured value being an improvement to the commercial instruments based on the focusing of a reticule.     

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0×10⁻⁴ corresponding to 1 °C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10⁻⁸ rad.     

Speckle shearing interferometer using a Savart plate

We describe a speckle shearing interferometer using a Savart polariscope. The purpose of this interferometer is to obtain the derivative of the out-of-plane displacement suffered by a scattering surface when put under stress. This information is useful to know the bending moments. The setup is compact, very stable, and does not require any stringent adjustment.     

Three-dimensional coordinate measurements using a multiple-pinhole interferometer

We propose a method for noncontact measurements of three-dimensional (3D) coordinates based on a Y-typed multiple-pinhole (MP) interferometer and demonstrate its feasibility in experiments. In this method, a Y-typed MP plate is inserted between the target and an image sensor to form a common-path interferometer. The 3D coordinates of the target are found by an effective algorithm using the discrete phase values on the measurement pinholes of the MP plate. These phase values can be directly extracted from a Fourier transform of the recorded intensity pattern without need of any iterative or phase-shifting algorithm. The method could be significant in real-time coordinate measurements and position tracking applications.