Asphere testing with a Fizeau interferometer based on a combined computer-generated hologram

Fizeau interferometers with an additional diffractive optical element are frequently used for measuring spherical and aspherical surfaces. We present a new (to our knowledge) optical test method, in which the Fizeau principle is now perfectly fulfilled by generating reference and measuring wavefront on the last optical surface, which carries a diffractive optical element. This method has been examined experimentally by testing a reference f/0.68 spherical mirror and can be applied identically for testing aspheres. Several advantages of this method are discussed and proved experimentally.     

Autonomous calibration method of the reference flat surface of an interferometer without using a standard flat surface

An autonomous method for calibrating the reference flat surface of an interferometer is proposed with the uncertainty analysis. The method consists of three phases; the first step is multiple rotating shifts of a specimen, the second is a linear shift, and the last is multiple rotating shifts again. The profile of the reference flat surface is basically determined by the linear shift. The linear shift errors that occurred during the linear shift are identified by the rotating shifts. The rotating shift errors caused by the rotating shifts can be compensated and the residual uncertainty can be reduced in proportion to the square root of the number of rotating shifts per one revolution. Finally, the uncertainty analysis is carried out in detail.     

Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile

The spectrum of the intensity profile of multiple-beam Fizeau interferograms is presented. Knowledge of this spectrum provides valuable information about the characteristics of Fizeau interferograms, allowing one to calculate the phase error when the Fizeau profile is evaluated by means of two-beam phase-stepping algorithms, as is usual for low-reflectivity coefficients.     

Wind-velocity lidar measurements by use of a Mach-Zehnder interferometer, comparison with a Fabry-Perot interferometer

We present the first wind-velocity profiles obtained with a direct-detection Doppler lidar that uses a Mach-Zehnder interferometer (MZI) as spectral discriminator. The measurements were performed in the lower stratosphere, between 10 and 40 km in altitude, at the Observatoire de Haute Provence (OHP), France, during nighttime. They are in excellent agreement with those obtained simultaneously and independently with the already validated double Fabry-Perot interferometer (FPI) of the OHP Doppler lidar (mean difference lower than the combined standard deviation). A statistical analysis shows that the random error obtained with this experimental MZI is 1.94 times the Cramer-Rao lower bound and is approximately half of that given by the FPI (both operating in photometric mode). Nevertheless, the present MZI measurements are sensitive to the presence of atmospheric particles and need an additional correction, whereas the OHP FPI is designed to be insensitive to particulate scattering.     

Evaluation of Measurement Uncertainty for Absolute Flatness Measurement by Using Fizeau Interferometer with Phase-Shifting Capability

It is important to precisely measure flatness of the optical flats, as many industries use these as reference standards to ensure the quality of precision measurements and fabricated components. This paper describes identification of sources of error and measurement uncertainty evaluation for three flat test. Three flat test is used for absolute flatness measurement of optical flats, with the help of Fizeau interferometer (VerifireXP/D, with phase shift interferometry) established recently at National Physical Laboratory, India (NPL-I). The absolute profile of reference flat with higher accuracy can be determined using liquid level reference but liquid flat reference is more difficult to realize practically. Therefore three flat test is frequently adopted in standard interferometric measurements and traceability of this test can also be established by using a traceable laser head. This paper describes three flat method in detail along with observations and evaluation of measurement uncertainty as per ISO GUM is also done. Factors contributing to uncertainty of measurement of surface flatness have been indentified and detailed evaluation of uncertainty in measurements has been reported here.     

Measurement of the refractive-index profile of planar waveguides by the use of a double Lloyd's interferometer

We present a nondestructive experimental method to measure monotonically varying refractive-index profiles of planar waveguides. The technique is a modification of the Lloyd's mirage setup proposed by Allman et al. [Appl. Opt. 33, 1806 (1994)] in order to have a reference phase distribution for the interference pattern. The theoretical calculations have been implemented to account for multiple reflections inside the sample. An application of the method to ion-exchanged glass waveguides is reported.     

Measurement of absolute displacement by a double-modulation technique based on a Michelson interferometer

A novel method is presented for of measuring absolute displacement with a synthesized wavelength interferometer. The optical phase of the interferometer is simultaneously modulated with a frequency-modulated laser diode and optical path-length difference. The error signal originating from the intensity modulation of the source is eliminated by a signal processing circuit. In addition, a lock-in technique is used to demodulate the envelope of the interferometric signal. The displacement signal is derived by the self-mixing technique.     

Measurement of gas-phase temperatures in flames with a point-diffraction interferometer

Experiments were performed to evaluate the performance of a point-diffraction interferometry (PDI) system to measure gas-phase temperatures in flames. PDI is an interferometric technique that creates the reference beam after the laser beam passes through the test section and directly provides the index of refraction in two dimensions. PDI-based temperature measurements were compared with thermocouple measurements of two-dimensional and axisymmetric thermal boundary layers, as well as two-dimensional and axisymmetric diffusion flames. The PDI system provided excellent agreement in the measurement of thermal profiles in the boundary layers and was within the uncertainties that are due to the radiation corrections for the thermocouple-based flame temperature measurements.     

Measurement of two-dimensional small angle deviation with a prism interferometer

A new technique for the measurement of two-dimensional small angular deviation is presented. A compound prism, which effectively produces a combination of two right-angled prisms in orthogonal directions, and plane reference surfaces have been utilized for the measurement of the orthogonal components of the angular tilt of an incident plane wavefront. Each orthogonal component of the angular tilt is separately measured from the angular rotation of the resultant wedge fringes between two plane wavefronts generated due to splitting of the incident plane wavefront by the corresponding set of right-angled prism and plane reference surface. The technique is shown to have high sensitivity for the measurement of small angle deviation. A monolithic prism interferometer, which is practically insensitive to vibration, is also proposed. Results obtained for the measurement of a known tilt angle are presented.     

Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer

A phase-stepped double-grating lateral shearing interferometer to be used for wave-front analysis is presented. The resulting interference patterns are analyzed with a differential Zernike polynomial matrix-inversion method. Possible error sources are analyzed in the design stage, and it is shown that the inaccuracy can be kept within 2-5 mλ rms. The apparatus was tested and evaluated in practice. Comparison with a phase-stepped Twyman-Green interferometer demonstrates that the accuracy of the two methods is comparable. Lateral shearing interferometry scores better on reproducibility, owing to the stability and robustness of the method.     

Rotation angle measurement based on white-light interferometry with a standard optical flat

We propose a simple white-light interferometric method of measuring a one-dimensional rotation angle with use of an optical plane parallel plate of standard refractive index. The phase change of the interference pattern of the interferometer during the rotation of the flat plate of known refractive index and thickness placed in one of the interferometer's arms is used for determination of the rotation angle. This method has been demonstrated for an accurate angle measurement over the angle range from 0° to 40° within a maximum uncertainty of 0.057°.     

Analysis of the enhancement of backscattering by nonspherical particles with flat surfaces

We examine backscattering by analyzing large nonspherical particles with flat surfaces for which where the size is much larger than the wavelength, using ray optics and diffraction theory. We show that the backscattering cross section for rectangles can be 1 order of magnitude larger than that for spheres with same geometrical cross sections, depending on the orientation of the particles. Then we show that there is a difficulty in estimating the backscattering cross section for hexagonal columns with the available solutions but that it is possible to estimate the integration of the differential scattering cross section over small solid angles in backward directions. The integral values for hexagonal columns are found to be more than 1 order of magnitude larger than that for spheres with the same volume. As an application, the use of power from hexagonal columns for lidar observations is analyzed. Unlike for spherical particles with their dependence on Z(-2) (where Z is the distance between the particle and the detector), for nonspherical particles such dependence varies with the particles' nonsphericity, such as shape and orientation: Z(0) for a hexagonal plate randomly oriented in the horizontal plane; Z(-1) for a hexagonal column randomly oriented in the horizontal plane.     

Measurement of small vibration amplitudes of a rough surface by an interferometer with a self-pumped phase-conjugate mirror

The application of a Michelson interferometer with a self-pumped phase-conjugate mirror to measure small vibration amplitudes of a rough surface is described. The distorted wave front of the light that is diffusely reflected from the rough surface is restored by phase conjugation to provide an interference signal with a high signal-to-noise ratio. The vibration amplitudes of a stainless-steel sample are measured with a precision of ~5 nm.     

Magnetohydrodynamic stability of boundary layers along a flat plate with pressure gradient

Summary The purpose of the paper is to consider theoretically the characteristics of steady two-dimensional magnetohydrodynamic boundary layer flow past a flat plate with pressure gradient in the presence of transverse magnetic field and its stability problem. The boundary layer equation is transformed into a non-similar one and numerical solutions are obtained by the difference-differential method. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity profiles obtained above. Numerical results for the magnetic parameter and pressure gradient parameter are given for the velocity profiles, coefficient of skin friction, displacement thickness and the critical Reynolds number.With 10 Figures     

Separation of DNA with different configurations on flat and nanopatterned surfaces

We demonstrate that electrophoresis on a flat Si substrate is an effective method in separation of DNA with different configurations, e.g., linear, supercoiled, and relaxed or DNA of different length, e.g., supercoiled DNA ladder. The surface separation arises from the different number of contacts due to the conformational differences between adsorbed DNA chains. Imposing a Au nanopattern on the Si surface further improves the separation effect. The simulation of electric field on this patterned surface by the finite element method shows that Au nanodots act as local pinning points for DNA segments due to dielectrophoretic force. The results of molecular dynamics simulation showed that the conformational differences between adsorbed polymer chains were amplified on the patterned surface and enhanced separations were achieved, which are consistent with the experimental results.     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer

A principal scheme for an external cavity technique for changing the polarization of a laser beam based on a modified Sagnac interferometer is proposed. The modified Sagnac interferometer includes standard optical components: a displacement polarizing beam splitter, an angle reflector, and a Dove prism. The radially polarized beams, obtained with the help of the developed scheme, allow the generation of a longitudinally polarized electric field by sharp focusing. The phase correction of radially polarized modes of higher orders leads to increasing the longitudinal field in the focus of the beam.