Holographically recorded axicon for grazing incidence interferometry

Abstract

A diffractive axicon for grazing incidence interferometry of cylindrical objects is presented. For industrial measurement, an element with a diameter of 8 cm was manufactured. The axicon was recorded in dichromated gelatine (DCG) with a high-precision rotating stage. The diffraction theory for the design of the element is presented. The axicon was tested interferometrically. Some possible errors are discussed.     

Phase-step calibration for phase-stepped interferometry

A novel method to set the proper phase steps, as used in phase-stepped interferometry, is presented. It is indicated how and when this method can be used. With only two images one can deduce the relative phase step between them by calculating the correlation between the two images. The error of the proposed method is shown to be smaller than 0.1%.     

Absolute distance measurement by two-point-diffraction interferometry

We present a point-diffraction interferometer that has been specially devised to perform absolute distance measurements in three dimensions. It is composed of two main parts: One is a target that moves in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The target is made of point-diffraction sources that emit two spherical wave fronts, whose interference is monitored by the photodetectors. Application of a phase-shifting technique allows the phase values of the photodetectors to be precisely measured, which are then fitted to a geometric model of multilateration so as to determine the xyz location of the target by minimization of least-squares errors. Experimental results show that the proposed diffraction interferometer is capable of measuring the xyz coordinates of the target with a volumetric uncertainty of less than 1.0 microm over a working volume of a 100-mm side.     

Phase-shift calibration algorithm for phase-shifting interferometry

We propose a novel phase-shift calibration algorithm. With this technique we determine the unknown phase shift between two interferograms by examining the sums and differences of the intensities on each interferogram at the same spatial location, i.e., I1(x, y) +/- I2(x, y). These intensities are normalized so that they become sinusoidal in form. A uniformly illuminated region of the interferograms that contains at least a 2pi variation in phase is examined. The extrema of these sums and differences are found in this region and are used to find the unknown phase shift. An error analysis of the algorithm is provided. In addition, an error-correction algorithm is implemented. The method is tested by numerical simulation and implemented experimentally. The numerical tests, including digitization error, indicate that the phase step has a root-mean-square (RMS) phase error of less than 10(-6) deg. Even in the presence of added intensity noise (5% amplitude) the RMS error does not exceed 1 deg. The accuracy of the technique is not sensitive to nonlinearity in the interferogram.     

Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry

Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.     

Absolute calibration of accelerometers at high frequencies

This paper describes the calibration of commercial accelerometers with mass load by laser interferometry at frequencies ranging from 2 kHz to 10 kHz. It is shown by experiment that the effect of mass load on the frequency response of commercial accelerometers with inverted centre mounted compression design is negligible. The comparison method adopted by some foreign companies has been analysed and the relative motion between the top of the mass load and the upper surface of a commercial accelerometer has been measured, thus explaining the obvious errors in frequency response curves obtained by using the comparison method.     

Primary calibration of ultrasonic hydrophone using optical interferometry

A primary calibration method for ultrasonic hydrophones which uses a Michelson interferometer to determine the particle displacement in an ultrasonic field is discussed. The acoustic pressure is derived from this measurement and used to determine the free-field sensitivity of a hydrophone in the frequency range 0.5-15 MHz. The random uncertainty of the method is typically 1%, whereas the systematic uncertainty varies from 2.3 to 6.6% over the frequency range. To obtain this accuracy, the performance of the system has been carefully examined and appropriate correction factors derived. The greatest difficulty in the method lies in determining the frequency response of the optical detection system, and two different approaches have been used to measure this response. Several acoustical effects have also been studied and the calibration procedure modified to take account of them. The calibration results are in agreement with those of other methods and with the theoretically predicted frequency response of a hydrophone. The method has been used to determine the temporal stability of a hydrophone over a period of two years.     

Oblique incidence and observation electronic speckle-pattern interferometry

In this paper we discuss an oblique incidence and observation electronic speckle-pattern interferometer, in which we use an anamorphic prism in front of the object. A collimated beam traveling through the prism is partly reflected at the base of the prism. The reflected light is the reference beam and the transmitted light illuminates the diffuse object, thereby generating the object beam. In this scheme the object and the reference beams are collinear. A new scheme that uses two prisms and permits phase stepping is also presented.     

Pulsed single-mode laser in four-arm grazing incidence cavity

Abstract

A four-arm grazing-incidence cavity (GIC) is demonstrated. It ensures stable single-mode operation in a pulsed-laser system by interferometrically enhancing mode selection; the corresponding standard GIC operates on five modes. We compare the four-arm GIC with the standard GIC and with two other multiple-arm GICs and show that it gives the best overall performance in terms of mode selectivity and threshold. An analysis has been developed that allows cavity parameters to be optimized for mode selection. The analysis has been verified experimentally.     

Absolute interferometric testing based on reconstruction of rotational shear

A method, believed to be new, for the absolute interferometric testing of flat or spherical surfaces is presented. It is based on the classic three-flat test, combined with additional measurements of one test piece in different rotational positions. Full-surface absolute maps for each test piece are determined with a data-processing technique based on the rotationally sheared maps of the rotated surface. An optimized numerical reconstruction algorithm employing linear filtering and superposition of the different rotational shear spectra in the angular frequency domain is used to reconstruct the rotationally sheared data. The technique does not require any assumptions about the surfaces under test; has low error propagation, even in the case of high spatial resolution; and is computationally efficient.     

Absolute calibration of a geodetic time transfer system

An absolute calibration technique is developed for geodetic Global Positioning System (GPS) receivers. An uncertainty budget for the system (receiver, cables, connectors, antenna) is evaluated, yielding 1.1 ns at each frequency, and 1.6 ns for a two-receiver experiment. Analysis of data on a short baseline yields 0.8 and 1.2 ns agreement on P1 and P2, respectively.     

Absolute interferometry with a 670-nm external cavity diode laser

In the past few years there has been much interest in use of tunable diode lasers for absolute interferometry. Here we report on use of an external cavity diode laser operating in the visible (lambda ~ 670 nm) for absolute distance measurements. Under laboratory conditions we achieve better than 1-mum standard uncertainty in distance measurements over a range of 5 m, but significantly larger uncertainties will probably be more typical of shop-floor measurements where conditions are far from ideal. We analyze the primary sources of uncertainty limiting the performance of wavelength-sweeping methods for absolute interferometry, and we discuss how errors can be minimized. Many errors are greatly magnified when the wavelength sweeping technique is used; sources of error that are normally relevant only at the nanometer level when standard interferometric techniques are used may be significant here for measurements at the micrometer level.     

Miniature Auger spectrometer with grazing incidence electron beam

The construction of a miniature Auger electron spectrometer is presented. The instrument is equipped with an electron gun of grazing incidence electrons and miniature retarding field analyser (RFA). Grazing electron beam of up to 3 keV as an excitation toll provides enhanced sensitivity to the top-most surface layer. Good energy resolution was achieved thanks to the aperture placed in the centre of curvature of the RFA. Combined with a normal electron beam spectrometer the system can provide valuable information about spatial distribution of atoms or molecules at probed surface layers. The example spectra obtained for a few substrate/adlayer systems measured by both grazing and normal electron beam spectrometers are presented. It is suggested that the differences in the relative signal amplitudes can answer the question which components are located at (or protrudes from) the top surface layer of the probed sample.     

Absolute calibration of accelerator beam energies by the crossover technique

An absolute method for the determination of the energy of a charged particle beam is described. The method is based on 0423 0450 V 2 scattering kinematics and exploits the variation with angle of the energy of particles scattered by elastic and inelastic processes 0423 0450 V 3 from different target nuclei. A determination of the angle at which particles scattered by two different reactions have the same 0423 0450 V 3 energy allows a precise calculation of the energy of the incident ion beam if the relativistic corrections are taken into account. A 0423 0450 V 3 simple system capable of supplying an absolute and accurate information on the beam energy in a short time has been designed and 0423 0450 V 3 tested. The system allows beam energy determinations over a wide energy range, from a few MeV up to several tens MeV and is not limited to some energy values in particular, in contrast with the use of resonance or threshold reactions. The system can in particular be employed for the calibration of accelerator beam energies in the energy interval typical of medium-energy commercial 0423 0450 V 3 cyclotrons, an increasing number of which are in operation in industry and in many fields of applied research. The paper briefly illustrates the theory underlying the “crossover” technique, describes the experimental apparatus and procedure and reports on experimental results for 12–36 MeV protons. The correction factors to be considered to fully exploit the accuracy of the technique 0423 0450 V 3 are discussed. The application of the method to the energy calibration of beams of deuterons and helium ions is described. A secondary and faster calibration procedure is also reported. This is derived from the main technique and can be routinely used once a number of energies have been determined and a sufficient data base of energy values has been built up. It is demonstrated that this secondary method is almost as accurate as the main technique.