The co-phasing detection method for sparse optical synthetic aperture systems

Co-phasing between different sub-apertures is important for sparse optical synthetic aperture telescope systems to achieve high-resolution imaging.For co-phasing detection in such a system,a new aspect of the system’s far-field interferometry is analysed and used to construct a novel method to detect piston errors.An optical setup is built to demonstrate the efficacy of this method.Experimental results show that the relative differences between measurements by this method and the criterion are less than 4%,and their residual detecting errors are about 0.01 λ for different piston errors,which makes the use of co-phasing detection within such a system promising.     

Phase-stepping interferometry: Five-frame algorithm with an arbitrary step

The present paper offers a new formula for calculating the phase in interferometric measurements by the phase-stepping method. The proposed five-frame algorithm utilizes equal phase steps with an arbitrary value. Results are presented on computer simulation of the errors occurring at a phase-step different from 90 ° and due to vibrations in the system ‘interferometer-object’.     

Measurement of thermal conductivity of fluids using 3-<Emphasis Type="Italic">ω</Emphasis> method in a suspended micro wire

A thermally controlled, compact device employing the 3-ω technique, used to measure the thermal conductivity of fluids, is designed, developed, and presented in this paper. The 3-ω method, which analyzes temperature oscillations data in the frequency domain, requires a microscopic sample and extremely low heating power. The functionality is derived from the approximate solutions of temperature oscillations of a line heater based on the infinite line-heater model over an empirically and analytically chosen range of frequencies. The method is devoid of errors related to transient measurements, fluid thermal stratification and mobility errors, which pose difficulties in other methods. A platinum (99.99% pure) wire of 50 μm diameter and a length of 30 mm, suspended in a sample volume of 25 μl of the test fluid, serves simultaneously as the heater and thermometer. Structure-wise, the device is designed to support measurements over a range of temperatures and fluid pressures providing modularity and flexibility to the instrument. The device is successfully employed to measure the thermal conductivity of de-ionized water for temperatures between 15 and 35°C with an accuracy of ±1.2% inmeasurement.     

A comparison of 2D and 3D PIV measurements in an oblique jet

A stereo PIV (SPIV) acquisition and analysis system was developed to measure three velocity components in planar flow fields. The analysis software is based on a third order mapping function method. The system was calibrated by imaging a square grid in three measurement planes with two Kodak Megaplus cameras oriented at 30 to the bisector between them. The camera images were dewarped into real coordinates by employing a set of transform matrices computed for each calibration plane. Bias and rms errors were determined by comparing displacements measured directly with displacements estimated from the dewarping and recombination algorithm. The bias errors in the directions parallel with the measurement plane were negligible while the bias in thez direction was about 0.6 pixel. The rms errors, 0.2–0.3 pixels, were largest in thez direction. These errors were thought to result from limitations in the calibration method. The SPIV system was tested in a two-dimensional oblique jet with Reynolds number of 1800. The three dimensional results were taken in a vertical (x, y) plane parallel with the jet span. The SPIV results were compared with LDV data and two-dimensional PIV data obtained in a vertical (y, z) plane of the same jet. The SPIV measurements yielded accurate values for the in-plane mean and rms velocity components. The measured out-of-plane mean component was underestimated due to the bias error mentioned above. The rms component was accurate in part of the field but overestimated in another part due to local variations in rms error. It is expected that in the future, the out-of-plane errors can be minimized by improving the calibration and transformation procedures.     

Errors in the Measurement of Cross-Correlated Relaxation Rates and How to Avoid Them

Cross-correlated relaxation rates Γ are commonly obtained from constant time experiments by measuring the effect of the desired cross-correlated relaxation on an appropriate coherence during the constant time T. These measurements are affected by systematic errors, which derive from undesired cross-correlated relaxation effects taking place before and after the constant time period T. In this paper we discuss the sources and the size of these errors in an example of two pulse sequences. Higher accuracy of the measured data can be obtained by recording a set of experiments with different T values. Cross-correlated relaxation rates are measured in constant time experiments either from the differential relaxation of multiplet components (J-resolved Γ experiments) or from the efficiency of magnetization transfer between two coherences (quantitative Γ experiments). In this paper we calculate analytically the statistical errors in both J-resolved and quantitative Γ experiments. These formulae provide the basis for the choice of the most efficient experimental approach and parameters for a given measurement time and size of the rate. The optimal constant time T for each method can be calculated and depends on the relaxation properties of the molecule under investigation. Moreover, we will show how to optimize the relative duration of cross and reference experiments in a quantitative Γ approach.     

The photonical, pure grid method

The paper presents an introduction on the pure grid method for deformation measurements in experimental mechanics. The pure grid method involves that the grid images are processed separately, and subsequently the results of these separate processings are substrated from each other in order to obtain a quantified deformation indication.The recording and processing of the grid images are currently performed photonically by means of digital image measurement systems. The basic data processing relations and set-ups of four different applicabilities of the photonical, pure grid method are presented in this paper. The applicabilities are discussed. Strains can be measured with errors smaller than 200 micro strain and displacements with errors smaller than of the diameter of the object as visible in the grid image. These figures can be improved substantially by future application of high resolving-power CCD cameras. Two examples are shown. The paper also contains an extensive bibliography for further explorations.     

Improving the accuracy of the n-dB method for determining damping of non-lightly damped systems

Damping measurements using the spectral magnitude remain popular and are studied here for non-lightly damped systems using the variable bandwidth n-dB method, which is advantageous for non-lightly damped systems. The most commonly used estimator (based on normalised bandwidth) provides significant errors for non-lightly damped systems. An existing more accurate method (using the squares of the frequencies used in the former method) is exact for hysteretic damping, but still provides significant error for viscous damping. Improved estimators are developed in order to correct either exactly, or to insignificant errors, measurements taken with existing estimators. Neither further data nor the individual frequencies are required; the previously calculated damping values are corrected. The application of the improved estimators is dependent upon the existing estimator used and the damping type; however a strategy is suggested to reduce errors if the latter is unknown.     

QED radiative correction for the single-W production using a parton shower method

A parton shower method for the photonic radiative correction is applied to single W-boson production processes. The energy scale for the evolution of the parton shower is determined so that the correct soft-photon emission is reproduced. Photon spectra radiated from the partons are compared with those from the exact matrix elements, and show a good agreement. Possible errors due to an inappropriate energy-scale selection or due to the ambiguity of the energy-scale determination are also discussed, particularly for the measurements on triple gauge couplings. Received: 22 February 2001 / Published online: 11 May 2001     

Optimizing and characterizing grating efficiency for a soft X‐ray emission spectrometer

The efficiency of soft X‐ray diffraction gratings is studied using measurements and calculations based on the differential method with the S‐matrix propagation algorithm. New open‐source software is introduced for efficiency modelling that accounts for arbitrary groove profiles, such as those based on atomic force microscopy (AFM) measurements; the software also exploits multi‐core processors and high‐performance computing resources for faster calculations. Insights from these calculations, including a new principle of optimal incidence angle, are used to design a soft X‐ray emission spectrometer with high efficiency and high resolution for the REIXS beamline at the Canadian Light Source: a theoretical grating efficiency above 10% and resolving power E/ΔE > 2500 over the energy range from 100 eV to 1000 eV are achieved. The design also exploits an efficiency peak in the third diffraction order to provide a high‐resolution mode offering E/ΔE > 14000 at 280 eV, and E/ΔE > 10000 at 710 eV, with theoretical grating efficiencies from 2% to 5%. The manufactured gratings are characterized using AFM measurements of the grooves and diffractometer measurements of the efficiency as a function of wavelength. The measured and theoretical efficiency spectra are compared, and the discrepancies are explained by accounting for real‐world effects: groove geometry errors, oxidation and surface roughness. A curve‐fitting process is used to invert the calculations to predict grating parameters that match the calculated and measured efficiency spectra; the predicted blaze angles are found to agree closely with the AFM estimates, and a method of characterizing grating parameters that are difficult or impossible to measure directly is suggested.     

Statistical and systematic errors in Monte Carlo sampling

We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the bin length (size of the statistical sample), both at and away from a phase transition. The formalism is tested using simulations of thed=3 Ising model at the infinite-lattice transition temperature. We show that for a 96×96×96 system noticeable systematic errors (systematic underestimation of response functions) are still present for total run lengths of 10⁶ Monte Carlo steps/site (MCS) with measurements taken at regular intervals of 10 MCS.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.     

Integrating nephelometer performance in fog and thick Haze

Summary In fogs and thick hazes integrating-nephelometer measurements are affected by the angular truncation error due to the integration of the atmospheric scattering function on a truncated angular range. A method of experimental investigation on the actual consequences of this error is exposed. Equations that take into account both truncation error and photometric systematic errors are proposed and validated through a field comparison by nephelometer and transparency measurements. It is shown that the integrating nephelometer can substitute the transmissometer in all visibility conditions if photometric errors are avoided. Paper presented at the 1° Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.     

The effect of out-of-plane motion on 2D and 3D digital image correlation measurements

The effect of out-of-plane motion (including out-of-plane translation and rotation) on two-dimensional (2D) and three-dimensional (3D) digital image correlation measurements is demonstrated using basic theoretical pinhole image equations and experimentally through synchronized, multi-system measurements. Full-field results obtained during rigid body, out-of-plane motion using a single-camera vision system with (a-1) a standard f55mm Nikon lens and (a-2) a single Schneider–Kreuznach Xenoplan telecentric lens are compared with data obtained using a two-camera stereovision system with standard f55mm Nikon lenses.Results confirm that the theoretical equations are in excellent agreement with experimental measurements. Specifically, results show that (a) a single-camera, 2D imaging system is sensitive to out-of-plane motion, with in-plane strain errors (a-1) due to out-of-plane translation being proportional to ΔZ/Z, where Z is the distance from the object to the pin hole and ΔZ the out-of-plane translation displacement, and (a-2) due to out-of-plane rotation are shown to be a function of both rotation angle and the image distance Z; (b) the telecentric lens has an effective object distance, Z_eff, that is 50× larger than the 55 mm standard lens, with a corresponding reduction in strain errors from 1250 μs/mm of out-of-plane motion to 25 μs/mm; and (c) a stereovision system measures all components of displacement without introducing measurable, full-field, strain errors, even though an object may undergo appreciable out-of-plane translation and rotation.     

Particle Size Distribution by Combined Elastic Light Scattering and Turbidity Measurements. A Novel Method to Estimate the Required Normalization Factor

Turbidity (T) and Elastic Light Scattering (ELS) measurements can be combined to estimate the particle size distribution (PSD) of a polymer latex. To this effect a “normalization factor” must be employed to adequately scale both measurements. In a real application, such factor is a priori unknown, and it must be estimated for determining the PSD. In a previous publication, a method was proposed to simultaneously estimate the normalization factor and the PSD by solving an inverse nonlinear problem. In this work, a simpler technique is presented which estimates the normalization factor and the PSD by sequentially solving two inverse linear problems. To evaluate the proposed technique, a synthetic example based on a polystyrene latex sample with a bimodal PSD was solved. It is shown that, for slight noise measurements, the errors in the estimation of the normalization factor are quite small and have a low effect on the PSD recovery.     

A Robust Method for Estimating Cross-Relaxation Rates from Simultaneous Fits to Build-Up and Decay Curves

This paper introduces a novel computational method for estimating relaxation rates among pairs of spin orders. This method simultaneously estimates all the auto- and cross-relaxation rates from the same measurements, and avoids the ill-conditioning problems associated with multiexponential fits. The method models the relaxation dynamics by a system of linear differential equations, and assumes that measurements of the spin orders have been made at an equally spaced sequence of time points. It computes a nonlinear least-squares fit of the exponential of the rate matrix at the shortest time point to these measurements. Preliminary estimates of the exponential matrix and initial spin orders from which to start the computations are obtained by solving simpler linear-least-squares problems. The performance of the method on simulated 2 × 2 test problems indicates that when measurements at eight or more equally spaced times spanning the maximum and inflection points of the build-up curves are available, the relative errors in the rates are usually less than the relative errors in the measurements. The method is further demonstrated by applying it to the problem of determining the cross correlation-induced cross-relaxation rates between the in-phase and antiphase coherence of the amide groups in the¹⁵N-labeled protein oxidized flavodoxin. Finally, the possibility of extending the method to other kinds of relaxation measurements and larger spin systems is discussed.     

Errors in measurements of atomic masses

The methods of measuring the atomic masses of stable isotopes with high-resolution static and dynamic mass spectrometers are examined. The typical measurement errors characteristic of both classes of devices are indicated. The greatest difficulty arising in such experiments is taking account of the effect of stray electric fields on the parameters of the motion of two types of ions forming a mass doublet as well as determining and introducing corrections for the corresponding errors in the measured mass values. This effect could be especially important in measurements of wide mass doublets. A method similar to the one employed in direct measurements of the magnetic moment of the proton in terms of nuclear magnetons with a magnetic resonance mass spectrometer with a two-section ion source is suggested for taking into account the effect of the stray electric fields in atomic mass measurements. Zh. Tekh. Fiz. 67, 100–104 (February 1997)     

Two-line planar fluorescence for temporally resolved temperature imaging in a reacting supersonic flow over a body

An instantaneous temperature imaging technique for chemically reacting, supersonic flows over bodies is described and demonstrated in a H₂/O₂/Ar shock tube flow (M=1.3, 0.7 atm, 1760K freestream). Based on a planar fluorescence measurement, the approach uses a two-line rotational population ratio to infer temperature. The measured 2-d temperature profiles qualitatively match the expected flowfield structure around the blunt body, and the temperature increase across the bow shock in a single-shot measurement agrees within 5–10% of the prediction of a 1-d shock analysis. The significant systematic error sources for the technique are detailed, and the random error effects associated with shot-noise-limited fluorescence images are statistically analyzed to identify transitions which minimize the temperature errors for instantaneous and average measurements. Even for average temperature measurements, the analysis predicts errors which can be as large as 5–10% when noisy fluorescence images are used in conjunction with low temperature sensitivity. In general, temperature errors can be reduced by increasing sensitivity, i.e., the energy separation of the two rotational levels, until the fluorescence shot-noise rises to a value of 30–50% within the temperature range of interest.     

Selection of response measurement locations to improve inverse force determination

The forces obtained by inverse methods are prone to errors. These arise due to a combination of errors in the measurements and high condition numbers in the matrix of transfer functions to be inverted. Ill-conditioning of the frequency response function matrix causes measurement errors to be magnified significantly. When the condition numbers are small, the measurement errors simply propagate without much amplification. Due to modal behaviour of the structure, the condition numbers can vary significantly over the frequency range and with the spatial location of the response measurements. The spatial variation can be quite considerable across the structure. The potential for using this characteristic to improve force determination is explored in this paper as an alternative to matrix regularization methods. The aim is to reduce error magnification in inverse methods by an ‘optimal’ spatial distribution of response locations. A method is proposed which is based on the minimization of the average condition number across the frequency range. If many possible locations are available, however, this can involve excessive calculation. An approximate method is therefore proposed which results in consistently good location selection for use in inverse force determination but involves much less computational effort. The error reduction in reconstructed forces is found to be significant in numerical simulations on a simply supported plate and in validation experiments.     

Systematic errors in dispersive fourier transform spectroscopy in a non-vacuum environment

A simple theory has been developed for the consequences of making dispersive Fourier transform spectroscopic measurements in a non-vacuum environment. Systematic errors are introduced which can be removed if the refractive index of that local atmosphere is known. The results of DFTS measurements on helium gas from 5.5 to 295 K are presented and used to correct previous measurements on the polymers TPX, low and high density polyethylene, and polystyrene in order to demonstrate the method.     

Errors of observation and systematic errors

Methods of displaying results of repeated measurements, and choice of measures of scatter are considered. It is argued that graphical displays and a 50 per cent probability as basis for expression of errors are simpler than, and in many cases as useful as, any other method.

The importance of allowing for errors which affect to the same extent all measurements of a quantity throughout an investigation is emphasized, and a method of estimating that sort of systematic error is described and illustrated by an example.     

Use of in-house primary standard blackbodies for accurate cathode temperature measurement

The interpretation of cathode behavior in traveling wave tubes is clouded considerably by the uncertainty in both the precision and absolute accuracy of cathode temperature measurements as determined by optical pyrometry. The sensitivity and potential accuracy of optical pyrometry is very good, but many sources of error are possible. Sources of error that were experimentally measured in this study can be classified in three categories: (a) instrument and calibration errors; (b) operator (subjective) errors; and (c) errors caused by obstacles or geometrical variations in the optical path. Possible methods of avoiding or correcting sources of errors are recommended, including the use of an in-house primary standard blackbody. The design and use of this device are described in detail. When the primary standard is used and coupled to cathode measurements through secondary blackbodies optical pyrometry is an extremely reliable method for cathode temperature determination.