Analysis of missile trajectory measurement accuracy for data processing

"Contract no. AF 30(602)-2138, Project 5554, Task 55102."

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 x 10(-4) corresponding to 1 degrees 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. (c) 2007 Elsevier Ltd. All rights reserved.

Measurement error of rearfoot kinematics during running between a 100Hz and 30Hz camera

Background: Measurement accuracy is critical for biomechanical gait assessment. Very few studies have determined the accuracy of common clinical rearfoot variables between cameras with different collection frequencies. Research question: What is the measurement error for common rearfoot gait parameters when using a standard 30Hz digital camera compared to 100Hz camera? Type of study: Descriptive. Methods: 100 footfalls were recorded from 10 subjects ( 10 footfalls per subject) running on a treadmill at 2.68m/s. A high-speed digital timer, accurate within 1ms served as an external reference. Markers were placed along the vertical axis of the heel counter and the long axis of the shank. 2D coordinates for the four markers were determined from heel strike to heel lift. Variables of interest included time of heel strike (THS), time of heel lift (THL), time to maximum eversion (TMax), and maximum rearfoot eversion angle (EvMax). Results: THS difference was 29.77ms (+/- 8.77), THL difference was 35.64ms (+/- 6.85), and TMax difference was 16.50ms (+/- 2.54). These temporal values represent a difference equal to 11.9%, 14.3%, and 6.6% of the stance phase of running gait, respectively. EvMax difference was 1.02 degrees (+/- 0.46). Conclusions: A 30Hz camera is accurate, compared to a high-frequency camera, in determining TMax and EvMax during a clinical gait analysis. However, relatively large differences, in excess of 12% of the stance phase of gait, for THS and THL variables were measured.

Optical Factors Determined by the T-matrix Method in Turbidity Measurement of Absolute Coagulation Rate Constants

Turbidity measurement for the absolute coagulation rate constant of suspensions has been extensively adopted because of its simplicity and easy implementation. A key factor to derive the rate constant from experimental data is how to theoretically evaluate the so-called optical factor involved in calculating the extinction cross section of doublets formed in the aggregation. In a previous paper, we have shown that compared with other theoretical approaches, the T-matrix method provides a robust solution to this problem and is effective in extending the applicability range of the turbidity methodology as well as increasing measurement accuracy. This paper will provide a more comprehensive discussion about the physical insight of using the T-matrix method in turbidity measurement and associated technical details. In particular, the importance of ensuring the correct value for the refractive indices for colloidal particles and the surrounding medium used in the calculation is addressed because the indices generally vary with the wavelength of the incident light. The comparison of calculated results with experiments shows that the T-matrix method can correctly calculate optical factors even for large particles, whereas other existing theories cannot. In addition, the calculated data of the optical factor by the T-matrix method for a range of particle radii and incident light wavelengths are listed.

Study on improving the turbidity measurement of the absolute coagulation rate constant

The existing theories dealing with the evaluation of the absolute coagulation rate constant by turbidity measurement were experimentally tested for different particle-sized (radius = a) suspensions at incident wavelengths (lambda) ranging from near-infrared to ultraviolet light. When the size parameter alpha = 2 pi a/lambda > 3, the rate constant data from previous theories for fixed-sized particles show significant inconsistencies at different light wavelengths. We attribute this problem to the imperfection of these theories in describing the light scattering from doublets through their evaluation of the extinction cross section. The evaluations of the rate constants by all previous theories become untenable as the size parameter increases and therefore hampers the applicable range of the turbidity measurement. By using the T-matrix method, we present a robust solution for evaluating the extinction cross section of doublets formed in the aggregation. Our experiments show that this new approach is effective in extending the applicability range of the turbidity methodology and increasing measurement accuracy.

Noninterferometric measurement of lead zirconate titanate inverse piezoelectric extension

A noncontacting and noninterferometric depth discrimination technique, which is based on differential confocal microscopy, was used to measure the inverse piezoelectric extension of a piezoelectric ceramic lead zirconate titanate actuator. The response characteristics of the actuator with respect to the applied voltage, including displacement, linearity, and hysteresis, were obtained with nanometer measurement accuracy. Errors of the measurement have been analyzed. (C) 2001 Society of Photo-Optical Instrumentation Engineers.

Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings

In this paper, we propose a novel method for measuring the coma aberrations of lithographic projection optics based on relative image displacements at multiple illumination settings. The measurement accuracy of coma can be improved because the phase-shifting gratings are more sensitive to the aberrations than the binary gratings used in the TAMIS technique, and the impact of distortion on displacements of aerial image can be eliminated when the relative image displacements are measured. The PROLITH simulation results show that, the measurement accuracy of coma increases by more than 25% under conventional illumination, and the measurement accuracy of primary coma increases by more than 20% under annular illumination, compared with the TAMIS technique. (c) 2007 Optical Society of America.

A high accuracy image sensor for sinusoidal phase-modulating interferometry

We proposed a high accuracy image sensor technique for sinusoidal phase-modulating interferometer in the field of the surface profile measurements. It solved the problem of the CCD's pixel offset of the same column under two adjacent rows, eliminated the spectral leakage, and reduced the influence of external interference to the measurement accuracy. We measured the surface profile of a glass plate, and its repeatability precision was less than 8 nm and its relative error was 1.15 %. The results show that it can be used to measure surface profile with high accuracy and strong anti-interference ability. (C) 2007 Elsevier GmbH. All rights reserved.

Even aberration measurement of lithographic projection system based on optimized phase-shifting marks

In the present paper, we propose a novel method for measuring the even aberrations of lithographic projection optics by use of optimized phase-shifting marks on the test mask. The line/space ratio of the phase-shifting marks is optimized to obtain the maximum sensitivities of Zernike coefficients corresponding to even aberrations. Spherical aberration and astigmatism can be calculated from the focus shifts of phase-shifting gratings oriented at 0 degrees, 45 degrees, 90 degrees and 135 degrees at multiple illumination settings. The PROLITH simulation results show that, the measurement accuracy of spherical aberration and astigmatism obviously increase, after the optimization of the measurement mark. (C) 2008 Elsevier B.V. All rights reserved.

Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry

As there exist some problems with the previous laser diode (LD) real-time microvibration measurement interferometers, such as low accuracy, correction before every use, etc., in this paper, we propose a new technique to realize the real-time microvibration measurement by using the LD sinusoidal phase-modulating interferometer, analyze the measurement theory and error, and simulate the measurement accuracy. This interferometer utilizes a circuit to process the interference signal in order to obtain the vibration frequency and amplitude of the detective signal, and a computer is not necessary in it. The influence of the varying light intensity and light path difference on the measurement result can be eliminated. This technique is real-time, convenient, fast, and can enhance the measurement accuracy too. Experiments show that the repeatable measurement accuracy is less than 3.37 nm, and this interferometer can be applied to real-time microvibration measurement of the MEMS. (C) 2007 Elsevier GmbH. All rights reserved.

Improved digital processing method used for image motion measurement based on hybrid opto-digital joint transform correlator

Hybrid opto-digital joint transform correlator (HODJTC) is effective for image motion measurement, but it is different from the traditional joint transform correlator because it only has one optical transform and the joint power spectrum is directly input into a digital processing unit to compute the image shift. The local cross-correlation image can be directly obtained by adopting a local Fourier transform operator. After the pixel-level location of cross-correlation peak is initially obtained, the up-sampling technique is introduced to relocate the peak in even higher accuracy. With signal-to-noise ratio >= 20 dB, up-sampling factor k >= 10 and the maximum image shift <= 60 pixels, the root-mean-square error of motion measurement accuracy can be controlled below 0.05 pixels.

Velocity measurement of pneumatically conveyed solids using electrodynamic sensors

Theoretical and experimental studies of cross correlation techniques applied to non-restrictive velocity measurement of pneumatically conveyed solids using ring-shaped electrodynamic flow sensors are presented. In-depth studies of the electrodynamic sensing mechanism, and also of the spatial sensitivity and spatial filtering properties of the sensor are included, together with their relationships to measurement accuracy and the effects of solids' velocity profiles. The experimental evaluation of a 53 mm bore sensing head is described, including trials using a calibrated pneumatic conveyor circulating pulverized fuel and cement. Comparisons of test results with the mathematical models of the sensor are used to identify important aspects of the instrument design. Off-line test results obtained using gravity-fed solids flow show that the system repeatability is within +/-0.5% over the velocity range of 2-4 m s(-1) for volumetric concentrations of solids no greater than 0.2%. Results obtained in the pilot-plant trials demonstrate that the system is capable of achieving repeatability better than +/-2% and linearity within +/-2% over the velocity range 20-40 m s(-1) for volumetric concentrations of solids in the range 0.01-0.44%.

Thermal conductivity measurement of liquids in a microfluidic device

A new microfluidic-based approach to measuring liquid thermal conductivity is developed to address the requirement in many practical applications for measurements using small (microlitre) sample size and integration into a compact device. The approach also gives the possibility of high-throughput testing. A resistance heater and temperature sensor are incorporated into a glass microfluidic chip to allow transmission and detection of a planar thermal wave crossing a thin layer of the sample. The device is designed so that heat transfer is locally one-dimensional during a short initial time period. This allows the detected temperature transient to be separated into two distinct components: a short-time, purely one-dimensional part from which sample thermal conductivity can be determined and a remaining long-time part containing the effects of three-dimensionality and of the finite size of surrounding thermal reservoirs. Identification of the one-dimensional component yields a steady temperature difference from which sample thermal conductivity can be determined. Calibration is required to give correct representation of changing heater resistance, system layer thicknesses and solid material thermal conductivities with temperature. In this preliminary study, methanol/water mixtures are measured at atmospheric pressure over the temperature range 30-50A degrees C. The results show that the device has produced a measurement accuracy of within 2.5% over the range of thermal conductivity and temperature of the tests. A relation between measurement uncertainty and the geometric and thermal properties of the system is derived and this is used to identify ways that error could be further reduced.

Rough-terrain groundspeed measurement:a radar-based commercial solution

Off-highway motive plant equipment is costly in capital outlay and maintenance. To reduce these overheads and increase site safety and workrate, a technique of assessing and limiting the velocity of such equipment is required. Due to the extreme environmental conditions met on such sites, conventional velocity measurement techniques are inappropriate. Ogden Electronics Limited were formed specifically to manufacture a motive plant safety system incorporating a speed sensor and sanction unit; to date, the only such commercial unit available. However, problems plague the reliability, accuracy and mass production of this unit. This project assesses the company's exisiting product, and in conjunction with an appreciation of the company history and structure, concludes that this unit is unsuited to its intended application. Means of improving the measurement accuracy and longevity of this unit, commensurate with the company's limited resources and experience, are proposed, both for immediate retrofit and for longer term use. This information is presented in the form of a number of internal reports for the company. The off-highway environment is examined; and in conjunction with an evaluation of means of obtaining a returned signal, comparisons of processing techniques, and on-site gathering of previously unavailable data, preliminary designs for an alternative product are drafted. Theoretical aspects are covered by a literature review of ground-pointing radar, vehicular radar, and velocity measuring systems. This review establishes and collates the body of knowledge in areas previously considered unrelated. Based upon this work, a new design is proposed which is suitable for incorporation into the existing company product range. Following production engineering of the design, five units were constructed, tested and evaluated on-site. After extended field trials, this design has shown itself to possess greater accuracy, reliability and versatility than the existing sensor, at a lower unit cost.