Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/iop-publishing/periodic-error-while-processing-data-from-a-velocity-interferometer-8qvHUPMC8A
References
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
- Copyright
- Copyright Published under licence by IOP Publishing Ltd
- ISSN
- 1742-6588
- eISSN
- 1742-6596
- DOI
- 10.1088/1742-6596/1787/1/012012
- Publisher site
- See Article on Publisher Site
Abstract
XXXV International Conference on Equations of State for Matter (ELBRUS 2020) IOP Publishing Journal of Physics: Conference Series 1787 (2021) 012012 doi:10.1088/1742-6596/1787/1/012012 Periodic error while processing data from a velocity interferometer system for any reflector 1,2,3 1,2,3 1,2,3 1,2,3 T V Kazieva , K L Gubskiy , A P Kuznetsov , V A Pirog 2,3,1 and I Yu Tishchenko National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Shosse 31, Moscow 115409, Russia Limited Liability Company “Laser Eye”, Kashirskoe Shosse 31, Moscow 115409, Russia 12 Central Scientific Research Institute of the Ministry of Defense of the Russian Federation, Sergiev Posad, Moscow Region 141307, Russia E-mail: [email protected] Abstract. When processing experimental data with systems such as velocity interferometer system for any reflector (VISAR), periodic measurement uncertainty arises. The appearance of its uncertainty is investigated and computer modeling of signal processing with random noise is carried out. Analytical dependences of the error value on the signal-to-noise ratio and signal phase are obtained. Methods of reducing this error are considered. 1. Introduction Velocity interferometer system for any reflector (VISAR) [1] is a widely used diagnostic tool in dynamic compression studies. A number of works are devoted to the analysis of the sources of errors and the accuracy of the method. Were considered: alignment errors [2]; correction of measurement results due to dispersion [3], availability of diagnostic windows [4]; radiation collection angle [5]. The limitations of processing methods were separately considered. The possibility of compensating for restrictions was considered [6]. In this paper, we investigated the dynamic error of VISAR data processing by traditional algorithms and the influence of various factors on it. 2. Theory The push-pull VISAR generates four interference signals that recorded by photomultiplier tubes (PMTs). As a result, signals of the following form are obtained: I = I (t) sin(φ(t)) + A(t); 1 0 I = I (t) cos(φ(t)) + A(t); 2 0 (1) I = −I (t) sin(φ(t)) + A(t); 3 0 I = −I (t) cos(φ(t)) + A(t), 4 0 where I are the recorded signals; I is the amplitude of the interference signal, contains the 1,2,3,4 0 multiplicative component of the interfering signal; A is the additive component of the interfering signal; φ is the phase, which contains information about the velocity of the object. The resulting Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 XXXV International Conference on Equations of State for Matter (ELBRUS 2020) IOP Publishing Journal of Physics: Conference Series 1787 (2021) 012012 doi:10.1088/1742-6596/1787/1/012012 combination of four signals allows subtracting multiplicative and additive noises. Equation for the velocity of the object is then: Δφ V (t) = KN + K , (2) 2π where Δφ is the additional phase shift, Δφ = arctan[(I − I )/(I − I )], N is the number of 1 3 2 4 recorded fringes; K is the velocity per fringe (VPF) of the interferometer is also called the fringe constant: cλ K = , (3) 4l n − 1 + δ where c is the velocity of light in vacuum, λ is the wavelength of the probe radiation, l is the 0 d length of the delay line, n is the refractive index of the delay line; δ is the correction coefficient for accounting for chromatic dispersion: n dn δ = − λ . (4) n − 1 dλ λ=λ The K constant is directly related to the VISAR resolution. To calculate the correct velocity, an integer number of velocity constants must be added to the signal obtained after processing. Therefore, the absolute velocity error is defined as 1 Δφ K 2 2 σ = N + σ + σ . (5) V φ 2π 2π The first term in (5) is determined by the characteristics of the delay line and the parameters of the laser radiation source. The refractive index and dispersion coefficient are tabular values: (n − 1)/n = β, dn/dλ| = α. Therefore, λ=λ ! ! 2 2 c cλ σ = σ + σ . (6) K λ l 0 d 1 1 4l β(1 − λ α) 4l β(1 − λ α) d 0 d 0 β β In this case, the wavelength of the laser source is λ = 532.0 ± 0.1 nm, the dispersion coefficient for VK7 glass α = −0.0546, the refractive index n = 1.51616, the error determining of the delay 2 2 4 −5 line length is 0.1 mm. Therefore, σ = (6.65/l + 2.01/l )10 . Consider the second term, K d d ′ ′ ′ ′ ′ Δφ = arctan(I /I ), where I = I − I and I = I − I are the signals recorded by the PMTs, 1 3 2 4 1 2 1 2 then ! ! ′ ′ ′ 1 ΔI I ΔI 2 1 1 2 σ = + . (7) 2 ′ 2 ′ ′ 1 + I I 1 2 The amplitudes of the signals are equalized by adjusting the voltage of the PMTs. So, if the ′ ′ ′ ′ ratio ΔI /I = ΔI /I = 1/SNR, where SNR is the signal-to-noise ratio, equation (7) becomes 1 2 2 2 σ = 1/(SNR[1 + (tan φ) ]), and 2 2 1 Δφ 6.65 2.01 K 1 −5 σ = N + + 10 + . (8) 2 4 2 2π 2π 2 l l SNR(1 + (tan φ) d d Figure 1 shows the dependence of the error upon the phase. The calculations were performed for a delay line 160 mm long VK7 glass. It is clear, that the error is periodic. As the phase increases, the value of the error will raise, because of the first component of equation (8). To reduce velocity uncertainty, Δφ calculation in formula (7) can be done by the following expression 2 XXXV International Conference on Equations of State for Matter (ELBRUS 2020) IOP Publishing Journal of Physics: Conference Series 1787 (2021) 012012 doi:10.1088/1742-6596/1787/1/012012 0 1 2 3 4 5 6 Phase (radian) Figure 1. Measurement uncertainty as a function of phase: black graph—calculations by (8); red graph—calculations are performed by formula (9); blue graph—averaging result. Δφ = arccot[(I − I )/(I − I )], equation (7) becomes σ = 1/(SNR[1+(cot φ) ]), and formula 1 3 2 4 φ (8), respectively, 2 2 1 Δφ 6.65 2.01 K 1 −5 σ = √ N + + 10 + . (9) 2 4 2 2π 2π l l 2 SNR(1 + (cot φ) d d The error value at the point of interest can be reduced by selecting the correct signal processing method. For the entire recorded signal, we use the average formula: 1 1 1 σ = + . (10) 2 2 2SNR 1 + (tan φ) 1 + (cot φ) 3. Simulation To confirm the obtained calculations, mathematical modeling of the deviation of the signal phase after processing and applying noise from the original value was carried out. For this, arbitrary phase sets were generated. Of these, signals were obtained to which white noise was added, and the reverse conversion was performed to obtain a phase containing noise. After that, the deviation of the values of the obtained phase from the original one was calculated and a graph of the dependence of the error on the theoretical value of the phase was built (figure 2). It can be noted that the signal has a periodic character and its period is π/2, as in figure 1. Absolute velocity error (m/s) XXXV International Conference on Equations of State for Matter (ELBRUS 2020) IOP Publishing Journal of Physics: Conference Series 1787 (2021) 012012 doi:10.1088/1742-6596/1787/1/012012 0.14 0.13 0.12 0.11 0 2 4 6 8 10 12 Phase (radian) Figure 2. Deviation of the calculated phase from the theoretical value. 4. Conclusion The analysis of the error while processing the quadrature data of the VISAR systems is carried out. It consists of constant and dynamic components. The constant is associated with the parameters of the delay line and the source of laser radiation. Dynamic determines the phase of the processed signal and the signal-to-noise ratio. The periodic nature of this error complicates the presentation of the final results, however, at the same time, it is possible to reduce the measurement error with the correct choice of the processing algorithm depending on the current phase. Averaging the phase value obtained by various algorithms also makes it possible to smooth out the influence of this source of measurement error. Acknowledgments This work was supported by the Russian Science Foundation, grant No. 17-72-20164. References [1] Koshkin D, Gubskiy K, Mikhailuk A and Kuznetsov A 2014 Proc. SPIE 9442 94420M [2] Neyer B T 1993 Proc. SPIE 2002 107–15 [3] Barker M and Schuler K W 1974 J. Appl. Phys. 45 3692–3 [4] Bhowmick M, Basset W P, Matveev S, Salvati L and Dlott D D 2018 AIP Adv. 8 125123 [5] Barker L M 2000 AIP Conf. Proc. 505 11–7 [6] Dolan D H 2006 Foundations of VISAR analysis Preprint SAND2006-1950 (New Mexico, CA: Sandia National Laboratories) Error of phase (radian)
Journal
Journal of Physics: Conference Series – IOP Publishing
Published: Feb 17, 2021