B.J. Peterson

E. A. Drapiko

National Institute for Fusion Science (NIFS-Repository)

      Image Reconstruction Methods for Bolometer Tomography and a New Study of Neural Network  Iwama, N. (School of Informatics, Daido Univ.) Teranishi M. (Dept. of ISM, Hiroshima Inst. of Tech.) Hosoda, Y. (Dept. of Inf. Sci., Fukui Univ.) Peterson, B.J., Tamura N.  Liu Y. (South-Western Inst. of Physics) Kostryukov A. Yu. (St. Petersburg Tech. Univ.)   The bolometer system for LHD plasma diagnostics, which is been developed from one-dimensional detecting arrays to 2-dimensional video cameras, gives a growing capability to observe the dynamic plasma behaviors. Study was made for refining the numerical methods of image reconstruction that have been developed for the 2-dimensional tomography in the semi-tangential cross section1), and also for exploring the possibility of 3-dim. one of the helical plasma. With respect to the two fan-beam camera system of bolometer installed in a semi-tangential plane with the 3.5U/4-O ports, the direct approach of treating each pixel value as an unknown without any parametric model is promising because of the triangular shape of magnetic surface region. To meet a large missing of projection data, strong regularization is required for solving the under- determined linear equation Hf=g in the sense of least squares. The projection matrix H, in which the effect of beam spread relating to the pinhole geometry should be taken into account, is sparse and ill-conditioned; the condition number is 607.4 when evaluated for HC−1, where C is the Laplacian operator, and the image and data vectors f and g have sizes of 322 and 40, respectively. In changing the type of regularization term in the Lagrange objective function, and with and without a nonlinear constraint of nonnegative pixel values, a software series of image reconstruction has been built up and examined on experimental data of LHD2): 1) the Tikhonov- Phillips method, 2) the maximum entropy method using the SMW formula, and 3) the Hopfield neural network. Efforts have been given to develop fast algorithms and also to get statistical tools of optimizing the plasma image with respect to the regularization parameter. Core software for movie production is ready to meet the long-time operation of LHD. Recent progress was obtained on the behaviors of the optimization criteria including the approximate GCV (generalized cross-validation) and the L-curve for the nonlinear methods of maximum entropy and Hopfield, and also on extending to the weighted least squares analysis. Additionally, a new study of neural network was started. The neural network collocation method (NNCM) proposed by Ma et al.3) is expected as another method that can be useful for sparse-data tomography. The method is based on a special usage of the perceptron; that is, the position coordinates of each pixel are fed to the inputs subsequently in order to give the corresponding pixel value as a single output. Training (learning) of the neural system is carried out so as to get a good least-square fitting for projection data. This usage of perceptron can be considered equivalently to be a series expansion of plasma profile with basis functions that are dependent on both the multi-layer arrangement of neurons and the projection data. This principle of nonlinear image reconstruction by NNCM can be explained well by revealing the acquired basis functions. With a 3-layered perceptron, which was equipped with the sigmoid and skimmer function in the hidden and output layer, respectively, a result of simulation is shown in Figs. 1 and 2. The NNCM may have an advantage of avoiding a large increase of unknown parameters even in the 3-dim. tomography, which is being planned for the purpose of studying the impurity behavior in LHD.  Feasibility was studied on applying the recon- struction methods to the large-sized inversion of 3-dim. tomography.                                                                   Fig. 1  Three basis functions which contribute to forming the edge of the semi-tangential cross section of LHD: the image region to [−1, 1] in both the x and y directions.         Fig. 2  Plasma image which was reconstructed by combining 12 basis functions as a result of training for numerically-simulated projection data of a phantom.  1) Peterson, B.J., Kostriukov, A.Yu., Ashikawa, N. et al.: Plasma Phys. Contr. Fusion, 45 (2003) 1167. 2) Iwama, N., Ichikawa, N., Hosoda, Y., Liu, Y. et al.: J. Plasma and Fusion Res. Series, 8 (2009) 975. 3) Ma, X.F., Fukuhara, M. and Takeda, T.: Nucl. Instrum.  Meth. Phys. Res., A 449 (2000) 366. Improved calibration technique for the IRVB.  Drapiko, E. A. (NIFS), Peterson, B.J. (NIFS)   The earlier developed technique1 based on using of the Ne-He laser to illuminate spots on a foil with 1 cm steps showed some issues. The foil was fixed and mounted inside the vacuum vessel while the IR camera and laser were outside. So the IR camera and laser beam were moved to provide coverage of the 9 by 7 cm foil. Such an approach showed high laser power nonuniformity on the foil inside the chamber due to vacuum window transition nonuniformity. In addition final analysis consists of solving huge amount of FEMs for every foil parameter. Also, a limited field of view of the IR camera with a fixed foil requires making the calibration by quadrants and venting the chamber four times during the calibration. To avoid the above mentioned problems a new calibration technique using a movable foil and UV LEDs mounted inside the vacuum vessel was developed.  In order to simplify the routine operation of foil calibration we have designed a new setup using the NI Labview controlled stepping motors for foil movement, camera acquisition trigger and LED pulse trigger. The NS375M-SFHM LED by Nitride Semiconductors was used. This is a high power UV module which consists of four 375 nm wavelength UV LEDs with 5.3 mm spacing, providing 450 mW of power. Such a spacing gives four clear temperature peaks, so four local characteristics on a foil could be determined from a one measurement. The module was placed as close as possible (about 0.5 mm) to the foil thus some corner parts of the foil was not reachable. The moving table allows calibration of  foils up to 10 by 13 cm with up to 1 mm steps. 3 mm pinholes were set in front of each LED in the module to collimate the beam and provide clear peaks on a foil with slightly reduced power. We were making a sequence of different width pulses with a 100 ms period. Right at the beginning and at the end of the pulse we trigger the IR camera to grab one image. Thus subtracting the image taken at the beginning of the pulse from the image at the end we can obtain the differential measurements of energy. The FLIR SC4000 IR camera was used. This camera can provide 320x256 pixels images at 420 frames per second rate. Also it works with an external trigger which was important for that experiment, because we have to grab the image exactly at the beginning and at the end of LEDs pulses. The main point of the experiment was to determine the specific thermal capacity. The idea was to avoid using FEMs in calibration procedure and make it less time consuming. So specific thermal capacity per unit area  cs=cvtf ,   (1) where cv is the volumetric thermal capacity and tf is the of thickness, could be measured directly using following equation ),(),(yxTyxec abss Δ= ,  (2) where eebs – absorbed energy. For an unknown profile ),( yxTAEcabsabss Δ= , (3) where Aabs – area of averaging. In addition knowing the cv for platinum we can determine the local foil thickness from Equation 1. Thus, the only foil parameter which needs FEMs to be defined is the specific thermal conductivity. Figure 1 shows the subtracted frames for 8 ms LED’s pulse at two different locations on the foil.   Fig. 1. Foil calibration results The same pictures ware acquired for 2,4 and 6 ms pulse width to check the linearity.  Table 1 shows the calculated thicknesses map for the foil 1.132983 1.417552 1.340046 1.333685 1.228959 1.476075 1.413709 1.41713 Table 1.  [1] B.J. Peterson, A. Yu. Kostrioukov, N. Ashikawa, M. Osakabe, and S. Sudo, RSI 74 N3 (2003).   179§30. Improved Cali ration Technique  for the IRVBiko, E. ., Peterson, B.J.

Improved Calibration Technique for the IRVB

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