2.1 Introducing the EAST device

EAST is a fully superconducting experimental Tokamak device with a non-circular cross-section. It consists of an ultra-high vacuum chamber, poloidal field coils, toroidal field coils, internal and external cold screens, external vacuum cryostat, and support systems. It is referred to as "fully superconducting" because all magnetic field coils are used to constrain the plasma (including the toroidal field coils, poloidal field coils, and central solenoid, which are all superconducting magnets); and it has a "non-circular cross-section" because the cross-section of the toroidal field coils and the plasma are in the shape of the letter D. The main technical features of EAST are as follows. It has a mainframe with a height of 11 m and diameter of 8 m, weights approximately 400 tons and has 16 large "D" shaped superconducting longitudinal magnetic magnets. It can generate a longitudinal field strength up to 3.5 T, and the 12 polar field superconducting magnets can provide a change in flux of ΔΦ≥10 volt·second. The main basic parameters are as follows: large radius, R₀, of approximately 1.88 m; small radius, a, of approximately 0.45 m; longitudinal field, B_t, of approximately 1.5~3.0 T; and plasma current, I_p, of approximately 1 MA.

2.2 Visible/infrared integrated endoscope system

To observe the position and shape of the plasma during discharge, a tangential fast visible imaging system was designed and installed on the EAST device. However, as many diagnostic systems are now installed on the windows of the EAST device, there is limited remaining window space, and to maximize the use of this limited remaining window space, a shared optical path was designed for the visible/infrared imaging system. The visible/infrared imaging system is installed in the G port, as shown in Fig. 1. The design of this optical system is based on the pin-hole imaging principle and light-splitting technology, and the optical system can achieve high resolution visible and infrared imaging of plasma discharge with the same aperture and field of view of 46° × 59° ^[12]. The system mainly comprises the fore-end of an endoscope, collimator lens group, beam splitting system, and visible/infrared receiving terminal. Considering the complex electromagnetic environment inside the device, and the possibility of bombardment from high-energy particles, a perforated plane mirror and a parabolic mirror are adopted in the front-end of the diagnostics system, as shown in Fig. 2. Here, the large field of view is achieved by pin-hole imaging, and the Cassegrain system is replaced by the beam splitting system to increase the amount of light within the system.

Fig. 1Full-screen View

Location of Visible/Infrared Imaging System

Fig. 2Full-screen View

(Color online) Optical path for visible/Infrared camera

2.3 Hardware and software design of imaging system

The plasma rotates extremely quickly during the discharge process and a low-speed camera is unable to adequately capture an image of its position. Therefore, a high-speed PCO.edge5.5 CCD camera (PCO; Germany) is employed to provide hardware support for high-speed acquisition. Compared with the Phantom V710 camera used previously ^[13], the PCO.edge5.5 camera is smaller, has a higher resolution, and is easier to use. The transfer rate of this image system via the Camera Link interface is up to 5.4 Gb/s. In addition, the highest sampling rate of this CCD camera reaches 100 fps at a resolution of 2560 × 2160 pixels, and the maximum sampling rate can reach 1651 fps under resolution reduction conditions, which is adequate for use in this experiment.

The image acquisition system primarily includes the PCO.edge5.5 camera, an industrial control computer used for image acquisition, a central timing control system, a real-time image processing server, and a display server, as shown in Fig. 3. In the plasma discharge experiment, the central control machine is responsible for sending the shot number and the acquisition time to the image acquisition computer, and also for sending the trigger signal to the camera to control the camera to begin image acquisition using the hardware triggering mode. The corresponding software for the high-speed CCD imaging system, which was developed in a VS2010 environment, has a simple interface with a user-friendly display. The interface is used to activate and deactivate the camera and to adjust relevant parameters. Figure 4 shows an original image of plasma discharge acquired by the PCO.edge5.5 camera in the G window during the rising phase of the discharge; this is the actual image prior to processing by the edge detection system. As seen in Fig. 4, the boundaries of the plasma in the original image are not very clear because it contains a lot of high-frequency noise, and the traditional edge detection algorithm is therefore unable to solve this problem.

Fig. 3Full-screen View

Hardware structure of image acquisition system used in EAST

Fig. 4Full-screen View

(Color online) Original image of plasma discharge

3.1 Traditional wavelet transform edge detection algorithm

Most of the edges in the image are non-differentiable and discontinuous; therefore, the traditional edge detection algorithm based on wavelet transform proceeds as follows. First, a smoothing function is used to smooth the image. The first or second order derivative of the smoothed result is then obtained; this result is taken as the wavelet-basis packet function, and maximum points or zero points are then identified as image edges. The traditional edge detection algorithm based on wavelet transform usually only calculates the absolute value of the modulus of wavelet transform for each row and each column in horizontal and vertical directions. For each point, the point is taken as the edge point if the maximum of the modulus is obtained at least once in the row and column; otherwise, it is regarded as a non-edge point and the gray value of this point is set to zero. All edge points constitute the edge of the image. However, edges obtained in this way will inevitably contain a large number of false edge with respect to noise. Therefore, after the initial edge is obtained, some of the pseudo-edge points are removed by setting a threshold: edge points below the threshold are removed and points above the threshold are reserved.

The detailed calculation process of the algorithm is as follows.

If we suppose that f(x, y) is the image, the result of f(x, y) after smoothing would be θ(x, y) = a(x, y) $\text{*}$ f(x, y), where a(x, y) is the 3 × 3 smoothing filter, as shown in Eq. (1),

${\phi }_x\left(x,y\right), {\phi }_y\left(x,y\right)$ are the directional derivatives of $\theta \left(x,y\right)$ in the x and y direction, respectively, and are represented as

If φ_x(x, y) and φ_y(x, y) are chosen as the wavelet-basis packet function, the wavelet transform can be expressed as follows,

The corresponding modulus and phase angle of the wavelet transforms are

where |ω_x(x, y)| and |ω_y(x, y)| are the moduli at point $\left(x,y\right)$ along horizontal and vertical directions, respectively.

When Eq. (7) or Eq. (8) is true, the image f(x, y) is set to 1, and otherwise it is set to 0. Finally, the points (x, y)∈{(x, y)|f(x, y) = 1} are identified as the edge of the image as

where |ω_x(i, j)| and |ω_y(i, j)| are the moduli at point (i, j) along horizontal and vertical directions, respectively; t is the global threshold and the ranges of i and j are i∈(x - 1, x + 1), j∈(y - 1, y + 1), respectively.

3.2 Improved Wavelet Transform Edge Detection Algorithm

The traditional wavelet transform edge detection algorithm has two main limitations. First, the moduli along horizontal or vertical directions are used to obtain the local maxima, which means that it is not possible to obtain the local maxima for the resultant moduli in both directions; therefore, the local maxima obtained by the traditional method is inaccurate. In addition, when the local maximum of the modulus of wavelet transform is solved using the traditional method, false edge information is often included in the obtained edge, and the effective edge is often missing. Second, the pre-set threshold in the traditional method is a fixed value. If the threshold is too small, there will be too much noise detected in the image, and if the threshold setting is too large, detailed information about the image edge will be lost. Therefore, this paper presents an improved method that ameliorates these two issues.

3.2.1 Determination of local maxima moduli in multiple directions

In this paper, the local maxima of the moduli of wavelet transform are directly searched in the modulus image, M, along the direction, A, of each phase angle ^[14]. According to the characteristics of eight adjacent points around each pixel in the image, the neighborhood of the pixel can be divided into eight sectors based on the phase angle, as shown in Fig. 5.

Fig. 5Full-screen View

Schematic diagram of gradient direction intervals

The eight sectors comprise regions sandwiched by -22.5°, 22.5°, 67.5°, 112.5°, 157.5°, -157.5°, -112.5°, -67.5°, -22.5°, and 22.5°, and these are labelled 0, 1, 2, 3, 4, 5, 6, and 7. Each sector represents the gradient direction of the area, and due to the symmetry of the gradient direction, only four directions of 0, 1, 2, 3 (or 4, 5, 6, 7) need to be considered in calculations. If the modulus M(x, y) of the image at a certain point (x, y) is greater than that of the two adjacent points along the A(x, y) direction, then the point will be considered as the local maximum modulus of the image. Since the local maximum of the modulus is selected in the same way along the four gradient directions, we only use the selection of the local maximum of the modulus at point (x, y) along the gradient direction 1 to illustrate the problem, as shown in Eq. (9),

$\{\begin{array}{l}M(x-1,y-1)\le M(x,y)\\ M(x,y)\ge M(x+1,y+1)\end{array}.$ (9)

If Eq. (9) works, then M(x, y) is taken as the local maximum at point (x, y). In the same way, all local maxima along the four gradient directions are preserved, and these form the initial edge points of the image.

3.2.2 Adaptive threshold setting

The traditional wavelet transform edge detection algorithm uses a fixed threshold to test the entire image, which thus removes high-frequency noise. Certain weak edge information about the image is also removed; however, some pseudo-edge information is retained ^[15-18]. Therefore, this paper uses an adaptive threshold to make improvements, and the associated equation is as shown in Eq. (10) ^[14],

$T=T_0+a_0\times {\displaystyle {\sum }_{i,j}{\lambda }_{i,j}},$ (10)

where T is the adaptive threshold, T₀ is the initial threshold, a₀ is a scaling factor, and λ_{i, j} is the corresponding wavelet coefficient for the current window. The size of the window of is 3 $\times$ 3, and T₀ and a₀ can be chosen according to the actual situation. When converting a grayscale image into a binary image during preprocessing, the parameters (T₀, a₀) are changed depending on whether or not the image edge is completely preserved.

The detailed algorithm flow is as follows. First, wavelet transform is conducted on the original image f(x, y), and the corresponding modulus value M(x, y) and phase angle A(x, y) are computed. The modulus image M(x, y) is then searched for to obtain the local maxima of wavelet coefficients along the direction A(x, y). The maximum value points are subsequently retained to obtain the possible edge image γ(x, y). Second, the possible edge image γ(x, y) is scanned using a 3 × 3 window, and based on the adaptive threshold calculation equation, the threshold T is obtained from wavelet transform coefficients. Finally, the points at which the local maxima of the moduli are greater than T in the image f(x, y) are taken as the edge outputs.

Figure 6 shows a summary of the algorithm flow chart. The detailed algorithm process includes the following steps: (1) enter the original image; (2) obtain a grayscale image of the original image, perform noise reduction and other preprocessing, and then perform wavelet transform on the image to obtain the modulus M(x, y) and the phase angle A(x, y); (3) find the local maximum points along the four gradient directions and retain the maximum modulus points to obtain the initial edge; (4) use the obtained adaptive threshold, T, to make further accurate positioning of the initial edge of the image and to output the final edge.

Fig. 6Full-screen View

Algorithm flow chart of edge detection

3.3 Edge fitting

The edges of the images obtained by the above method are usually discontinuous and unsmooth; as this result is not conducive to data analysis, it is necessary to fit the actual detected curve to obtain one that is more accurate. In this respect, the image of plasma discharge can be captured by the high-speed camera used in the current experiment, and edge detection and curve fitting for images of plasma discharge throughout the whole process can thus be achieved. According to the principle of plasma discharge and a large amount of experimental data, the edge of the plasma during the start-up phase of discharge is approximately circular, and the edge of the plasma during the latter stage of discharge is an elliptical curve. Therefore, this paper uses the least square iterative method to fit the circular and elliptical curve edges.

3.4 Method for Reconstructing Plasma Boundary

Assuming that plasma is toroidally symmetric during the plasma discharge progress, we used the OFIT method mentioned in Ref. [21, 22] to reconstruct the plasma boundary from the images acquired by the high-speed camera. The main problem in the reconstruction is the transformation between the Cartesian coordinate system (u, v, w) and the Tokamak coordinate systems (R, Z, θ); more information about this is shown in Fig. 7. The coordinate axes, v and Z that have identical origins in both coordinate systems are overlapped. The projection plane of the camera is chosen as the vertical (u, v, 0) plane, and after the camera location is obtained (u_c, v_c, w_c) and the projection properties of the optics from the camera are calibrated, then the trajectories of all lines of sight are determined and each can be projected onto the projection plane ^[21,22]. Using the method shown in Ref. [21,22], the optical plasma boundary can be reconstructed from camera images.

Fig. 7Full-screen View

(Color online) Relationship between Cartesian coordinate system and Tokamak coordinate system