Reconstruction performance

The reconstruction process was tested using the simulated data from section 4.1.

First, the ‘ideal’ line-integrated brightness and phase images in figure 4.2(b) and (c) were inverted to establish the performance of the inversions with idealised input data. This also tests the validity of the flow line integral in equation (4.2.4), since this relationship was not assumed in the generation of the data. The results are shown in fig. 4.12(b), with the original input profiles in (a). The emissivity profile appears generally well reconstructed, but is somewhat noisy in the Private flux region (PFR) and outside the outer divertor leg. Artefacts following the paths of sight-lines can be seen in the PFR adjacent to the sloping section of divertor coil

4.6. Tomographic Inversion 92

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Figure 4.12: Testing of tomographic inversion of emissivity and flow. (a) Top: OSM-EIRENE profiles used to generate test data. (b) middle: Profiles reconstructed from simulated phase & brightness images in figure 4.2(b) and (c). (c) Bottom: Profiles reconstructed from demodulated, noisy test data, as in figure 4.2(a).

4.6. Tomographic Inversion 93 armour and leading out from the outboard strike point. These are very similar to artefacts seen in tomographic inversions of camera data from the same plasma view on MAST in independent work [Lisgo et al., 2009], suggesting these features are related to the viewing geometry. The flow profile is also generally well reconstructed, however significant differences from the ideal profiles are seen in the private flux region. These may be partially caused by the errors in the emissivity inversion in this region. Deviations from the ideal profile are mainly in grid cells with very low emissivity, and which therefore contribute little flow information to the line-integral measurements and are poorly constrained in the inversion. This behaviour is expected, since naturally flow information can only be obtained from parts of the plasma where light is being emitted.

The reconstruction was also tested as part of the complete data analysis chain:

the brightness and phase were demodulated from the noisy simulated data in figure 4.2(a), and then inverted. The overall appearance of the emissivity reconstruction is not much different from the ideal data inversion, however the artefacts seen in that case appear more pronounced. The flow inversion appears significantly worse than the ideal data case, both in recovery of spatial features and the presence of noise and artefacts. Again as expected this is particularly the case for parts of the profile where the emissivity is low, both due to the poor constraint of these grid cells as previously stated, and the low SNR of the corresponding measurements when noise is included in the simulated data. When viewing inversions of real data, for this reason the flow inversion is only considered where the emissivity profile lies above a threshold value. Some artefacts in the image coincide with those seen in the emissivity reconstruction, indicating the effect of the emissivity reconstruction on the flow. The effects of the anisotropic fringe phase noise can be clearly seen in the inverted profile. Apart from the artefacts mentioned for the ideal data inversions,

‘blobs’ of positive and negative flow appear near the poloidal field coil in the top right of the image (R ≈ 0.8 − 1m, Z ≈ −1.2m). These are due to residual ringing artefacts at the coil edges from the phase demodulation.

The agreement between the ideal and reconstructed flow profiles is illustrated in figure 4.13, which shows horizontal slices through the flow profiles above and below the X-Point. Both the idealised data inversions (green lines) and full analysis chain tests (red lines) generally show good quantitative agreement with the input profiles, however the noisy data inversion does show loss of fine spatial detail (e.g.

in fig. 4.13(b), R = 0.4 − 0.55m) and spurious flow artefacts (these slices also do not illustrate the ringing artefacts previously mentioned). The flow noise level in parts of the profiles away from any artefacts is not significantly amplified over the noise

4.7. Summary 94 level on the line integrated measurements. Future possibilities for improving the quality of reconstructions from noisy data include applying smoothness constraints to the flow reconstruction, and accounting for the anisotropic spatial resolution when building the response matrix. These tests also do not account for possible errors from uncertainty in the viewing geometry calibration, errors in EFIT, the presence of reflections in real images or the presence of cross-field or non-axisymmetric flows.

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Figure 4.13: Horizontal slices of the v|| profiles shown in figure 4.12 at Z = −1.15m (top) and Z = −1.31m, showing ideal and inverted profiles.

4.7 Summary

This chapter has presented the data analysis methods used with MAST CIS data, including numerical experiments investigating sources of measurement error. This was achieved using simulated line-integrated data based on plasma profiles from OEM-EIRENE simulations of MAST.

The data analysis process begins by removal of bright spots and streaks in the

4.7. Summary 95 images due to D-D fusion neutrons in NBI heated discharges, before the underlying brightness image is extracted using frequency domain filtering and boxcar smoothing perpendicular to the fringes. The extracted brightness is then factored out, and the flow information (fringe phase) is extracted using the analytic signal representation of the resulting signal. Windowing in Fourier space and apodisation of the input data around sharp jumps in brightness are used to reduce artefacts due to sharp spatial features and image noise, at the cost of smoothing the spatial response to flows.

Pixel-based tomographic inversion using the SART algorithm has been imple-mented in MATLAB and tested with simulated divertor data, including integrated testing with the interferogram demodulation. The results show good quantitative agreement between the plasma profiles used to generate the test data and the re-covered profiles from the simulated measurements. However, for noisy data the flow inversion shows some ringing artefacts at sharp image edges, and larger errors for parts of the plasma profile with low emissivity. These must be kept in mind when applying the techniques to real data, and inverted flow profiles can only be obtained from parts of the plasma which are emitting sufficiently brightly.

In the next chapter, we go on to present experimental characterisation of the MAST CIS diagnostic and its constituent components.

Chapter 5