1. An Image Filtering Technique for SPIDER Visible Tomography N. Fonnesu M. Agostini, M. Brombin, R.Pasqualotto, G.Serianni 3rd PhD Event- York- 24th-26th June 2013

2. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Introduction My research activity is focused on: Optical diagnostics for Neutral Beam (i.e. tomography) Analyses and numerical models dedicated to characterize the ion extraction from the source, beam optics in the accelerator and beam transport in the injector Fast neutron measurements on RFX (Reversed field pinch device) The ITER Heating Neutral Beam (HNB) injector, based on negative ions accelerated at 1MV, will be tested and optimized in the SPIDER source and MITICA full injector prototypes, using a set of diagnostics not available on the ITER HNB. SPIDER (Full size prototype of the HNB source, ions accelerated at 100 kV) MITICA (Full size prototype of the HNB, ions accelerated at 1 MV)

3. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Tomography: what is it? why is it important in SPIDER ? tomography code and inversion technique The role of instrumental noise in tomography reconstructions Filtering technique in the spatial domain and results Conclusions and future works Outline

4. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu What is tomography? Tomography is the reconstruction of a cross-section (or a slice) of an object from its projections (i.e. integral of the image at a given angle). Every projection is made of a large number of lines of sight (LoSs) Fan of LoSs Fan of LoS Fan of LoSs

5. E/O PC Diagnostic room PC O/E viewport lens CCD beam source 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Observing the emission of Hα (Dα) radiation (due to collisions between background gas and ions) on a plane perpendicular to the beam with a set of 3127 lines-of-sight, will allow a tomographic reconstruction of the two dimensional beam emission function, which is proportional to the beam density. SPIDER Visible Tomography Main target: measurement of the beam uniformity with sufficient spatial resolution and of its evolution throughout the pulse duration. The maximum acceptable deviation from beam uniformity is ±10% the deviation of the reconstruction from the real emissivity of the beam has to be sufficiently lower than this value

6. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Inversion technique: the pixel method I j : line-integrated signal of the line j ε i : emissivity of the pixel i a i,j : fraction of area of pixel i observed by line j SART METHOD PIXEL METHOD From the line integrated measurements we want to obtain the 2D map of the beam emission 1280 beamlets divided into 16 beamlet groups j-th line of sight Integrated Hα (Dα) radiation along the j-th line of sight Emissivity of the beam The unknowns are the emittivities ε i of each pixel i of the image which can be obtained by inverting the matrix a Pixel i

7. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Instrumental noise in the line integrated signals Phantoms (i.e. 2D emissivity profiles) that reproduce different experimental beam configurations (non-uniformity of ±10%, uniform profile, two beamlet groups turned off) are simulated and reconstructed by the tomography code with satisfactory results. ±10% However, if we simulate noisy input data, errors in the reconstructed image shows that noise acts as a limiting factor for the maximum achievable resolution. Reference phantom …adding a random noise (unif. distr., max 20%)

8. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu npix Errors in the reconstructed beam profile

9. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Filtering in the spatial domain The filtering algorithm is based on Lees formula [1] that allows to calculate the estimated noise-free pixel intensity just considering its neighborhood: this value will represent the filtered intensity for the corresponding pixel. [1] J.S. Lee, Optical Engineering 25 (5), 636-646 (1986) Pixel i,j filtered value of the pixel i,j at the step l+1 value of the pixel i,j at the step l local average pixels value at the step l parameter (variance,mean of the pixels neighborhood) Pixels neighborhood is defined by a squared window (5x5 pixels gives better results)

10. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Filtering in the spatial domain In order to minimize the reconstruction errors, the algorithm applies iteratively the Lees formula.

11. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Filtered reconstructions: linear emissivity variation

12. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Filtered reconstructions: constant emissivity

13. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Filtered reconstructions: 2 beamlet groups off The algorithm tends to smooth the boundary of the zero-emissivity area present in the case a beamlet group is switched off, affecting the entire profile. It is necessary to introduce a delta function that allows not to consider pixels with quasi-zero emissivity in the local statistics (for the calculation of the mean of x and k parameter).

14. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Comparison with a low pass filter FFT+ Low Pass (Hann) filter Lees filter

15. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Conclusions The maximum errors (in reconstructions with 640 pixels) are reduced to values up to 3.5% considering different operating conditions of SPIDER. Filtering in the spatial frequency domain could give similar results (for the same level of noise) just considering a lower number of pixels (i.e. 32 or 64). A higher number of pixels can go beyond the simple detection of the lack of uniformity of the beam, giving information about its causes and suggesting possible solutions. Encouraging attempt to demonstrate the feasibility to suppress instrumental noise by a post-processing algorithm that does not increase significantly the processing time.

16. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu Future Works Filtering algorithm for MITICA visible tomography Development of the tomography code for N1O (60 kV negative ion source)

17. 3rd PhD Event- York- 24th-26th June 2013 – Nicola Fonnesu THANK YOU FOR YOUR ATTENTION !