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

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

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)


• 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


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 LoSs

E/O

PC

Diagnostic room

PC

PC

O/E

viewportlens

CCD

beamsource


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


Inversion technique: the pixel method

jii

ij aI ,

Ij : line-integrated signal of the line j

εi: emissivity of the pixel i

ai,j: fraction of area of pixel i observed by line j

1 aI 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 sightEmissivity of the beam

The unknowns are the emittivities εi of each pixel i of the image which can be obtained by inverting the matrix a

Pixel i

dxdyyxfjl

j ,


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%)


npix

Errors in the reconstructed beam profile


Filtering in the spatial domain

The filtering algorithm is based on Lee’s 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

,ll

jill

ji xxkxx

[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 pixel’s value at the step l

parameter (variance,mean of the pixel’s neighborhood)

Pixel’s neighborhood is defined by a

squared window (5x5 pixels gives

better results)


Filtering in the spatial domain

In order to minimize the reconstruction errors, the algorithm applies

iteratively the Lee’s formula.


Filtered reconstructions: linear emissivity variation


Filtered reconstructions: constant emissivity


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).

i j ji

i j

ljijil

ji

xx

,

,,1,


Comparison with a low pass filter

FFT+ Low Pass (Hann) filter Lee’s filter


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.


Future Works

•Filtering algorithm for MITICA visible

tomography•Development of the tomography code

for N1O (60 kV negative ion source)


THANK YOU FOR YOUR ATTENTION !

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

Documents

rd phd event york

nicola fonnesu tomography

nicola fonnesu filtering

beam uniformity

line j i

value slide

nicola fonnesu introduction

beam transport