1

Limitations to Flat-Field Limitations to Flat-Field Correction Methods when Correction Methods when used with an X-ray Spectrumused with an X-ray Spectrum

David W. DavidsonDavid W. DavidsonUniversity of University of

GlasgowGlasgowCo-Authors:Christer Frojdh, Hans-Erik Nilsson: ITM, SundsvallVal O’Shea, Mahfuzur Rahman: University of Glasgow

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Medipix ChipMedipix Chip Designed by M.Campbell Designed by M.Campbell

(CERN)(CERN)

Single photon counting chipSingle photon counting chip

Tunable thresholdTunable threshold

64 x 64 pixels64 x 64 pixels

Silicon detector for X-raysSilicon detector for X-rays

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Flat-Field CorrectionFlat-Field Correction Used to correct for inhomogeneity of response in X-ray Used to correct for inhomogeneity of response in X-ray

imaging sensorsimaging sensors Numerous images are taken with the sensor exposed to Numerous images are taken with the sensor exposed to

a uniform fielda uniform field The sensitivity of each pixel is determined by the The sensitivity of each pixel is determined by the

average response and a gain map calculatedaverage response and a gain map calculated Further images can be corrected by dividing by this Further images can be corrected by dividing by this

gain mapgain map If the gain map is functioning correctly the variations If the gain map is functioning correctly the variations

remaining should be due to the statistical variation of remaining should be due to the statistical variation of the noisethe noise

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Flat-Field Correction Flat-Field Correction WorkingWorking

Raw flood image taken at 70% exposure limit

Image corrected using a gain map calculated from 50 such images

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Gain Map VariationsGain Map Variations It has been seen that the gain map, taken for one It has been seen that the gain map, taken for one

source, will not correctly adjust for all sources using source, will not correctly adjust for all sources using the same chipthe same chip

Test effect of map on flood imagesTest effect of map on flood images

Set of flood images with non-monochromatic source Set of flood images with non-monochromatic source to test for consistencyto test for consistency

The variation of efficiency map with incident spectra The variation of efficiency map with incident spectra is obtainedis obtained

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Variation of gain mapVariation of gain map

The incident spectra after various thicknesses of perspex shows beam hardening

Change in gain map from no perspex to 40mm of perspex

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

What effect does the What effect does the wrong map have?wrong map have?

Each map was generated Each map was generated by 50 flood imagesby 50 flood images

A flood image for each A flood image for each input spectra was then input spectra was then adjusted using each mapadjusted using each map

The distribution of counts The distribution of counts was then examinedwas then examined

The standard deviation The standard deviation drops below Poisson value drops below Poisson value only for the correct maponly for the correct map

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Explanation of gain map Explanation of gain map variationvariation

Each photon absorbed in detector releases chargeEach photon absorbed in detector releases charge This charge depends on photon energy and ionisation energy This charge depends on photon energy and ionisation energy

of detector materialof detector material Charge is drifted to electrodesCharge is drifted to electrodes Loss in material included in charge collection efficiency (CCE)Loss in material included in charge collection efficiency (CCE) Lack of uniformity across detector brings in use of gain Lack of uniformity across detector brings in use of gain

correction factor per pixelcorrection factor per pixel Any variation in effective thickness of detector medium will Any variation in effective thickness of detector medium will

result in a variation of absorption efficiency dependent on result in a variation of absorption efficiency dependent on incident energy spectrumincident energy spectrum

This gain correction factor will be dependent on the energy of This gain correction factor will be dependent on the energy of the photonthe photon

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Mono-energetic X-raysMono-energetic X-rays Signal per pixel for integrating and photon counting systemsSignal per pixel for integrating and photon counting systems

Sint = Ge * e * (1-exp(-e * t)) * Qe

Scount = Ge * e * (1-exp(-e * t)) If Qe > Qth

Ge = Gain constant

e = No. of photons entering the pixele = Linear attenuation coefficient

t = Effective detector thicknessQe = registered charge per photon

(includes CCE)

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Spectrum of X-raysSpectrum of X-rays Signal per pixel for integrating and photon counting detectorsSignal per pixel for integrating and photon counting detectors

Sint = ∫ Ge * e * (1-exp(-e * t)) * Qe de

Scount = ∫ Ge * e * (1-exp(-e * t)) de If Qe > Qth

However in practise the gain map is applied for all However in practise the gain map is applied for all energiesenergiesSint = G* ∫ e * (1-exp(-e * t)) * Qe de

Scount = G* ∫ e * (1-exp(-e * t)) de If Qe > Qth

This would only be correct if G were independent This would only be correct if G were independent of energyof energy

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Potential SolutionPotential Solution Possibility of calculating theoretical gain mapsPossibility of calculating theoretical gain maps

Forming a database of gain mapsForming a database of gain maps

Reducing amounts of preparation work for any set Reducing amounts of preparation work for any set of resultsof results

Interpolating between available gain mapsInterpolating between available gain maps

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Interpolating MapsInterpolating Maps First simple test for First simple test for

different spectradifferent spectra

Result -Result -• Improvement of factor Improvement of factor

1.51.5• Brings distribution to Brings distribution to

below Poisson (just below Poisson (just like correct map)like correct map)

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

SummarySummary Correct flat-field adjustment is required so as to Correct flat-field adjustment is required so as to

avoid phantom images (Artefacts)avoid phantom images (Artefacts)

Flat-field adjustment requires correct gain mapFlat-field adjustment requires correct gain map

On each separate pixel the gain adjust is dependent On each separate pixel the gain adjust is dependent on energyon energy

Some calculation of theoretical gain maps is possibleSome calculation of theoretical gain maps is possible

University of Glasgow David W. Davidson IWoRiD 2002 Amsterdam

Final SolutionFinal Solution The use of monochromatic sources would remove The use of monochromatic sources would remove

this effect and allow correct adjustment of the this effect and allow correct adjustment of the image regardless of objects placed in the beamimage regardless of objects placed in the beam

The inclusion of an ADC on each pixel would allow The inclusion of an ADC on each pixel would allow the incident spectrum to be found and a correction the incident spectrum to be found and a correction for the relative intensity of each energy present for the relative intensity of each energy present would be possiblewould be possible

or