image quality parameters and their measurementimage quality in x -ray detectors icmp, september 1,...
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ICMP, September 1, 2013 / Brighton, England 1 Image Quality in X-ray Detectors
Image Quality Parameters
and their Measurement
John M. Boone, Ph.D., FAAPM, FSBI, FACR
Professor and Vice Chair of Radiology Professor of Biomedical Engineering
University of California, Davis
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2 Image Quality
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3 Image Quality
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Image Quality Parameters
and their Measurement Linear Systems / Stationary Behavior
Spatial Resolution
field measurements
scientific characterization
Contrast Resolution (noise)
field measurements
scientific characterization
Signal to Noise Ratio
field measurements
scientific characterization
Summary
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary
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Image Quality Parameters
and their Measurement
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary
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Response of a 400 speed screen-film system (Fuji)
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Response of a Varian 4030CB Flat Panel Detector
high gain mode
low gain mode
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Response of a Fuji Computed Radiography (CR) System
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stationary
non-stationary
Image Quality
point spread functions (PSFs)
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Image Quality Parameters
and their Measurement
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary
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Field Measurement
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spatial resolution
line pair phantom
star pattern phantom
wedge
resolution test tools
Image Quality
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system input
system output
blurring
Spatial Resolution: Measurements in the Field
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modulation
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can resolve 4 bars?
yes
heck no
no
yes
yes
yes
limiting spatial resolution
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Limiting spatial resolution (~10% of MTF)
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Scientific Characterization
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Image Quality
The Point Spread Function (PSF)
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Image Quality
The Line Spread Function (LSF)
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The Edge Spread Function (ESF)
Image Quality 20
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Image Quality
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The Line Spread Function – lsf(x) – “slit image”
measures focal spot resolution measures detector resolution
slit
slit
focal spot
detector
{
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The Line Spread Function – lsf(x) – “slit image”
resulting image of slit measurement geometry
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The Line Spread Function – lsf(x) – “slit image”
resulting image of slit actual lsf(x)
position (mm)
gray
sca
le (d
n)
orthogonal trace thru slit
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Fourier Representation
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different phase
different amplitude
different frequency
sine waves 101
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2( )( )
( )
ifxlsf x e dxOTF f
lsf x dx
∞ − π
−∞∞
−∞
= ∫∫
( ) ( )MTF f OTF f=
2 2( ) [ ( )] [ ( )]MTF f OTF f OTF f= ℜ + ℑ
complex
real imaginary real
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lsf(x)
MTF(f)
2( )
( )
ifxlsf x e dx
lsf x dx
∞ − π
−∞∞
−∞
∫∫
normalizes area to 1.0
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modulation transfer function
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top view of detector array
side view
Direct Digital Detectors (eg Selenium)
a
aperture – lsf(x)
lsf(x) = RECT{x/a}
∆
pitch – Nyquist
FN = 1 2 ∆
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other considerations
Pre-sampled LSF / ESF
Type of Image Processing
flat fielding OK
dead pixel correction OK
“for presentation” not OK
Paralax issues
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Image Quality Parameters
and their Measurement
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary
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Field Measurement
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contrast resolution
1.2 µR/frame 1.8 µR/frame 3.8 µR/frame
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( )2
2
1
1 ( , )1
N
ii
I x y IN =
σ = −− ∑
2σ = σ
N = number of pixels in ROI hi(x,y): the data in the ROI
“noise”
First Order Determination of Noise
region on interest (ROI)
digital image
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Scientific Characterization
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σ σ
But “noise”, or the standard deviation σ, does not tell the whole story
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( )( )2 2 ( )
1
1( , ) ( , ) x yN
i f x f yx y ix y
iNPS f f I x y I e dxdy
N∞ ∞ − π +
=−∞ =−∞=
= −∑ ∫ ∫
The Noise Power Spectrum (NPS) or Wiener Spectrum
10 20 30 40 50 60
10
20
30
40
50
60
N regions on interest (ROIs)
10 20 30 40 50 60
10
20
30
40
50
60
10 20 30 40 50 60
10
20
30
40
50
60
10 20 30 40 50 60
10
20
30
40
50
60
average
analytical equation
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The Noise Power Spectrum (NPS) or Wiener Spectrum
10 20 30 40 50 60
10
20
30
40
50
60
N regions on interest (ROIs)
10 20 30 40 50 60
10
20
30
40
50
60
10 20 30 40 50 60
10
20
30
40
50
60
10 20 30 40 50 60
10
20
30
40
50
60
average
discrete implementation
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The Noise Power Spectrum (NPS) or Wiener Spectrum
10 20 30 40 50 60
10
20
30
40
50
60 radial average
spatial frequency (mm-1) N
PS (m
m2 )
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The Noise Power Spectrum (NPS) or Wiener Spectrum
10 20 30 40 50 60
10
20
30
40
50
60 radial average
spatial frequency (mm-1) N
PS (m
m2 )
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The Noise Power Spectrum (NPS) or Wiener Spectrum
spatial frequency (mm-1) N
PS (m
m2 )
σ2
2 ( )NPS f dfσ = ∫
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uncorrelated noise correlated noise
convolution
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Image Quality Parameters
and their Measurement
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary
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Field Measurement
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Signal difference to noise ratio (SDNR)
Contrast to Noise Ratio (CNR)
signal
background
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detail detail detail
cont
rast
cont
rast
cont
rast
A B C
the contrast detail curve
Image Quality 49
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the contrast detail curve
interpretation
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lower dose higher dose
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Scientific Characterization
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22 ( )( )
( )outMTF fSNR fNPS f
=
2 2 ( )( )( )
k MTF fNEQ fNPS f
=
The Noise Equivalent Quanta (NEQ)
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2 2 ( )( )( )
k MTF fDQE fq NPS f
=
( )( ) NEQ fDQE fq
=
2
2
( )( )( )
out
in
SNR fDQE fSNR f
=2 ( )inSNR f q=
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2 2 ( )( )( )
k MTF fDQE fq NPS f
=
k = mean GS value
q = mean photons/mm2 for this acquisition
Image acquired to compute NPS(f)
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detective quantum efficiency (DQE)
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2.94 x 107 photons / mm2
120 kV / 1.0 mGy air kerma incident
To determine q: …some spectral modeling required
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57 IEC values courtesy Nicole T. Ranger on line presentation
RQA3 50 kV 10 4.0 RQA5 70 kV 21 7.1 RQA7 90 kV 30 9.1 RQA9 120 kV 40 11.5
IEC: International Electrotechnical Commission (IEC 61267-1)
Radiation Quality
Designation Tube Voltage
~added Filtration (mm Al)
HVL (mm Al)
150
cm
DQE measurement geometry
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Image Quality Parameters
and their Measurement
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary
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Field measurements of image quality are adequate
but are subjective and imprecise
Scientific measurements are useful in detector evaluation
but their quantitative nature is desirable
Digital radiography QC should convert to quantitative measures in time
Clinical Medical Physicists should understand MTF, NPS, NEQ, DQE
Summary
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Image Quality Parameters
and their Measurement
Linear Systems / Stationary Behavior
Spatial Resolution
Contrast Resolution (noise)
Signal to Noise Ratio
Summary