X-ray Detection & Noise Flashcards

1
Q

xray Absorbed energy is either

A

(1) directly producing an image (analogue)
(2) processed electronically (digital)

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2
Q

xray Detector Characteristics

A

⚫ Spatial resolution
⚫ Spectral resolution
⚫ Dynamic range
⚫ Noise
⚫ Read-out time
⚫ Quantum efficiency
⚫ Field of view

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3
Q

Spatial Resolution types

A

𝑃𝑜𝑖𝑛𝑡 𝑠𝑝𝑟𝑒𝑎𝑑 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 (𝑃𝑆𝐹): 𝑛𝑜𝑡 𝑝𝑟𝑎𝑐𝑡𝑖𝑐𝑎𝑙 𝑡𝑜 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 →𝑙𝑜𝑤 𝑓𝑙𝑢𝑥

𝐿𝑖𝑛𝑒 𝑠𝑝𝑟𝑒𝑎𝑑 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 (𝐿𝑆𝐹): 𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑡𝑜 𝑎 1𝐷 𝑙𝑖𝑛𝑒 𝑖𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛

𝐸𝑑𝑔𝑒 𝑠𝑝𝑟𝑒𝑎𝑑 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 (𝐸𝑆𝐹): derivative of ESF = LSF

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4
Q

1𝐷 𝐹𝑜𝑢𝑟𝑖𝑒𝑟 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝑜𝑓 𝐿𝑆𝐹 𝑔𝑖𝑣𝑒𝑠 𝑡ℎ𝑒

A

𝑀𝑇𝐹 (𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛)

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5
Q

Dynamic Range, refers to the range

A

between the minimum and maximum detectable signal levels. It indicates the ability of a system or device to capture and represent a wide range of signal values accurately.

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6
Q

Dark Current

A

Noise without input (illumination)
e.g. thermal fluctuations of el.-holes-pairs

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7
Q

Read-out Noise:

A

Errors during read-out procecure

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8
Q

dark current is dependent on ………., while read-out noise only depends on the ……….

A

dark current is dependent on exposure time, while read-out noise only depends on the read-out speed or ‘frame rate‘

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9
Q

‚Frame rate

A

Exposure time + read-out time

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10
Q

CCD (Charge-Coupled Device)

A

transition from film-based photography to digital imaging.

A CCD chip is a silicon-based semiconductor device that can convert incoming light into an electrical charge

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11
Q

Digital X-ray detector types

A

Conventional detectors
e.g. CCD, Flatpanel

Photon-counting detectors

Spectral detectors

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12
Q

CONVENTIONAL TECHNOLOGY FLOW

A

X-RAY

SCINTILLATOR (X-RAYS ARE CONVERTED TO LIGHT)

PHOTODIODE (LIGHT IS CONVERTED TO ELECTRICAL SIGNALS)

ELECTRIC CIRCUIT

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13
Q

PHOTON-COUNTING TECHNOLOGY flow

A

X-RAY

DIRECT CONVERSION (X-RAY IS CONVERTED TO
ELECTRICAL SIGNALS)

ELECTRIC CIRCUIT

PULSE HEIGHT ANALYZER

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14
Q

general definition of noise

A

any unwanted signal (image)

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15
Q

we will use the following definition of noise

A

random, uncorrelated signal (image)

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16
Q

Probability Density Function (PDF)

A

𝑃 (𝑎 < 𝑥 < 𝑏) = integral from 𝑎 to 𝑏 (𝑃(𝑥) 𝑑𝑥)

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17
Q

Expectation Value

A

𝐸 [𝑥 ] = integral from −∞ to∞ (𝑥 ∙ 𝑃(𝑥) 𝑑𝑥 ) = 𝜇

18
Q

variance

A

𝑉𝑎𝑟[ 𝑥 ]= 𝐸 [ (𝑥 − 𝐸[ 𝑥 ]) ^2]

19
Q

Skewness (symmetry)

A

𝑆 [𝑥] =𝐸 [(𝑥 − 𝐸[ 𝑥 ]) ^3]

20
Q

kurtosis (peakedness)

A

higher central moments
𝐾 [𝑥] =𝐸 [(𝑥 − 𝐸[ 𝑥 ]) ^4]

21
Q

Central Limit Theorem

A

sum of independent and identically distributed variables converge towards the normal distribution

22
Q

Poisson distribution:
Probability mass function
expectation
variance
occurence

A

𝑃 (𝑥 = 𝑘) =(𝜆^k exp(−𝜆))/ 𝑘!
𝐸[ 𝑥 ]= 𝜆
𝑉𝑎𝑟 [𝑥 ]= 𝜆
𝑝ℎ𝑜𝑡𝑜𝑛 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑜𝑟 𝑒𝑚𝑎𝑖𝑙 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔

23
Q

other distributions

A

Wrapped normal distribution
Rice distribution
Lorentz distribution
Gamma distribution

24
Q

Detector noise (for CCDs)

A

− shot noise (photon statistics, Poisson)

− dark current (thermal electronic fluctuations in semiconductor, Poisson)

− readout noise (fluctuations during amplification and digitization, Gaussian)

25
dark frame measures ......, bright frame measures .......
dark frame measures detector noise, hot pixels, dead pixels bright frame measures gain differences and imperfections (dust, etc)
26
contrast
𝐶 = |𝑆 (𝑥2) − 𝑆(𝑥1)| absolute difference of signal intensities in two different pixel locations
27
Visibility (Michelson contrast)
𝑉𝑖𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 = (|𝑆 (𝑥2) − 𝑆(𝑥1)|)/ (𝑆 (𝑥2) + 𝑆(𝑥1))
28
Contrast-to-noise (CNR)
𝐶𝑁𝑅 = |𝑆 (𝑥2) − 𝑆(𝑥1)|/ (sqrt(𝜎(𝑥)^2+ 𝜎(𝑥(1) ^2))
29
Noise power spectrum (NPS)
Power spectrum of pure noise image 𝑛 (𝑥, 𝑦) ⇔ 𝑁(𝑢, 𝑣) 𝑁𝑃𝑆 = 𝐸 [𝑁(𝑢, 𝑣)]^2
30
NPS Connection to auto-correlation
inv fourier of abs(N(u,v)^2) = autocorrelation
31
Weiner-Khinchin theorem
𝑎𝑢𝑡𝑜 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑛𝑜𝑖𝑠𝑒 ⇒ 𝑛𝑜𝑖𝑠𝑒 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑑𝑒𝑛𝑠𝑖𝑡𝑦
32
red noise white noise blue noise
low freq high power constant power high freq high power
33
White noise in spatial domain means
white noise in frequency domain
34
White noise is perfectly
uncorrelated (Auto-correlation of white noise is the delta function)
35
Noise reduction by averaging requirement
additive noise, zero mean
36
Denoising by linear filtering
Noise reduction possible, but at cost of sharpness (blurred)
37
Median filtering Good for
getting rid of 'outliers'
38
Median filtering Less sensitive to
Less sensitive to outliers in pixel ensemble, better edge preservation
39
Bilateral filter similar to
Gaussian filter, which is a weighted average of intensity of adjacent pixels with a decreasing weight with spatial distance
40
Bilateral filter takes into account the
variation of intensities to preserve edges
41
Bilateral Filter The kernel shape depends on
The kernel shape depends on the image content
42
Describe the way indirect detection works
X-Ray Photons Scintillator Visible Light Photons Photodiode Read-Out Circuit