X-ray Detection & Noise

Question 1

xray Absorbed energy is either

Answer 1

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

Question 2

xray Detector Characteristics

Answer 2

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

Question 3

Spatial Resolution types

Answer 3

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

Question 4

1𝐷 𝐹𝑜𝑢𝑟𝑖𝑒𝑟 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝑜𝑓 𝐿𝑆𝐹 𝑔𝑖𝑣𝑒𝑠 𝑡ℎ𝑒

Answer 4

𝑀𝑇𝐹 (𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛)

Question 5

Dynamic Range, refers to the range

Answer 5

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.

Question 6

Dark Current

Answer 6

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

Question 7

Read-out Noise:

Answer 7

Errors during read-out procecure

Question 8

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

Answer 8

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

Question 9

‚Frame rate

Answer 9

Exposure time + read-out time

Question 10

CCD (Charge-Coupled Device)

Answer 10

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

Question 11

Digital X-ray detector types

Answer 11

Conventional detectors
e.g. CCD, Flatpanel

Photon-counting detectors

Spectral detectors

Question 12

CONVENTIONAL TECHNOLOGY FLOW

Answer 12

X-RAY

SCINTILLATOR (X-RAYS ARE CONVERTED TO LIGHT)

PHOTODIODE (LIGHT IS CONVERTED TO ELECTRICAL SIGNALS)

ELECTRIC CIRCUIT

Question 13

PHOTON-COUNTING TECHNOLOGY flow

Answer 13

X-RAY

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

ELECTRIC CIRCUIT

PULSE HEIGHT ANALYZER

Question 14

general definition of noise

Answer 14

any unwanted signal (image)

Question 15

we will use the following definition of noise

Answer 15

random, uncorrelated signal (image)

Question 16

Probability Density Function (PDF)

Answer 16

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

Question 17

Expectation Value

Answer 17

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

Question 18

variance

Answer 18

𝑉𝑎𝑟[ 𝑥 ]= 𝐸 [ (𝑥 − 𝐸[ 𝑥 ]) ^2]

Question 19

Skewness (symmetry)

Answer 19

𝑆 [𝑥] =𝐸 [(𝑥 − 𝐸[ 𝑥 ]) ^3]

Question 20

kurtosis (peakedness)

Answer 20

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

Question 21

Central Limit Theorem

Answer 21

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

Question 22

Poisson distribution:
Probability mass function
expectation
variance
occurence

Answer 22

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

Question 23

other distributions

Answer 23

Wrapped normal distribution
Rice distribution
Lorentz distribution
Gamma distribution

Question 24

Detector noise (for CCDs)

Answer 24

− shot noise (photon statistics, Poisson)

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

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

Question 25

dark frame measures ……,
bright frame measures …….

Answer 25

dark frame measures detector noise, hot pixels, dead pixels

bright frame measures gain differences and imperfections (dust, etc)

Question 26

contrast

Answer 26

𝐶 = |𝑆 (𝑥2) − 𝑆(𝑥1)|

absolute difference of signal intensities in two different pixel locations

Question 27

Visibility (Michelson contrast)

Answer 27

𝑉𝑖𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 = (|𝑆 (𝑥2) − 𝑆(𝑥1)|)/ (𝑆 (𝑥2) + 𝑆(𝑥1))

Question 28

Contrast-to-noise (CNR)

Answer 28

𝐶𝑁𝑅 = |𝑆 (𝑥2) − 𝑆(𝑥1)|/ (sqrt(𝜎(𝑥)^2+ 𝜎(𝑥(1) ^2))

Question 29

Noise power spectrum (NPS)

Answer 29

Power spectrum of pure noise image
𝑛 (𝑥, 𝑦) ⇔ 𝑁(𝑢, 𝑣)
𝑁𝑃𝑆 = 𝐸 [𝑁(𝑢, 𝑣)]^2

Question 30

NPS Connection to auto-correlation

Answer 30

inv fourier of abs(N(u,v)^2) = autocorrelation

Question 31

Weiner-Khinchin theorem

Answer 31

𝑎𝑢𝑡𝑜 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑛𝑜𝑖𝑠𝑒 ⇒ 𝑛𝑜𝑖𝑠𝑒 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

Question 32

red noise
white noise
blue noise

Answer 32

low freq high power
constant power
high freq high power

Question 33

White noise in spatial domain means

Answer 33

white noise in frequency domain

Question 34

White noise is perfectly

Answer 34

uncorrelated (Auto-correlation of white
noise is the delta function)

Question 35

Noise reduction by averaging requirement

Answer 35

additive noise, zero mean

Question 36

Denoising by linear filtering

Answer 36

Noise reduction
possible, but at
cost of sharpness (blurred)

Question 37

Median filtering Good for

Answer 37

getting rid of ‘outliers’

Question 38

Median filtering Less sensitive to

Answer 38

Less sensitive to outliers in pixel ensemble, better edge preservation

Question 39

Bilateral filter similar to

Answer 39

Gaussian filter, which is a weighted average of
intensity of adjacent pixels with a decreasing weight with spatial distance

Question 40

Bilateral filter takes into account the

Answer 40

variation of intensities to preserve edges

Question 41

Bilateral Filter The kernel shape depends on

Answer 41

The kernel shape depends on the image content

Question 42

Describe the way indirect detection works

Answer 42

X-Ray Photons
Scintillator
Visible Light Photons
Photodiode
Read-Out Circuit