PD Stefan Bosse - AFEML - Module X:

X-ray Imagaing and Data

PD Stefan Bosse - AFEML - Module X: Further Readings

Further Readings

PD Stefan Bosse - AFEML - Module X: X-ray Radiation

X-ray Radiation

• X-rays belong to the group of electromagnetic rays, hence, they follow the rules of electromagnetic radiation.

Berger, Yang, Maier, Medical Imaging Systems, 2018 Wavelengths and frequencies of the different groups of electromagnetic radiation. X-rays lie in the range of 0.01nm up to 10nm.

PD Stefan Bosse - AFEML - Module X: X-ray Radiation

X-ray Radiation

• In industry, X-rays are often the method of choice, for example to test for very small cracks in metal parts in the field of non-destructive testing.

• The photon energy E is proportional to its frequency f and inverse proportional to its wavelength λ, that means the higher its frequency, the higher its energy:

$${E}_{{p}}=\frac{{{h}{c}_{{0}}}}{{\lambda_{{p}}}}={{f}_{{p}}{h}}$$

• Typical energies in NDT: 30-120 keV ⇔ 0.04nm - 0.01nm

PD Stefan Bosse - AFEML - Module X: X-ray Generation

X-ray Generation

PD Stefan Bosse - AFEML - Module X: X-ray Generation

X-ray Generation

• The anode is tilted by a certain angle to direct the emerging X-rays in the right direction. The angle determines the Focal Spot Size (FSD), and hence the imaging resolution, discussed later!

Berger, Yang, Maier, Medical Imaging Systems, 2018 Vacuum X-ray tube: The image on the left shows a schematic how electrons are accelerated from the cathode to the anode to generate X-ray photons. The image on the right shows a historic vacuum X-ray tube.

PD Stefan Bosse - AFEML - Module X: X-ray Generation

X-ray Generation

The production of X-rays is caused by two different processes:

1. Electron Interaction (Discrete)
2. Nucleus interaction (Continuous)

The firs process: The electron interacts with an inner-shell electron of the target, characteristic X-radiation can be produced. This kind of X-rays results from a sufficiently strong interaction that ionizes the target atom by a total removal of the inner-shell electron.

• The transition of an orbital electron from an outer-shell to an inner-shell is accompanied by the emission of an X-ray photon, with an energy equal to the difference in the binding energies of the orbital electrons involved.

PD Stefan Bosse - AFEML - Module X: X-ray Generation

X-ray Generation

Another type of interaction in which the electron can lose its kinetic energy delivers the second process of X-ray production:

• Caused by the interaction of the electron with the nucleus of a target atom.
• As the colliding electron passes by the nucleus of an anode atom, it is slowed down and deviated, leaving with reduced kinetic energy in a different direction.
• This loss in kinetic energy reappears as an X-ray photon. This type of X-rays is called Bremsstrahlung,
• The amount of kinetic energy that is lost in this way can vary from zero to the total incident energy ⇒ Continuous energy distribution!

PD Stefan Bosse - AFEML - Module X: X-ray Generation

X-ray Generation

Berger, Yang, Maier, Medical Imaging Systems, 2018

PD Stefan Bosse - AFEML - Module X: X-ray Material Interaction

X-ray Material Interaction

Berger, Yang, Maier, Medical Imaging Systems, 2018 Principles of photon-matter interactions

PD Stefan Bosse - AFEML - Module X: X-ray Material Interaction

X-ray Material Interaction

• The reduction of radiation intensity is a reduction of the number of photons that arrive at the detector.
• That process is usually referred to as attenuation.
• There are several different physical effects contributing to attenuation, including a change of the photon count, photon direction, or photon energy.

PD Stefan Bosse - AFEML - Module X: X-ray Material Interaction: Absorption

X-ray Material Interaction: Absorption

• Absorption is the main effect that contributes to X-ray imaging:

$${I}={I}_{{0}}·{e}^{{−µ{x}}}$$

with x as the material thickness and μ as the absorption coefficient that is dependent from the photon energy!

PD Stefan Bosse - AFEML - Module X: X-ray Material Interaction: Absorption

X-ray Material Interaction: Absorption

Hahn, Mary, DGZfP-Proceedings BB 84-CD , "A general approach to flaw simulation in..", CT-IP 2003 Absorption coefficient µ for aluminum against X-ray energy

PD Stefan Bosse - AFEML - Module X: X-ray Measuring Technologies

X-ray Measuring Technologies

PD Stefan Bosse - AFEML - Module X: X-ray Measuring Technologies

X-ray Measuring Technologies

PD Stefan Bosse - AFEML - Module X: X-ray Measuring Technologies

X-ray Measuring Technologies

https://umsystem.pressbooks.pub/digitalradiographicexposure/chapter/focal-spot-size/ The FSD depends on the filament size of the tube and the anode angle

PD Stefan Bosse - AFEML - Module X: X-ray Measuring Technologies

X-ray Measuring Technologies

https://umsystem.pressbooks.pub/digitalradiographicexposure/chapter/focal-spot-size/ Larger focal spot sizes increase penumbral unsharpness (but depends on magnification, too)

PD Stefan Bosse - AFEML - Module X: X-ray Measuring Technologies

X-ray Measuring Technologies

PD Stefan Bosse - AFEML - Module X: X-ray Radiography

X-ray Radiography

PD Stefan Bosse - AFEML - Module X: X-ray Radiography

X-ray Radiography

$${R}_{\text{limit}}=\frac{{p}_{{D}}}{{M}}$$

PD Stefan Bosse - AFEML - Module X: X-ray Tomography

X-ray Tomography

PD Stefan Bosse - AFEML - Module X: X-ray Detection

X-ray Detection

PD Stefan Bosse - AFEML - Module X: X-ray Image Intensifier

X-ray Image Intensifier

Berger, Yang, Maier, Medical Imaging Systems, 2018 Schematic principle of an image intensifier detector. The X-rays are first converted to light, which is converted to electrons. An optic accelerates the electrons towards a fluorescent screen which converts the electrons to light, which eventually results in an image.

PD Stefan Bosse - AFEML - Module X: X-ray Image Intensifier

X-ray Image Intensifier

Berger, Yang, Maier, Medical Imaging Systems, 2018 Detailed principle of an image intensifier detector. The X-rays are first converted to light, which is converted to electrons. An optic focuses the electron beam to a fluorescent screen or film material which converts the electrons to light

PD Stefan Bosse - AFEML - Module X: X-ray Image Intensifier

X-ray Image Intensifier

(Left) Vignetting artifact, i. e., luminescence drops at image periphery (Right) Distortion artifacts due to external fields, field inhomogeneities and optical systems

PD Stefan Bosse - AFEML - Module X: X-ray Image Intensifier

X-ray Image Intensifier

Example image (USAF 1951 test target, steel foil 100μm) from a cheap OV2940 CMOS camera with mini lens optics using a Thales XRII (8"), 55kV, Tungsten X-ray tube (FSD 0.8mm)

PD Stefan Bosse - AFEML - Module X: X-ray Image Intensifier

X-ray Image Intensifier

Advantages:

• High sensitivity
• Medium area (about 10000 mm²)
• Medium resolution, about 4 LP/mm

Disadvantages:

• Expensive
• High voltage generators required (up to 30 kV)
• Geometrical distortions (can depend on environmental conditions, external fields, ...)
• Sensitivity degrades during radiation exposition irreversible!

PD Stefan Bosse - AFEML - Module X: X-ray Images: Geometrical Errors

X-ray Images: Geometrical Errors

Errors by:

PD Stefan Bosse - AFEML - Module X: X-ray Images: Geometrical Errors

X-ray Images: Geometrical Errors

http://m43photo.blogspot.com/2012/05/geometric-distortion-correction.html Barrel vs. pincushion distortions

PD Stefan Bosse - AFEML - Module X: X-ray Images: Geometrical Errors

X-ray Images: Geometrical Errors

• Corrections by various algorithms and methods

• Commonly using a reference set of points (Ground truth points) and affine or non-linear polynomial transformation

• Fisheye Distortion Correction

PD Stefan Bosse - AFEML - Module X: Affine Transformations

Affine Transformations

https://neutrium.net/mathematics/basics-of-affine-transformation/ Affine transformations are typically applied through the use of a transformation matrix M and its inverse M^-1

PD Stefan Bosse - AFEML - Module X: Affine Transformations

Affine Transformations

For example to apply an affine transformation to a three dimensional point, P to transform it to point Q we have the following equation:

$${Q}={M}{P}\\ {P}={M}^{{-{1}}}{Q}$$

• When dealing with affine transformation points are represented as P = (P_x, P_y, P_z, 1) while vectors are represented as v = (v_x, v_y, v_z, 0) = v = (v_x, v_y, v_z).
• Where multiple transformations are to be performed a single compound transformation matrix can be computed.

$${M}={M}_{{2}}​{M}_{{1}}\\ {M}^{{-{1}}}={{M}_{{2}}^{{-{1}}}}​{{M}_{{1}}^{{-{1}}}}$$

PD Stefan Bosse - AFEML - Module X: Affine Transformations

Affine Transformations

Translation and Scaling

$${M}_{{\text{trans}}}={\left(\matrix{{1}&{0}&{0}&{m}_{{x}}\\{0}&{1}&{0}&{m}_{{y}}\\{0}&{0}&{1}&{m}_{{z}}\\{0}&{0}&{0}&{1}}\right)}\\ {M}_{{\text{scale}}}={\left(\matrix{{s}_{{x}}&{0}&{0}&{0}\\{0}&{s}_{{y}}&{0}&{0}\\{0}&{0}&{s}_{{z}}&{0}\\{0}&{0}&{0}&{1}}\right)}$$

PD Stefan Bosse - AFEML - Module X: Camera Calibration

Camera Calibration

https://euratom-software.github.io/calcam/html/intro_theory.html

• Using:
  • Rectilinear Lens Distortion (RLD) Model
  • Fisheye Lens Distortion (FLD) Model

The RLD model takes in to account radial (barrel or pincushion) distortion, and tangential (wedge-prism like, usually due to de-centring of optical components) distortions.

The fisheye distortion model only includes radial fisheye distortion.

PD Stefan Bosse - AFEML - Module X: Camera Calibration

Camera Calibration

RLD Model

$${\left(\matrix{{x}_{{d}}\\{y}_{{d}}}\right)}={\left[{1}+{k}_{{1}}{r}^{{2}}+{k}_{{2}}{r}^{{4}}+{k}_{{3}}{r}^{{6}}\right]}{\left(\matrix{{x}_{{n}}\\{y}_{{n}}}\right)}+\\ {\left(\matrix{{2}{p}_{{1}}{x}_{{n}}{y}_{{n}}+{p}_{{2}}{\left({r}^{{2}}+{2}{{x}_{{n}}^{{2}}}\right)}\\{p}_{{1}}{\left({r}^{{2}}+{2}{y}^{{2}}\right)}+{2}{p}_{{2}}{x}_{{n}}{y}_{{n}}}\right)}$$

where r = √(x_n²+y_n²), and k_n and p_n are radial and tangential distortion coefficients, respectively. The polynomial r² in in the first term describes the radial distortion while the second term represents tangential distortion.

PD Stefan Bosse - AFEML - Module X: Camera Calibration

Camera Calibration

FLD Model

$${\left(\matrix{{x}_{{d}}\\{y}_{{d}}}\right)}=\frac{{\theta}}{{{r}}}{\left[{1}+{k}_{{1}}\theta^{{2}}+{k}_{{2}}\theta^{{4}}+{k}_{{3}}\theta^{{6}}+{k}_{{4}}\theta^{{8}}\right]}{\left(\matrix{{x}_{{n}}\\{y}_{{n}}}\right)}$$

where r = √(x_n²+y_n²), and θ=tan^-1(r).

PD Stefan Bosse - AFEML - Module X: X-ray Images: Geometrical Errors

X-ray Images: Geometrical Errors

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Flat Panel

X-ray Detector: Flat Panel

Wotirz, Digital X-ray Sensors, Circuir Cellar, 2012 Principle construction of a flat panel X-ray detector with a scintillator material, a light guide (fibres), and a CMOS/CCD image sensor

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Flat Panel

X-ray Detector: Flat Panel

Advantages:

• Nearly no geometrical distortions
• Moderate sensitivity
• Large area (about 250000 mm²)
• High or medium resolution, real pixel size about 50-200 μm (theoretical resolution limit), up to 30 LP/mm

Disadvantages:

• Expensive
• Practical and theoretical resolution differs (especially in lower cost systems, far away from film-based imaging!)
• Noise (including X-ray induced noise)

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Optical Screen Imaging

X-ray Detector: Optical Screen Imaging

Self-made low-cost X-ray screen imaging detector (Bosse, 2023)

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Optical Screen Imaging

X-ray Detector: Optical Screen Imaging

Self-made low-cost X-ray screen imaging detector (Bosse, 2023)

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Optical Screen Imaging

X-ray Detector: Optical Screen Imaging

• Scintillator Screen: OrthoFine 100 foil (for medical radiography using films), green light emission

• CMOS image sensor: Sony IMX290 1920x1080 pixel (monochrome), exposure time 100-5000 ms

• Resolution limit: 3x3μm × M_opt=13 ⇒ 40μm

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Optical Screen Imaging

X-ray Detector: Optical Screen Imaging

Some recorded samples, contrast, and spectral light emission of scintillator versa camera sensitivity

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Optical Screen Imaging

X-ray Detector: Optical Screen Imaging

Advantages:

• Inexpensive
• Using only widely available components
• Medium area (about 4000 mm²)
• Medium resolution, real pixel size about 10-50 μm, up to 10 LP/mm

Disadvantages:

• Geometrical distortions (but known and independent from environmental parameters)
• Noise (including X-ray induced noise)
• Low sensitivity, long exposure times
• Lead glass placed before detector introduces additional geometric distortions

PD Stefan Bosse - AFEML - Module X: X-ray Detector: Optical Screen Imaging

X-ray Detector: Optical Screen Imaging

The optical imaging system is sensitive to "popcorn" noise induced by incident radiation (even a mirror do not eliminate such kind of noise due to scattering). Algorithmic noise cancellation is required by using multiple images.

PD Stefan Bosse - AFEML - Module X: X-ray Noise

X-ray Noise

• Similar to noise, artifacts are image degradations that also find their source in physical effects during the scan.

PD Stefan Bosse - AFEML - Module X: X-ray Noise

X-ray Noise

Berger, Yang, Maier, Medical Imaging Systems, 2018 Overview of noise related processes in X-ray imaging

PD Stefan Bosse - AFEML - Module X: X-ray Noise

A common quality measure for imaging is the signal-to-noise ratio (SNR).

In X-ray imaging it makes sense to use the definition based on statistics, i. e.,

$$\text{SNR}{\left({x}\right)}=\frac{\overline{{x}}}{σ}=\frac{{{E}{\left({x}\right)}}}{\sqrt{{{E}{\left({\left({x}-\overline{{x}}\right)}^{{2}}\right)}}}}$$

For random variables x following a normal distribution (Gaussian), x is the mean value and σ represents the standard deviation.

PD Stefan Bosse - AFEML - Module X: X-ray Noise: Popcorn Cancellation

X-ray Noise: Popcorn Cancellation

σ0 := Σ[1]
∀ (x,y) ∈ coord(σ0) do
  if σ0[x,y] > γ then
    ∀ σ ∈ { Σ / σ0 } do
      if σ[x,y] < γ then
        σ0[x,y] := σ[x,y]
        break
      endif
    done
  endif
  ∀ σ ∈ { Σ / σ0 } do
    if σ[x,y] < γ then
      σ0[x,y] := σ0[x,y] + σ[x,y]
    else
      σ0[x,y] := σ0[x,y] + σ0[x,y]
    endif
  done
  σ0[x,y] := σ0[x,y] / |Σ|
done