Presentation by Nityanand Gopalika on X-Ray Spectrum Modelling. The paper was presented at NDE 2003 conference.

1. Evaluation of Mathematical Models
for X-ray Spectrum Generation suitable for Industrial
Radiography Applications
Nityanand Gopalika, A. V. K Satish, V. Manoharan
Industrial Imaging and Modeling Lab
Imaging Technologies
John F. Welch Technology Centre
Bangalore

2. Presentation Outline
 Different X-Ray generation models
 Validation approach:
 Variation of Photon Fluence / mR with Average
Energy
 Relationship between Average Energy and kVp for
different filters
 Half Value Layer (HVL) for different cases
 Dose validation with experiment
 Summary

3. Birch and Marshall model
Intensity produced in a solid target
Governing Relationships dT
Nρ
T −1
 
v
Iv =
A ∫  dx 
T0
Q

dT Physics
• Theoretical model
Effect of target absorption • Target absorption taken care
T = (T02 − Cxρ ) 0.5 (improvement over Kramer's theory)
Substituting the above gives
−1
Nρ
Tv
 T0   dT  µv
Iv = ∫ 1 + m0C 2
 Q
  dx  exp( (T 2 − T02 ) cot θ ) dT
A T0    Cρ
Characteristic Intensity
I ch = K (U 0 − 1)1.63
Drawbacks
 Applicable only from 30-150 kV.
 Small target angles greater error.
 Back Scatter not considered.
Suited for medical applications

4. Ellery Storm Model
Thick target energy loss as an integral of thin target energy loss:
E0
 dE  dE = Energy loss in thin strip of target
I E0 ,K = ∫ I E0 ,k ,E  
E >k  −dE /dx  E = Initial electron energy at photon emission
Correction for electron backscatter losses, photon attenuation and target angle
E0
 dE 
I E0 ,k = ∫k
E>
I E0 ,k ,E  (1−ηε E 0 ,k )*exp( −µ k x/ tanα )
 −dE /dx 
Emission per unit solid angle in the photon energy
−3 k
11 ( E0 −k )(1−e ) Ek 1.0
I E0 ,k ≅( Z ) f E0 ,k ,α
4π 1 E0
( k / E0 ) 3 (1−e Ek )
40 kV
60 kV
Photon Attenuation Correction Factor C E0 , k
f E0 ,k ,α ≅ exp(−0.2C E0 ,k ℜ E0 µ k / tan α )
100 kV
0.5
200kV
E0  Initial Electron Energy
Ek  K Edge Energy 300 kV
K  Photon Energy 0.0
10 20 40
Z  Atomic Weight Photon Energy (keV)
Best suited for industrial applications

5. Photon Fluence /mR & Average Energy
Photon Fluence per Roentgen
Photon Fluence
4.E+10
3.E+10
/ mR
2.E+10
1.E+10
Photon Fluence /mR =
∫Θ( E )*E*dE
0.E+00 ∫Θ( E )*(µ ( E )/ ρ )*E*dE
0 50 100 150 200 250 300 350
Average Energy
Average energy
70
60
Average energy kev
no filter
Average Energy =
∫Θ( E )*dE 50
40
1 mm aluminium
2 mm aluminium
∫dE 30
20
3 mm aluminium
4 mm aluminium
10 5 mm aluminum
0
0 50 100 150
kVP
Literature data available below 150 kVp

6. Model Performance Verification
Average Energy Vs. kvp (Simulation) Photon Fluence per roentgen Vs.
Average Energy (Simulation)
140
120 3.00E+05
Average Energy
Thick = 1mm
Photon Fluence / mR
100 Thick = 2mm 2.50E+05
Thick = 1mm
80 Thick = 3mm 2.00E+05 Thick = 2mm
60 Thick = 4mm 1.50E+05 Thick = 3mm
40 Thick = 5mm 1.00E+05 Thick = 4mm
20 Thick = 5mm
5.00E+04
0 0.00E+00
0 100 200 300 400 500 0 20 40 60 80 100 120 140
kvp Average Energy
Average Energy Vs. kvp Photon Fluence / mR Vs. Average Energy
(Simulation & Liturature) (Simulation & Literature)
140 3.E+05
Photon Fluence / mR
120 3.E+05
Average Energy
100 2.E+05
80 Thick = 5mm, Simulation 2.E+05
60
Thick = 5mm, Literature 1.E+05 Thick = 5mm, Simulation
40 Thick = 5mm, Experimental
5.E+04
20
0 0.E+00
0 20 40 60 80 100 120 140
0 50 100 150 200 250 300 350 400 450
kvp Average Energy
High accuracy in the range of 30 – 150 kVp

7. HVL Study: Comparison with NIST Data
Tube HVL Dose Dose
Potential Inherent (mm) - Before After
Cases (KvP) Filter Added Filter Object NIST Object Object % Error
1 100 1 mm Be % Difference in HVL
1.98 mm Al Al 2.77 12.668 6.744 -6.475
2 100 3 mm Be 5 mm Al Al 5.02 6.080 3.043 -0.106
3 100
8 3 mm Be 4 mm Al + 5.2 mm Cu Al 13.5 0.025 0.012 2.393
4 100 6 3 mm Be 4 mm Al + 5.2 mm Cu Cu 1.14 0.025 0.012 3.496
5 120 3 mm Be 6.87 mm Al Al 6.79 6.887 3.440 0.100
6 150 4 3 mm Be 5 mm Al + 0.25 mm Cu Al 10.2 8.405 4.177 0.610
% Difference
7 150 3 mm Be 5 mm Al + 0.25 mm Cu Cu 0.67 8.405 4.125 1.851
8 150 2 3 mm Be 4 mm Al + 4 mm Cu + 1.51 mm Sn Al 17 0.187 0.092 2.147
9 150 3 mm Be 4 mm Al + 4 mm Cu + 1.51 mm Sn Cu 2.5 0.187 0.087 7.005
10 200 0 3 mm Be 4.1 mm Al + 1.12 mm Cu Al 14.9 9.782 4.831 1.217
11 200 3 mm Be 4.1 mm Al + 1.12 mm Cu Cu 1.69 9.782 4.785 2.169
12 200
-2 3 mm Be 4 mm Al + 0.6 mm Cu + 4.16 mm Sn + 0.77 mm Pb Al 19.8 0.141 0.070 1.665
13 200 -4 3 mm Be 4 mm Al + 0.6 mm Cu + 4.16 mm Sn + 0.77 mm Pb Cu 4.1 0.141 0.068 4.188
14 250 3 mm Be 5 mm Al + 3.2 mm Cu Al 18.5 9.624 4.740 1.504
15 250 -6 3 mm Be 5 mm Al + 3.2 mm Cu Cu 3.2 9.624 4.695 2.425
16 250 3 mm Be 4 mm Al + 0.6 mm Cu + 1.04 mm Sn + 2.72 mm Pb Al 22 0.206 0.101 2.119
17 250 -8 3 mm Be 4 mm Al + 0.6 mm Cu + 1.04 mm Sn + 2.72 mm Pb Cu 5.2 0.206 0.102 0.613
18 300 3 mm Be
75 125 4 mm Al + 6.5 mm Sn
175 225 Al
27522 4.395 2.169
325 1.280
19 300 3 mm Be 4 mm Al + 6.5 mm Sn Cu 5.3 4.395 2.201 -0.149
20 300 3 mm Be
kVp
4.1 mm Al + 3 mm Sn + 5 mm Pb Al 23 0.164 0.083 -0.839
21 300 3 mm Be 4.1 mm Al + 3 mm Sn + 5 mm Pb Cu 6.2 0.164 0.086 -4.415
% Difference in HVL between NIST and simulation is within +/- 8%

8. Experimental Dose Measurement
Experimental Conditions: Simulation Conditions:
X-Ray Tube: Target Voltage : 20 < kV < 420 kVp
Current : 1 mA
1. KM16010E-A MicroFocus Target Material – W
2. Seifert ISOVOLT 420/10
Dose = 1.828*10-11∑φ(E).(µ(E)/ρ) air.E.dE
Dosimeter: Keithley 35050A Dosimeter
% Difference in Dose : Kevex, SDD = 1m % Difference in Dose: Seifert, SDD = 1m
(Experimental and Simulated) (Experimental and Simulated)
6 8
0.4 mm Cu Filter
4 6
9 mm Al Filter
4
% Difference
2
% Difference
2
0
0
-2
-2
-4 0.4 mm Cu Filter -4
-6 9 mm Al Filter -6
-8 -8
30 50 70 90 110 130 150 170 30 130 230 330 430
Tube Potential (kvp)
Tube Potential (kvp)
KM16010E-A MicroFocus Seifert ISOVOLT 420/10
Less than 7% difference is observed between simulation and experiments

9. Summary
 Ellery Storm Model best suited for X-ray Spectrum Generation
 Model performance metrics:
 Accuracy for Photon Fluence / mR > 95%
 Error in Average Energy < 5%
 Deviation in HVL < 8%
 Simulated Dose is in good agreement with Experiments