Spatial Resolution and Modulation Transfer function – Lab
Objective:
The overlying objective of this experiment was to understand the limitations of an
imaging system. More specifically the concept of spatial resolution was explored by
assessing it both qualitatively and quantitatively. This was done by calculating the
Modulation Transfer Function (MTF) using a Line Pair Phantom and then plotting
the relative modulation as a function of spatial frequency.
Data / Analysis
𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑓) =
(𝑚𝑎𝑥. 𝑏𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 − 𝑚𝑖𝑛. 𝑏𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠)
(𝑚𝑎𝑥. 𝑏𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 + 𝑚𝑖𝑛. 𝑏𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠)
𝑀𝑇𝐹(𝑓) =
𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑓)
𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛(0)
*Observe the minimum and maximum peaks of the line profile as it intersects each
of the groups of line pairs. Record your results in a table like the one below
Spatial Frequency
0.5
0.67
1.0
Maximum
46144
47232
46848
1.3
Minimum
Modulation
MTF
44608
10432
9920
10944
13952
0.631
0.653
0.621
0.523
0.966
1
0.951
0.648
2
39424
16576
0.408
0.624
4
41152
26624
0.214
0.328
Line Profile
60000
Value
50000
40000
30000
20000
10000
0
0
50
100
150
200
250
300
350
Pixels
Sample Calcs:
47232 − 9920
= 𝟎. 𝟔𝟓𝟑
47232 + 9920
𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑖𝑠 0.653
0.631
𝑀𝑇𝐹 𝑜𝑓 𝑆𝑝𝑎𝑡𝑖𝑎𝑙 𝑓𝑟𝑒𝑞 0.5 =
= 𝟎. 𝟗𝟔𝟔
0.653
𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛(𝑓) =
Spatial freq. vs MTF
1,2
1
MTF
0,8
0,6
0,4
0,2
0
0
0,5
1
1,5
2
2,5
Spatial Frequency
3
3,5
4
4,5
3D – Very High Voxel size (0.25mm) (3Dhighbil)
Spatial Frequency
0.5
0.67
1.0
Maximum
2.451
1.942
1.111
1.3
Minimum
Modulation
MTF
0.451
2.11
1.194
0.723
0.219
0.075
0.239
0.212
0.346
0.194
0.619
.549
.896
2
0.582
0.258
0.386
1
4
0.436
0.278
0.221
.573
3D - High Vox
3
Value
2
1
0
0
20
40
60
-1
80
100
Pixels
Spatial freq. vs MTF
1,2
1
MTF
0,8
0,6
0,4
0,2
0
0
0,5
1
1,5
2
2,5
Spatial Frequency
3
3,5
4
4,5
120
3D – Very Low Voxel size
Spatial Frequency
0.5
0.67
1.0
Maximum
1.954
2.208
2.452
1.3
Minimum
Modulation
MTF
2.026
1.639
1.926
1.751
1.554
0.088
0.068
0.167
0.132
0.527
0.407
1
0.790
2
1.402
1.297
0.039
0.234
4
1.910
1.577
0.095
0.569
3D - Low vox?
3
Value
2,5
2
1,5
1
0,5
0
0
50
100
150
200
250
Pixels
Spatial freq. vs MTF
1,2
1
MTF
0,8
0,6
0,4
0,2
0
0
0,5
1
1,5
2
2,5
Spatial frequency
3
3,5
4
4,5
3D - No filter
Spatial Frequency
0.5
0.67
1.0
Maximum
6.440
7.371
6.455
1.3
Minimum
Modulation
MTF
5.373
6.051
6.219
4.804
4.478
0.031
0.085
0.147
0.091
0.161
0.443
0.766
0.474
2
4.932
4.441
0.052
0.271
4
3.909
2.650
0.192
1
3D - No filter
8
Value
6
4
2
0
0
10
20
30
40
50
60
70
80
3
3,5
4
90
Pixels
Spatial freq. vs MTF
1,2
1
MTF
0,8
0,6
0,4
0,2
0
0
0,5
1
1,5
2
2,5
Spatial Frequency
4,5
100
Wrap Up Questions
1.) Based on the MTF curve, the clarity of the image decreases as features
become smaller. Blurring begins to occur at spatial frequency 1.0.
2.) When the voxel size is made larger, the spatial resolution of the image
decreases. This is mainly due to increased signal to noise ratio (SNR).
3.) When there is no back-projection filter, the clarity of the image decreases.
4.) Filter back projections are used to produce high quality images where every
section is visibly contrasted. These filters are used to reduce the frequency of
photons so that the beam can focus more readily on specific areas.
5.) The spatial resolution is highly dependent on the contrast and noise of the
surrounding structures in the region. The number of images showcase each
angle of the region. Therefore, a large number of images gives the user a
better understanding of what the region looks like from all angles.