# How CT projection image and intensity plot are related?

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Anand Ra il 3 Mag 2022
Risposto: Image Analyst il 16 Gen 2024
Hello
I am looking to interpret the CT projection image and I am lacking basics.
From my X-ray system:
• I have one CT projection image of a copper wire (1.8 mm thickness). Image pixel height =1452 and width = 1651
• And also I have the intensity plot ( intensity vs Y-current) corresponding to the above mentioned CT projection. This intensity plot has 1452 data points (Y-current) which is equal to the pixel height of the image.
• My detector size is 2mmX2mm
Iam trying to understand the the relationship between
1. Image width and pixel
2. Image height and pixel
3. Number of intensity data points to the thickness of the material thickness of the sample
For 3 in the above list
I am looking fit the intenity data to the Xray abosrption model to find the attenuation length - t ( attenuation length/ thickness is a variable in the model). The model is:
I = Io*e −[µ/ρ]ρt ,
where,
Io : is the initial x-ray beam intensity.
I : is the final beam intenisty after the xray passed through the Cu wire smaple.
µ : absorption coeff.
Io will be a single intenisty value without any object in the xray path
whereas I will be an array (n- data points corresponding to the pixel?)
I am unssure how to make sense of the array when trying to fit them in the above mentioned model.
Thanks for help.
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### Risposte (2)

Image Analyst il 16 Gen 2024
t = -1*(1/µ)*log(I./Io)
note that I is a 2-D array, so the log is also a 2-D array, and thus t is also a 2-D array. So even though µ and Io are scalar constants, you still get a 2-D array out. You get a material thickness, t, for every pixel in the image.
To calibrate the system you should construct a calibration step wedge of copper foils. Then, using the known mass attenutation coefficient of copper you can construct a curve of gray level versus thickness of copper. Then you can fit a curve through that to get a model where you can predict thickness given a gray level. It would be best if the step wedge was in every x-ray image (along with the wire) because the x-ray exposure can vary slightly from shot to shot.
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Shreeya il 16 Gen 2024
Given the image width w and height h, the number of pixels p are then calculated as p = w*h. According to the beer’s law of X-Ray imaging:
Where Io is the incident intensity
µ is the mass attenuation coefficient
t is the thickness of the sample
From this relationship, it can be inferred that as the thickness increases, the intensity passing through the material decreases, i.e. the relationship between intensity and thickness is inversely proportional.
To fit the intensity data to the model where I is an array and Io is a single value, the element wise operation in MATLAB can be used. To calculate the thickness of the sample across various intensity values(I), the below code can be used:
t = -1*(1/µ)*log(I./Io)
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