X-ray inspection of household typical bags of sugar to find iron in it

Imagine that you should design a system for X-ray inspection of household typical bags of sugar. Your goal is to find 1 mm thick pieces of iron that might have gotten into the bag during the processing.

1. Decide on a simple chemical and geometrical model for a package of sugar (and motivate it!).
2. Based on this model, derive the estimated transmission in the sugar and in the iron, and the contrast between these two in dependence of the X-ray energy (start your derivation from the atomic scattering factors).
3. Based on these calculations, motivate which X-ray energy you would use in the experiment e.g. with help of a plot.
4. You will have to make many assumptions, so make sure that you state them and the respective sources clearly. It is recommended to use Matlab or Python for this task.

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

[Lucifer]

looking forward to do same also working on it but have a deadline till 25th won't be able to complete till then. So please share code if you can, THANKS IN ADVANCE 😊

[Image Analyst]

I did share code below. Did you even try to adapt it? Because I can't just turn over a complete solution to you. I'm sure your university would get angry with you if they found out you turned in my or @Steven Lord's code as your own.

[DGM]

I'll note that the project seems to largely be a written description of a hypothetical model, its materials, geometry and the resulting transmissive properties. You need to describe your optimization choices, and the research on which you based everything.

So find attenuation coefficients for your given materials (hydrogen,oxygen,carbon,iron) as a function of xray energy. In one case, your beam penetrates a given thickness of sugar. In another case, it penetrates a similar thickness of sugar and a specified thickness of metal. Calculate the attenuation over those paths. Plot the resulting intensities as a function of energy. Where is the contrast highest? As a student, you might have tables for these things in your book. If you don't, you probably have better access to reference material (e.g. a library) on this topic than I do.

If you choose to model steel as elemental iron, that's something to explain in your writeup. How you choose to model the reduced bulk density of granulated sugar is another choice you'll have to make. Neither are particularly difficult, but these details are why the assignment emphasizes that your assumptions are described.

See also:

https://www.nde-ed.org/Physics/X-Ray/attenuationCoef.xhtml

[Rik]

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

If you want to cheat, make sure to do it offline.

[Rik]

You saw I was able to easily restore your question. Why edit it away again? Do you think you will be more stubborn than I am?

If you have an actual reason why you want to remove the question, post a comment or contact Mathworks support.

Copy of the original question:

X-ray inspection of household typical bags of sugar to find iron in it

Imagine that you should design a system for X-ray inspection of household typical bags of sugar. Your goal is to find 1 mm thick pieces of iron that might have gotten into the bag during the processing.

1. Decide on a simple chemical and geometrical model for a package of sugar (and motivate it!).
2. Based on this model, derive the estimated transmission in the sugar and in the iron, and the contrast between these two in dependence of the X-ray energy (start your derivation from the atomic scattering factors).
3. Based on these calculations, motivate which X-ray energy you would use in the experiment e.g. with help of a plot.
4. You will have to make many assumptions, so make sure that you state them and the respective sources clearly. It is recommended to use Matlab or Python for this task.

Answer 1

[Image Analyst]

I imagine the iron particles would show up as dark spots in your x-ray image. So threshold for dark spots.

See my Image Processing Tutorial in my File Exchange:

Image Analyst's File Exchange