Introduction

This document describes some ideas for laboratory works in the MSc degree program in physics using commercially available X-ray Micro-CT equipment as well as our inhouse built micro-diffraction equipment. At our university (University of Helsinki) such laboratory works give 3-4 ECTS depending on the amount of work, so the total work amount should be kept between 70 to 100 hours maximum. In practice the measurements take only a few hours, and therefore the major part of the work is the perparation by learning about the theory and practice, and then the data analysis and reporting. 
One of the main ideas in the physics laboratory works for students is to learn to design experiments in order to test theories or observe quantitatively some phenomena of interest.  The experiment can be include building of equipment (such as electronics or optical systems), or it can be an experiment made with a readily existing equipment. In the case of X-ray microtomography the student is typically using the existing equipment for performing X-ray imaging, and due to the short nature of the visit at the lab these imaging experiments are typically made under guidance of an experienced person, so as not to make the equipment use the primary goal of the laboratory work. Here is a list of topics that either have good potential to be used as lab works, and some other topics that may not be as good but which have already been used for some students. Some of the topics are very simple in principle, so that a student can get on with the lab work without having to exceed the 70 to 100 hour limit. There should however be more difficult topics that may require extra work for those students who are looking for extra challenge and are willing to work more to learn more. 

Physical concepts that are present in MicroCT and micro-diffraction experiments

First there are some fundamental concepts that are present in the experimental apparatus and techniques. Some of these form already suitable topics for students to try to understand the technique and learn more about specific aspects:
Then another side is the physics in the system under study. This is a much wider field, and we should try to find some examples where the physics can really be analyzed based on the image data. Calculating numbers such as porosity or surface area is possible for students to do, but this is not yet a physical insight. Some of the students did exactly this, but the results were not very good from the learning point of view. To really understand some physics of a material, several measurements are probably necessary. We should try to find materials science lab works that offer high quality insights, that are well defined (so that we know a good student will get reasobale results), and that do not require too many hours of machine time. Here are list of potential physical aspects that could be interesting to look at:

List of Topics Available Now or Possibly in the Future

  1. Contrast, SNR and sensitivity. In this work the student measures how small differences in material properties can be seen in the micro-CT images. The experimental setting can be for example to measure tubes that have water with different concentrations of salt dissolved in it. By choosing suitable amounts of salt the student can extrapolate to get the limit of detection under given experimental conditions.
  2. Image resolution.  In this work the student prepares to measure the image resolution. The student should come to understand difference sources of blurring in the image, i.e. the detector point spread function and the source size. These have a different contribution at different magnifications. The source size effect can be measured using a structured sample at sufficiently high magnifications (few levels of zoom required for good accuracy). The detector PSF can be measured when doing a low resolution scan, although a slanted knife edge measurement would probably be the best. We do not have really a proper test pattern for these measurements. The student also does not a priori know at all in which ballpark these figures will be, so it will be difficult to independently plan the measurements.
  3. Classification of materials based on the X-ray image. If we have known material compositions, eg. Al, polymer, graphite, the student could make a microCT measurement, and then the main part of the work would be to show why the materials have differing contrast. In this work the planning stage is not emphasized if the form of the work is like this, we shouls still add a part that makes it necessary for the student to do some preliminary work to plan the experiment. 
  4. Testing the exponential absorption law. The student would use known materials of known thickness to see how the absorption works. There will probably be some discrepancy with the exponential form due to the polychromatic nature of the beam. The student could study this phenomenon and report their findings. We have to test this ourselves, does it make any sense, but one could probably get a value for an effective ยต for each material that fulfills the exponential law sufficiently well that would be \(\mu_\mathrm{eff} = \mu(E_\mathrm{eff})\). Probably the student would find that for different materials the \(E_\mathrm{eff}\) do not agree due to different amount of beam hardening in the materials. Then the student could also make a CT scan to see how the beam hardening causes artefacts in the image. More advanced students could try to find a way to undo the beam hardening at the projection level based on the calibration images from known thickness materials. 
  5. Phase contrast imaging. Use propagation based phase contrast to get an image of  a thin nylon thread. The edge enhancement effect is visible at high magnifications, and some comparison with theoretical values could be made. Then additionally the task would be to do phase retrieval to get back to the electron density. This is quite demanding from the point of view of the equipment, but should give some reasonable results according to our own preliminary tests. Some edge enhancement contrast can be seen both in the Bruker equipment as well as the GE equipment. The student could compare these two devices as well as their generalized coherence lengths.
  6. Micro-diffraction study of crystalline and amorphous materials. 
  7. SNR and tomographic reconstruction. In this work special attention is paid to the SNR properties of the reconstructed image. Tradeoff between projection SNR, number of projections and the resulting slice could be studied. For more advanced students special reconstruction methods including regularization could be used. For this to work we need to work in the fan geometry (to be simple), and we should have a set of standard macros for octave where the student can take the data and start experimenting different things.