 So, this will be the very first lecture of this fairly packed week. And I will aim to link all the information in this one hour lecture to all the things that will happen later during this week. And I will go over some basic concepts, definition, interaction mechanism of neutrons with matter, and then also touch briefly on different imaging modalities that we can use with this neutron imaging. So a little outline of what I will cover in this hour in a bit more detail. So I will first provide a broad overview of characterization techniques in a bit more general terms, and then the definitions of what makes neutron imaging, neutron imaging, and also how we get neutrons in the first place. And then I will talk about the accessible length scales and put them into relation to other neutron techniques. And very basically, I will also go how an image is recorded and then show the derivation of the Bialambad law. I will touch on that briefly and then talk a bit more detailed on the imaging setup itself. And the principles of tomography will actually be covered by Anders in great detail during this week. So I will only mention it fairly briefly in this one hour. And then the different imaging modalities that come in with all the advanced imaging methods that have really come up mainly in the last decade, I would say, the last 10 years have seen very many activities around neutron imaging. And last but least, I will say a few words about neutron detection, which is actually a scientific field in itself. So when preparing this lecture, I realized that we have only one hour. So I will skip over some parts of these slides rather quickly, but I wanted to keep them in here as they will also be online in a slide form and also as video, hopefully. So I wanted to keep them in here so you can go back to the slides and that you have some reference to go back to later on. So let's get started. But before really getting started, I want to say just a few more words before we will spend quite some time together online this week that you may know a bit more about my background and hear you actually listening to. So as I already said earlier, I'm actually a mechanical engineer by default and work a bit in the automotive industry. And then in 2006, I went to the United States to the University of Tennessee where I worked first with General Motors on some topic of lost form casting of aluminum engines. And also as part of that, I built a portable stress train rig that was fitting actually into a large shamba electron microscope, which is actually a 2 by 2 by 2 meter shamba, so really large and you can climb inside. However, doing that was a bit like shooting with cannons on little birds. And in the PhD program, we wanted to couple this information from the small scale from the large shamba SCM actually with something on length scales, on the more macroscopic length scales. And that's when neutron imaging came in and we started a collaboration actually with Nikolai Kardilov, who is one of the lecturers that week. And my dissertation that I carried out where I was termed energy selective neutron imaging for the characterization of polycrystalline materials. For that, I modified the stress train rig and then we took it to a lot of different neutron facilities, both imaging and diffraction also to synchrotrons. And then we did imaging and diffraction and eventually combined the two. And this will also come in later in the lectures of the advanced imaging methodologies. And as I already said, since February 2015, I'm now at ESS and really excited to build the most powerful neutron source on the planet, basically. And while, again, now starting out this lecture, I think it's very important to emphasize that there, of course, neutrons cannot, even if you have the most powerful neutron source, you can, it's not enough. You cannot just throw away all the other techniques. So there's a lot of different characterization techniques. And they're obviously very complementary to each other. So if you take this unknown object, then if you have some lab methods, they will tell you one thing. And if you have electron microscopy, they may tell you another thing, and so on and so forth. So depending on your problem, you may need a range of techniques to really answer your full problem. And this is something I like you to keep in mind throughout this whole week. Even if you have advanced methods, you may need to use additional techniques, maybe neutrons, maybe lab techniques to really answer your scientific question. To give you a somewhat more realistic example for imaging techniques, I like to consider here available 3D tomography, tomographic techniques. And tomography, in case you don't know that yet, you will surely know it by the end of today, after Anders' lecture, is the use of imaging to reconstruct the 3D structure of an object. And there's a range of tomography techniques, each providing a certain level of information over a final length scale. You can use, for example, atom probe tomography, which has a subnanometer resolution. And you can also use electron and focused ion beam tomography operating on micrometer sized sample volumes. And then x-ray and synchrotron tomography can investigate larger samples. They have submicrometer resolution and can, for example, visualize individual grains and polycrystalline samples, what you see on the top left here. And OK, these are the images that I was talking over. And the neutron tomography really attaches to this upper right part of this graph, where you can investigate larger samples. And the spatial resolution starts just a little bit beyond one micrometer. And you can really, but it allows you to study larger samples than any of the other techniques. So you can already see this is really complementary. In an ideal world, you would maybe start this neutron tomography, get the information before you cut your sample into smaller pieces or zoom into regions of the sample and get information in greater detail with some of the other techniques that are available. And since the topic of this one-week long class is neutron imaging, I like to go through some basic definitions of neutron imaging by the International Atomic Energy Agency. I believe Nikolai, I'm not sure if Anders was also involved in defining this. So neutron imaging is a technology to produce visible information of objects and structures by using beams of free neutrons. And it uses the high penetration power of the neutrons to visualize the inner features of objects. And therefore, it's a suitable tool for non-destructive testing for applied research. So it falls into the category of non-destructive testing methods. And moreover, I already said it's a non-destructive technique. It can be used for visualization and also for quantitative determination of material and of macroscopic samples and objects. And this is, again, the sample resolution. There's not yet an example where you get below one micrometre, at least not with the direct imaging methods, only indirectly by the advanced imaging methods that we will cover later. And you can cover fairly large object sizes in principle, even larger than 20 centimeters. There has been the first time I got into neutron imaging was actually for neutron radiography of full engines being cast. This was this collaboration with General Motors, where they did in-situ casting of full engine blocks. And what motivates this, what's the physical background, is why we need this is because matter, as you obviously know, is generally not transparent for visible light, except a few exceptions. And there you can use different types of radiation to penetrate this matter and then to do this non-destructive information. And again, this is all a bit repetitive, but I like you to remember these things, that neutrons can penetrate thick several centimeters layers of materials that cannot be penetrated as many other forms of radiation. And what's already important here, it can do that for heavy materials, but you are very sensitive to light elements. So you can heavy elements, you can penetrate, but you can be sensitive to light elements. So they are maybe, many of the light elements are attenuating a neutron beam strongly. And this is opposed to what X-rays do, for example. And with that, I'm already coming to X-rays now. You will hear this comparison possibly quite a lot during this week. And X-rays are possibly the most commonly used for radiography or tomography. And as you know from the hospital, for example, you typically get an X-ray done. And the fundamental difference is that neutrons interact with the nucleus of an atom and X-rays interact with the electron cloud. And you can imagine the nucleus to be the size of a marble. And then the atom itself is the size of a football stadium to just give you some perspective here. As a result of that, neutrons interact with your sample only when they hit the nucleus. So the chances are much lower. And as a result of this, again, neutrons can penetrate this very thick lead container and, for example, reveal these flowers inside of them. And as you will see in several examples later on, neutrons and X-rays are very highly complementary. Here are some radiographs of a model airplane engine and a bullet, for example. And you can see different parts of these objects in different grayscales. A very useful thing to generally look at when you want to decide if neutrons are actually useful for you is this type of periodic table that compares the attenuation for neutrons and X-rays. For X-rays, we have a proportional dependence of the elemental number. And for neutrons, this appears much more unsystematic. And the interaction is even different for different isotones of the same element for neutrons. And this is really exploited in many of the neutron scattering techniques and also in neutron imaging nowadays. And what you will also see later during this week is that this attenuation, or we will speak more generally about the cross-section, also depends on the energy of the radiation. And that is actually true for X-rays and also for neutrons. And you can then, of course, make use of this during experimental investigations. The total neutron cross-section describes the observed attenuation by a material and it depends on different scattering contributions as well as absorption, what you see in this formula on the bottom right. And then the scattering contributions can further be divided, subdivided into elastic coherent, inelastic coherent, elastic incoherent, and elastic incoherent scattering. And this can be then exploited for some of the advanced techniques that we will talk about later. So just remember that different contributions to what you are observing as an intensity of neutrons on your neutron detector. And this slide now should mainly serve you as a reference for later that summarizes properties of the neutrons. And more importantly for the purpose of this lecture is to chose the relevance when doing neutron imaging with neutrons and what it can be used for. The fact that they have a spin allows you to do, for example, polarized neutron imaging and so forth. And what I did not clearly state so far is that neutrons can be described as a classical particle with a mass m, but it shows also a wave character which can be described by the de Broglie wavelength lambda. And then we can convert between energy wavelengths and velocity with this formula. So again, this should be some of the references that can be useful for your future work when you want to use neutrons. But then the actual question is how do I actually get neutrons that I can use for my experiment? Well, for that there are many large-scale user facilities around the world that operate neutron sources and the ESS here in Lund will be one of them. And when it's completed, it will be the most powerful one to date. And one of the two main methods to create neutrons for scattering and imaging experiments is by fission in a nuclear reactor. And these are not nuclear reactors that are used for producing electricity, but actually they are very specialized research reactors that have typically also much less power than those power plants. The other method to producing neutrons is by a process called spallation. And here's a nucleus of a target material is smashed by a powerful beam of particles, typically protons, to release and free neutrons from that. And by default, since you're using an accelerated beam, you will also create a pulsed neutron beam. And this leads to fundamental instrumentation concepts that we will also cover during this week. And it is spallation source, for instance, because of this time structure, then there comes in a concept that is called time of flight that allows wavelength selection right away. And this slide I want to just mention briefly, because these are the most advanced neutron sources and there was a recommendation that these advanced neutron sources should be built spread around the world. Already operational is JPEG in Japan, the spallation neutron source in the US, and we will soon have the ESS in Europe. There also is now a spallation source in China already by the way operational. And coming now to this concept of a pulse source versus a reactor source. The reactor source is typically a steady state source. This graph is quite useful to see. The neutron beam spectrum from both sources is quite similar. Let's see if something came in. Okay, that was Steve's question. Steve said that you can ask questions and we can collect them and they are definitely asked away. And the neutron spectrometer pulse source or reactor source is not too different because of moderators that are used, also that I will cover in the lecture on instrumentation. So you have neutrons of different wavelengths and the intensity distribution is slightly different depending on what kind of source you have. And if you use a reactor source, okay, now it's progressing, then you are selecting one wavelength typically of this of your of your neutron source or actually imaging. I should also say you can also use a full spectrum, which we call wide beam imaging, then you get the most intensity because intensity because your neutrons that are depicted here in blue, yellow, red all together to use all of them at the same time. But for more advanced method and also literally all the scattering methods, they need monochromatic neutrons. So at a reactor, you would use a monochromator and you pick out one wavelength that you get all the time because neutrons are produced all the time. So you get the same wavelengths at a certain intensity for the whole time. And you can change your monochromator to a different wavelength. And you get the same wavelengths all the whole time and again, the red one. And the pile source works a little bit the other way around. You are creating this spectrum in every neutron pulse and it travels a distance when you when it's created at the neutron source and it travels through your sample and your detector and the neutrons get separated over while they travel over this distance in time. And that determines what wavelengths these neutrons have. So you just stop the timing of the neutrons and you know what wavelengths they have. And so you're getting these pulses every so often and that depends on the repetition of your neutron source. And this part I will cover in a bit more detail tomorrow and also in the time of flight lecture I will go into detail of the time of flight and I believe Nikolai will likely go into the monochromatic part at a steady state neutron source at a reactor. So now it's already time to draw an in-between summary for the use of neutrons in our experiments and then of course like with anything we do in life their advantages and disadvantages to that. So advantages include neutrons have no charge. So often that allows for a deeper penetration but they do have a magnetic moment that means we can do polarized neutron imaging with them for instance. We do have a higher sensitivity for light elements. Hydrogen is a very prominent example where neutrons are used and we can also differentiate different isotopes that makes neutrons very powerful. And also we have energy selection using time of flight at pulse neutron sources now and that comes basically for free. However disadvantages include even the most powerful neutron sources have still a limited intensity especially compared to the most powerful x-ray sources in form of synchrotrons these days of reelectron lasers and we have no direct detection. So it's kind it can be a very inefficient process to detect actually neutrons because we need some secondary process to do that and that will also limit our spatial resolution. And because they carry no charge we can also not focus them very easily and that limits also again our spatial resolution that is possible by neutron imaging. And moreover there's always a risk of sample activation so before you carry anything to a neutron source you should study if this sample may activate. Okay so I'm not sure if there are any questions in between I don't see any otherwise you can also just peek in. I like to now go a bit about talk about neutron methods and length scales and compare imaging to other neutron methods that are available. So here you can see a rough range of length scales on the x-axis and if you're interested in really the atomic structure or the magnetic structure of materials then atomic lattice basings that are actually on the angstrom regime can be probed by neutron diffraction. So you have a specialized neutron diffractometer for instance and another popular technique is neutron reflectometry where you typically investigate surface and interface structures on length scales ranging anywhere from the sub nanometer up to the several hundreds of nanometer range and then on a similar level we also have small angle neutrons scattering which can be used to study all sorts of substances on substances on similar length scales as reflectometry between let's say one nanometer and up to a few hundred nanometers. These length scales can be further be extended towards a micrometer range by a method called very small and ultra small angle neutrons scattering and while all of these measurements are performed in reciprocal space or Fourier space, neutron imaging actually operates in real space and the accessible length scales are determined by the achievable spatial resolution of the instrument and detector system which are already set is nowadays as good as a few micrometers and of course again neutrons can shine through tens of centimeters of many materials at the same time. Moreover what's important to note and remember is that all these scattering techniques although they are sensible to the small length scales they then probe an average volume of the material. So you are you are illuminating a bigger volume of the material and then you are getting the average size information about the property for this volume and imaging on the other hand as I already explained is a real-space imaging technique so you are seeing the size of the objects in real space and the spatial resolution how it's distributed within your sample and for now I would like to showcase you some examples where neutron imaging can be extremely useful and most applications even today on if you look at neutron imaging beam lines worldwide they simply exploit attenuation differences between different elements and isotopes and by doing that you can for example study the water uptake in this root soil system of a plant and you can see water moving up in the soil which is invisible here when you can see the root system or you can review for example hydrogen inside of metals where it causes embrittlement and leading to dramatic failures like they have been like when you see collapsing bridges or oil platforms very often hydrogen embrittlement is an underlying cause of that. Also you can look for example lithium transport in batteries of course that's a very popular application these days and due to its non-destructive nature there is a big user community in the cultural heritage sector and from museums and so on and here you can see a lead statue that is actually rather big 55 centimeters as you see and since neutrons can easily penetrate the lead one can reveal the inner wooden kernel of the statue and moreover even locate no regions inside that have been sold or corroded and then this can be used by by the people from the museum how to restore this figure and or understand how it was made in the in the first place. Applications to this of course also exists in the medical sector you can see an example on the top actually from Lund University on bone structures and implants and of course one can also look at larger assemblies all together like this diesel diesel particle filters and separate the ash the soots and different components of a diesel particle filter after it has been in operation and while this guy is interrupting me knowing he wants to see more examples this is not yet the time for it we will have some applications later we should look a little bit more about now into the peculiarities of neutron imaging itself and what one needs to consider so let's continue with that how do we actually record an image or I should say how do we actually record a transmission image so if you ever wondered how you do that and take an image as a snapshot of reality then images that you normally take with your camera well I guess you use a smartphone these days captures a visible light that is reflected by the objects in the direction where you are aiming this camera and the camera principally consists of a black box and some optical lens so if you want to record now an image let's say of Homer Simpson then the reflected light is projected through the lens onto a ccd ship when the old days it was filmed placed on the backside of this black box and then we obtain an upside down image of Homer so how about we want to record images new using neutron rays instead of light rays and as I already said neutrons are not as easy to focus as visible light or x-rays which means we don't have efficient optics like like this to make images with comparable resolution to what you could do with state-of-the-art x-ray images or optical microscopy so if you like maybe to join in I have a little pop-up quiz here so how would one record an image now of Homer when you don't have optics or visible light so I'm not sure if anybody wants to answer one of these three pre-choices scintillator well we will probably need some scintillator that's true and there's something else that we get some some sort of spatial resolution and the choices are minimize the distance between object and box maximize the distance between object and box or using a small pinhole okay somebody answered a small hole yeah a small pinhole that is the right answer actually in this case that is the most efficient way to do that and I can show you why we even then we do that uh it's also called maybe you have heard the term camera obscura and that will then produce an image on the wall inside of the box by just a simple projection and you see if you would make the hole bigger you will get a more blurring of of the image that is actually depicted here now so if you make the hole bigger you get more light in but you have more blurring and while we have now just seen how to create an image on the surface of an object this visible light we want to actually investigate the internal structure of objects so we need to look inside and for that we can use x-rays or neutrons and you of course now this already you can take images of your body for example where only part of the beam passes through and then we will observe the transmission image called a radiograph on the detector placed behind the hand just to highlight this here radiograph is this 2D projection when you just take one image and a tomograph is you would rotate either the source and the detector or the the object around and then you'd use computer tomography to take to get a 3D image of this and actually Willem Röntgen has taken this nice image of that so I like to just give you just a brief history here this was the invention of x-rays and typically x-rays have always driven the developments of of neutrons later on because neutrons were also discovered after the x-rays and this is again this is one of the first images taken in 1895 actually he used the hand of his wife apparently and we also had shortly after the discovery of neutrons then actually images already shown with neutron so these are some of the first neutron radiographs ever taken so I'm wondering does anybody know by chance when the neutron was discovered so by whom and when not sure if somebody wants to ship in the answer for that any guesses 1932 in Chadwick yes that is that is very good that should give an extra point exactly so should we discover it and here's a picture of the article that appeared the possible existence of a neutron so thank you and okay looks like we got everything we need let's go and take some neutron images then well unfortunately it's even a bit more complex and that we should consider a few more things and one of the things is now the Bialambad law for attenuation based imaging which is the underlying principle to describe the attenuation in this case of a neutron beam by assemble and it describes the intensity I that we observe or record when incident beam intensity I0 that you see on the left side passes through an object in view of time and seeing the rest of the lecture we still have in front of us I would mainly like to see you these next few slides and I will go over them rather quickly to go to the final Bialambad law but it's basically about you divide the sample into differential slices and then you are going through that with certain assumptions and we are ending up basically at this final Bialambad law at the end and if you have several absorbers it looks like that now what's important here for you to remember is we are having a macroscopic cross section which is material specific defined by the sigma is equal to n times sigma and the unit is a centimeter to the minus one and this can also be expressed this is the other important thing to remember as attenuation coefficient and the written form like I've shown in now in the top right of this slide is what I will show on the next few slides with underlying with some examples and again you have the intensity I the incident intense the observed intensity the incidence intensity I0 and you have an attenuation coefficient that is material specific which you can look up in different tables and this is it for example the table that is uploaded on the indico page already by spheres then you can find these attenuation coefficient for different materials that's why it's uploaded there and it depends on the sample thickness that and again this law written a slightly different way and what we are measuring really in neutron imaging is the transmission it's it's a relation between again the observed intensity by the incident intensity I0 what we have the terminology in in neutron imaging and this is actually I stole this from a slide that Anders will present later you have an image of an object which is this bright one on the left top side and you have the same and then you take an image you remove the sample from the beam afterwards so you have a sample image and the one on the bottom left we call typically an open beam image in the lingo used in neutron imaging and depending on your detector system you may also have some dark noise or readout noise on your detector system which we call a dark field image so this is just a constant offset of the single so you should subtract that from both of them and what you get out is then the transmission image so you're normalizing out the different neutron beam intensity of your source and also anything that is related in specific to your detector system and in inverted formats it reads like that and we can obtain the thickness D if we know the material specific cross section or the density or composition can be derived as a thickness is known but in all of this and then you go through the derivation of the Bialamban law there's a couple of assumptions that have been made and I like you to be aware of these assumptions for later when you perform a neutron imaging experiments one thing is it assumes that the absorbers are independent of each other that these absorbers are diluted meaning they don't shadow each other from one side to another and the tunation does not depend on the wavelengths or in other words the Bialamban law is derived from monochromatic neutrons and as I already said many of the neutron imaging applications are actually using wide beam imaging so it means it uses the whole part of the neutron spectrum in order to have more intensity it also assumes that the beam is somewhat parallel and that the absorbers are not influenced by the radiation itself and also it assumes that this is important that no scattering is present and when we go through that we can see okay this one is true for most applications number two is true for most elements well number three we can maybe deal with it or use monochromatic neutrons to start with that this is true and the beam is somewhat parallel well this becomes true by the L over D ratio which I will cover still in this lecture and that the absorbers are not influenced by radiation well that's also true for most elements and it also assumes that no scattering is present okay and actually as I will show this is just plain wrong for most elements and causing tremendous challenges when we want to do quantitative neutron imaging and what you see on this table is actually a couple of elements on the x-axis so different elements and then it shows the contributions from absorption versus scattering and what you see actually that for most elements scattering is actually in blue and it's often the very dominating factor for many of the elements and there are just a few exemptions lithium boron cardmium and gadolinium for example and these actually are also the materials that are used in neutron detectors well you can see already in the distribution of this graph that you will always and what you should take away you should consider how much scattering your sample produces because if you have a very pure absorber then these assumptions that were made before are actually decent enough so we have just a few more things to cover and one thing is now the neutron imaging setup itself and what geometrical considerations need to be done and then again I'll talk a bit more about scattering versus absorption here and first let's go back to this image now if you want to require a transmission image so what's important to realize is that we this neutrons we have actually a point source of radiation so neutrons are produced in some point basically and we are creating a point then also with this pinhole so in order to create an image of homo and since we do not have efficient optics we actually need to put a pinhole that will then determine the resolution and exposure time of our image so it looks like that and this is then actually exactly how a neutron imaging experiment is performed neutrons are coming from this neutron source which as I already said is usually a research reactor or a spallation target in this example it's a reactor and then the direction towards the object is defined by a collimator just to make it clear again in this reactor neutrons actually going in all directions around and there's actually different neutron beam lines in what we call beam ports in in different directions as well and you just use this collimator and pinhole to make sure that you're only getting the neutrons and that going by by chance into this direction and then the sample can be positioned and rotated for tomography and the detector is placed that in the direct beam behind the sample and it requires a shadow image of homo in this case and for a time of light beam lines it then should also require the time of arrival of the neutrons so if you assume now we want to take a radiograph of actually this sample not of Homer Simpson anymore and let's assume it's made from two different materials and it has also varying thickness so what will be what will we see on the detector well the neutron beams neutron beam it travels along the direction that with an incident intensity denoted as i0 as I already told you before and the transmitted intensity on the detector is as I already touched on is defined again here we have to be a Lambert law and you can see this little formula again now it depends on the attenuation attenuation coefficient mu and the thickness of the sample that so to make it a bit more practical if you assume now we have one centimeter of material this attenuation coefficient of one this means that of 100 percent intensity i0 we have only 37 left intensity left on the other side and if this beam passes now through two centimeters of material only 13.5 percent of the initial beam intensity would be left and the thicker part of the yellow material the hands appear darker than the thinner part but how about now the attenuation from the blue material compared to the attenuation from the yellow one so this transmission depends on the attenuation coefficient mu again which are we told you as material specific so if you if you assume 0.8 for the blue material we will actually measure a beam intensity of 45 percent and as I also highlighted before the attenuation coefficient for material depends on the probability that the neutron is removed from the direct beam which can be done in one of the two main processes either absorption or scattering and then this total attenuation is the sum of the neutron attenuation from these two types of processes inside of your sample so I'm repeating these points quite a few times because they are quite important and in order to understand a bit more details what happens to a ray when it hits the sample we have to look in detail what goes on between the atoms inside the sample and the ray and I already mentioned it to you once here I like to visualize it let's first look again at x-rays and when an x-ray hits an atom inside the sample it interacts with the electron cloud of the atom and it can also be absorbed or scattered whereby it leaves the atom often in another direction the attenuation of the x-ray beam scales with a atomic number what you see here in this chart you see the atomic number versus the attenuation coefficient and there's like a linear relationship between those two and that's of course due to the electrons in the electron in the in the cloud and as you will typically measure a lump of material rather in a single atom the unit on the y-axis of the plot is the mass attenuation coefficient which is attenuation coefficient divided by the mass density of the sample material again you can go through this later to understand this maybe a bit better and if you have now a neutron ray instead if it hits the sample it can interact with the nucleus it interacts as I already said with the nucleus instead of the electron cloud and again also here it can happen either an absorption or scattering and then the attenuation coefficient can be calculated for every material by knowing the microscopic total cross section sigma total and the atomic density n and the neutron cross section that is shown shown here quantitatively describes the interaction between the neutrons and matter and as it comprises of the different contributions that I highlighted before and in more detail it's actually the coherent and incoherent scattering and absorption and these properties are isotope specific and also depend on the neutron wavelength so this all goes back to what I explained earlier in this lecture and you can look up these different neutron cross sections for example in these different tables and there are some links to websites from NIST where you can find very comprehensive information as well as on this paper that is uploaded on IndieCo. So a complete discussion of all of this is obviously beyond the scope of this lecture but the important thing to remember is that the attenuation coefficient moves to some of these different contributions from absorption and scattering and as we saw before it's fairly simple to predict the x-ray attenuation coefficient of a material for x-rays and it increases monotonously with the atomic weight of the material as seen in this blue line and the neutron attenuation coefficient does not look so simple to predict and if you take a closer look at the red points however we see some tendency that many light elements attenuate the neutron beam strongly as you can see by the high value neutron attenuation coefficient for atoms with lower atomic number and you can also see a tendency that most metals and heavy elements there's a few important examples do not attenuate neutrons well this means that most metals and heavy elements are semi transparent to neutrons and I like to go back now to our imaging geometry again and we have so far seen only how to calculate the theoretical transmitted neutron intensity through a sample but what can we expect about the sharpness of the image the so-called spatial resolution so if you're doing imaging we want to take images with as good as possible spatial resolution of course and you can easily see that the neutron rays from different angles can pass through the collimator and hit the sample it can hit the same part of the sample and this causes then the so-called penumbra blurring and it can be described by the L over D ratio and in order to make this D small we need to minimize this distance L and you can also increase the sample to aperture distance L by moving the sample further away do that now from the neutron source but that would result in longer acquisition times at the detector the reason is that the source emits neutrons in all directions not just towards the detector as I already said and hence the flux of neutrons decreases quadratically with the distance from the source the blurring is also minimized by choosing a small aperture size D of course and this will again reduce a result in longer acquisition times because we have less neutrons and maybe these slides maybe didn't play quite in the right order but I have another a little pop-up quiz for you somebody wants to answer which image has the highest and which one has the lowest L over D ratio here in this example are there any takers so if you want to take an image really fast versus taking a good acquisition time so I can reveal it for you so here is L over D ratios of course and the one on the right has an L over D ratio of over 500 so it produces the sharpest image but most likely it will also have taken a longer time to acquire this image and the next few slides will deal with the principles of tomography but of course Anders will talk about this in great detail so I will not talk about this too much I just like to highlight to you this small animation so if you have an object that consists of two materials again and we take one projection we're getting some intensity distribution on our detector and if we have a sample again two materials but this time it's a blue material instead of the yellow one inside it can produce exactly the same image if the distribution inside of the sample is actually different so one projection doesn't tell us really a solution but what if you take two projections now of this sample from this side let's say then hey we're getting a different image actually this time we are seeing a different distribution will this produce us a unique solution well we can actually find easily another example where two projections will up again give us the same solution for two different samples so obviously this is still not a unique solution and it would only exist if we have an infinite number of noiseless continuous projections actually and that is what tomography will do and we are rotating the sample through the beam and as I said you will start hearing about this from Anders Kessner already today and there will be a couple of tutorials that you can reconstruct 3d images by yourself and now I like to go this is the last coming to the last part of this lecture talk about advanced neutron imaging methods and when we come back to this slide and it will come back to the fact that many materials are actually rather strong neutron scatterers rather than absorbers that is actually affected by neutron scattering is such a successful technique after all and I already told you that we have only a few materials that are really absorbers among them are gadolinium boron cupium and lithium but this also means that the information about the missing scattered intensity is embedded in the attenuation signal so the fundamentals are actually there that we can use and expand imaging towards these these regions and this recent paper that is also uploaded to press a review paper of advantages in neutron imaging it highlights some of these developments that have taken place and then they are in there you will find many references to other research papers for different aspects in in in exploiting more the scattering aspects in in neutron imaging and practical examples of that include for example to exploit diffraction contrast in neutron imaging to for example obtain strain distributions in metals you can see for example two fasteners two screws and how the strain distributions is different in them or people have for example studied microstructure changes in ancient vikings warts or one can follow phase crystalline phase transitions for example in metallic alloys or in energy devices such as solid oxide fuel cells or one can also exploit actually a phase contrast and I believe Nikola will talk about this in more detail to reveal internal lattice defects in metals or also visualizing magnetic domains and this can be then used to example for example to study and optimize electrical steels like those used in electric motors and as I said earlier in this lecture due to the neutrons having a nuclear spin and a magnetic moment one can also exploit this for imaging of magnetic fields and again these are some of the lectures that will go into more details on these advanced techniques and there are those things coming in like the neutron grating interferometer the polarized neutron imaging setup and simply exploiting the wavelength selectivity or energy selectivity and as you've seen earlier on the slides the term that you don't get confused the term energy and wavelengths are very interchangeable used some people will say energy selective neutron imaging some people will say wavelength selective neutron imaging it's the same thing after all so just don't get confused by terminology as this is a quickly developing field also the terminology is it's not very fixed so I will wrap up with this I just want to make the point basically that we need to detect the neutrons after all we can set up the best experiments if you don't have a good neutron detector and the problem is that we can't directly detect slow neutrons as they carry too little energy so we need to produce some form of quantitative and accountable signal and we need to use some form of nuclear reaction to convert neutrons into charged particles for that and there are different detector technologies some gas proportional counters ionization shembrous cindillator detectors or semiconductor detectors and cindillation detectors are some of the most prominent ones for for neutron imaging and this is just what you need to remember because they have zero charge they cannot be directly detected and instead we need to detect the charged particle and as I said already a few times during the lecture some nuclides have a high neutron capture cross section those are the again the ones here and those are the ones that we are using typically for neutron detectors and the elements are highlighted again in this chart and what's important for the neutron detection as well as when we investigate materials these cross sections are also dependent on the energy and the energies we are talking about and this is one of the last points of the lecture now is we are operating typically in in this energy and wavelengths regime anywhere anywhere between slightly below one angstrom and maybe one maybe now with more cold neutron imaging maybe up to 20 angstroms and these are some of the important capture reactions for thermal and cold neutrons that can be exploited in neutron detectors and the one that you see on on on lithium boron gadolinium are the ones where excuse me neutron detectors are built on and how do we choose an absorber I need to drink a briefly something so if you have actually no a scintillator detector how do we choose which absorber and which sickness for a scintillator to use as a rule of thumb the sickness and the spatial resolution are coupled together because the scintillators are made from powders and this is something Nicolai will talk about in greater detail I believe and these are images of what we call a seaman star it's a resolution mask to show the resolution of an image and a thinner scintillator will then typically put use a sharper image and that's of course not the end of the story so I'm referring with that to Nicolai's lecture