 Thank you very much Fernando for those nice words So our director is a very busy man. He's actually on his way to catch a plane So we're very thankful that he was able to take some time to talk to you about ICDP So I wore the tie just to wake you up Anyway, actually I'm known to wear loud ties I won't spend too much time here because I want to bring up Maria Calvo one of our Directors and she's going to introduce the rest and so Maria Won't you come up at while Maria is here. I Just want to emphasize a point we emphasized it last week that there were there's a lot of there are a lot of experts here Including Maria who are going to help they really have done a lot to prepare what's going to happen And so I I think we I'd like to see all come here on time that means the morning lecture so they don't come and see a half empty house It's very important that you're there. You're here and a ray will keep emphasis I don't think we have to emphasize this thing No, last week was really incredible as far as I understood everybody was was really there on time and Well, anyway, there's probably another reason for that. It's a very special college this year So anyway, here's Maria and she can introduce the program Thank you very much Joe. Good morning everybody. My name is Maria Calvo I am one of the co-directors of this winter college of this year and Just very briefly to Let you explain That this is quite new as the director right now for Nando Kavedo say If for many many years It is the first time that we are just organizing a college in which you're going to have hands-on Activities and all these hands-on activities are in the afternoon, but please don't get lost in the afternoon okay, so Just very kindly remind you that you are the guest of the ICDP ICDP put a lot of effort just to organize this college and we of course You just expect the best from us and I think that is reciprocal Which is expect the best from you The idea is that you can have theoretical training that's going to be in the morning and Experimental laboratory training is going to be in the afternoon Let me introduce the other co-directors at this college couldn't be possible because of this special Conversation without the support of the other three co-directors So let me introduce you Victor Lisciuk. Please Victor Do you Nicoleta Tosa? Me introduce you unberto cabrera Please identify please identify unberto because he is the responsible co-director of the labs So whatever you need to clarify if there is something that you don't understand in terms of Organization as I say don't get lost We are here to interact with you. Do not forget that So apart from being lecturers We really want to interact and we want to know your opinions Just to be sure That the spirit of this college is fine and that we could continue on a future colleges So we all are responsible for the success of this college this year So that's all from my part and now I introduce you unberto He has to explain you something specifically about the organization of the lab. So please pay attention many thanks Good morning. As you know this Winter college is very particular because we will have Experiments in the afternoon many spending around 15 Then we need very high level of organization Then I encourage you to be on time in the experimental session for that I will explain every day the specific point because Maybe we will have some change, but I will explain the same days there the same day and please Follow the organization of the groups Who's follow you must be there with your groups at the spending you have Any thoughts about this? Please contact in advance For today, we will have at 4 a very fragile experiment in M lab And after that we will have also optical lithography Then you must be there in the in the lobby ten minutes before four Because we have to walk there to the lab Then I also want to say that the poster session will start Tomorrow and if you have your poster ready, please you can add around this lecture How you can add your poster because the evaluation committed will start Evaluation right tomorrow Then I think that's all Let's we study microscopy and To take advantage of the experimental session If you have any comment or question, please you can ask me or Other directors, okay, we try there is a Federica the secretary you can go there and we can Organize this and finally I want to say also that the with the student of the preparatory school we had Experimental session and we had six students that I know very well To these groups, but they will have with me additional experiment. We have to coordinate with them But I will contact okay and now I Well, thank you very much in virtual So we'll continue every day. You'll get from a virtual day the very last information About the organization of the college and I just for me a pleasure to introduce to you Professor Collin Shepard who will deliver the first opening lecture Professor Collin Shepard is a senior scientist at the Italian Institute of Technology in Genoa in Italy Collin right. Thank you very much. Okay. So it's very nice to be here I actually this is not my first time at this winter college I was I think I was last year 16 years ago around that sort of time. So quite a long time ago and right, so I'm down to give lectures today and tomorrow and Actually the the the the slides I've grouped actually into into three files And I don't know whether you can actually download them. I'm not quite sure what's happened about these things yet My files were too big to send by email. So but I think they're Yes, good. Okay, so But anyway, so I I've grouped them into into three files and I'll start With the I don't know how much of the second one I'll get through today. So we'll see how it goes now so Maria Let me just explain a little Maria says as you can see that I'm from Italy I work in Italy in the Italian Institute of Technology in Genoa and I've been been there for four years now and If you look on these various lists, I noticed that some places I'm down as being Australian some places I'm down as being British It says British on my badge, but it says Australia on the thing Well, I'm both of those but originally from from the UK and and then I worked in in Sydney for 15 years and Became an Australian citizen when I was there and but then subsequently moved to Singapore for nine years and and now in Italy and So I'll introduce some of the things I've done in in these different places as the talks go on So but now in Italy So the first group of lectures are about microscope imaging So I've heard that you you've a lot of you have done this preliminary course and learn a lot about microscopes already. So I hope I'm not going to Cover too much that you already know The other thing I ought to say my Maria made the point that we like a lot of interaction in this course so Please interrupt me at any point and I'd be pleased to you know To have some discussion I'm going to be here for for the next two weeks. So You'll have plenty of time to ask me any questions If you want more details about any of the things Okay, so Microscope and so here's a picture of a very nice. So this is not a modern microscope You can see it's a beautiful brass thing. They don't make them like this anymore but On the on the left I I list here The the really what you might think of as the three important parts of a microscope on the one hand You've got the objective lens. You've got the eyepiece way out the way you view the image And you've got the illumination system and I put the objective lens first because actually that's really the most important part of a microscope It's really the objective lens which is going to control the resolution that you can get from that microscope and Because of that very often the objective lens is also the most expensive part of the microscope Recently in our lab We we had on loan to microscope objectives from Olympus These were special objectives designed with a very long working distance so you could look deep into tissue The purchase price of these lenses was 16,000 euros each right, so I Know you could buy a microscope for a lot less than that But but this is just one micro microscope objective You can easily pay that sort of money for it. So they can be very expensive And right so last week, I think you would have learned that The resolution of the microscope is determined primarily by the numerical aperture of the of the objective lens so numerical aperture n sin alpha n is the refractive index of the of the immersion Medium and alpha is the semi-angle of the lens so the the bigger the aperture of the lens the better resolution you'll get of course the the resolution also depends on the wavelength of the lights and We'll talk about that later But I'm going to say a bit more about the objective lens so so that you know that it's very important you choose the right lens for the right thing and and so you can You you can get air air objectives or immersion objectives water immersion objectives are becoming more and more popular as people want to look in into biological tissue you want to focus deep into the into the tissue and Water is quite a good refractive index match to many tissues, so This is the why the reason we're going in that direction But when it comes to resolution, of course, you want this the refractive index to be as high as possible And so oil has got a refractive index, which is pretty close to that of glass so 1.514 I think is the what there's the standard for the refractive index of oil I might add that another feature that we sometimes find in experiments in sensitive experiments is that the refractive index of oil depends quite strongly on temperature and So be aware of that if you if your lab is very hot you'll find that the refractive index of the oil is not what you think it's going to be Okay, and then Objective lenses are corrected for a cover slip or maybe not corrected for a cover slip so typically Lenses that are designed to look at metallographic specimens surfaces Are not corrected for a cover slip, but but if you for biological systems usually they are And and they're corrected for a particular thickness of cover slip The standard is what's called a number one and a half So they range through different numbers starting from one is the thinnest but one and a half is the most standard and it's 170 microns thick You'll find That sometimes they vary in thickness if you buy good quality ones from Zeiss or someone you you probably can Rely on them being pretty well what they say they are if you buy cheap ones you'll find that they vary a fair bit So you may be a good idea to check them with a micrometer to make sure that you've got the right thickness so changing these things the the the the immersion fluid and the cover slip Are going to change the aberrations of the lens So the lens is corrected to work with a particular thickness of cover slip a particular Emotion fluid and so on Now the other thing is What happens on the other side of the objective nowadays most objectives are corrected for infinity They bring of they bring they focus to produce an image at infinity This this is actually only happened over the last I'm not really quite sure now 10 or 20 years. Let's say before that most most Microscoped objectives were designed to bring an image Somewhere inside the tube of the microscope. So typically it would have been 160 Millimeters or something like that in those days virtually every manufacturer had their own standards for this so 160 170 210 Pretty well every company they did different things nowadays people have Standardized or on correcting for infinity But the way that they're corrected does vary and you have to be aware of that too Xi subject is for up for example corrected so that Some of the final chromatic Correction is done by the by the eyepiece Right so the lens itself is not completely acromatic so if you use If you use that sort of lens Then you have to what you use it with a tube lens which which is going to the combination Will produce an acromatic effect. So that's basically Why you have to be careful of these things? So you can't just take different components from different manufacturers and think that they're going to work well when they go together Okay, and they're so they're finally on the objective lens If you read if you look on the objective lens, you'll find something like this. So this tells you all the information 100 times magnification 1.4 numerical aperture oil immersion 0.17 means the thickness of the cover slip infinity is where it brings this image and So all that information is written on the objective Okay, now so a bit more about resolution You remember there's this thing called the airy disc. This is a picture. I took from Bournemouth this the sort of standard book on Optics got lots of good information in there But I'm not I'm sure that you people who've looked in it realize it's not actually a very good book for Beginners to learn optics from it's it's definitely a serious book for people who are experts really But anyway, this is an experimental picture of an airy disc And the airy disc is the image of a point object if you have a let's say a metallic screen with a small hole in it very small hole Then you get look at an image of that in your microscope, of course because of the fraction effects You will you won't see a point you'll see some blur and this is what it would look like You'll see a central central bright spot surrounded by a series of rings So now this is photograph from an experiment But note that actually, you know when they've taken this photograph. It's overexposed if you if you look at it with your eye You wouldn't see you wouldn't be able to notice as many rings as this because they they become weak quite quickly So this has actually been overexposed. So this central lobe is Saturated so that you can see these outer rings. This is a cross-section through this picture and Now the interesting thing Is that the whole idea of the numerical aperture? And you know the size of this spot is going to depend on the numerical aperture and also the wavelength But the shape of this curve is the same It doesn't it doesn't depend on the numerical aperture or the wavelength And so we plot this Against this normalized quantity This is what's called the optical coordinate if you look in Bournemouth. I think this is probably where it was first divine defined V is the optical coordinate. It's a dimensionless quantity Dimensionless distance if you like and it's defined like this. There's a missed out Sorry, there should be an R in here. It's a normalized radius So it's the radius multiplied by two pi over lambda, which is K the wave number And multiplied by n sine alpha the numerical aperture, right? So if you plot this curve against this normalized quantity V then the same curve is going to apply for any system and And this is what it looks like it turns out that you can express this term in terms of Bessel functions mathematically the amplitude is given by this thing and So the intensity as I've plotted here is the modular square of this And the reason why we put this to there Is to make it so that this thing becomes one when V equals naught So here it's plotted here. You can see it's got a normalized intensity of one When V equals naught So this is a Bessel function J1 and For people who might feel frightened by Bessel functions Bessel function is really nothing more than a It's it's it's very similar to a cosine. It's very similar to a decaying cosine wave Except that the zeros are not regularly spaced as they will be for a cosine wave, right? So it's nothing to be Afraid of Okay, so that's the image of one point. What happens now if we look at the image of two points and this was a Criterion of resolution that was introduced by Lord Rayleigh So this is one of the two major Ways that you specify the resolution of a microscope one way is in terms of Rayleigh's criterion for two-point resolution The other way is ABBA's Resolution limit and I'll go on to that in a minute but actually Historically ABBA's was before Rayleigh's right Rayleigh's was about I think six years after ABBA's Criterion was introduced so Rayleigh said yes, well, okay If you've got if you're looking at the image of two points Then you can see If they are if they're well separated you can see there are two points there if they're too close together You're not really sure. Is there is this really two points or is it just one sort of slightly elongated point? Well slightly elongated region, right? So He came up with this idea this Criterion and he said that some that the points are just resolved If I go back to the previous slide if you place the second point over the first The dark ring of the first one. So if you place it here, then We'll say they are resolved if they're closer together than that. We say that they're not resolved Very arbitrary really It's not that you know anything magic happens of that figure It's just around there that things happen. Okay. This is what I've just said two points are just resolved if the second point is placed on the first start ring of the first points and if you if you do that Then you find that this is what the separation is The value of this V or rather to V is equal to 3.84 if if that is a condition is achieved this is basically the first zero of the Bessel function J1 and So 0.61 is a figure that you maybe have come across it often Comes up in you know diffraction experiments and so on as the spacing between things and Or even sometimes you see Twice this figure 1.22 as being a magic number that comes up to do with diffraction by circular aperture So this is you know rarely recognized that this is rather an arbitrary Concept this rule is convenient on account of its simplicity And it is sufficiently accurate in view of the necessary uncertainty as to what exactly is meant by resolution So he's saying that this isn't everything. It's just a rule that you might come up with But it's you know at the moment actually as I've defined it so far This is actually quite restrictive Because it assumes that you've got a perfect imaging system. It assumes you've got circular apertures It actually assumes you've got incoherent light This is a very important thing when Rayleigh first came up with this concept He was really thinking of telescopes not microscopes. He was thinking of two stars And if you've got two stars The light from two stars is obviously going to be there's no phase coherence between the light between two stars So so they're basically incoherent with respect to each other, right? So if they're incoherent, you can add the intensities of the two points so this was all assumed in In Rayleigh's original concept But in a microscope that might not be true You know if you illuminate two points you might illuminate them coherently And then the resolution is going to depend on how you illuminate them And this is going to be one of the things I say quite a lot about in the in these lectures is about how the Resolution of a microscope is going to be affected by The coherence of the system So how do we deal with this? To generalize this Rayleigh criterion so we can apply it in in more general cases And so it's all based on this idea here We find according to Rayleigh That the intensity for this special case when it's a perfect imaging system incoherent illumination the intensity midway between the points if You divide that by the intensity at the points themselves This ratio is naught point seven three five This is the how big the dip is that you'll see in that image of two points and we take that As the as a definition of resolution for the more general case This is called the the generalized Rayleigh criterion. You'll find quite a lot of literature about about this Right, but first of all, let's say a bit more about this Co this incoherent case Here I've plotted the image of two points incoherent points and This could this one here is for the the case where they just satisfy the Rayleigh separation So this the ratio between this and this is naught point seven three five What happens if you make them slow slightly closer together? What happens if you make them slightly further apart? Well, this is what I show here This is 10 percent closer 10 20 percent closer 10 percent further apart 20 percent further apart So not a very big change in the distance between these points. You see that actually It changes very quickly the shape of this image right so although I said that this You know this this Rayleigh criterion was rather arbitrary You'll see that it's about right and You know because a lot happens over a very small change in distance between the two points Changing from ten percent bigger to ten percent smaller. You see the size of this didn't change is appreciably right so So what that really means is that maybe if you if you'd change the resolution the actual details of the resolution By to something different. It wouldn't really give a very different result Okay, now I said resolution depends on coherence And this is all to do with the illumination system of the microscope And so here I show a microscope. This is the objective lens very simple this And this is the condenser lens. So the sample is placed here It's illuminated with light from the condenser lens And produces an image in this plane here So this this pictures he has taken from born and wolf again. This shows what's called critically illumination. I I've heard that You you you've also heard about curler illumination system I Think I probably I'll say something about that in a minute It doesn't really make a lot of difference from the point of view of the performance of the microscope In terms of theoretical terms But in this case here, you've got a condenser lens and you see that this is illuminating the object With lights coming if you think of it as being plane waves their plane waves Coming in from different directions right, so One of the important features is what is the aperture of this condenser lens? And the can the aperture of the condenser lens is fixed By this aperture stop So any microscope would have a control that you can change to change the aperture of the illumination system and And so we change this this iris diaphragm here And if you stop this down, it would become a smaller aperture obviously, okay? And so here I've written Alpha C alpha O The out so these are the angles alpha O is the is the angle the semi-angle of the objective This is what determines the numerical aperture of the objective lens And alpha C is going to Determine the numerical aperture of the Condenser lens right and it turns out the ratio between these is the important thing And sometimes we call this the coherence ratio a lot of a lot of Sources talk about this as being capital S. I think born on Wolf called it's capital S You might find some other papers that call it different things But this coherence ratio is the ratio of the numerical aperture of the condenser to the numerical aperture of the objective and basically the the coherence of the illumination and therefore of the final image For the image for motion formation process depends on this ratio So if s equals zero We're effectively just illuminating with a plane wave. It's when the numerical aperture of the condenser lens is very small So it's effectively coherently illuminated Right, it's just illuminated with a plane wave. You get this result if you shot a laser at your sample Then as we increase s it becomes partially coherent and as s tends to infinity If we could really illuminate With an angles that were much bigger than the numerical aperture of the object of the objective lens It would tend to become incoherent illumination And now very often you can't do that, of course Because there's a limit to how big these angles can be our alpha here can't be any bigger than pi by two All right, so if our if alpha zero has got some big Compact, you know comparatively large value. There's no way that this can be much bigger than this Right, so some of these you can't really get into this regime if you've got a high numerical aperture objective lens So s tends to infinity is incoherent illumination so you could apply Rayleigh's Criterion directly to this case if you could achieve it in an experiment Now in between there's a very important case Which people quite often use in practice is where s equals one? When s equals one it means that this aperture is equal to this aperture Note then this the numerical apertures So if this is if this is an oil immersion lens, this would have to be an oil immersion lens Right, so if it's very often if we want the ultimate resolution in a microscope We have to it oil immerse the condenser lens as well as the objective lens And Yeah On the other hand so this is what this is what happens if you've got what's called a trans illuminated object So you've got your objects on a slide you illuminate it it could be in a transmission could be in reflection But that all that all this would apply for either case But it but it's illuminated from outside. It's it's different from what you might call a self luminous object and Like stars I was just describing in astronomy This a star is a self luminous object And you can think of fluorescence as being like a self luminous object. So The reason for that is that if you've got a fluorescent object Fluorescent die for example, you illuminate it with light But the fluorescence is incoherent and and the reason for that is because you remember that they went when you Excite fluorescence you excite an electron from a lower level to an upper level And then it hangs around the electron hangs around in this upper level for maybe a nanosecond Which is many many periods of light, right? So when it pops but down the phase of the light is arbitrary basically so fluorescence behaves as incoherent imaging and No, it's interesting to note. I'm going to talk a bit about Abba's Resolution theory in a minute You know that this was actually proposed before fluorescence microscopy had been thought of So not about 1910 the first fluorescence microscopy was done. So a lot later but this idea that Illuminating by over range of angles is going to give Could give effectively incoherence was actually first described by Lord Rayleigh About 1890. I think it was Okay, so So let's now look at what happens to our imaging of two points as we change the aperture of the condenser lens So I give three three examples here a small condenser Equal apertures and a large condenser So large condenser. It's incoherent. So this is this is Rayleigh's case. Let's look at this one first I've shown here four curves the one in blue the curve in blue is pretty close actually to being the Rayleigh separation It's It's really 1.9 something I think we said it was So this one this one is close to being the red Rayleigh Separation so these two points are resolved Let's go to this one now This is the small condenser coherent illumination were close to coherent illumination Again, now I've shown four curves here the blue one here is the same separation as this one What can you see here they're resolved Here they're not resolved right, so So this is one thing that we've learned which is a very important thing If you stop down your condenser lens the resolution is not so good You open up the condenser lens you get better resolution from the point of view of this two-point resolution, right? in between Equal apertures is this blue curve actually it turns out this blue curve is identical to this blue curve However these other curves are Different from these ones So it turns out that the resin that the Rayleigh resolution limit is the same but What happens if we're not quite at the Rayleigh resolution limit is slightly different and I'm making a big point about this because there are very many papers that you you read where they They get this wrong. They think that this is incoherent illumination and it's not It's a partially coherent illumination and But it just so happens that when there's points two points are separated by this particular distance you get the same image Okay, so this is plotted in born-and-warf again And he this is a picture. I've taken from born-and-warf. This is this coherence ratio s And so here you see he's got it going from zero up to two This is the the match condition in the middle here And what he's plotting here is that the distance between two points for them to be just resolved according to this generalized Rayleigh criterion this 0.735 ratio of intensities And and this is what you get you see that here. This is coherence The resolution is not so good the distance between the points is further Apart and then as you open the aperture you see this decreases It comes to a minimum. It comes to a minimum at this where this s this ratio is about 1.4 And you see then it starts increasing Eventually it's going to tend to 0.61 So actually if you plotted this curve further it would start oscillating like this and tend to 0.61 eventually Okay, and Yeah, that's right. So here no 0.61 is this point here as well two point resolution Right, so this is another way of Presenting this information what I've what I've done is I've plotted here this ratio of the intensity midway between the points to the intensity at the points themselves As a function of the separation between the points And so for the incoherent case, let's this is Rayleigh's case is this curve here You see it rises up and then drops down again, and then does some oscillations where this curve Crosses this 0.735 line Corresponds to the two-point resolution for that microscope For coherent illumination you see it's this curve And so the the the resolution is poorer the distance between the points is further apart For the coherent case, so I show a few different ones here I also show a couple of confocal ones. I'm going to talk a lot about confocal my microscopes in the in later part of this These lectures, but you see that confocal reflectance Or confocal fluorescence We're in we're in we're improving the two-point resolution Right, so this is what I've talked about here the generalized Rayleigh criteria So you'll find that that is the what they assume in many many papers Including Bournemouth It's defined as the ratio between the intensity midway between the points to the to the intensity at the points themselves But actually This actually this definition does have a problem From the point of view of actually measuring this Because you don't necessarily know where the points are If you've got aberrations, for example If you've got a system with aberrations the magnification might not be very well determined That's so sometimes people Take the definition as being not that the at the points, but the intensity at the maxima So you get a dip surrounded by maxima and you take that ratio instead So this has been called The modified Rayleigh criterion rather than the generalized Rayleigh criterion So this is getting a bit detailed really, but this is by far the most used Expression that people use So there are some other things I mentioned here. I'm not even going to talk about that It's confusing, but I do have a bit of a discussion about these these different definitions in this paper That's resolute. It was actually about solid immersion lens microscopes And so this is from when I was in Singapore So in Singapore So this is a paper by Rui Chen who's still in Singapore actually When I was in Singapore, I was in the National University of Singapore in the bioengineering department and So this was some work we were doing there on solid immersion lens microscopes Okay, so Yeah, this is just pointing out something that's going to be important in Tomorrow's lecture really Is that Imagine you've got an object which is a phase object Imagine your object can be described by this complex number. It is a modulus term and a phase term And so this is what we call the object transmission transmission or transmittance and I wanted to point out that if you could produce a perfect image of this if you had a perfect microscope What you would see is just the modular square of this wouldn't you and the modular square of this is just a squared Right, so this is quite interesting, isn't it? It's this is a limitation of perfect imaging if you've got a perfect imaging system. You don't see the phase So maybe you want to see the phase so What this is suggesting is that if you want to see the phase the best thing is for it to not be a perfect imaging system You have to mess it up in some way And in lecture tomorrow. I'll talk about some different ways you can mess it up in order to make it make the phase visible Okay, now so what happens then we've spoken about two points We can generalize that to more general objects How can we calculate what the image is in these different types of system? First of all, we'll take the coherent case Let's imagine we've got two points This is the image of one point. It's the amplitude image of one point, right? This is this is this some vessel function thing 2j1 of V over V But we have to because this is coherent We have to add the amplitudes coherently Here we're assuming that these two points are Giving out light in phase with respect to each other, right? So we add We add together the amplitudes of the two points And it gives this solid line here This is still an amplitude. You see it goes negative And then what we actually observe is the intensity So we actually observe the modular square of this amplitude which looks like this. So now this is our area disk Right, so this is the area disk for this. Sorry. This is not the area disk This is the image of these two points. Sorry, but but you see there's not a lot of indication that you've got two points there Right, these are actually I've chosen these two points to be Actually at the Rayleigh distance So this is the case where they would be resolved if it was incoherent But not if it's coherent. Okay, so we generalize that that's two points How can we treat some arbitrary objects? This is our arbitrary objects. We break it up into lots of points We say each of these points is like a This 2j1 of v over v type curve and then we add all of these two together And then we have to do the modular square To calculate the intensity. So this is our final expression the image that you see the image intensity is The amplitude point spread function. We call it this shape of this curve Convolved with the object's amplitude So all this is saying is that for each point of the objects you have to place one of these and then we add them all together And then finally we have to find the modular square in order to find the total intensity of that object So this is how we can calculate the image of an arbitrary object in a coherent system Now the other way of doing this is in in Fourier space Right, so we introduce The well if it's a periodic object We can introduce the Fourier series for our object So this gives you an example Imagine your object is as got is a square wave grating like this. So bright and dark regions We can resolve this square wave objects into its Fourier series It consists of a constant term a first harmonic a Third harmonic There's no second harmonic for this particular case because of the symmetry And if we added together these first three components that I've just mentioned constant first harmonic third harmonic Some of them together we get this so so you see we're already getting something which looks quite reasonably close To our square wave objects right, so so this is a way of another way of treating Imaging in a in an optical system is in terms of the What we now call Fourier optics It's interesting that You know Fourier optics really I in some ways Was invented by Abba in with his diffraction theory of the microscope but Other people were not very happy with this idea at that time especially Lord Rayleigh it seems Who didn't think it was a very good way of doing it You have to remember that Fourier transforms also were not really very well known at that time In the 1800s, right? So Nowadays we feel very happy. We're taking Fourier transforms all the time You don't need to use a Fourier series You can use a Fourier transform in it doesn't have to be a periodic function anymore because we know we can still use Fourier transform So the basic principle of Fourier optics Is that a lens produces? performs a Fourier transform operation So if you've got some amplitude in the front focal plane a distance f in front of a lens Then if you look in the back focal plane of the lens the amplitude is going to be given by the Fourier transform of it So this is our amplitude here. This is the Fourier transform of it and Optically basically what the Fourier transformations doing Is changing? positions to slopes and Slopes to positions. So here I'm showing some rays This is at a particular radio distance from the axis and the lens converts this ray to a particular Slope particular gradient The further away is from the axis the bigger the slope and vice versa a slope is converted into position right, so this is our our lens Fourier transforms a signal And so this is showing it again here. We've got some objects This is a lens and if we look at the back focal plane of the lens We will see the Fourier transform of this as a simple example of that What happens if we put our square wave grating here or any form of grating if we've got a grating We illuminate it with light The light is going to be diffracted. Isn't it? You'll get different diffraction orders So the different diffraction orders will appear in this plane here, right? So the example I gave of a square wave grating has got a Constant component which is going to appear at the origin It's going to have a first harmonic, which is going to be Somewhere out here according to the spacing of the grating and there'll be a third harmonic fifth and so on getting further and further away and Abba realized this He realized this in 1850 or whenever it was very very before its time, I think really to have appreciated this idea back then and He realized that then you can think of a microscope as being simply two of these one after the other two units This is our sample We take the Fourier transform the second lens Takes another Fourier transform The Fourier transform of a Fourier transform is actually the same as doing a Fourier transform And then an inverse Fourier transform Except that it flips over This is why you get a negative image in an in an optical system and so The here I showed the object. This is the the frequency content of the object But the of course the aperture of the system is not infinitely large here. I show this aperture stop This is the aperture of the objective lens. This is the objective lens. This is the tube lens Here we are drawn this like we normally do in Fourier optics books This is what's sometimes called a 4f optical system all these distances f But in in a microscope It's not a 4f system because these two lenses would have a different focal length Because you want to magnify if you make the focal length of this bigger than this one then you get a magnified image and so Anyway, we've got this aperture stop. So you see this this object has got this frequency content and it goes on forever, maybe and So the further away from the axis corresponds to the finer detail in the object And you see that this fine detail doesn't get through this aperture stop like so only the Part of this that goes through the aperture stop produces is into the goes into the final image so this Explains why a Microscope has got a certain resolution and why it depends on the aperture of the lens so nowadays because of the the way we think of in terms of Fourier optics as being you know a bit like Communications theory we tend to we tend to this think of this as being a low-pass filter The low frequencies are transmitted The high frequencies are not transmitted Mathematically, this is the way we write these things. This is our object transmittance that I mentioned before We this is the the Fourier transform of this. So this is what we call the object spectrum So this is the Fourier transform of this object and then That is going to be filtered By some sort of transfer function, which is a description of that aperture Any aberrations the system might have or whatever I mean that we described this in terms of this See I've written it here C mn. So this is this is our object These m and n are spatial frequencies in the x and y direction We have to filter that by this What we call the coherent transfer function of the system. So once we've multiplied by that this tells us now The the spatial frequencies would are which are in the image We then have to do an inverse Fourier transform to get back into real space the second lens and then finally we have to do a modular square in order to calculate the intensity and So this is the expression then you can use this to calculate The image of any arbitrary object in a coherent system. What happens if it's not a coherent system? Well, it turns out this in this this modular square of this double integral. We can actually write as four integrals Which I've written in this next line here. So we just multiply this by its complex conjugate, which I've done here And now we've got an integral over four spatial frequencies M and n are in x and y directions P and Q are also in the x and y directions I'm sorry for this terminology, but this was the way it was developed originally by Hopkins And it's described like this in Bournemouth, too so M and P are two spatial frequencies In the x-direction both in the x-direction N and Q are two spatial frequencies both in the y-direction And you see in the final image you see what we get we get M minus P. So basically these these these spatial frequencies mix And this is because we're looking at intensity not to do not amplitude All right, and so so this is how we can write this expression again expanding this as these four into the two integrals as four And you see here. We got this coherent transfer function appearing twice It turns out if you want to treat a partially coherent system Then all your this expression still works except that These two things don't separate anymore so you have to replace that product by some function of four spatial frequencies and I'm not going to go into a lot of detail about how this is done. This is called the transmission cross coefficient But as I say here, this is all complicated. It's probably more complicated than you really need to know Let's go to the other simple case Let's let's the other a limiting case incoherent illumination Now what we've said is we have to add together the intensities rather than the amplitudes And so here we see we add together two airy discs Get the total you see now there. It's nicely resolved. This is at the Rayleigh separation again, and if we if we generalize to many points We think of our object here. This is now an intensity object We break it up into lots of points each of these points is imaged like an airy disc Then we add them all together and we get the final intensity in the image, right? So so this is and now our expression for the final image It's the modular square of the amplitude point spread function gives the intensity point spread function the airy disc And the modular square of T gives the intensity transmission of your object and you convolution of these right so just to Compare that with what we had earlier and right now, so let's say about the The the the spatial frequencies get that gets through for an incoherent system It turns out for a coherent system if it's a perfect system The aperture stop tells you everything The the the spatial frequencies inside the aperture stop get through the spatial frequencies outside of the aperture stop Don't get through so we can recognize we can represent this as a circle. It turns out for the incoherent case What we call the optical transfer function of often called the OTF is given by the the Autocorrelation of this circle The auto correlation of the circle We have to move one of the circles relative to the other and calculate the area of overlap if you calculate this You can actually express it analytically like this And it looks like this This is sometimes called the the Chinese hat function Because of its shape right so here I've tried to draw a Three-dimensional view of what this looks like in 3d If you've got a system with circular objectives Circular apertures and so on this has got circular a cylindrical symmetry And if we do a cross-section through here, we get some curve that looks like this So this is the transfer function for an incoherent system So these are these are the two cases the two limiting cases You've got a coherent transfer function for a coherent system an optical transfer function for an incoherent system You see that there's some differences between these the first thing to note is That the cutoff of this one is actually twice as big as this one and I guess Certainly to a first approximation anyway This is the reason why an incoherent system has got better resolution than any than a coherent system because it's Got twice. Whoops. Sorry Twice the the bandwidth Right on the other hand, maybe we can't really compare these two things You know, I put them on the same picture here, but they're not really the same This one operates on amplitudes. This one operates on intensities Right, so you can't really compare them completely One with the other for that reason You notice the other thing is that this one slopes off. This one's got a flat top. This one decreases So although this has got twice the bandwidth of this you see that the The transfer function is actually dropping off So these higher spatial frequencies are not actually imaged as strongly as the Higher spatial frequencies here This again is another picture. I took from Bournemouth, but originally it was done by a calculated by Harold Hopkins And what it shows here, this is the OTF. I've just shown you for an incoherent system These other curves here correspond to two different amounts of defocus as you defocus the system so that you see the these curves start falling off it means that the Spatial frequencies are not transmitted as well by the optical system So this explains very simply why if you defocus your optical system the images and there's good Right because the spatial frequencies don't get transmitted as well There's a very interesting thing about this though that maybe you can't see too well If you look at this axis here, this is the origin. This is zero here And so these are positive Constitutes this is actually going negative So this OTF although if it's in focus is is always positive if there's defocus it actually starts going negative and This is really bad news If you think in terms of that square wave grating, you know, we resolved it into its Fourier track Fourier Fourier components What this would mean is that some of them get reversed in sign Right if the value of the OTF is negative it means that that component is flipped over So it's not going to produce the right sort of result at all in that case And so I've got an example of this This is actually not for the incoherent case. This is this is actually for this case s equals 1 but these these are some calculations done by One of my former students from Singapore shall in meter So he's now at marine biological labs in Woods Hole and So he calculated images of this Zeeman star. It's called The Zeeman star you see is like a square wave grating as you go round But the period of it gets higher at the closest you get to the center And so this is the in focus image This is a defocused image. This is another defocused image And I hope you can see what what this sign change can do This is the defocused image. You see that what what? What was what bright becomes dark what was dark becomes bright So you actually get a contrast reversal right so Obviously, this is not a good thing if you want to get an image which tells you exactly what your object looks like Okay, so this is taken from one of shall in's papers. You see it's in biomedical optics express And he's I think he's got this program He calls micro leth that you can download from somewhere for free and it will calculate partially coherent images for you another object is a straight edge Let's say you put a razor blade in your microscope You look at the edge of the microscope on one side. You're going to see bright on the other side You're going to see dark but of course it doesn't change suddenly from dark to bright because of the resolution of the microscope and So these are some experimental Plots that were published a long long time ago now by this guy what trust of its Two different values of this coherence ratio Showing what the image of this edge looks like And actually is one interesting thing. This is s equals one You see that actually at the edge if you normalize this study is 10 into one Actually at the edge the intent is a third it's always Amaze me why it should be a third And there have been a few papers actually published that prove that it's a third But it's not trivial to prove it by any means if it was incoherent Then it would be a quarter Because by symmetry if you've got an edge like this the amplitude actually at the edge would have to be a half and Therefore the intensity would have to be a quarter If it's purely coherent Sorry, I've got it wrong like for if it's coherence. It's a quarter a half squared gives gives a quarter if it's incoherent It's a half so In the experiment he just did these two values. So here you can see it's because it's tending to wards Well, it's not much actually much different from a third there, but it it Let's see what it is Yes, not far off a quarter. This is this is 50% here So it changes from a quarter up to a half as you change the aperture of the condensers The other thing you'll notice here Is that if it's coherent illumination you get this quite large overshoot Fringes here you don't see fringes So that's another difference and this is actually often used in practice in the semiconductor industry If they're if they're trying to measure the width of lines features integrated circuit They use close to coherent case Because it turns out that this is actually steeper than this. So this is this is an example Where coherent is actually better than incoherent The steepness of this transition region is is greater for the coherent case than the incoherent case so some of these things are I've Summed them up here the intensity at the edge for these three cases the slope at the edge you can calculate what that is and it comes to this and So as I say for these particular examples when you're measuring the size of things People are found that nearly coherent systems have got some advantage Right, I think that's going to be the last slide right so So that's the first Part of my lecture. I was going to do a bit more today But maybe we'll have a five-minute break so that people can and I can get my senses as well Before I carry on and so so let's break for five minutes And then I'll carry on and talk a bit about confocal microscopy It's time for questions. Oh, yeah, of course either now or or yeah, please You investigate this parameter. Yeah for different system optical system and I don't know why you called it coherency because as We know coherency is related to wave optics and related to a phase difference between different objects, I think it's just a Comparison between two numerical aperture Am I correct or not? Thanks. I Yes, you are correct. That's I you know, this is just one very small part of it And so actually the you know, I shall say a bit more about partially coherent imaging tomorrow I think this was actually the big missing link that that was you know while Abba came up with this theory and Everyone was arguing with him and not understanding quite what was going on Part of the problem was that nobody knew at that time how to treat partially coherent systems And all this was solved eventually by Harold Hopkins again actually who I just mentioned who Did an amazing amount of Really, you know high quality work on diffraction imaging And he came up with the idea, you know, basically he calculated the system by In terms of what you're saying about the the wave theory of partial coherence You can propagate the the mutual Coherence through the optical system, and that's what he did in his paper 1953 I think it was so you You you you you you propagate them the partial coherence through the system the mutual intensity and and then finally you get an expression for the Mutual intensity of the image And then from that you can calculate the intensity of the image And so yeah, you're you're right. So basically what happens is if you've got a Condenser lens, which has got a certain aperture and let's say it's got a circular aperture then the Mutual intensity of the illumination is given by the Fourier transform of that which is Again this 2j1 of V over V So that means that if you've got a two-point object If you're imaging this point the coherence of this point is Depend on the aperture of the condenser lens. So that's how it all connects But I think you'd have to read the papers to fully understand this Yeah, okay So so what I'm saying is that this this this mutual intensity of the illumination is given by the Fourier transform of the condenser lens And the width of that curve is going to be again a Bessel function the the the scale of it is determined by the Aperture of the illumination system. So this is why This is where the aperture of the illumination system comes in and the important thing is how big it is Compared with the numerical aperture of the objective lens Right, so this this ratio determines how how broad The mutual intensity function is at the sample compared With how big the point spread function of the system is Okay, I mean this is a power a White light illumination not laser Illumination yeah, but but but let's call it Quasi monochromatic Yeah, I'm assuming a particular well In in the results I showed we're all done for a particular wavelength We're not taking color into account But it but it's from a it's let's say filtered white light So, you know what you might have from a halogen lamp or a tungsten lamp with a filter Not a laser. Yeah, this is not a laser in this case. It's a It's either a tungsten lamp or a Halogen lamp or arc source something like this So it assumes that I haven't really said this yeah, so this source here is basically according to Hopkins theory this source is incoherent And I think you know that as light propagates the the coherence increases and So although the light when when it comes from the source is purely incoherent by the time it gets to here It's actually partially coherent. So please read. I know actually I will say a bit more about that You can read it in Bournemouth But I find the account in Bournemouth very difficult It's much better to go back to Hopkins original paper where I Think it was in the proceedings of Royal Society Where he describes it much clearer way I think Okay, any more questions. Yes here and thank you for your informative lecture It's for it was so nice and I guess He was asking about the temporary and the special Coherency and I guess you were talking about the special spatial coherence and the other question is is there any difference between the objectives in a Reflective and microscopy and transmissive and microscopy or not So the question is are the objectives for transmission and reflection microscopy different The biggest difference is to do with this cover slip You know because biological ones are normally corrected for a cover slip Whereas ones for looking at metal surfaces and so on don't are not corrected for a cover slip But apart from that they should be pretty much the same Just another one. You said that the perfect Object image is that we don't see the phase. Yeah, but what do you mean by that? We don't see the face for example if we have a coherency and full coherence special and temporary We will see the fernel diffraction fridges. So it will maybe Say show the phases or you mean something else Yeah, okay, so so I guess the question there is saying pointing out that that actually Diffraction does depend on the phase and yes, that's true. No, I mean What do you know when we we have an image? So it will about the amplitude not the phase, but we can Mission the phase with holographic fringes. Yeah, yeah. Yeah. Yeah. Yeah. Yeah, yeah So of course if you if you haven't some sort of reference beam, then you can measure the phase If you have a microscope without a reference beam Then if it's a perfect microscope, you won't see the phase In the talk tomorrow, I shall talk about how you can see the phase even without having interference So, thank you. Okay. Is there room for another question? Yeah So, sorry. Thank you for the nice presentation, sir my question was firstly about where you have Defined that in the coherent imaging we add the amplitudes. So By amplitude, do you mean the complex amplitude? You mean you also at the phase phases of the object exactly. Yeah What I saw there was that you added the curves, which was the real part of the absolute value of the amplitude. So Are we assumed that the phases on that image? Well, I think yeah, okay First of all, yes, you're correct. You add the complex amplitudes and Sorry, I seem to not be connected to this anymore I Think I don't know it is there. Hold on. I can't find my cursor. Sorry. I've lost my cursor Maybe I'll just have to say in words The example I gave of two I gave an example of two points Sure, or maybe more many points, but if you've got two points each point is going to be like a 2j1 of v over v which is purely real. It goes negative, but it's not that that's so for the particular picture I drew it just happens to be real Yeah, but in general as you say you have to add In phase and if it's not bad time I was just very simple short question about the reflective that Peggy mentioned In the reflective microscopy as long as I think and I I hope I'm not wrong the condenser and the objective lens are the same I mean the same thing that condenses the light is the same thing that sees light So it would be very sensitive to tilt. Isn't there any kind of objective? Which kind of is ready to correct this tilt aberration by itself because sometimes the object is not Finally, you know in detail to be correct by the tilt. It doesn't go back to objective simply the way it was eliminated. I Don't know of anything that's quite like that So, you know, so in a reflection microscope as you say often you're using the same lens to Yes, and illuminate the sample handle to collect the light And so that optical system will we'll have a a plane of focus Which is perpendicular to the axis and you're saying that that might not coincide with your surface You know sometimes of course Some microscopes do have very sensitive tilt chart tilt stages in order to correct for the for these angles But I don't know And the very optical way of Thank you, sir Hi in some of microscopy methods based on Radiation of the sample for example fluorescence microscopy or Raman microscopy The radiation is direction dependent and I think we have to define a modified Koreans ratio. Is it correct? Probably yes It's I think the sample dependent for Image formation. Well, you know it in fluorescence Actually, of course the light in fluorescence is incoherent full-start So, you know the the details about the source are really not very important in Determining the coherence right so Because it's only the intensity of the light that matters So I guess the same will be true in Raman, ordinary Raman So this afternoon you'll have the chance to keep in maintaining these questions with Professor Collin Shepard because he's going to be in the lab and this afternoon Some of you you are going to make the Abe Defraction experiment which is what he was explaining right now and in the other group you're going to To study some aspects on microscopy So this is quite a very important lecture Okay, thanks Okay, so Did you we just carry on now or do you want to have a break? What do people want? I'll continue for 20 minutes. Yeah, that's a good idea. Okay, right. So I'm going to change gear a little and talk about Confocal microscopy and a bit about super resolution and so so this let this lecture I shall start now and Carry on with it tomorrow before I then go on finally to face contrast So so mainly I'm in this lecture. I'm going to be talking about a lot of it is to do with fluorescence imaging rather than Bright field and so we don't have to think about coherence Okay Yeah, so first of all I wanted to Introduce the fact that there are actually two fundamentally different ways of producing an image the first is what you do in an ordinary microscope and So here I've called it imaging using a detector array So nowadays, of course, we very often don't bother with an eyepiece. We just have some detector we we Record the image store in a computer and so on So this shows how an ordinary image is formed So here I've got some objects This is the image a magnified image It's inverted as I was saying earlier And we can record that image using some detector array But that's not the the only way you you can make an image The other way is to use a scanning system and interestingly, I think the This was really first done with electrons before it was done with light for some strange reason and Anyway, so it's this is how it's it's done how an image is formed in a scanning electron microscope but also in a scanning laser microscope and So what you do is you have some source It's effectively a point source So here I've got I've limited the size of this so that it's very small and we use a lens to produce a probe of lights and Then we scan that probe of lights over our objects and We pick up some signal here. I've just shown a detector picking up Signal and we see how that signal changes as we scan the lights and This gives us an image Here I show this this this intensity that the signal we measure is shown on a on a some sort of TV display Now it's quite interesting. This is actually probably this was this method was first thought about in optics this is actually the principle of John Logie Baird's first television system that he developed in 1920 something so 1920 a something It was based on this method This whole idea has recently been sort of reinvented and it's called being called the single pixel camera Which is a very fancy name. You have to call something if you want it published in physical review letters But actually all you're doing is talking about something that was really done in 1928 That's me being cynical But anyway, you've got this single-endiment detector That allows you to record an image by doing this scanning And It's quite interesting that there are these two different ways of producing an image there Yeah, I've got a couple of points here. The detector doesn't image it only collects light And the magnification of the image is just given by the size of the scan compared with the size of the display So that doesn't depend on the numerical aperture of the lens The resolution does but the magnification doesn't whereas in a Microscope an ordinary imaging system The two are linked usually a higher numerical aperture lens has got a higher magnification right, so doing this Scanning with this focus probe Allows you to do lots of interesting things And You can produce an image as I've just described But you can actually use this illumination spot to produce all sorts of different other effects So these are one one sort of Experiments we were doing very long time ago. This is back when I was in Oxford And this is looking at semiconductor This is a reflection mode. This is what we call the photo voltage mode Illuminating with the focus spot of light Produces induces a voltage you can measure the voltage you scan the sample you get an image of your sample Which is not an ordinary image now because it tells you something about the electrical properties of the sample This is another one. This is a transistor And you see these these black lines this is done in a Optical beam induced current mode is called obiq is sometimes called These black lines are defects in this in the in the crystal the silicon Stacking force actually You don't see these in an ordinary image But by by using this special way you can you can do that. So this is just you know there are many many different types of Different contrasts you can pick up According to different signals you can pick up in fact any sort of You know physical or chemical type Interaction could be used as the basis Producing an image spectroscopy of course is something that we very often use to do spectroscopic Images this was from a another paper. I had when I was in Oxford with my student Ingemar Cox who at that time there was a lot of interest in the Acoustic microscope where you use sound waves rather than light But it also in the photo acoustic microscope where you use a Modulated light beam to induce an acoustic wave This has also become very very popular nowadays actually But it first started back in the if this was 1984 I guess in around 1980 people were first doing experiments on this And but now you've got you know, you might have a few different stages in this process the light beam Produces acoustic waves Actually what it does you see is it heats up the sample you have a modulated light beam It periodically heats up the sample. So it produces thermal waves And then these thermal waves induce acoustic waves so it all becomes a very complicated process all together and It gives you some idea that you can Investigate the thermal properties the acoustic properties. Well, in this case the electronic properties and so on right net let's go back now to these two types of microscope an ordinary microscope and a scanning microscope Which one gives the better resolution? It turns out that under most circumstances they both give exactly the same resolution And that there was if you look in the literature, you'll see there was a lot of arguments about this This all might mainly it started When for the from the electron microscope field when the scanning transmission Electron microscope was invented and So people thought is this going to give a better resolution than a transmission electron microscope or not And eventually it was shown that they give exactly the same it's called the equivalence theorem equivalence of scanning and conventional microscope and it's based on the principle of reciprocity Which means that effectively you can reverse the rays in your in your ray diagram of the optical system and this this is going to hold It holds even if there's loss or multiple scattering But not any elastic scattering, so it won't work for fluorescence for example Because if you've got an ordinary system You you you actually image the fluorescent light Which as you know has got a longer wavelength than the incident light in a in a scanning system The resolution is determined by the wavelength of the illuminating light So there they're not going to be equivalent This is a series a whole list of papers where people have discussed these these things the first ones all for electron microscopes Right, so I said you can just reverse the rays, so let's shut out a bit more about that this is a Conventional microscope here again. I've shown this as critical illumination But basically you got these two lenses the condenser lens and the objective lens Here I'm showing Having some sort of detection system where you measure the image here I'm showing it by scanning a Very small detector around in this plane, but it might be a CCD detector producing the image This is a scanning system And I want you to compare these two ray diagrams. You see that they look very similar except the one is Inverted respect to the other here. You've got a large area source and a point detector Here you've got a point source and a large area detector If you change the direction of all these rays you get this go from this one to this one So the equivalent equivalence theorem, which is based on reciprocity Says that this microscope and this microscope will give exactly the same resolution As long as you of course this this this objective lens here the aperture of this has to be equal to the Aperture of this first lens here, which you might call the probe forming lens There's another diagram. I've got on this on this plot here and this slide and this shows a confocal microscope This is not the same as either of these It's got a point source and a point detector And it turns out that the imaging properties of this system are completely different from either of these These are the same as each other, but this is different from them and it turns out that Here you see is this second objective which is primarily Giving the numerical aperture of the system. It's responsible for determining the resolution To a secondary degree it does also depend on the condenser lens, but it's primarily the objective lens Here it's the first lens Here it's both lenses Because we focus a spot of light onto the sample And this detector is only collecting light which comes from a very small spot here It turns out the overall effect of this is that you have to multiply these two point spread functions together and you end up getting An improved resolution slightly improved resolution as a result of that so So this is a confocal microscope normally done in reflection mode Light from a laser focused on to the sample the light comes from the sample It might be reflected light or it might be fluorescent light Is is refocused onto a detector, but we put this small pinhole in front of the detector and Probably the most important property of the confocal microscope Is that the lights which is coming from other planes of the sample? Let's say the light from here is going to come to a focus here Light from here is going to come to a focus further away So only lights from this focal plane of the system comes to a focus where the pinhole is Right, so the light that comes from Other regions won't get through the pinhole Nearly so well So we we produce what we call optical sectioning if we've got a thick object We can look at the light that just comes from this plane So so this is the confocal microscope, of course at the moment We've just looked at one point as I've described it here. We have to build up an image by scanning And in practice we can usually we scan the beam using Galvo mirrors or something like that But you can scan the sample you can scan the lens you have to scan something anyway and It's done in reflectance or reflection microscopy or in fluorescence Mostly in fluorescence now because this has become very very useful in biological studies I've show here the the covers of two books that I've written about this method over many years. So this one 1984 Backs from Oxford days So so this one was written with Tony Wilson who was one of my students when I was in Oxford He's still there This is a later book also written while I was in Oxford actually but But published Eventually after I'd left and gone to Australia and this was written jointly with David Shotton Who is in the zoology department at Oxford? This one is a pretty theoretical book That describes the theory of the imaging in different types of microscope and so on this one is much more of a book for the user and describes different systems How you should use it and some examples of some images right optical sectioning This is a demonstration of optical sectioning and all we're looking at here is The surface of a of an integrated circuit So this reminds me of this question about the because this this is very typically to do with this actually You see this is two pictures here of this Integrated circuit This is with the pinhole This is with the pinhole removed Without the pinhole there we collect all the lights. There's no optical sectioning with the pinhole there We get optical sectioning. We only get a Signal from the part of the object which is in focus. So here here and here The object is either too close or too far So we just image this band like this it without the pinhole. This is what we get Now if you look very closely at this region, I don't think you can see this on this Display here, but you would find that this this region here and this region here are blurred because they're out of focus The region in the stripe across here would be a better focus. You can't really see that So this I think was the the first real demonstration of Optical sectioning in a confocal microscope shown in a paper in optics letters 1981 So, yeah, we could optical sectioning we sometimes call it depth discrimination. So these are almost analogous terms So confocal microscope the advantages Optical sectioning there's there's two main ways you can use that you can look at a thick object and You can look at sections through a thick object like tissue Or you can look at a surface and you can actually measure the height of the surface and Related to that is another effects Reduce scattered lights because this pinhole As well as getting rid of light that comes from the wrong part of the sample is also going to get rid of light that comes from Anywhere else. So if light reflects inside the system or from other parts of the sample This scattered light is going to be removed by the pinhole So that means that if you're looking say at some biological tissue, you can look deeper into the biological tissue And the third advantage improved resolution It's I mentioned this already. It's quite interesting. This is what was driving us to do this in the first place when we Built these systems back in the 1970s and 1980s But it turned out that optical sectioning was what was the important thing the resolution point of view really went away and Then eventually People came back to it again with the structured illumination microscope, which I should talk about later on But but now it's going full circle and we're coming back to thinking about resolution in confocals again And I'll say more about that tomorrow it will be right so reflection Methods fluorescence methods Reflection you can use for various industrial appellate applications looking at semiconductors manufactured items surface profiling More recently, it's also now being used for some biomedical type applications looking for skin cancer And so on But in the bio area nearly always it's done in a fluorescence mode And we either use also fluorescence from the sample itself or we label it with some fluorescent marker And and we can look at fixed samples or we can look look at living samples And now we've really got so you know why the confocal microscope has become so important You can look at living samples And whereas, you know electron microscope has got much higher resolution But you have to kill it chop it up slice it put it in a vacuum Coat it in metal do all sorts of nasty things to it. It's certainly not living by then Right, so in confocal microscope, you can look at living things. I might mention one other thing about this the Industrial applications. I was once told by someone from Zeiss Zeiss of course is one of the many the main manufacturers of confocal microscopes This guy from Zeiss told me they have sold more confocal microscopes For industrial applications than they have for biomedical applications. So it's huge Every company has got one to look at the surface of something that they've manufactured to you know fault finding So there's there's been tens of thousands of them sold so This is an example of surface profiling I've got two images here We call this one an autofocus image this one a surface profile image what we do is We we move the sample axially until we get the maximum signal We record the maximum signal and how far we've moved it How far we've moved it corresponds to the height of the sample, right so brights means closer to you Black means further away from you This one though is an autofocus image Every point on there is brought to the best focus So the depth of focus of this system Is much much more than you can get with an ordinary microscope? It's it's it's in principle unlimited except that eventually you bump into the lens right Here these heights you can't see very well because the dynamic range of the system But we can record these two images directly into the into the into a computer we can then process those images So this this is the surface profile So this is this is this is actually calculated from these two images Nowadays the way when we first did this it we would do it like that We would record these two images and then calculate that nowadays Computers are so big Now you would record a complete three-dimensional image Then you can you can get this from them or this from them or anything, right? But in the early days we couldn't do that because our computers weren't big enough But now you can see this surface This is a Bonding pad on the surface of the sample. This is silicon This is aluminium this that's why this is brighter than this because it reflects better And you can see the height of this sample and so on So that's an example of Autofocus and surface profile Right, I think I better stop at that point And tomorrow I'll I'll carry on with how can focus microscopes work from a theoretical point of view And then more recent developments In terms of super resolution or something. Oh, thank you very much Professor Shepard Okay, so we have now break lunch break with one hour and health so Please be here on time for the afternoon lecture Thank you. I ought to ask if there are any questions now But or we could we could save it or later We could continue in the discussion this afternoon in the lab