 Good morning, welcome in the second day of our winter college. I hope everybody is here. We will continue today with our presentations. In the morning, we will have two lectures. It's the first basic principles of photothermal techniques and their applications. We'll present Professor Ernesto Marín Moráez from Instituto Politecnico Nacional, Mexico. And then we will have, after coffee break, the second lecture of Professor Colin Shepard is co-focal microscopy and super resolution and phase contrast microscopy. Then we will have the lunch break at half past 12. And then we will have, starting with 2 o'clock, the experimental session for Hanson. And I will try to pay attention about the schedule. For the person, it's about group one, two, three. I advise you to take the lunch in Adriatico. Guess how's because these groups will have an experimental session there. It's about, in computer lab, it's about low-cost microscope, automation, hardware, embedded software development. And there are also another groups there, they. As it is written on the program, you have to be there with 10 minutes before two. Be careful. Then you will have to come for a poster session. Everybody will have to put their posters at the lunchtime or after lunchtime because we will start the evaluation of all posters. So the groups one, two, three will come by walk from Adriatico because there is no shuttle after. Yes. OK, sorry, four, five, six. Yes, that groups, I made a mistake. One, two, three will be in my ML lab. So you will come by walk to be here for poster session. So two o'clock, experimental session in Adriatico. And then starting with four is the poster session. And four groups, one, two, three, there are experiments up in the ML. It's about a diffraction with Humberto. It's a continuation. Then it's about a partner with experimental session digital lock in photothermal shadow graph metal and laser induced breakdown spectroscopy. So for all information about experimental session, you have to contact Humberto, the guys who didn't attend these sessions are required to address to Humberto to be able to do these activities. But it's the last chance to have these activities. And now with your permission, I will invite Professor Ernesto Marin to make his presentation. Please. Thank you for the presentation. Thank you, the organizing committee, for inviting me. And thank you for your presence. I will talk to you about a group of experimental methods that are based in the common principle of periodic area heating example with light and measurement of the induced temperature changes and on the use of this measurement for material characterization. Let me introduce me before going into matter. I am from Mexico. Mexico is not only a country of great ancestral culture, tequila, mariachis, and so on. There are also several high education universities. And I am from one of them from the National Polytechnical Institute. This is the greatest technological university in Mexico. And in particular, I am in a research center in which there are three graduate programs. Two of them are for physics and mathematics education. They are virtual distance programs for use to the preparation of teachers. And there is a multi-program in advanced technology. This is a multidisciplinary program with different research lines, for example, nanotechnology, biomaterials, instrumentation. And there is a photothermal techniques laboratory in which I do my work. The graduated program is evaluated by the Mexican Council of Science and Technology as a program of international competence and as a consequence, the students of this program can have access to scholarships from different institutions of Mexico. I will divide my presentation in four main points. In the first one, sorry, I will tell you about the photagoustic technique. This was the first developed photothermal method. Then I will tell you about the physics behind these techniques. Then I will describe some different photothermal techniques. And at the end, I will tell you about some applications in the fields of spectroscopy, measurement of thermal properties, depth profiling, microscopy, et cetera. The photagoustic effect was discovered by Alexander Graham Bell while working in the photo phone. The photo phone was a device which was Bell tried to transmit information at large distances using sunlight. The experimental setup consists basically in a minor couplet to a loudspeaker so that the reflected light can be modulated by voice and the telephone receiver. With these instruments, Bell was capable to transmit information to distances about 200 meters approximately. Changing the telephone receiver circuit by a hearing tube with an enclosed sample, Bell discovered that when light is shining onto the sample, a song is produced. And he described this effect in this publication. In other experiments, Bell discovered that the photagoustic effect can be attributed to the absorption of light by a sample. He did the following experiment. He modulated the intensity of a light beam using a chopper and directed the light onto a sample enclosed in a recipient connected to a hearing tube. And he had a song when light is focused onto the sample. Using the so-called spectrophone, Bell discovered that the song intensity is changed when the wavelength of the light also changes so that the effect is attributed to the optical absorption of light by material. This is a color selective process. Each material absorbs, as you know, electromagnetic radiation in different forms. You can do a similar experiment in your home using an stethoscope. All what you need is a light bulb driven by alternating current, for example, the line current, and a stethoscope. If you put the stethoscope head close to the light source, you will hear a song like, and if you chop the light, this song will be modulated at the chopping frequency. There are several similar experiments that you can perform with very simple apparatus. Some of them are described in these articles that are published in teaching journals, such as American Journal of Physics, et cetera. What is the cause of this effect? When intensity modulated light is absorbed by the diaphragm that closes the stethoscope head, this diaphragm is heated periodically, and the heat is transmitted to a thin layer of the air enclosed in the stethoscope head. This thin layer of fire will expand and contract following the light modulation frequency and act as a piston on the rest of the enclosed air so that an acoustic wave is produced. There are four main mechanisms involved in the generation of the photoacoustic signal. The first one is the absorption of light energy. And this process depends on the optical properties of the sample. Then there is a process of energy conversion. The absorbed light energy is converted into heat. And this process depends on several properties depending on the kind of material, but we can define a conversion efficiency for this process. This is the ratio of the produced heat and the absorbed light energy. Then we have a head diffusion process that depends on thermal properties of the sample. We will see later which thermal properties are these. And there are also some wave producers that depends on the elastic properties of the sample. And this is the motivation for using this effect for material characterization. You can design an experiment to measure some of these properties or physical processes in which these properties are involved. I will do a rough estimation of orders of magnitude. Suppose that the power of the light pulse is 0.1 milliwatt. And the duration of the pulse is five milliseconds. So you can calculate the energy absorbed by the sample. And using the laws of thermodynamics, you can calculate the temperature increase that is produced by the absorption of this energy during this time. And you obtain a value in the order of many Kelvin. With this value of the temperature increase and considering the gas as an ideal gas, you can also calculate the generated pressure increase. And you become approximately the end to the minus 2 Pascal. So that we can say that we are within the range of the audio and music in a graph of pressure between a virtual frequency. We are situated here for these values. These small values are the motivation on how to detect or the motivation for developing methods for the detection or for the measurement of these small quantities. We'll see later. Several scientists of the 19th century were interested in the photagoustic effect. But due to the absence of light sources like the lasers or electronic methods to detect these pressure variations substituting the air, the effect remains forgetting. There were two attempts, Ronjan discovered that the photagoustic effect can be also produced in gaseous. And this is the fundamental for applications in spectroscopy, in gas materials that were developed by Viennese Luf in the 20th century. The 1970s can be considered the years of the rediscovery of the photagoustic effect, mainly due to the work of Alan Rosenway in the Bell Laboratories in the USA that reported the first theoretical model describing the effect and which reported the first application of the effect mainly related to spectroscopy in solid materials or in condensed matter samples, solids and liquids. Since then, there is a grow in the applications of the photagoustic effect in different fields of research. This is a graph from 2012 showing the increasing number of papers produced in different kinds of applications. This is only about the photagoustic technique. If we add here the applications of the other photothermal techniques, these values will be sure to increase. This is a scheme of a typical experimental set-up for applying the photagoustic effect. You have a source of light, for example, a lamp, a white light lamp. A monochromator, if you want to do a wavelength-resolving experiment, a chopper or another kind of light modulator. The modulated light is focused on the sample that is implausible in a photagoustic cell. The photagoustic cell is similar to the head of the stethoscope that I showed before. A photagoustic signal is generated and it is measured using a microphone also enclosed in the sample. And the signal provided by the microscope is measured using equipment that can help to measure the small values of the pressure and temperature that are produced inside the cell. These kind of instruments are known as phase-sensitive detection systems or simplest locking amplifier, Li-A. This is a herd of photagoustic experiments. These kind of instruments measure only the signal that is produced at the light modulation frequency and filter all the noise that is to beared with this signal. They are very expensive, not very, but expensive locking amplifiers. But you can also construct a very inexpensive one using, for example, developed arrays such as FPGA or data acquisition cards, et cetera. You can do the measurement in the photagoustic experiment as a function of the light energy or light wavelength for spectroscopic applications. You can also do measurements at a fixed wavelength and varying the light modulation frequency when you want to determine transport properties. For example, thermal properties of materials. But you can also do time-resolving experiments to monitor the time evolution of different processes, for example, photocatalytic process as shown here. I will describe now briefly the principles of this technique. It differs a process involved in the generation of the photagoustic signal with the optical absorption. Optical absorption, under certain conditions, is described by the Lambert Birlau. The intensity of the transmitted light at a given distance from the sample surface is given by the product of the intensity at the surface of the sample. And the exponential of minus the product of the absorption coefficient beta and the distance at which this intensity is measured. The optical absorption coefficient is proportional to the concentration of the absorbing species in a given sample. This allows, for example, application in which the concentration of a solution must be determined. Then we have a process of light energy into heat conversion. The amount of heat generated per volume in the light of the sample in an element of thickness dx at a given depth is given by the following question here. Eta is the quantum efficient for heating. So the quotient between producer heat and incident energy. R is the optical reflection coefficient. E is the light intensity. This is the derivative of the light intensity. And x is the coordinate. Then we have a process of heat conduction through the sample and its surroundings. There are three modes of heat transfer. Wherever temperature difference exists, there is a heat transfer from the hot to the cold region. And there are three modes of heat conduction. One is the convention. In its simplest form, natural convection, this process can be described by the Newton law of cooling. That states that the heat flux density, also the energy per unit time and surface area unite is equal to the product of the heat transfer coefficient and the temperature difference between the two regions through which heat transfer takes place. In the case of radiation, the heat flux density is described by the Stefan-Borsman law of radiation. In this law, sigma is the Stefan-Borsman constant. E is the spectral emissivity of the material surface. The series is the ambient temperature, for example, and this is the temperature of the other medium. If the temperature difference is very small, when compared with the ambient temperature, you can do a Taylor development of this equation around ambient temperature. And you linearize the Stefan-Borsman law. And you can introduce a radiation heat transfer coefficient given by this equation. The third mechanism is heat conduction that is described by the Fourier law. The heat flux density by conduction is the product with a mere sign of the thermal conductivity of the sample and the temperature gradient. In the case of one-dimensional heat conduction and for homogeneous and isotropic samples, you can approximate the gradient by the quotient of the temperature difference and, for example, the length of the sample. And in this way, you can also introduce a heat transfer coefficient for conduction as the quotient of the thermal conductivity and the thickness of the sample. If you use the Fourier law to calculate the heat flux across a sample of thermal conductivity, k, thickness l, and cross-sectional area, a, you can define the thermal resistance of the material as the quotient of the length of the sample, the thermal conductivity and the thermal conductivity and area product. This is often known as the Ohm's law for thermal conduction because it's very similar to the Ohm's law of the electricity. The inverse of the thermal resistance multiplied by the surface area, excuse me, you can define a heat transfer coefficient for the processes of convection and radiation. And here is an error, here must be radiation, yes? And the quotient between the heat transfer coefficient for radiation and convection and the heat transfer coefficient for conduction is known as the Biot's number. And it describes the fraction of material thermal resistance that the post-conventional radiation hit the losses. If you combine the Fourier's law of conduction with the energy conservation law, we can obtain the heat diffusion equation. In its homogeneous form, the heat diffusion equation is this one. Here is the Laplacian of the temperature field. Alpha is the thermal diffusivity of the material. This is the quotient between the thermal conductivity and the product of the density and the specific heat. And this product is defined as the specific heat capacity of the sample. And this is the line derivative of the temperature. If you plot the thermal conductivity as a function of the thermal diffusivity for different materials, you observe that, for example, for condensate matter samples, all values are grouped around a stretch line whose slope is approximately the specific heat capacity of these materials. In other words, for condensate, so the same occurs for gases. And this means that the specific heat capacity is almost a constant parameter for matter. And its value is approximately 3 times 10 to the 6 joule cubic meter Kelvin to the minus 1. This is the consequence of the Doulomb and Petit rule for the molar heat capacity of solids that states that this quantity is nearly a constant parameter for temperatures near ambient temperature and below the device temperature of solids. OK, now, suppose that we have an isotropic and homogeneous same-infinite solid. Same-infinite means that you can neglect what happens at the back surface of the sample. And suppose that this solid is heated with light that is absorbed only at the surface of the solid. And that the heating is uniform so that you can try the problem as a one-dimensional problem. I call this a beautiful sample with all good properties that can have a sample to ask as a model. If you want to calculate the temperature distribution across the sample, you must solve the heat diffusion equation given before with the properly boundary condition. The boundary condition states that the heat flux produced at the sample surface will be proportional to the optical energy absorbed by the sample. If you suppose that the temperature field can follow the time dependence of the heating, you can do a variable separation in this equation and you transform this partial derivative equation in an ordinary differential equation of second order with constant coefficient, a very simple equation. And the boundary equation becomes this for the spatial part of the temperature field. Here is also an error, sorry. This T must be related here. This is only the spatial part of the temperature field. The solution of this equation is this one. And here is the light intensity epsilon is another thermal parameter. This is the thermal effusivity. The thermal effusivity is the square root of the product of specific heat and thermal conductivity. Q is given by the quotient of 1 plus E, is the complex unit. And the so-called thermal diffusion length that is given by the square root of 2 times the thermal diffusivity divided by the angular modulation frequency. This equation has the same form as an attenuated wave, so that it is known as a thermal wave equation. And as you see, there are two thermal properties involved in this equation, the thermal effusivity and the thermal diffusivity. So that measurement of this temperature field can allow us to determine the thermal properties of the material. In the thermal wave equation, we can define an amplitude given by this term and a phase given by the sum of these two terms. If you plot this amplitude as a function of distance, you have an exponential function. And the thermal diffusion length can be defined as the distance from the sample surface at which the amplitude of the temperature wave is reduced E times. In other words, the distance at which the thermal wave amplitude is reduced in 60% approximately. The thermal wave length is defined as the product of the thermal diffusion length and 2P. So that in one thermal wave length, the thermal wave is almost completely attenuated. They are very attenuated waves. And this is very important for several applications. In this process, you have an alternating heating. In electricity, for direct current, you define an electrical resistance. But when you use alternating current, you define a thermal impedance. In heat transport, it works the same. For a stationary heating, you define a thermal resistance that was defined before. And for alternating heating, as in this case, you can define a thermal impedance of the sample. And the thermal impedance depends on the thermal effusivity of the sample and on the light modulation frequency. You can also define a velocity of the wave. And the velocity of the wave depends also on thermal effusivity and the light modulation frequency so that you can change the velocity by changing the light modulation frequency. At the interface between two regions with different thermal properties, you can define a reflection and transmission coefficient for the thermal waves. And you can demonstrate that for normal incidence of the thermal wave, these coefficients depend on the ratio of the thermal effusivities of the form materials. So that the thermal effusivity is a parameter that describes phenomena that takes place at the sample surface or at interface between two regions. There are several experimental phenomena whose interpretation is given in terms of thermal effusivity. For example, if you touch a metallic object and an object made of wood during a very short time interval, you will feel that the metallic object is colder than the other object. But both objects are at the same ambient temperature. And this phenomena is explained by the thermal effusivity, as well as you calculate the time during which you can touch a very hot object using also physics that is related to a thermal effusivity concept. Talking about orders of magnitude, for a typical solid material, you can calculate the wavelength of a thermal wave. And you become approximately a dozen micrometers. Some micrometers you can obtain for a typical solid material and at the modulation frequency of 10 kilohertz. The wave velocity at this frequency becomes approximately some meters per second. For a comparison, the wave length of acoustic waves at the same frequency is about 1 centimeter. To obtain acoustic waves with this very short wavelength, you must have frequencies larger than some megahertz. And this technically is a very difficult task. We will see later why we can use this fact to do a kind of microscopy using thermal waves. The thermal wave concept is not new. Fourier, in his classical and very known work, the Analytical Theory of Heat, described the thermal wave for the first time. And he and Poisson proposed that you can use the thermal waves to characterize the thermal properties of the air crust of soils, for example. I don't, this kind of experiments and this kind of experiments is often done for the thermal properties characterization of soils. If you measure the temperature at different depths inside the soil using a thermometer, during one day you obtain an almost sinusoidal behavior that can be fitted with the thermal wave equation to obtain the thermal diffusivity of soils in a straightforward way. Fourier published his work in 1822, but the theory was first developed approximately 20 years before Fourier sent his work to publication to the French Academy of Science. But the reference of his article was among others, Leandre and Laplace. Fourier was a guy very involved in politics and his work was rejected one more time by the reference and finally Fourier decided to publish his work himself. He printed his work and he published the work. I do always this comment to my students, don't worry if your work is rejected for publication, you have always the possibility to publish it yourself or to send the work to journal such as some open access journal that can publish your work. But remember that the Fourier's book is still one of the masterpieces of the scientific leader. At the same time, Fourier's work, Anstru, developed a method for the measuring of the thermal diffusivity of a solid in the form of a bar. And the experiment is very similar to the experiment described before. You have a solid in the form of a bar, you have a periodical heating element in one string of the bar, and you can measure the temperature at different distance. And you also obtain a temperature oscillation whose amplitude and phase change with the distance. So that we assist today to a rediscover of 19th century physics by modern science as also in modern fields of research. Before, I talked about a beautiful sample with superficial light absorption in the case that the light energy is absorbed through the bulk of the sample. The temperature field will also depend on the optical properties of the sample. For example, the optical absorption coefficient. Because the optical absorption coefficient depends on the colors of the light, you can do a kind of optical spectroscopy by detecting this thermal. We have seen that thermal waves can be detected using a microphone or directly using a thermometer. But beside this wave of detection, we have another wave to detect thermal waves. When you hit a material, the temperature changes. But also all material parameters and all materials of the medium surrounding the sample depend on temperature so that you can use the detection of these changes in these parameters to indirectly measure the temperature. For example, you can modulate with heating the refractive index of the sample and detect the changes in the refractive index to measure temperature. This will be the theme of another presentation tomorrow and next week. You can also measure the infrared radiation that is emitted by the heated sample using, for example, thermographic cameras or other kinds of infrared detectors and so on. This is one example of a photothermal technique. When you hit the surface of a sample, the air in contact with the sample will be also heated. And the temperature becomes different at different distances from the surface. The refractive index also changes so that if you chime onto the sample another light beam, the intensity of this light beam will be changed due to the changes in the refractive index. This is the basic of one technique known as a mirage effect or beam deflection. This is an illustration of the technique. This is the sample. This is the heating light beam. This is an illustration of the changes of the refractive index. And with another light beam known as the probe beam, you can monitor these temperature changes. This is an experiment in which the probe beam is divided in several beams. And this is, I will show you tomorrow this video. This is an image of these light beams projected onto a screen. And they are deflected by the heating in the central ratio of the sample. I will tell you now about some application of the photothermal techniques. The first application that I want to describe is a photoacoustic spectroscopy and the possibility to do depth profiling in this kind of applications. Here is the phot acoustic spectrum of a sample of neodymium oxide, showing some characteristic peaks. And this is the phot acoustic spectrum of holmium oxide, showing also the characteristic absorption bands. Suppose that you have a two layer sample composed on the top by a neodymium oxide and at the bottom by holmium oxide, OK? You will do phot acoustic spectroscopy in the following way. You hit the sample from the top at a certain frequency and you measure the phot acoustic signal. When the light modulation frequency issues that the thermal diffusion length becomes inside the top ratio of the sample, you will obtain a phot acoustic spectrum similar to that obtained in a single sample of the same material. Then you can repeat the experiment at a lower frequency so that the thermal diffusion length becomes higher so that the thermal wave propagates also into the lower layer of the sample. And as a result, you will obtain that some peaks will appear in the spectrum that are characteristics from the bottom layer, from the holmium oxide sample. And if you made the light modulation frequency more lower, the thermal wave will diffuse more and more into the whole sample. And you obtain a spectrum that is the combination of both the holmium oxide and the holmium oxide contribution. There is a method using the phase of the phot acoustic signal that is known as phase-resolving analysis which you can resolve the spectrum of the two components from the obtained phot acoustic spectrum without the necessity of changing the modulation frequency and of repeating the experiment at different frequencies to obtain this result. So I have shown that you can do photothermal spectroscopy and you can resolve things that are below the surface of the sampling in a straightforward way. You will hear about more spectroscopic application of photothermal techniques in the lectures of Professor Marcano and Professor Franco during the next days of this school. Thermal characterization, how can we do thermal characterization using thermal wave? This is, again, the thermal wave equation. The thermal wave equation, and suppose that the temperature field is measured at a given distance, L, from the sample surface. This is the amplitude of the thermal wave and this is the phase of the thermal wave. You can see that if we plot the logarithm of the product of the amplitude at the square root of the modulation frequency as a function of the square root of the frequency or if you plot the phase as a function of the square root of the frequency, you become a straight line whose slope depends on the thermal diffusivity of the material. This is known as the slope method. You can measure the amplitude and the phase. You can do these plots. You can do these plots and from the slope you can determine the thermal diffusivity if the distance is well known. But you don't always measure directly the temperature. Sometimes you measure the temperature indirectly and you introduce a proportionality factor between the measured quantity and the temperature field and this parameter that is known as the instrumental factor of the experiment can be frequency-dependent so that to use this method, you need some normalization procedures or some experimental artifacts to remind the thermal diffusivity. But looking at this equation, you can see that the same dependence that exists for the modulation frequency is given for the length. So that if you plot the logarithm of the amplitude as a function of the length of the phase as a function of the length, you also will obtain a straight line with slopes that depend on the thermal diffusivity. And if the modulation frequency is well known, you can determine the thermal diffusivity of the material. This is the principle behind the main methods developed for thermal diffusivity measurement of materials. For example, the Fourier-based method that I showed before used the slope method. Here are the temperature oscillations as a function of time taking at different depths below the surface of the air. And you see how the amplitude of the thermal wave is reduced with increasing depth. And you can also see a phase lag between the different waves. So the minimum is at different time positions for each wave. For each distance, you can measure the amplitude of the wave, the peak-to-peak value. And you can plot this peak-to-peak value as a function of depth. And you become a straight line. Well, here is only four points, but it's not easy to do these measurements inside the soil. But you obtain a straight line. And from the slope of this line, you can obtain the value of the thermal diffusivity of the sample. This is another experiment proposed for thermal characterization, in this case, of liquid samples. In these experiments, you have, for example, a metallic foil that is heated with electromagnetic, with periodical electromagnetic radiation so that thermal waves are generated. And this metallic foil acts as a source of thermal waves. And these thermal waves can propagate and can be measured using a pyroelectric sensor, a sensor that gives an electric voltage when the temperature changes. Because you have here a cavity. The method is known as a thermal wave resonator cavity or thermal wave interferometer by other authors. If you measure the real part and the imaginary part of the temperature field measured by the photo pyroelectric detector, you obtain a behavior with maximum and minima that is characteristic of wave interference phenomena. Now, suppose that we put a liquid sample in this recipe, a volatile sample, so that the vapor from this sample diffuses into the thermal wave resonator cavity that is filled by air. You can measure the amplitude of the photo thermal signal as a function of time. And you see that at certain times, after certain times, you will obtain a constant behavior. That means that the thermal wave resonator cavity is saturated by the liquid sample vapor. And at this moment, you can change the distance between the aluminum absorber and the photo pyroelectric sensor, and you can monitor the pyroelectric signal as a function of length. And then you can use the slope method to measure the thermal diffusivity. This is the result of one experiment made with hydrocarbons samples. As a result, the characteristic time of this graph shows a linear relationship with the number of carbon atoms in the linear chain of the hydrocarbon molecule. In another application, this behavior was used to propose a method for the measurement of octane. For example, here, the thermal diffusivity was measured for different mysteries of octane and exane. And the thermal diffusivity is plotted as a function of the motor octane number. And you obtain a relationship between both magnitudes so that you can use the thermal diffusivity of these mysteries to define an octane scale for characterizing, for example, gasoline. And this is a result in which samples of gasoline were adultered with different products. And if you measure the characteristic time shown before, this characteristic time, as a function of the thermal diffusivity of these samples, you obtain a conformity grid. And the values corresponding to the non-adulterated gasoline are inside this rectangular grid. All other values correspond to adulterated samples. Alternation of gasoline is a grid problem in several countries of the world. This is a world that was developed in Brazil some years before. You can also use the slope method to characterize the thermal properties of non-conventional samples, for example, very thin filaments, for example, spider silk. In this work, a group from Bilbao in Spain do the following experiment. Here is the sample. This is a spider silk filament that is located inside a cavity in which bacon is performed to eliminate convection that can affect the measurement procedure. You hit the sample with a laser and with an infrared camera, you can measure the temperature distribution as a function of the distance from the heating point along the sample. And plotting the phase of the signal as a function of distance and the logarithm of the signal as a function of distance, you can obtain the thermal diffusivity in the way described before if the light modulation frequency is no. You can also use all optical methods to do measurement of thermal properties of materials. For example, the thermal length technique is not only useful for spectroscopy, but also for thermal characterization of materials. Here, we have implemented the technique using an optical microscope. In blue is the heating laser beam that is named the boom beam that is focused using the microscope objective into a very small ratio of the sample. And here is another laser whose way front is disturbed by the produced changes in the refractive index of the sample. And these intensity changes can be measured with an optical photo detector. Using this method, you are able to do measurements of the thermal properties of very thin material, for example, two-dimensional materials like graphene. If you look at these graphs of the thermal length signal as a function of time, you can see that the amplitude of the signal changes with the number of graphene layers in the sample so that you can use the thermal length method or similar methods to do maps of graphene samples where you have different small ratios with different numbers of graphene layers. These are some examples of this kind of photothermal maps. They were taken using a modulated thermoreffectance setup. This is you have a heating laser and you have another laser that measures the changes in optical reflectivity of the sample that are produced by the temperature changes. And here are images taken at different modulation frequencies in which we can see different ratios with one, two, three, and seven graphene layers distributed across the sample. This is a typical optical reflectance setup. Here you also have a PUM laser beam in blue and this is the probe beam. This is a continuous laser that impinges on the sample and is reflected and you can measure the intensity changes using a photo detector. This setup can be combined with a photacoustic setup to do a combined measurement using reflectance and using photacoustic detection in the same experimental setup. The sample here in this experiment is an integrated circuit that is glued onto a piezoelectric sensor and located in a photothermal reflectance microscope. With the heating beam, you scan the sample surface and for each point, you can measure both the photoreffectance signal and the photacoustic signal. Here the heating is not produced by light. It is produced by electrical current that passes through the microscope. Here these are electrical tracks. Here different electrical contacts. This contact is connected to ground and the other to a constant voltage value so that when you do the photothermal measurement, you obtain these images. For example, this is a photoreffectance image and this is the photacoustic image. You can see the direction of the track where heat is dissipated. For example, here in red. But in the photacoustic image, we also see this track here. This is this track in the sample that is not connected to any electrical circuit. And the cause of this track appears in the photacoustic image was demonstrated using some mathematical modulations that show that there is a drift current across this electrode and this can be shown by the photacoustic image but not by the optical image of the sample. Here is also a photacoustic microscope. This is the sensor. This is the PCT piezoelectric transducer taken from a commercial booster. The sample is glued onto the sensor and you scan the surface of the sample using a laser, a modulated laser beam. And for example, this is an image taken. This is an optical image of a lottery ticket. This is from scratch and wing. Lottery ticket, of course, after scratching the surface. But before that, we have taken the photacoustic image. This is the amplitude image and this is the phase image. And you can see the X in both images so that photacoustic experiments can be used to reveal superficial things of a given sample like this. This is another image taken in a system composed of a cadmium telluride grown on cadmium sulfide and glass as a substrate. This is an optical image and this is the photacoustic image. Here in this sample, the cadmium sulfide layer is some hundreds of nanometers thick and the cadmium telluride is some micrometers thick so that I can show here that photacoustic technique can resolve a structure that are only some nanometer thick. This is the same image but in another field. You can see the glass, the cadmium sulfide and the cadmium telluride layer in the image. Tomorrow I will talk to you with more detail about the photothermal characterization of samples and in particular about the new development technique that is known as the shadow graph technique. You will also learn about this technique in the afternoon in one of the experimental sessions. These are some institutions that support our work. Thank you.