Optical Turbulence Effects on Laser Beam Propagation

[00:00:00]Thank you, Laura. Thank you for the nice introduction. It's a pleasure for me to be here today to introduce my course, actually. The title, as you can see here, is a little bit different. The title of my course is Optical Turbulence and Laser Beam Propagation. Of course, I cannot cover all these topics today, so I prefer to put a different title, a little bit more specific, because here the goal is give you a basic understanding of optical turbulence and focus on some main effort that optical turbulence induce on a laser beam.

[00:00:38]Okay, so Anyway, I put here the outline and not of this presentation, but of my course. In red that you see the topic that today I, let's say, partially cover. And unfortunately, I don't have time to talk about what you see here in black. So today I'm going to talk about optical turbines, how we model optical turbines using a strutter function power spectrum. I'm going to show you what kind of regime we can propagation to the to the atmosphere can phase?

[00:01:15]We separate this regime as a weak, moderate, and strong. I'm going to show you a little bit of what I mean with propagation to atmospheric turbulence, not time of oceanic today, but also oceanic turbulence is issomething that you can model, let's say, using this kind of approach. Okay, all these things, of course, you can, if you're interested, you have to go, you can see the details in my course. You can learn from there.

[00:01:49]I'm going to talk about effort caused by turbulent laser beams and images, such as beam spread, beam wander.

[00:01:57]Then I'm going to give you an idea how we measure optical system performance and what is the impact of turbulence on this performance. Of course, they are deleterious, turbulence is deleterious.

[00:02:14]And finally, I just one slide what I mean with non-Kolmogorov turbulence. Okay, but let's focus on on the main question. So why do we need to deal with optical turbulence? I mean, optical turbulence is very complicated, right?You will see required a lot of help for the mathematics, physics. So why we have to stress ourselves on that? The answer is simple. The answer is that optical turbulence, in particular atmospheric turbulence, is affected any kind of light or laser beam that go through the atmosphere itself. So we have many applications of this kind. We have, for example, free space laser communication.

[00:03:02]We have a satellite laser communication in the case of uplink and downlink, where the beam anyway have to go to the atmosphere. We have a direct energy, so energy laser weapons, where the laser beam is propagated through the atmosphere. We have astronomical observation. This is the actually where, you know, concept like scintillation, other stuff come from, right? When we were looking at the star, we have the problem that the star twinkle because of our blur, because we have the atmosphere, we have atmospheric turbulence.

[00:03:33]Application like laser radar, remote sensing, imaging. So as you can see, this is a topic of big interest in the field because it can go through many applications, okay, involve many applications. But What is atmospheric turbulence? Atmospheric optical turbulence in general? Optical turbulence is simple. I mean, it's a fluctuation of the index of refraction. And why we have a fluctuation of the index of refraction?

[00:04:01]We have a fluctuation because we have a fluctuation of temperature. So in the air, in the atmosphere, but also in the ocean, or also in the human tissue, for example, we have a fluctuation of temperature that induce A fluctuation of industrial refraction. And then we havewe have optical turbulence in the specific of the atmosphere, we call it atmospheric turbulence. So as you can see here, for example, N0 is roughly one in the atmosphere, is the refractive index, the mean value, and then we have a fluid plate in part. This fluid plate in part is random, so we need all the random process theory, random field theory, in order to model this stuff, the atmospheric turbulence.

[00:04:49]So, you see that this N1 is a random deviation from its mean value, a small fluctuation, but they are random, so we cannot use an approach that is deterministic. And also, we usually we the time variation that are often suppressed in the term of optical wave propagation. Okay, so now why, as I was telling you, turbulence is complicated. It's complicated because it has a random nature, Okay, is basically random in space and time.

[00:05:21]And then we need to use a statistic approach, the theory of random process, random field, in order to model it.

[00:05:30]We need to use also all the parameters that are going to describe basically turbulence are random, so are a random variable, random process.

[00:05:41]This makes things more complicated, of course, required also some strong approximation, and make also tool bullet field a quite interesting topic because it's very challenging. So I hope that some of you is going to be interested and is working actually on this field because still there are many, many other challenges that need to be faced and solved. So as I will say, we need to focus around the refractive index. And we modeled the random refractive index with actually a subter function, which is a subter function power spectrum.

[00:06:22]So, as you can see, basically, to summarize, random process optics and wave propagation, because then there is also the fact that the laser beam go through turbulence, so there is also the propagation aspect. is a mix of scientific field that have to converge in order to treat these things.

[00:06:45]Okay, so, but what is Kolmogorov turbulence? Kolmogorov, why Kolmogorov turbulence? It's said that Kolmogorov was the first to introduce to introduce a power spectrum that is still you said that today, after more than 85 years, the Kolmogorov theory basically still apply. Most of the time it works. And Kolmogorov was so smart that was able to understand, let's say, in the inertia range, you will see what is inertia range, the power law of the refractive index fluctuation is mean 11 over 3. This is a magic number there, a magic slope that most of the time works in the inertia range. And I have to say it's quite, was really, really smart to find this.

[00:07:41]So we will see also that the Kolmogorov sometimes fail. Unfortunately, this brings some to the tension. We are also, that's why we are also interested in what we call a non-Kolmogorov two points because sometimes we will see in the last slide, Kolmogorov doesn't work. But anyway, let's see now.

[00:08:05]I move. I don't understand why it's not moving.

[00:08:11]Yes, okay. Let's see now the energy cascade Richard's theory. What is it?

[00:08:16]Basically, the Kolmogorov theory is based on Richardson theory. What is it? Imagine now that we have the ground, okay, ground, and then you have some energy injection. like coming from the sun, wind shear, convection, all these kind of energy that are going to build up the biggest cell of turbulence. We can visualize turbulence like many vortex in hair, many optical vortex. And the biggest one inertial range is called the outer scale. Then there is an energy transfer, energy transfer, energy transfer, until you reach inner scale, in inertial range of this energy is inertial, is transferred inertially, right? Then you reach the smaller scale, which is called the inner scale, and beyond that, you have only it.

[00:09:12]Okay, so we start to visualize now these cells as a turbines, but we have to model these cells. We have to deal with that. How we do? Well, let's associate to each of them, a spatial wave number, spatial frequency basically.

[00:09:31]You see, if we have the cells of different size, L1, L2, L3, we can define a kappa 1, kappa 2, kappa 3, like 2 pi over L1 and so on. So basically, we can represent in a Fourier space, you will see in a power spectral space,all these sides, okay? So, and what we do at the beginning? Well, first we have to start from a subtle function. What is a subtle function?

[00:10:00]Imagine that you have a specific volume and you look at two point and you look at as the fluctuation of index or refraction are correlated in this two point.

[00:10:13]Then you basically you are you see that you are calculating the structure function and then you can do the Fourier transform in order to get to the power spectrum. But to be more specific, the structure function here is basically a square of the difference in two different points. You have a job in many, many realization. The higher is the number, the better it is, usually 100, 500, 1000. And then you can, when you construct your starter function, because you do it for several distance R, you are you and you are able to calculate the power spectrum. In the case of Kolmogorov turbulence, if you assume isotropy, homogeneity, that's a strong assumption of Kolmogorov, the starter function is this, where CSC square R2 over three. This is a typical three-dimensional starter function for Kolmogorov. CN squared is the structure constant, okay, which represent the strength of the turbulence.

[00:11:15]You see that in case of, as I say, homogeneity, you can, you're a Fourier transform basically, well, a little bit more than Fourier transform, but anyway, basically it's a Fourier transform. you can look like this and you can obtain the Kolmogorov power spectrum, which is this typical and well-known power spectrum, 0.033 CN squared kappa minus 11 over 3. 11 over 3 is the magic power law that Kolmogorov was able to understand using a dimensional analysis. Okay, and you see that is the range that that we are going to focus on in our calculation. So, from the outer scale to inner scale, you have this different scale of two different size turbine cells, and and outside of this range, of course, you have a different range which is called, for example, energy distribution range for a scale smaller than the inner scale. But let's start now to look at at the propagation aspect here.

[00:12:22]Most of you probably know this kind of formula. This is something that I actually downloaded on Wikipedia is a standard formula that describe our Gaussian beam that is collimated, the transmitter evolve as it propagates. So you see, as you know, if it's collimated, the transmitter is going to diverge with an angle theta and a total angle spread.

[00:12:46]given by this data here, and then, okay, we can define also the LED stance, blah, blah, blah. But what is the point here? I think this is a specific case when your beam is collimated at the transmitter, but we want to be more general. We want to end up in case where also I can have a divergent beam, focused beam, and also collimated beam as this one. So what we do, we can introduce a random I'm sorry, we can introduce that wavefront radius of the wavefront F0. You see that we can have three different cases. The case is the case where F0 is lower than 0, then we have a divergent beam. The case where F0 is higher than 0, and then we have a convergent beam. And the case where F0 is infinite, and then of course we end up in the previous case, which is a collimated beam. Okay, so we model this.

[00:13:37]I tried to put out all the formula.

[00:13:39]People that know me know that I put a lot of formula in my paper stuff. I don't want to stress you out on this. Here I would like just to catch the concept, the main concept. But here I need just two, three slides where I have to put some formula, but not so hard, I promise. So this is a basic actually equation that describes the complex amplitude of a Gaussian beam. you know that we define the spot radius as basically W0, then we have the phase radius of curve zero, we have a K which is 2 pi over lambda, which is the well number, so the carrier basically radiation. And you see that these are the transmitter plane. If we go in the receiver plane, so basically at distance zeta equal to L, And we obtain from you and Fresnel integral, the solution give us this equation. In this equation, you see that this Pl. which is usually called the propagation parameter, show 2 main coefficients. One is called the two main parameters, sorry, theta 0, lambda 0. where the theta 0 described the amplitude change due to focusing, so described basically the refraction parameter is a refraction parameter. A lambda 0 described the amplitude change due to diffraction, so it's basically a diffraction parameter, which is called also Fresnel, okay, parameter.

[00:15:10]Why this is nice, it's a quite powerful, it seems this data lambdas and type people can get confused, but it's quite powerful because with this theta 0, lambda 0, you basically can characterize the geometry of beam. Okay, for example, if you want to end up in a case of plane wave, I can set the theta 0 equal to 1, lambda 0 equal to 0, because it means that the basically W0 is infinite, so lambda 0 is 0, and F0, in that case, also, in this case, you have also theta 0 equal to 1, because you have F0 equal to infinite as well. So, also you can characterize the if you are in the far field in your field, but basically what I mean here to to why I would like to introduce this T.0 Lambda 0 actually it's something that was done from Anders and Phillips. By the way, all the my course is based mostly on Anders and Phillips and other publications mostly on Anders and Phillips book. So, you can see a couple of parameters, theta 0 and the transmitter, and a couple of parameters, theta, lambda, which is related to the theta 0, lambda 0, they are related to theta 0 by a conformal transport. Okay, so when you know these theta 0 and the 0 theta transmitter or lambda theta, the receiver, you know how to characterize the Gaussian beam at the transmitter of the receiver. So it's become quite powerful. For example, what about if I want to know what is the spot radius a receiver in zeta equal to L? Using this approach, theta 0, lambda 0, you can see that you can express, we are talking about the spot radius in free space, not turbulence. I didn't include any turbulence so far in this equation here, okay? So this is the spot radius at distance L, basically due only to diffraction in free space, okay? So you have the W0, which is the spot size of the transmitter, and then you can express either in either way using the transmitter parameter or the receiver parameter. If you look at the intensity, also you can get this expression here.

[00:17:23]But now let's focus on something that hopefully you can enjoy a little bit more, which is, okay, I have a beam, I have a beam that go through the atmosphere, there is the atmospheric turbulence, and how this beam is affected, as I was telling you before.

[00:17:41]Okay, first the case where we don't have turbulence. As you know, if you don't have turbulence, of course, we have only diffraction and you get this diffraction limit, this red spot here. Okay, so your beam may look quite uniform.

[00:17:54]What happened now if there is turbulence?

[00:17:56]There are different sides. Each of them affect the beam in a different way. And now, The biggest one, so basically the cells that are bigger than the sides of your beam are going to induce B wonder and the smaller induce diffraction.

[00:18:12]So you have this combinational effect that play a big role. So as you can see here, I use the mouse, over you can follow me. The red disc is the diffraction limited spot.

[00:18:26]Because you have further diffraction in the smaller scale, you end up in the yellow spot, okay?

[00:18:33]But then you have also the cells that are bigger in your beam, that are going to move your beam along the direction of propagation. So these yellow of these here are moving, randomly are moving, okay? And on the long-term period, you have a bigger spot where you can see this green circle here. So, in the end, they are going to have, for example, spot sides, and we call long-term long-term beam spread. OK, which is now not only the which is given by the the spot radius that you you have when you don't have turbines, so only by diffraction, which I call it the pupil here. Let me move over here, otherwise I don't see. OK, W pupil. I put Google because here we are not in the focal plane. This is analysis on the, let's say, a distance set. And then we have this term T, okay, this third thing that is basically related to turbulence, is the spread due to turbulence. Okay, so I have to speed up a little bit, I guess.

[00:19:43]So the long-term be spread. can be calculated. You, if you use, which is called, I don't have time today to talk about this, but usually we use a turbulence regime. We use what is called the Ritov method. And if you look on Andrew's book, but all these details are given also a little bit more in my course, you can calculate this T term. If you use Kolmogorov power spectrum,you see that this T term is given by 1.23 sigma R lambda phi over 6. So what is a sigma R?It's the rate of variance, which is the scintillation index for plane wave. I will talk about it later a little bit.

[00:20:25]Okay, so basically what is this theory?

[00:20:27]It's a parameter that describes spread on your beam due to turbulence, and that's why I include the parameter that is on variance that is higher when you have higher turbulence. Okay, and lambda, which is something that is related to the beam. OK, and this is a main parameter for a free space optical communication. Why? Because it is the parameter that is going to tell you how much power you're losing due to turbulence. Okay, now, okay, so if you look at the intensity, well, as we say, we start with a beam that is Gaussian. In free space, we know that remain Gaussian. Is that true also in turbulence? I mean, the beam remain Gaussian. Yes, and this film showed also that it's quite good approximation that the beam remain Gaussian. And the intensity look like this. Well, now you see that you have WLT, the long-term spread here, that of course is bigger than your diffraction limited spot radius. Okay.

[00:21:37]The on-axis value of your intensity is basically given by this ratio here.

[00:21:44]Okay. This means basically also that the turbulence is completed.

[00:21:52]If you know the W0 and WLT, W0 is something that you know because you know there's both sides of the transmitter. If you are able with formula and this stuff that also show in my course to calculate WLT, but you can also, if you know how to use this formula here, you can calculate with this formula, you are able to know also what is the on-axis intensity.

[00:22:15]Now,What I showed you before was at the pupil plane, as I said, distance of the transmitter. For practical application, like for example, free space optical communication, of course your fiber or your sensor is located at the focal plane. So basically, I don't have time to show you this, but you can think of this, you're going to get it if you want to know the spot sides on the focal plane after propagation turbulence. The approach is very similar, I mean, but you have to use ABCD formulation. There are details in this paper that they published on Optical Engineering last year. Okay, and you can end up with a similar formula here, where now you have the both sides here on the focal plane, the defocal, which is a term related to the spread of turbulence, but on the focal plane. Okay, so, okay, I think I'm pretty much there as at the time. Let's now move on on scintillation. What is a scintillation?

[00:23:14]Scintillation are a spatial temporal fluctuation of intensity. Okay.

[00:23:19]Yeah, we are at the pupil plane.

[00:23:22]It is basically the variance of intensity scaled by the square of the mean intensity. Mathematically, this is the formula. Okay.

[00:23:32]scintillation is affected at the most from turbulent cells of the Fresnel scale, which is given by square root L over K or square root lambda L, depends how you prefer to express it. Okay.

[00:23:47]And as you can see, scintillation is a problem.

[00:23:52]Why? Well, because if you want to do, for example, optical communication, this fluctuation of intensity means that sometimes you have also dark zone across your beam, which means that you're going to blind your sensor. We will say this later. But let's start to understand the physics behind the scintillation, why that's happened in turbulence. Okay, think about a flat phase, okay, here on the left. This flat phase starts, let's suppose you have a plane wave, started to look at the middle of a huge Gaussian beam or whatever, you're going to approximate with a flat face. And this phase started to propagate to turbulence. And you see that start to get aberrated. And then you see, if you think of it with the ray optics, that you have some ray that are diverging, others that are converging, so they are going to bring out, bring away sunlight or focus sunlight, and you get these different bright, different zones with different brightness. So you're going to end up with darker,In the brighter region, this region of course, a more random scintillation is a random process again. I mean, it's moving randomly and they require all this kind of statistic approach. That's why we use, you know, power spectrum, etcetera function, blah, blah, blah. Okay, so of course, I cannot go into details today. I'm sorry, but Okay, what is the rate of variance?As I say, rate of variance is the scintillation index for plane wave. Okay, so the scintillation index for a plane wave, why is it important? Because we have here to, how we can say that we are, that our beam is propagated to weak or strong turbulence. We don't, we cannot say that if we have only CN square, which is the information about our strength in the turbulence, or L, which is the length of the path, we need basically both of them, because maybe I have a very high CN square, but my team is going to propagate a few centimeters, then in that case, I mean, probably, or the opposite case when CN square isvery, very high, very, very, sorry, very, very small. Let's suppose I'm, you know, a 10 kilometer of altitude and the propagating might be for many kilometers, but still probably I mean with the regime, because in this case, the number is lower than one. So, basically, when the number is used to distinguish the regime, And when it is lower than one, it means that you can use a return method and that you are in a weak turbulence regime. Okay, So here, just to give you an idea about how the beam look like, you see that 350 meter, and A5 kilometer, so they are two different distances, but down we have also when we increase the value of the CN square, the strength of the turbulence. So you see, for example, in the bottom right, you have a beam that is totally broken, and you cannot do nothing. Of course, you cannot do optical communication with this beam, right?So, but let's say up to, you know, weak, moderate turbulence, we canquite succeeded in our application. There is a method that we just called the standard method to also, let's say, to extend the theory of, but this was done by Anders and Phillips, but still, I mean, it's an empirical method that still need to be improved, let's say. So, we, there is not too much we can do when we have very strong turbulence, because, as I will say here in this plot, Basically, what happened that when I think a sigma R number, basically, sorry, when the rate of variance is lower, the one you are with turbulence, when you start to increase the strength of the turbulence, okay, or in this case, is the square, so is sigma one here, is the square root, you increase the value, and then you see that there is a zone here, call it the focus regime. And then, because the multi-scattering start to play a role, your bill will get totally destroyed, and you go to saturate, your scintillation is going to saturate to one. Okay, so I go fast here because I would like to show you in this 10 minutes main application which is free space optical communication. Why free space?optical communication is interesting. Well, first for the bandit, because we have for the fiber, a bandit that use optical frequency, so is higher than in microwave. So we have higher data rate, can be deployedvery quickly. I suppose you have a disaster recovery scenario where you have to go there, you put your telescope and this telescope can look at each other and then I can transmit information. I mean, you don't need to make, you know, to build like for the fibre and invest months and months of work and you have to prepare where you have to put your fibre or whatever. So, it's also easy. There is an easy integration with the fiber system because it's similar technologies, again, for example, still use a 1.55 micometer as a wavelet. There is no spectrum license required, and a narrow beam, right? A narrow beam, because they are optical beams are very narrow, and from the security point of view, this is a big benefit. So, but what are the problem here?The problem is that because the beam go through the atmosphere, we have optical turbulence, like I said, but also we have what is the main problem when it's present, which is fog, because here we have also atmospheric turbulence is treated separately from scattering absorption. Okay, enter the question of budget leak separately, we'll see later.

[00:30:23]But of course, when you have a situation where you have a 225 dB over kilometer of attenuation here, you cannot do free space optical communication. You have to maybe have a hypid system or find a different path that microwave can succeed, let's say. So it's very important. But even with this, why optical turbines of interest, because even a clear day, clear sky day, turbulence is there. Is there is any way need to be kept in count in order to build correctly your system.

[00:31:03]Okay, so what I would like that you see here that basically I have a few slides to go, I think I'm on time.

[00:31:14]This is the well-known equation for budget link, right?When you want to build up a system, you have to receive a certain amount of power, the receiver.

[00:31:23]So you have your transmit a certain amount of power, you have to submit your trade-off of variable here.

[00:31:30]But what is important here, that where atmospheric turbulence enter this equation, atmospheric turbulence enter this equation here, in the divergence of your beam, because it's going to spread the more your beam. It's not going to enter here where alpha range here, this is the typical atmospheric attenuation, so you see there are two independent terms, the exponential one. Is that one due to the usual you can calculate it in or other kind of software you know is due to scattering that's option and here in the divergence you have you have the differential your beam due to the threshold limit spread, but also two points. Okay, so our turbulence now impact, for example, coherent system. As you know, coherent system is a system where I transmit as a constellation of bit. And, because of the atmosphere, you have you see what happened to your constellation, the receiver is spread, spread and moving. This means that there is a chance that you're going to make a mistake when you're going to when you're going to decide what is the symbol. So, you increase basically the symbol rate due to turbulence.

[00:32:46]Okay, because of turbulence, you increase the symbol rate. This is 1 effort, Okay, for this is what happened for equivalence system, but let's look at the free space system performance for direct detection system.

[00:33:04]We're going to look at probably the fade signal to generator, bit error rate, just a main concept. What is probably the fade?

[00:33:11]What is the fading? Fading is intensity drop at the receiver. So, basically, let's suppose this is at the pupil. Let's suppose that the green circle here is not here, but is behind on your focal plane. And then you focus this beam on your focal plane, but you still have this kind of scintillation here that basically you see that your sensor, I suppose, is going to be blind in some moment. So your intensity is going to drop. There are this yellow region here on the plot. The intensity is going to drop a given threshold and then you lose information.

[00:33:46]This is the fate. Okay, very simple.

[00:33:50]just a mathematical formula here, the signal-to-noise ratio. The signal-to-noise ratio without turbulence, as you know, is given by the RMS signal power over RMS noise power, okay? In turbulence, first you have to note the notation here.

[00:34:08]We have a bracket because these are basically random variable, okay? I mean, sorry, our average mean value, our mean value. So we put a bracket there.

[00:34:17]And also is interested to note that is going to be, even if you increase your signal, the power of your signal in principle to infinite, so your SNR 0, which is the signal to noise ratio without turbulence to infinite, you see that the signal to noise ratio in turbulence is driven by scintillation. So you see that in this plot, if you plot, sorry, if you plot signal to noise ratio in turbulence as a function of signal to noise ratio when you don't have turbulence,You have this line here, the forty-five degree line that is, of course, the ideal case, but when you start to increase the scintillation, this curve will move away, so you have a penalty thermal signal to noise ratio.

[00:35:01]Okay, on the bit error rate, I think I'm there, the bit error rate same when you have a sequence of bit 01, okay?And you have a scintillation, you have also noise, you see that there are bits that you're going to lose. So you're going to lose a bit error rate due to scintillation. Okay.

[00:35:24]And finally, I would like to spend a few words about non-commodal turbulence also because probably most, maybe 99% of all my paper are on this topic, more than 50.

[00:35:40]It's a topic of interest because, as I say, sometimes Kolmogorov turbulent doesn't work. So we have to find, let's say, a different model that is able to, let's say, describe a situation where we have a different overlook from Kolmogorov, for example, or there are cases where the hypothesis of isotropydoes not apply. For example, when you transmit a beam very close to the ground, you don't have a perfect mixing, you start to have some anisotropy, okay, anisotropic turbulence, that is going to affect your beam in a different way.

[00:36:17]There are papers, there is a paper that we published in Miami, for example, where we measured anisotropy using intense intensity correlation over a field that there are American football field. Okay, I think this is pretty much all.

[00:36:37]Unfortunately, of course not too much time. Hopefully you have an idea about optical turbulence and also if you are interested to know more deeply this what a tuber is, how would it affect the beam, how is modeled, you know, my course is about 8 hours where I can almost 200 slides to 180. So there is more time, you're free also to interact with me all the time, but this can do also it now. But hopefully I can see you in Orlando on April 15 and then see you there. Thank you for your attention. Thank you so much, Itola, for that fantastic presentation. You can tell that there's a lot of information to. cover on this topic here. And as Italo has said, he covers so much more in his full day course at the Defense and Commercial Sensing. So let's take some time here. We have about a little bit more than 15 minutes or so to address any questions from the audience.

[00:37:38]Again, if you have any questions, please put them in the Q&A box.

[00:37:43]and then we'll call your name if you include your name. And it looks like we've got a few questions here.

[00:37:50]The first one is from Jay Sethi.

[00:37:54]I apologize if I've mispronounced your names, Jay. If you'd like to unmute your mic and ask Dr. Taselli your question.

[00:38:02]Hey, thanks. Yeah. Wonderful presentation, Dr. Taselli.

[00:38:07]Just what is the max attenuation do you see in laser comm or open space laser comm?Like how much of a loss are we talking about?Like 100% on a normal day or I just want to understand what is the challenge like? Yeah.

[00:38:27]Well, you mean attenuation do you only do turbulence or? Yeah, yeah.

[00:38:33]Atmospheric, yeah. Yes, but again, for atmosphere, you have basically two kind of attenuation. One due to the fact that the beam spread due to turbulence. Another one because you have a sorption scattering. If you suppose a clear day sky, now I don't remember, I have a plot on the presentation.

[00:38:50]Remember, I think it's a 2DB.

[00:38:54]that the notion should be a kilometer or something, I don't remember. But this is only for the scattered soldier. From the optical turbine point of view, depends how you, how long is the path, how strong is the turbines, what kind of aperture you have at the transmitter, all these things. So I cannot tell you exactly what is the loose that you have. But let's say usually you can have a power in, you can quantify this with also power in the bucket. Maybe you can get, I don't know, 40, 50% probably in the bucket in a good day with not too strong turbines. I don't know. So the second part of this question was, of course, I think the wave number also, well, it depends on the wavelength. So can we assume like if it's a higher wavelength?

[00:39:42]Yes. Okay. Yes, of course there is. If you look in the Lenny Andrews book, you look at this well-known formula of scintillation, for example, you have the K term that is always I had the equation. So this K term is 2 power lambda, which is the wavelength.

[00:39:59]It means that in microwave, you still have scintillation, but it's not so strong like in optical bandwidth. Okay.

[00:40:09]Yeah, okay, got it. Sorry, just the last one. Modulation.

[00:40:15]Does some sort of modulation still help with getting more data across, even if you have a lot of scintillation?Like can you use a lock-in amplifier or some FFT system to extract data, even if it's jumbled up with a lot of turbulence in between? Well, there are many effective, many techniques in order to improve your performance, let's say. First, I have to keep, I didn't talk to you about averaging, so you can increase the aperture. If you talk about only modulation, of course, if you go, if you're able to do a coherent is better than, as you know, then you have you have a more bandit or whatever, you have more degree of freedom and then the detection. If you use a forward error code that are going to help. Also, I mean, this year, that's what I said before, is very interesting that this kind of field, free space optical communication, is a relatively new field, but can also take from the fibre optics field, or the technology, or the techniques, in order to, from the modulation point of view, for example, in order to, you know, to also to be effective, let's say more effective.

[00:41:33]Of course, yeah, the situation is different. You are not in the fabric, the medium is different. But I would say there are so many aspects to consider that it is hard to answer with only, you know, one basic phrase, because here it depends what kind of beam. I talk about only Gaussian beam, but there are so many exotic beam that you can use that can be improved performance.

[00:41:57]I mean, many things that are there in the lecture that you can take a look. And these are for me to tell you what is the best, to be honest. Right.

[00:42:07]And I guess this book that you were using throughout the presentation is the best resource to go find some stuff on.

[00:42:16]The book listed Beam Provagation to Random Media was published on 2006 by Anders and Phillips, the 2nd edition. It was 6, 7, or 5, but then there is also another version. So I, let's say, spent most of my time as a science on that book. So I know very well the book I can recommend, but I don't want to be, let's say, there are many good books in the field. Also, Sashiella book can look it look quite with a bit formalism. All these books are published by SPIE, by the way, by SPIE. So the format seems quite strong, but when you manage it, it's quite powerful because let's say it's more engineering oriented. You can also build up some, you know, you're going to apply that theoretics, other stuff, a filter function. So I recommend, as a science, I don't recommend a book. I recommend to study several books.

[00:43:21]But of course, you're going to have your book that you like the most.

[00:43:28]Right, thank you. But yes, these are all these very good. If you are somebody that is in the field, I will have on my shelf for sure Henderson Philips' book. As I can, I will have Tapaskio or other book, I guess, but where they also older one, but they are good book, I guess. Right, thanks. I'm just giving a little bit of background. I'm just starting in this.

[00:43:54]I'm coming from a mechanical engineering background, so any direction is really appreciated. Thank you. Thank you so much. You're welcome. And very usual could be also the field of guide, which is a small book with all this formula maybe to put in your pocket that can be useful.

[00:44:13]Don't be lost in the mathematics, because in this book there is a lot of mathematics. Try to understand the main concept. That's why it's important also to read paper, read the several books, read a different book, say the same things in a different way, because you don't need to be focused only in the mathematical, then you have to know the color of what you're looking.

[00:44:36]Right. Thank you. You're welcome. Thank you so much for your question, Jay. Thank you, Dr. Taselli. We've got quite a few more questions coming in, so I'm going to move right along here. It looks like I apologize for any name, if I say your name incorrectly, Justice or Justus Burskis.

[00:44:56]If you'd like to unmute your mic and ask Dr. Taselli your question.

[00:45:02]Hello, so thanks for the presentation.

[00:45:06]I was also wondering about like many, many times I hear about Gaussian beam and so on, but basically we also have some more interesting light structures.

[00:45:18]This Bessel beam, which has this elongated profile and does not diverge so much. Also, it is robust to some turbulence to my knowledge, like was any investigation done on this topic and like how would you see the influence of such light structures on the on the field on basically? No, there are many papers actually coming out also this day by, for example, Forbes from South Africa that these people work on structured light.

[00:45:51]And yeah, there are what we call, some people call also sorting beam. There are these kind of beam that have seems to have a better performance. Sometimes there is a feeling or they spread less. So it depends. Also, if you look at so many Olga Korokova, Pebershy, Multi Gaussian, there are several kind of investigation. But to be honest, I think it really depends on what kind of system you need to build up.

[00:46:21]and how much you are going to complicate your life when you don't use a Gaussian beam because everything for Gaussian beam is pretty much at least with turbines calculated. So you have your expression there, you can calculate your spot size and with that in the other way you have to go more maybe to well simulation which is also works but maybe take longer analytically and also you need the probably also to generate this beam to manage this kind of beam that require probably more expensive technology. So really depend on from what you need. But of course, they are very promising.

[00:46:59]Thank you. Thank you so much. We have another question here from Ian Wallhead. Ian, if you'd like to unmute your mic, there's a couple of questions there from Ian.

[00:47:14]Hello, can you hear me? Yes, yes, you sound great. Yes. Okay.

[00:47:19]One question I have is regarding the CN squared value. Well, one question is what's the typical value of this?It obviously varies with the level of turbulence and is it a fixed, is it a constant then or is it wavelength dependent? OK, there is a slight depends from the wavelength, but this is negligible, at least this this is negligible.

[00:47:44]If you look at how OCN Square derived from City Square, you have to look on the theory of this, butCN square is considered a constant. Usually terminal 14, terminal 13, let's say a strong value starts to be terminal 12, terminal 13, terminal 14 is what is a standard, what you get ground level. The more you go up in altitude, of course, the atmosphere become less dense, then you start to reduce also the value of your CN square. So, there is, for example, profile, which is a well-known profile used in academia, which of course need to be improved. The people are working to improve it to make it more precise, but there you can an idea how the CN square evolve change, let's say, with altitude. But a typical standard value that you actually you use this value in this model ground level is about, I guess, 1.7, 10 minutes, 14 meter to men or two over three.

[00:48:51]This is the standard value, yes.

[00:48:54]And a second question. Obviously, turbulence has a detrimental effect to the propagation of the beam. How does it compare with atmospheric scattering? Would you consider it worse in general? In general, I would say if you are in a clear sky there, you're slightly foggy there, slightly, thenyou have to be worried also about turbulence.

[00:49:22]If you are in a very, you start to have a quite good fog, I don't think you care more about turbulence because of course when scattering assortion are going to dominate, they're going to dominate a lot and Actually, you have to see if you're able to to be successful with your link in this case. For example, in oceanic turbulence in in in the ocean, also we have turbulence, we have a filtration of of temperature and we call oceanic turbulence. But in the ocean, you cannot go behind the 50, hopefully 100 meters one day because your scattering becomes devastating. So I would say turbulence, count to consider turbulence is important, but of course is less relevant when you're in very scattering environment. Okay, thanks.

[00:50:17]Thanks for your question, Ian. We have about 5 minutes left. And we have a few questions left, a couple of people here. Francesco Nardo, if you'd like to unmute your mic and ask your questions. And then after that, we have one more in the Q&A. So if we can try to get it wrapped up in about 5 minutes here.

[00:50:44]Hi, Francesco, are you able to unmute your mic?

[00:50:51]Unmute. Yeah. Can you hear me now?So sorry. I simply have two questions. You can just answer in simple words. That's what I really need. The first one is what is the difference between the modified Von Karma spectrum and the Kolmarov power spectrum? Why is it the modified or in which scenario is the first one?

[00:51:10]If I remember well, this is the beginning Andrew's book. The modified include also You have a basic this spectrum include a roll-off in the inner scale and outer scale, let's say the buoyancy range, and they would just call it dissipation range. So, basically, for the modifier, if I remember well, you have inner scale and outer scale. Okay, you introduce an exponential where you have you include the effort of inner scale and you include an inner scale and a number scale that one that is not modified yet.

[00:51:49]Unfortunately, I don't have another book.

[00:51:51]Maybe there is only one of them. But there is not a big difference. I mean, also there, it depends on why you need to use the spectrum, because most of the time what I did, for example, when the calculation long term is spread, that I showed you before, the T-term I showed you before, if you look through the slide, there you need to use a spectrum that is not Kolmogorov, because Kolmogorov diverge. So you have to introduceyou have to use up the One Karma spectrum. But when I think about One Karma, I usually think that one that includes both the inner scale and other scale. I'm not so worried if it's modified and modified. I mean, there is otherwise there is other spectrum that describe better a bump near the inner scale, which is theHenderson Henderson spectrum, for example, or you sometimes people use a different one, but here the main concept is that when you don't use Kolmogorov, usually you are still using, so you're keeping count also in the scale of the scale. And this sometimes, because as exponential, it's going to help to solve the integral. So, from the mathematical point of view, sometimes when you have a singularity on Kolmogorov, it's better if you use this kind of spectrum. Because you also sometimes can get, make your integral converge. Okay.

[00:53:08]So it's more a mathematical, let's say, concept than. Because, to be honest, also, the the the the the Mont-Carmen is not really really physical, if you think about that. This way is an artifact that we found in order to make this roll off mathematically, but in practice, we have we we should we should be only in the inertial range in this kind of hypothesis, because there is isotropy, there is homogeneity.

[00:53:34]Yeah, I mean, that was my problem. No, you have four or five different power spectrum and you have to pick one. And for me, the easier, the better, no? And really, and that was my question, or if you have a preferred one, if I should.

[00:53:46]The preferred one is the part that I use most in my paper, if you see, is the.

[00:53:51]Again, it depends from what kind of parameter you have to use. If you have to calculate the scintillation, then maybe I will use only Golmogorov, unless you need the information like what is the input order scale or in the scale of my scintillation that I calculated. Okay, then I have to use Von Karman. But it depends what you need. If you need to know how outer scale, for example, impact on your B wonder, which is usually quite remarkable becausehow the scale impact on B Wonder, then you have to use a spectrum that include other scale. You cannot include the, you cannot use, for example, the Commodore.