 Welcome back we are going to continue our discussion of optical diagnostics applied to sprays we will look at a couple of different techniques today involving laser diagnostics just as a quick recap in the previous classes we have studied basic imaging although we did not really look at image processing we looked at PIV we looked at phase Doppler particle animometry and started to talk about other techniques today we are going to discuss three more techniques one called laser interferometric droplet droplet sizing we will also look at laser induced fluorescence and end with shadow graphing laser interferometric droplet sizing I will use the acronym LIDS is known by several acronyms commercially IPI is an acronym that is used by a company called DANTEC I LIDS is a company is an acronym that is used by I believe TSI I am not sure and there are other companies that make this as well the basic principle of operation is similar to a PDPA in the in the sense that it takes advantage of coherence so if I take a droplet and have a laser impinging have will have some have a laser light source approaching the drop if I do a very quick ray trace this is a typical ray that is twice refracted through the drop of diameter D there is another possibility of light reaching this observer here so if let us say this is me the observer there is another possibility by which this same light can reach this observer which is through the through the mode of reflection so either a ray down here is reflected or it could reach the same person through the medium of refraction a combination of these two modes of transmission of light or scattering of light through to the to this observer if I focus when the light is focused you see a drop with two bright spots corresponding to the two predominant sources of light coming to the observer so this is in fact common observation that if I see a raindrop if you see a picture of a raindrop that is in perfect focus you will see two points of bright light on either side of the raindrop now if I take the same light and instead of focusing it on to a plane so if this is my focal plane when I create this focused image I see this if I take the same same modes of transmission and if I image the light say this is a focusing lens so instead of placing the plane the imaging plane at the focus I place it at a slightly defocused part what you will see at the defocused part is a set of interference fringes so if I draw that out we are likely to see and all of this is the envelope of a circle because that is what is scattering the light so you see bright and dark interference fringes this these interference fringes especially the fringe width contains information about the size of the drop and it is a it is really a hard signature that is coming directly from the sphericity of the drop and the size capital D of the drop okay so it is actually very rich in information this fringe pattern we will see how to take advantage of it a little later so let us see how do I practice this is the basic principle of operation of this lids laser interferometric droplet sizing now how do I take advantage of this in a real system what we do is I have a spray nozzle I have a spray that is formed I take a light sheet pass it through the spray now potentially I have a lot of drops in this light sheet of different sizes and where the where your eye is currently you is where the collection optics and the focusing optics are set up so if I now look at the scattered light coming towards me with in fact with in a sort of a defocused sense every one of these drops will create a circular footprint and an interference pattern in that circular footprint because of this coherent light coming from two different optical path lengths the reflected light and the refracted light takes separate optical paths therefore you create interference okay now when I when I view each of these drops I have a full circular pattern so if I have a I mean a light sheet of some finite thickness which is say 1 mm and our drops are typically much smaller than that the if I have two drops that are one slightly behind the other they are both going to create an interference pattern and this circular interference pattern is going to interfere in some sense spatially in the image with the interference pattern created by the drop slightly behind it so as a result you will see a whole set of interference fringes but I need to identify a set of interference fringes with a particular drop in order for me to get to the drop size the way this is done is by using only the information that is required by only allowing the information that is required and discarding the rest when I have a circular interference pattern a circular footprint with interference fringes along the length of the circle along the vertical cross section of the circle all I care about are the is the fringe spacing I do not care about the full circular footprint so what is typically done at the collection optics level there is a so I can place a slit and this is a in some sense a horizontal slit that looks like this. So the vertical fringes when looked when visualized through a through a horizontal slit essentially create you only see a part of the fringes that looks approximately like this you will not see these vertical lines on top and bottom but you will just see something like this for every drop something like this is seen for every drop. So if I have multiple drops even if I have two drops that are slightly behind each other I am able to only take a thin slice of the interference pattern created by each of the two drops and as long as those two slices do not overlap I have enough information to get the size of each of the two drops even if they are close to each other spatially inside the light sheet okay so once I know the this fringe spacing and once I have information related to the position the once I know the fringe spacing and I have a bunch of these for every one of these drops we are able to extract drop size information for every for every one of the drops now like I said these fringes actually if you do the if you do the even in some sense the the wave calculation of optical wave transmission calculation through a spherical drop you will find that this fringe spacing is not exactly uniform throughout and that contains information that is specific to that drop in terms of sphericity for example or some kind of some kind of a difference in the refractive index of the drop now so I am able to relate every drop and by knowing let us say the midpoint of this pattern I am able to determine the size and its position uniquely so if I use lids which is laser interferometer droplet sizing along with double pulse photography where I take two pulses and get two images lightly apart in time because I am able to uniquely identify every drop in this image we can calculate the velocity vector of every one of the drops so essentially an extension of this so first of all lids is based on relating the fringe spacing to size now if I combine lids plus double pulse imaging you can get lids plus particle tracking velocimetry which allows us to measure the velocity of every particle in the spray we have looked at several different techniques for both particle sizing or drop sizing and velocimetry let us quickly see the advantages and disadvantages of the various techniques first of all so let us list for each one of the various techniques the advantages and disadvantages but before we do that maybe we should look at one more technique called shadow graphing is similar to the one we used before it is actually in some sense the simplest of all light of all imaging techniques you potentially have a very bright light source passing through a diffuser and on the other side is your camera typically this has to be a high speed camera in order to be able to image the spray the basic principle of operation you know when I am looking at a bright light directly in front of me I am going to see the shadow of any object that is between me and the light and so the camera sees shadows of these drops so you might see drops that are back here as well as drops that are in front all cast a shadow on the image but I could have a specific plane in on which I focus the camera and only look at the shadows in that focused plane and discard the images on either side so essentially this is the clarity of the image depends on the depth of focus the smaller the depth of focus the higher the clarity but smaller the depth of focus the less chance I have of capturing a sufficiently large number of these drops in any one image so they are contrasting requirements of this system once I have an image ideally I would like an image with like dark shadows that are circular or it doesn't they don't have to be circular but let us say they are of some very clearly defined shape in reality what you will end up seeing is one of two things you will see a little bit of a blur where the drop is may be dragged through a certain distance this is because in spite of using the highest speed camera the exposure time on some of the high speed cameras may be still long to get a crisp frozen image of the drops so the solution to that very often used is to have instead of a bright light diffuser you they are fluorescent emitters emitter plates if you will that are excited by a laser pulse so this would be a substitute to the bright light source the advantage of this tech of this light source is that you have first of all a laser light source that is impinging on a fluorescent on an absorbing medium a medium that absorbs that wavelength and emits a slightly longer wavelength but the emitted intensity is relatively uniform and is only controlled by the concentration of the fluorescing agent in reality of course even that intensity is not important the fact that that emission occurs over a very short period of time is what is important so the fluorescence lifetime of these agents is very short typically much shorter than the exposure times on your high speed cameras so if you can synchronize the high speed camera to the to the initiation of the fluorescent fluorescing time or the pulse initiation time one could capture a very crisp image of the drop the biggest advantage of shadow graphy is that I get I am able to capture sizes of drops that are known to be a spherical you look at the previous techniques whether it is phase Doppler particle analyzer or lids they are all they all assume sphericity in order to get to the size so this is a technique since you are directly visualizing the blobs of liquid in motion frozen however you do get you are able to see images of drops that are not spherical and by appropriate image processing get you know shapes of like a you are able to characterize the shape of the drop apart from just the size so if I now look at an image coming from the fluorescing agent I am able to see drops like that that are spherical but I may also have a second drop that is slightly behind the first drop and in my image I may create a shape that looks like this okay and both these drops may still be within the depth of focus of what I need what of my imaging optics so I can now I can with my naked I see that there is two separate drops and I can use appropriate image analysis techniques so start with edge detection and look at sudden change in the gradients of the edge and from there identify this composite image of two drops one behind the other as actually being two separate drops and you can ascribe a size to each of the two drops now if I have a ligament of sort say typically like if I am now very near the nozzle I may be I may actually see a drop that looks like this I can use this technique to not only get the size of that drop in the plane of the image but also get some feel for what sort of non equilibrium shapes are existing in the near nozzle region so this is a slightly more versatile technique in the sense that you are able to image drops that are not spherical one of the biggest disadvantages of this technique is that you really still cannot go very close to the nozzle in spite of you know talking about non spherical drops because once your droplet number density becomes large a tip a classic case is a diesel spray it is very very difficult to image the near nozzle region in a diesel spray to get to some kind of indicators of what sort of drop sizes may exist in that part of this in that part of the near nozzle region of the spray now we did not talk about another technique in fact one of the oldest techniques for for particle sizing is what is called diffraction particle sizing the pioneer in this field is called was a company called malvern which is which was in fact it preceded all other forms of optical diagnostics for sprays except photography now the basic principle here is that I have basic laser source that puts out a light beam the light beam light beam is shines through a spray and all the little drops that are in the in the light beam are scattering light so essentially by the medium of diffraction by the mode of diffraction so every drop again assuming sphericity creates what is called an airy pattern of diffraction so I am going to exaggerate this part just to just to make the point if I take this particular drop the it creates a pattern where the light intensity versus radius takes on a pattern that looks like this so you see a very bright spot in the middle one more bright spot a certain angular deviation away and a third bright spot so you see these clear peaks this is called the airy diffraction pattern from a spherical drop and this airy diffraction pattern has these clear peaks and these peaks are response are directly related to the drop size so the way remember this creates the diffraction creates an angular diverging pattern so with again some appropriate imaging optics so it is quite usually it is just a single lens is enough and the detectors are semicircular arrays so I mean the airy diffraction pattern for a circular drop in a laser beam is symmetric about the center line it is axisymmetric so typically the detectors that are used to detect this light are photo diodes or photo detectors that not photo diodes but photo detectors that essentially are arranged in in rings around the axis and these rings are the spacing between the between the first two peaks of the ring or the position of the first peak on the ring position of the first peak of the airy diffraction pattern tells us what the sizes now as you can see this works if I have one drop in that long laser going through the spray I mean this principle of operation is clear but if I have multiple drops I will get a superposition of peaks and there are algorithms and that is Malven's contribution to take the to take the intensity distribution from many different rings coming from many different drops and and obtain a mean diameter for the drop size for the distribution of drops in the resident in the laser beam we will talk a little bit about this algorithm and continue our discussion towards laser fluorescence laser induced fluorescence in the next class we will continue our discussion of optical diagnostics and towards the end of we have completed our discussion of the phase Doppler particle analyzer a diffraction particle sizer lids which is laser interferometric droplet sizing of course our standard techniques associated with PIV particle imaging velocimetry and how PIV can be used to extract some averaged size information averaged surface area information today we are going to talk about another technique called cliff or planar laser induced fluorescence planar laser induced fluorescence is a technique that basically relies on this property called fluorescence ok so what is fluorescence very quickly typically when a photon interacts with a molecule molecule has discrete energy levels for the electrons and an electron from one of the lower energy levels can absorb the energy coming from a photon and be pumped up to some high energy level but on the way back but on the but in the process of relaxing from this higher energy level down to the ground state it may not emit a photon of the same wavelength or frequency there is some amount of inelastic this is essentially a phenomena called inelastic scatter because the incident photon and the emitted photon are of different frequencies the emitted photon has a lower frequency essentially lower energy in relation to the incident photon which automatically means that the incident wavelength of the light is less than the emitted wavelength of the light so this is also called in some sense this is slightly red shifted that is shifted towards red on the spectrum now the way this actually works is you have to find a wavelength whose photon energy h nu is exactly equal to the spacings the between two discrete energy bands two discrete energy levels and so that in itself is a big field of research so for example in the in some of the work that we have done we use this so to find a molecule that has a pair of energy levels one being the ground state another higher energy level whose difference is equal to the photonic energy is the is the photon energy is basically an art of choosing what is called a dye so this kind of this kind of a molecule is often referred to as a dye so for example there are many different dyes there are many different classes of dyes but say for example rhodamine 6g is a dye that is very commonly used in the spray community and rhodamine 6g has an absorption line at 532 nanometers wavelength which happens to be the wavelength of argon ion laser so this happens to be green in fact and it happens to be the wavelength emitted by an argon ion by an argon ion laser so if I take just to give you an idea if I take a beaker full of water okay so this is water with rhodamine 6g in some concentration and shine a argon ion laser through there and see it from where my eye is placed I will essentially at least to start with see green a green band going through that water which is dyed with this rhodamine 6g that is because of what we have already seen as me scatter so there is lots of particles and you know some entities in there that are scattering light towards the observer and that scattered light is exactly the same wavelength as the incident light so this is referred to as elastic scatter so the you have a lot of elastic scatter in any real system that has some scattering of scattering entities in it and then if I wear safety glasses in any of you that has worked in a laser lab usually you have a pair of safety glasses that have a cutoff filter for the wavelength of the laser that you are using so essentially that wavelength light would be invisible to you if you wear that if you wear those safety glasses so if I wear those safety glasses and look at this beam going through this water which is dyed with rhodamine 6g I will see a slightly orangish glow in the region where the laser is passing through the water and hardly any glow or hardly any light coming out of the rest of the beaker in all in other words the rest of the beaker is practically dark the beam before it enters the beaker is invisible the beam after it comes out of the beaker is invisible only the part inside the beaker when the beam is resident inside the beaker is responsible for this fluorescence emission from the rhodamine 6g dye the intensity of that rhodamine 6g dye the intensity of that fluorescence emission is directly proportional to the concentration of the dye present in the solution so the intensity of the light to not the wavelength of the fluorescence emission but the intensity is directly proportional to the volume concentration of the fluorescence of the fluorescent of the dye in the solution now sometimes this fluorescence emission is a slightly broader band in other words it is not a discrete wavelength because these molecules are typically very complicated so there are many energy levels from which you can get this fluorescence this inelastic relaxation so and because of which fluorescence is sometimes especially in the commercially used dye is not one single wavelength emission but a slightly broad band but it is always redshifted so it is always slightly longer in wavelength than your incident light can never be shorter and in and it also is much lower in intensity than your intensity than your mescater okay because mescater is a is a phenomena which is where the intensity of the light is directly proportional to the scattering surface area okay so let us be there are two things happening here one is I me which is proportional to surface area and I fluorescence which is proportional to the volume concentration so let us see how this is applied to a spray so if I take a spray nozzle and I take my argon ion laser sheet and in this sheet you know you may have little drops of the spray that you want to visualize and these drops typically have these drops are of the liquid where you have the dye present in the liquid so the drops themselves may be let us say an aqueous solution of water and rhodamine 6g and your and a camera is placed where your eye is placed and typically the camera may have collecting optics but it may also have a filter it is called a notch filter or a at 532 nanometers so in other words it passes all wavelengths below and above 532 nanometers this is called a notch filter or I could use a a low pass filter that or a high pass filter that cuts out anything below 532 nanometers or slightly above 532 nanometers so I am only going to see wavelengths that are longer than the cut off cut off wavelength okay but a notch filter is like it is fairly commonly used because it is easy to make it using diffraction patterns so essentially if I place a notch filter in front of my imaging optics I see I do not see the me scattered light I will only see the fluorescence emission coming from the drops themselves so if I create an image of the fluorescence emission this is essentially an image of the volume concentration of the rhodamine 6g okay now for most commercially available pulsed argon ion or frequency doubled nda both give you very close to the same wavelength so either argon ion or it could be a frequency doubled nda laser so both of these even at some even at the highest pulsed pulse energy of the light sheet coming into the spray the fluorescence intensity is so weak that it may not be visible on a regular CCD or a CMOS array so very often we have to use what is called an intensified CCD camera so this is like very low light imaging so that is essentially the reason you require some way to intensify the image so your regular CCD camera is able to detect it so this intensified CCD camera with a notch filter will be able to visualize the fluorescence intensity distribution in the light sheet and the fluorescence intensity distribution if which is now a function of let us say some spatial if this is my image this is proportional to the volume of the drops so if I for a moment assume that I only have monosized drop or if I look at this phenomena at the single drop level the fluorescence intensity is proportional to d cubed and the me scatter intensity which I can visualize without the intensifier and actually without the notch filter is proportional to d squared so if I do multiple double pulse images one pulse giving me the fluorescence intensity distribution and the second pulse giving me the me scatter intensity distribution from that I can get essentially and if I do a time averaging of those pulsed images I am accruing sigma d cubed in time in one sequence of images and sigma d squared in time on the other sequence of images and if I ratio them I am actually directly getting the souter main diameter that is the advantage of using pliffin sprays that you by this appropriate ratioing you may be able to get the souter main diameter directly so let us just quickly write that down if which is a function of x and y is equal to some kf times d cube this kf is a function of the volume concentration which is the I mean at this level we will just say it is a function of the concentration of the rhodamine dye in the liquid so this is like the concentration of the dye in the tank in a tank sitting upstairs somewhere above your sprain also right the me scatter on the other hand is some km times d squared we found that this km is slightly more complicated we have already done this calculation to show that it depends on this thing the alpha your scatter angle between the laser source and your imaging plane and your image it is the angle made by the ray coming in from the source and the ray going towards the observer and that angle could be different for different parts of the image so that complication which was which applied to any kind of a me scatter imaging also applies to using cliff for droplet sizing so if I do a time sequence on these so remember if we set this kf is only a function of alpha I can factor that out if k sorry kf is only a function of x I can factor that out if km is only a function of alpha I have I can factor that out and make sure I still retain the fact that it could be a function of my x and y coordinates in the image because different parts of the image have different angle angle through which light is scattered so if I I can get this outer main diameter at one point in the image but that value is not comparable to another to the outer main diameter at another point in the image because the denominator km is a function of x and y and that is not very easy to get in a real situation this it is still a somewhat active area of research to identify that okay so this while in principle works is still not been implemented fully commercially there are people who claim to have done it and you can actually buy this pliff me sizing instrumentation but as far as I know this is not been implemented commercially in a very robust situation yet so there is some room for you to play around with and do some some development work there let us quickly recap all the different measurement techniques we have studied we have referred to this both as non-intrusive and optical okay we started with simple photography videography and then we looked at phase Doppler particle analyzer this may not be in the same order as the lectures but it summarizes all of the all of the techniques we have discussed particle imaging velocimetry we looked at laser interferometric droplet sizing and then we looked at planar laser induced fluorescence the phase Doppler particle analyzer is a superset of our standard laser Doppler animometry or LDV or LDA so if you discard the particle sizing part in the particle in the PDPA you have essentially an LDV or an LDA and somewhere along the way I think we also photography videography we also intended to mean high-speed imaging so this these sets of techniques are fairly widely and commercially used they are there in the last let us say 20 to 30 years the prevalence and use of these instruments in spray and spray related to understand spray related issues has really revolutionized our idea of what we can do in combustion systems especially if not in other spray applications okay we will continue our discussion in the next class