 So, the next session is Geometrical Optics 2 Paraxial Theory, Microscopic Imaging and Color Regulation Objectives and IPG by Dr. Mumberto Cabrera Morales from the Venezuelan Institute of Scientific Research at the ITV. Thank you. Good morning. Okay. In previous lecture we read about length, image formation and other topics related with that. What we will do today is to use this theory and to apply it to the microscope and we will see how length works inside the microscope because in the microscope we have length, we have length for creating the image but also we have a set of lengths for the illumination of the sample and the same principles apply. As I say you before, I have here some objective, this is Nyko, this for example is around the maximum set of lengths around 17 lengths here but as I say you before is the image formation is based on the length maker equation and what we started before and then we will see that but we will start with simple lengths, single lengths in each case as a simplification and finally we will explain about the objective, how it's going on with this. Remember and start again with the length maker equation and image formation. You know that using the length maker equation taking into account the distance how far away is place the object from the length, we will have the image and taking into account the focal length of the length, we can calculate where to put the detector but also we can build it using the three law that we studied yesterday as we know a parallel beam of light coming through the length we have an object in this case place a leader before, a leader after the focal length of the length. In this case a parallel beam of light we know that this object for example is a light source a point source can be emanating a lot of light and this light are collected but this length this parallel beam of light path through the focal length of the length. We can build the image as I say before using two of these rides, the ride passing through the center will be directly and we have the tip of the image here. We can use another ride coming from the focus also but he will be in this case coming again to create the image as we know and we studied yesterday. As we can see in this image in different colors the three rides representing the three laws. Let's now we start to apply this for a microscope objective that I say you now is represented here by a single length this is the the objective that we know can be a set of lengths. If you have a microscope from 1970 or even 80s they are called finite objective lengths they are working based on this principle what that that is meant it means that for this kind of a microscope or this kind of microscope were designed in a way that the the object is placed a little after the focal length of the length very very at very short distance this is what we had in the previous in the previous image similar to this okay then we will have a projection here of the of the image of this object in this case if we use the length maker equation we know that this object or this image this is called intermediate image plane we will have at the the final of this lecture we will see and we will study about the the image plane in the microscope. The image will be created here in this place normally in this kind of microscope or in this design because it is a design this distance is around 150 millimeters okay and after that we have the eyepiece which is another length that take this image and create a parallel beam of light together with the with the length of our eyes create the same image in your retina okay in some case you don't need to use this if you have a ccd camera and you want to see you put there directly the sensor as we will see after this slide and you will have there an image we will see in the lab that in some case we don't have enough magnification to see this image even with a ccd camera and we need a second lens but doesn't matter it depends on the magnification do you want because each lens as we will see in the in the next slide give an additional of the relation between the focal length of the lens produce so called the the is called the or is it related with the magnification of the system in the in the for more recently microscope you have microscope from the 90 even now they are they they were based on a different design in this kind of my microscope the image or the object is exactly at the focal length of the objective lens as you know when you have the object here after the lens you have a parallel beam of light this parallel beam of light gives you no image no image formation there you need the second lens that in this case is called tube lens why this this gives you a flexibility in in the design of the microscope for example you can add their additional components blanks filters and so on and also this additional lens gives you an additional magnification as I say you before the magnification of the system is related with is a ratio between the focal lengths of this lens that normally usually is larger than the focal length of the objective then we have an additional magnification there these are the main reason why this new design was taken into account and in any case I will be referring to both design to remember you that point okay what happened after the the object is take this image as I say you before I will add both system and what happened how we can detect this image oh we can detect of course directly in our eyes if we have the first system we have intermediate image here the eyepiece parallel beam of light then focus onto the retina if we use the second system that I say you has less magnification because this lens gives an additional magnification we have also parallel beam of light and also the image there then we can have also norm nowadays for example a ccd camera where to add where to locate the ccd camera we have different options if we have a system with a tube length as here we can add the ccd camera after the tube length here because the tube the tube lengths take the parallel beam of light here and create the image as I say you before if you need an additional magnification you can add a second length we will play with this in the lab with different lengths for image formation and also for color illumination and you will see that this is only applying the concept that we studied here it's very easy okay and this is another kind of a system for example using laser this is a fluorescent microscopy for example you decide the sample here you get the fluorescent there and you can add the camera here of course this is what I say you before that this this system allow you to add additional elements there filters mirrors and so on normally or nowadays many microscope has a the possibility to add or to incorporate a blazers they they have they have plates for mirror and for filters and so on due to this new configuration of an infinite a infinite image okay but also you can add a ccd camera after the the eyepiece and you have an additional magnification there because you will have the magnification of the tube length and the eyepiece and you can normally you uh you know that some microscope has the the ccd camera here or normal camera camera okay but let's we were here in this review okay the objective and we study how this image is created in our eyes or in a ccd camera but we need also to illuminate the sample to see the details of the of the specimen there and for that we have this system here in which we also use lengths normally we have a lamp we can use different kind of lamp depending on the application or laser we will have in the lab boss possibility we will use even lead and laser boss normally we have a collector length which of course collect the light coming from the light source and focus the image of this light source in a the back the front focal plane of the condenser length we will see also in the lab and we will check how to create this image in the correct plane taking into account the focal length of the of the collector length the the location of the diaphragm of the of the condenser diaphragm and also in some microscope nothing or you have a collector length a fill length boss together the function is to take the image of the of the of the of the lamp and to create this image in the front focal point of the condenser we have there you okay you can create it when you know applying the the length maker equation normally normally for the objective also we have back focal plane normally is the the region where you have a ring there but you calculate it using the length maker equation in the lab we will see that if you know the focal length of the collector length you know where this image will be then if you have a condenser length of course you know the the focal length of these lengths you add there this image at the at the focal distance of the collector length of the condenser length because as i will explain now you need for for color illumination or for an even illumination uniform illumination for example you need a color illumination it means parallel beam of light you add your front focal point exactly at the focal length of these lengths then you do you have a parallel beam of light you create it we will see in the app yes we measure the the focal distance and so on and normally companies do it when you have this objective the the back focal plane is is there where you have in the back plate you have a ring intentionally they did there and you know that the back focal plane is there due to that in the lab we will have a objective and also length because for for clear understanding and for working and looking at these planes we need lengths because normally in the in the microscope objective is inside this plane as you cannot see there but in the lab we have similar we have an open microscope with larger distance large focal length you to be able to play there to measure but you can calculate it okay I am explaining here what company can do but also what we can do we can build the microscope we have there in the lab okay then normally we have in some microscope you don't have field i will in the lab we will have only collector lengths a condenser lengths a condenser condenser diaphragm only that but we can add if we have good image we don't need a fill a fill length of course if you have a fill length also there is a fill diaphragm okay here normally this diaphragm or iris are i located in the in the four planes image plane and source planes of the microscope and you can see simultaneously all this plane i will explain this later okay wait the the the condenser as i say you create a parallel beam of light not nowadays we use a color illumination not critical illumination in critical illumination we focus the image of the of the light source in the specimen it means that we have we will have also in the ccd camera or or in the eyes we will have the image of the specimen but also the image of the light source this is not good this is why nowadays we use color illumination and we will play with this in the lab all these complex okay now as i say you we need color illumination for color illumination i will explain here in this each time i add both configuration and for better understanding okay we have here this technique is recommended by all manufacturers of modern laboratory microscopy because it can produce specimen illumination that is uniformly bright and free from from there allowing the user to realize the microscope full potential okay in color illumination as i say you the image the image of the source will be in the back in the front focal plane of the condenser and on to the sample we have parallel beam of light this parallel beam of light will be collected by the objective and we will have we will have again this plane is conjugated with this plane and is conjugated with this plane normally in the eyepiece you can see all this plane there you see this this iris you see the image and the iris you open down the the iris you have less or more illumination but you see the iris there and when you add and you can see very clear this iris it means you are in the correct uh or your your your iris is in the correct place is in the in the back focal from focal plane of the condenser then this this all uh plane are the uh the field planes they are simultaneous you can see there this plane simul simultaneous okay when we have a color illumination and for checking the color illumination we will see in the lab this plane here this is a back focal plane of the objective we will place for example here a deflation grating what we will have here in the back focal plane of the objective we will have the deflation pattern of this grating and we will play there in the lab with this deflation pattern and we will remove some details of the image okay and how we can see this deflation pattern hey in the case of the of the grating in the case of uh of this we will see uh of course there and with a second lens we create we take this image and we will see in in in other plane this this this image very very clear but also we will have another lens or moving the lens we will have the the location of this plane and with the with the focal length of the lens we can separate this this plane normally in microscopy you cannot see these planes but there is an additional line that this color Beltran lens you add this lens there and instead of the image plane you can see the the field planes okay but how to check about color color illumination when you have the sample you have the sample if you want to check that you have perfect in this case with a lead color illumination normally when you have color illumination you have parallel beam of light how to check and to see the image of the light source and to check that you have perfect color illumination you use a second lens and you know that when you have a parallel beam of light this lens can be located in any in any in any place but at the focal length of this this lens you will have the the image of the light source if your lens as we will see in the lab is 10 centimeters and as in our case at 10 centimeters you will have a perfect image of the lead source if not you don't have perfect color illumination because you don't have parallel beam of light you will have maybe the image after for sure at 11 or 12 centimeters this is it this is the way to check about color illumination and what we will do in the lab okay here in this in this diagram I show you the conjugate field planes as we will explain here and upper two planes here in this case as I say you this is the image of the of the of the sample here this is the intermediate plane also the the the field diaphragm this is what you can see through the eyepiece of the microscope together with the image you will see all these iris I'm playing with the these iris for example with the condensate diaphragm you change the illumination of the sample if you play with the field stock the diaphragm you change the the field of view also this is the this is the the importance of of diaphragm and due to that they are located in this plane because I allow you also to play with the illumination with the field of view of view that are also very important parameters in microscopy okay now let's we speak about critical illumination so say you in critical illumination the image of the lamp the filament in this case will be created here together will be together as as we can see here with the with the with the sample and this is not good because you don't have even illumination and you will see together with the sample the image of the of the filament it's very clear why is not a good this this setup okay now color illumination versus a critical illumination I review here but we spoke about this light source image planes you know I repeat again lamp filament condensate diaphragm back focal plane of the object of this and the eye as a point and the specimen image plane they are they are represented here also both the field diaphragm the specimen intermediate image plane and the edge retina or camera or camera sensor okay now we uh again review about uh uh conjugate planes and define as a simultaneously in focus and appear they appear superimposed all this plane without belt and lens or belt and lens you can chief in between this set of plane but this is very very important concept in microscopy but now let's we start and we concentrate on the objective properties as I say you the objective we have here an objective from the from the 1970s this is finite uh working system and this is recently this is this is the another kind of objective okay then in the for the objective as I say uh before we have many class we have for example uh a a chromat that uh has around five lengths or we can have more complicated objectives we have we have a fluoride that are better quality but of course so more expensive this is around 17 lengths a combination of lengths you can see there of course it's more expensive but is without a a a chromatic aberration a spherical aberration all corrected there of course this is proportional to the price of the objective high quality high price okay uh they are mainly and all of them are a plan version this is uh I say that I will only concentrate in the main or the main or more complicated aberration in the microscope but we have also coma we have but Miguel will explain about this we have astigmatism also we have a this flat field distortion all of these are corrected for the the flat field okay but acromats okay they are axial corrected for red and blue for these two wavelength for the chromatic aberrations but for a spherical aberration for the green light at this way wavelength they are also correct okay fluorides are uh or so-called it's also semi semi api axial for two to four colors and a spherical two to four colors also and the more sophisticated apochromats they are corrected axial of course for four to five color we have for violet for blue green and red we can use all these wavelengths and all available in plan plan versions okay I will explain there how to identify these properties when you buy an objective now let's we concentrate on the numerical aperture we wish this is they are the more sophisticated objective what I show before they have around 17 lengths they are uh corrected for chromatic aberration for spherical aberration even for for coma for a foul field distortion for astigmatism all due to that they are so expensive hey you know I will explain after that when you have a chromatic aberration corrections objective you must select the correct immersion oil normally uh companies say you if you buy this objective you must buy for example nicon you need also oil from nicon if you use another oils you will introduce I will I will explain about this uh independent of this that you have corrections you can introduce a also distortion if you use another kind of oil mainly for chromatic aberration because you are introducing another medium there I will explain about chromatic aberration you know it's related with the dispersion of the media and if they sell you this kind nicon for example of oil you use this because they match the refractive index of this oil with the objective if you if you use another it's another the refractive index you will have chromatic aberration you you will introduce and and for spherical I will explain also there are different ways to correct this kind of aberration okay now this is the most important property of the of the objective the numerical aperture I I say you before that also is related with the resolution and this is one of the most important properties we will see that the resolution is you you have to separate the resolution with the magnification you you can have a lot of magnification but the first objective the objective is is the element which define the resolution and you can magnify this but with the same resolution there was a paper I don't know Miguel know about that was published in 70s 1970s not remember exactly they reported even a super resolution technique using a photocopy machine you know they add and was published after some people understood that this is not correct we will see this in the lab you add the sample in the photocopy machine and then you get the image this image again you increase the the magnification and they reported even they were looking at the atoms there this is not possible it's wrong because the magnification is a one property that is not related with a with the resolution is different and for example in this equation we have the refractive index of the medium between the sample and the objective I as I say you before you can use air water a different medium is different I will explain why this increase the the resolution and we can have also different numerical aperture depending on this angle this is a gathering angle that the objective can collect of course if you have a if this angle is bigger you have a higher numerical aperture the the image will be bright okay as you can see here also the working distance that is another property of the normally this is not the focal length of the objective the working distance is where you have to add the sample because for example for finite objective it's in different place is not at the place of the focal distance and is where you have to place the the the sample to have the proper image formation at this distance also depend on the numerical aperture we have here an example with different angles gathering angles and we have different numerical aperture okay now in this case we have another example of the we are comparing they are different numerical aperture with different angles and different working distance of course the working distance or also depend if you you don't need so high resolution depend on which sample you you will use here and as we will see in the lab also allow you to add their a mirror for example in thermal length we will have there a mirror for the resonator for that you have to use long focal distance of course you don't have a very high resolution but maybe it's enough for your application it depends okay this is a trade-off and now why in immersion media okay of course why immersion media increase the the numerical aperture okay because you avoid total internal reflection what immersion media do is that if you have a glass the refractive index of the glass is around 1.5 as we saw before and normally a immersion oil has around 0.5 if you have a here what happened the the beam coming there will be refracted in this direction you lose you lose you lose resolution because you are you are you are losing there the the right coming at a higher angle from the from the from the sample as we will see in the lab this contain very valuable information but if you put here an oil in immersion media you will collect all this ray coming from there and you will increase of course you avoid total internal reflection this is the point and you increase the numerical aperture and of course the resolution okay this is an example of the this is around 1.5 this is the the maximum value it's around there we can obtain using the best oil of course without introducing introducing additional distortion and using blue light you know this is another example of a calculation of the numerical aperture and how this angle correspond with the numerical aperture we have here some examples the the angle using specific numerical aperture objective the angle we can obtain this is the maximum angle we can obtain using the maximum numerical aperture objective oil immersion of course okay now let's quickly concentrate in the chromatic and spherical average I will not speak speak about a comma and so on but also this average are present in the microscope but these are the more complicated and more common average you know that when we have a dispersion different colors bent in different way the blue light is the more a banded light there and the red is less in the lens we have the same the blue light will be projected the focus of the blue light will be projected here closer to the lens and the red light after that then you have there a dispersion which will introduce a mistake or will will distort the image okay if you are you are using white light okay but how to correct a chromatic average normally we use another a dispersive element with different refractive index it's very clear here that if we have the blue light is focused close to the lens and the red one there when you introduce this element here with this shape the blue light will be diverging in this case and the red light will be coming to the focus okay and this is a way when we use this doublet we we have it inside or inside the design of the of the objective and this correct here is an example that of this how it's gone how the chromatic average can be avoid in the objective here an example very well corrected objective for chromatic average ratio but what happened with the spherical average ratio spherical average ratio as i say you yesterday when we have a spherical surface they are not perfect focusing elements and we know that the rise coming even for monochromatic light when we have a monochromatic light the light coming from here will be focused normally here and the light passing close to the center will be focused more far away and we have also a dispersion here and of course a distortion of the of the image this corrections this aberration but before to continue with this i have to say but i i say you before that for chromatic aberration also you must select the correct oil image media if not you introduce aberration for chromatic for a spherical aberration is different it's not related with the with the of course with the with the media there there are other methods for correcting this kind of aberration correction colors correction colors is a kind of set i will explain now of set of lengths with a ring that you can move there and you correct this mainly the the peripheral beings to coincide with the central beings we will see now how how we can do that in the microscope this is the case oh this is correction color for a spherical aberration this is a correction color adjustment ring how it goes okay normally for a spherical aberration what we have is this okay here we have some part of the light is focused here and part of the light is focused here we have a distortion in the image this is due to that the fact that the length is and this right are spread off more than the central right what the correction color do is to move this right inside to come parallel and this that is represented here in red to coincide with the this right to correct the spherical aberration normally you move this color and you you make this right to come parallel this is the way to correct this kind of aberration normally in the microscope in the objective it's right in there it has correction color okay yes i will explain about this now but not so much as for a chromatic aberration okay not so much we can discuss about this it's related you are right it's related because i will i this is what i will explain now the for example there are additional aberration due to the sample the microscope slide and so on you know you can have a sample in which you have you have a specimen there a cell i don't know you have water inside the refractive index of this each elements are different and for calculation of the this correction colors and for chromatic aberration you have to take into account you have to assume a model which refractive index will have your specimen it depends on this and if you have a specimen there with a water and other components that have different refractive index you will have a mixture there and you have to assume some average value and of course this this influence but mainly the the the the the chromatic aberration because the spherical aberration as the as the names say is is mainly related with the spherical surface there that are not perfect of course if you have but in a specimen a some component that also refract the light in different way you have an additional spherical aberration okay but in this way but we can discuss about this also okay now as i say you before uh we can the the magnification of the objective is related with the magnification of the the of the system at all magnification of the uh objective the eyepiece and you can have intermediate factor there and other elements i don't know the two planes and so on and the overall magnification is the is uh is depending on these all components but depending on on your application you you can amplify more or less okay and now uh i will i i think today i will have time i was thinking maybe to start the other lecture but i will see we'll see is still uh 12 30 i think we will have so much time i will i will finish uh 12 maybe okay let's now uh we look at the properties of the objective but we can have uh many questions because this is a very interesting topic and also important uh let's we look when you buy objective what is important there okay uh this is the magnification of course plan means is corrected for the fulfill distortion miguel will explain about this uh kind of aberration a apochromat we so before they are corrected for many wavelengths many many colors uh this means of course the manufacturer as i say you flat field correction it's plan apochromatic correction this is the magnification this is a numerical aperture of course this is what i discussed with you before dick mean uh or here is represented uh the main application of this uh objective what you can do is this you can do a a interfering contrast microscope with this no this is the main application of this objective what does this means this infinity here what does it mean this is what i say before is is not finite correction is infinite infinite correct okay you need a tube length for this kind of objective and you need to add the sample or in the microscope they use this objective normally usually the sample is located at the focal length of this objective uh this is the cover glass that you can use with this objective normally cover glass are around point 17 it's an average value uh this means that for this objective you need to use a cover glass in these lines if not you will have aberrations okay this is the working distance this is where you have to put the sample here we have a cover glass okay and another this is later was the magnification these are the main the main properties of the objective that you have to look when uh you need to buy a objective for any kind of application or a specific application i i want to stop here because this ratio was not so uh maybe we can have discussion here