 Hello, welcome back. In the last class we have just seen the concepts of depth of focus and depth of field and then we moved on to the concept of contrast and then we looked at the meaning of the very definition of the contrast and then we just started discussing about the lens defects. So, we will again start look back that the classification of the lens defect. If you look at it I just mentioned lens defects are basically of two types one is on-axis aberrations other one is off-axis aberrations and then we have a distortion which is also going to impair the quality of the images. So, I started off describing the first defect and very important defect spherical aberration yesterday. So, let us look back and look at this defect again. I mentioned that the spherical aberration is a very difficult aberration to eliminate for any lens because this aberration causes because of the spherical nature of the lens. So, let us look at the review the remarks again once again it is still worth it. The aberration is caused by the spherical shape of the lens surfaces it is more severe the greater the aperture of the lens and it occurs for the most positions of an axial object point, but for certain positions it becomes 0. Such aberration free object and image points are aplanotic points the for the spherical surface one pair of such points lies at a distance nr and r by n from the center of the curvature where r is the radius of curvature. As I mentioned yesterday this parameter aplanotic points is used to fabricate a high power objective lenses. So, this aberration can be largely but not completely eliminated by use of combinations of converging and diverging lenses of different refractive index. We will see that in detail when we complete all the definitions of the defects and then we will see how it can be overcome by the combinations of different lenses which have different optical characteristics. So, the one the image which is shown in the right hand side here what I have just try to bring to your attention is what happens to this spherical aberration when you view the specimen with the cover slip. Yesterday we have seen that the numerical aperture and and it is a light grasping power of an objective lens with oil immersion for a dry lens as well as immersion lens as well as a bare sample a sample with the cover slip. Normally if you look at this image what you have seen is normally this cover slip on the specimen is kept at a specific thickness about 0.17 mm and if you do not have this a designed 0.17 mm distance of a cover slip or if you have an arbitrary length or thickness of the cover slip then what happens to this spherical aberration that is what is being illustrated here and if you look at carefully thus the rays which is emanating from the specimen surfaces just get diffracted or rather I would say refracted from this cover slip in this manner and then if you trace this they refracted ray and then these two rays are differing with the distance of H1. You can see that if you trace this ray and it falls here and if you trace this ray R2 it falls here and these two rays are emanating from the surface of the length H1. On the other hand if you if you just allow the rays to pass through a cross slip which is of arbitrary length than the 0.17 mm then you can see that the refracted ray goes like this that is R1 and R2 and if you trace their path optical path they differ in the range of H2 which is much higher than the H1. Obviously the quality of the image will be much affected because of this optical path difference between the a standard cover slip thickness versus an arbitrary cover slip thickness. So now we will move on to the next defect called astigmatism and curvature of field. Look at this image carefully as I mentioned this is off axis aberration and if you look at the schematic you have this optical axis and then you have this lens here and there are two different planes are defined here that is the tangential plane t, t dash and then and sagittal plane ss dash and you see that if you let me read the remarks first and then we will come back to the description of the effect of this image quality effect of this defect on the image quality we will discuss after going through this remarks. Astigmatism is a defect in which the images of points of of the optic axis are drawn out into blood lines or discs. So like this this is the discs two discs we are talking about it increases with the distance from the optic axis and causes poor definition of images formed away from the axis. So as the distance increases from the optic axis the image quality also will go back. So let us now come back to this schematic again. So you have this what this the the line passing through this t, t prime form an image t it that is a tangential image and then the rays which are passing through ss prime plane form an image is. So you can see that in a tangential image the tangential lines are sharp and then radial lines are unsharped on the other hand if you look at the sagittal image that is this this ss prime plane image the radical sorry the radial lines are sharp and tangential lines are unsharped. So the circle of least confusion lies between these two images and the correction is done once these two circles are brought together but still the image will be lying on the curvature of the surface. You can appreciate that the the tangential image lie in a sagittal plane and the sagittal image lie in a tangential plane. So this is a very nice schematic to appreciate the defect of astigmatism and we will see the curvature of field the curvature of the image field arises from the change in focal length of the lens as the position of the point on the lens moves away from the optic axis and it depends on the lens geometry and refractive index. We will also see when we look at the correction of this objective lenses how this curvature of the image is also being taken care. The next defect is coma and distortion and before we look into the description let us look at the preliminary remarks coma causes the image of a non axial point to be reproduced as an elongated coma shape lying in a direction perpendicular to the optic axis. It is a form of asymmetrical spherical aberration affecting non axial object points. You can see that your non axial points are appearing as I1, I2, I3 and then this forms an elongated coma shape perpendicular to the optic axis like this that causes an image distortion and it is a kind of asymmetrical spherical aberration okay. The correction is achieved by figuring the lens surfaces so that the ratio of sine angle of incident divided by sine angle of emergent refracted ray is constant. We will discuss this again when we talk about a correction of lenses and the distortion which we have seen in the introductory slide of the lens defects is arising because of variation in the magnification with the distance of the object point from the optic axis that means the magnification is varying with the distance of the object from the optic axis that is from this optic axis as you move from the optic axis the magnification changes and it occurs in both objectives and eyepieces and more common in later and it is difficult to eliminate completely. So you have to live with some defects the next aberration which we are going to talk about is chromatic aberration it is very different from what we have discussed the previous ones arises when the light is non-monochromatic whatever the defects which we have discussed before you talk about coma or astigmatism or spherical aberration they they occurs when we use monochromatic radiation and this one that arises when the light is non-monochromatic you have to remember this is very important point. So let us look at the remarks when the white light is focused by a lens light of different wavelength is brought to focus at different distances from the center of the lens violet light being focused closer to the lens than the red light. So we are talking about the visible spectrum that means your violet light will have a different wavelength compared to the red light so they are all being focused at different different distances and it occurs because the refractive index of a transparent isotropic material is greater for light of shorter wavelength than for the light of longer wavelength this you already know and so the effect of this aberration is like if you have an image the periphery of your image is filled with a different color that means every color will focus at a different different focal point so you will see that the periphery of your image is filled with a color fringes it will appear like a color fringes we will see how to correct this So we will now summarize this lens defects and we will see how they are characterized or corrected based upon the different degree of corrections. So the objective the most important critical component in the optical microscope is made up of number of glass lenses and sometimes fluoride lenses also lenses are subjected to spherical and chromatic aberrations minimization and correction of these undesirable physical effects greatly aided by modern computational techniques is possible and objectives are classified according to the degree of correction that is a chromates fluorides they are also called semi apochromates apochromates like that lenses are usually coated in order to increase the light transmission. Now let us see some of the typical characteristic of objective lenses is stable here look at this table carefully as I mentioned depending upon the degree of corrections they are being classified and you see that yam is a magnification and this is a type of objectives and you have the medium and this is the working distance WD is a working distance in millimeter this is numerical aperture D minimum is the minimum resorbable distance this is depth of focus in meters and B stands for brightness. So you see that depending as the magnification increases and then how this values are changing okay and then you can also see that how the refractive index also influence the other parameters especially depth of focus and minimum resorbable distance and so on. So it gives you a broad idea about what kind of corrections we can make or we can take up and then probably I will just show you some of the correction which is made on a blackboard. So let us try to give one example how this correction is being made let us write like this different kinds of glass different relative dispersion dispersion mu. So let us in fact it is reciprocal reciprocal relative dispersion mu is defined as Nd-1 divided by Nf-Nc where Nd is refractive index of sodium d line and Nf is the refractive index of hydrogen f line Nc is the refractive index of hydrogen you can also note down this values 589.3 nanometers 486.1 nanometer 656.3 nanometers. So I am just giving you this because you should know how this correction is made and what is the basis these are all spectral values and then different kind of glass will have a different reciprocal relative dispersion mu which is defined by this formula and for example you can take you can take example a crown glass will have around 60 mu value of 60 and a flint glass will have the value of 38. So consequently these two lenses can be combined we will write these two lenses combined weaker diverging lens of flint glass so that chromatic abrasion cancels for certain lambda. So this is one case study how this correction is done in the case of chromatic abrasion there is a parameter called reciprocal relative dispersion mu and this value for characteristic of different lenses so for the crown glass it is 60 for a flint glass it is 38. So these two can be combined because with a weaker diverging lens of a flint glass and that will correct the abrasion chromatic abrasion for certain lambda so we can also draw some schematic how that corrected doublet will look like so you have this lens and then so this is a crown glass and this is a flint glass this is an a chromatic doublet. So I just gave an example how this corrections are being made it gives you an idea so similarly all those listed in that table follows certain procedures to take care of the kind of correction which is required or the degree of corrections which is required and based on which these subjective lenses are classified. So now we will move on to the next item that is eyepieces and oculars I just want to mention the important functions of these eyepieces we have talked a lot about objective lenses because they are very critical and important as I mentioned in the last slide. So let us have some idea about what these eyepieces are doing in a microscope they are also called an oculars and eyepieces have three main functions and they are to examine and magnify the primary image and they are also to correct the residual chromatic aberration and especially for photo micrography and they are to flatten the field of view with just which we have seen that is a problem and correct astigmatism. So these are the three primary functions of an eyepieces a single lens eyepiece would produce a cone of rays with an angle greater than that which the eye can accept so that the eye would be unable to view the entire field simultaneously consequently all eyepieces consist of two lenses the field lens and the eye lens there are several types of eyepiece depending upon the degree of correction required and the uses to which they are to be potent. So similar to objective lenses you have in eyepieces also have different types based upon the degree of corrections and as you know that depending upon the kind of sophistication one one require to build a microscope the combination of an objective eyepiece or ocular being selected if you recall that table which we have shown that you know the kind of useful magnification which produces the combination of these two apertures now you will get an idea how a quality of a microscope is decided and how these two lenses where objectives and eyepieces are being selected okay. So now we will move on to some other important parts of microscope I would like to talk about this few filters for adjusting the intensity and the wavelength of illumination look at this slide and for getting a full brightness illumination is also an very important aspect of it and if you most of you you will see that in some of the microscopes you will have lot of color filters just after the illumination source I am going to show you and you should know what are these filters doing so this is about that so look at this plot this is percentage transmission versus wavelength plot you have a short pause a band pause a long pause the name itself tells that the filters for isolating the wavelength of illumination short pause long pause filter sometimes called edge filters block or transmit wavelengths at a specific cutoff wavelength you can see that it is 50% cutoff it is peak transmission and the band pause filters exhibit broad band or a short band transmission centered on the particular band of wavelength here you can see that and this filter performance is defined by the central wavelength and by the full width at half maximum this is full width at half maximum so another term for full width half maximum is half band width so let us look at some more remarks on this filters neutral density filters regulate light intensity whereas colored glass filters and interference filters are used to isolate specific colors or bands of wavelengths there are two classes of filters that regulate the transmission wavelength edge filters and band pause filters edge filters are classified as being either long pause that transmit long wavelengths and block short ones or short pause which transmit a shorter wavelengths so I think this is a kind of introduction to these kind what are the filters and what are their primary functions are we will now move on to another important filter an interference filter look at this slide and what you are seeing is an action of an interference filter we will be using this filter in one of the variants of the optical microscope called differential interference contrast microscope so let us look at this function of this interference filter you have the incident wave coming here and some of them are raise are reflected are modified by interference and some of them are transmitted and we have to know how it is done correctly so you see that the two metallic layers are coated on the dielectric material in a such a way that they are optical path length is lambda by 2 so when the wave incident wave which comes and enters this filter perpendicular to the phase and only those wavelengths will be allowed to pass through and then rest of them will be reflected back since all the transmitted waves are in the phase they will be allowed to constructively interfere and then and becomes a transmitted wave so this is the function of these interference filter we will see the usage of this filter much more detail when we actually take up the variant of this microscope in the coming lectures let us see few more remarks on this filters interference filters often have a steeper cut in and cut off transmission boundaries than the colored glass filters and therefore are frequently encountered in a fluorescence microscope where sharply defined bandwidths are required interference filters are optically planar sheets of glass coated with dielectric substances in multiple layers each it could be lambda by 2 or lambda by 4 thick which act as selectively reinforcing and blocking the transmission of specific wavelengths through constructive and destructive interference this is what just I mentioned so this is about the interference filter we will now look at the another important parameter called optical path length we will be using this concept in one of the again another variant of the optical microscopy so let us see what is this optical path length the number of vibrations experienced by a wave traveling between two points in optics the optical path length OPL through an object or space is the product of refractive index N and the thickness T of the object or intervening medium so OPL is equal to N times T that is optical path length is a product of thickness and the refractive index of the medium if the propagation medium is homogeneous the number of vibrations of a wave of a wavelength lambda contained in the optical path is determined as number of vibration is equal to N times T divided by lambda the overall optical path length expressed as the number of vibrations and including the portions in air and in glass is thus described as number of vibrations equal to N1 T1 divided by lambda 1 plus N2 T2 divided by lambda 2 where the subscripts 1 and 2 referred to the parameters of the surrounding medium and the lens as we will encounter later on the optical path length difference between the two rays passing through a medium versus through an object plus medium is given by delta equal to N2 minus N1 times T so as I mentioned we will be using this parameter in one of the variant of the optical microscope which I will be discussing it that is why I have introduced this concept we will now see the general description of light microscope so what I have done is if you look at all the three classes I have taken some of the cons fundamental concepts which you required to understand before we get into the use this light optical microscope I hope it will be it was it will be useful to in order to understand the the functions of different variants of optical microscopes so now what I am going to do is I am going to just describe what a general light microscope does and I will just disc I will also take you to the lab and then show some of the videos of actual light microscopes which we have in our laboratory so let us look at the description of a light microscope why do we use this light microscope so examination in the as polished condition which is generally advisable will reveal the structure features such as shrinkage or gas porosity cracks inclusion of foreign matter and for that we need to do something called etching I will be dealing with it in much more detail when I when I talk about a sample preparation for all this microscopy techniques however you just look at the initial remarks etching with an appropriate chemical reagent is used to reveal the arrangement and size of grains phase morphology compositional gradients sometimes called coring orientation related edge pits and the effects of plastic deformation these are all only a some of the features which I have just mentioned but in reality we will see how how much we can use this or how effectively we can use this microscopic techniques for various applications in material science and and so on. So we have something called a bright field illumination light is reflected back towards the objective from the reflective surfaces causing them to appear bright and then you also have a dark field illumination reverses this effect and causing the grain boundaries to appear appear bright. So I will just take up this to I mean the actual microscopic part when we discuss a specific application and this is just to give you an idea of what kind of method even in a light microscope a basic imaging techniques one is bright field illumination another is a dark field illumination and the image quality is depending upon the degree of chemical attack is sensitive to the crystal orientation and an etched polycrystalline aggregate will often display its grain structure clearly. So we will also talk about this etching behavior we will see what is etching and then how it affects the image quality and so on in a in a coming class and this is just to give you an introduction about this microscope you have an objective you have the specimen here it is a schematic of an etched surface and you see that light is being reflected at a different orientation because due to their different orientation of the grain we will see actually the experiments. Now you can look at this references very important references you can follow for this course one is fundamentals of light microscopy and electronic imaging by Douglas B Murphy 2001 Wiley List International USA and second important reference optical microscopy of materials by Heinz 1984 international textbook company UK. You can also refer this inflexible video of material characterization surfaces interfaces thin films by Richard Brunel Choll's events and Shawn Wilson Butterworth's Raymond Pulf Heinzmann Boston USA you can also read this transmission electron microscopy by DB Williams and Barry Carter Springer USA for some of the basic concepts of optics then the physical metallurgy and advanced materials by R. E. Smallman and A. H. W. Nagan Elsevier publication you can also go through the website www.microscopy.com so now what I am going to do is I am just going to introduce you to the some of the microscopes what is coming on the screen is a typical metallurgical microscope. So one is there are two basic types of microscopes one is vertical type another is inverted type so what you are now seeing is an inverted optical microscope. I will just show some of the main parts which we have talked about like this is specimen stage this is a vertical since a vertical microscope it is a the specimen stage will be on the top and these are all oculars and eyepiece just we have we have now read about quite a bit on this how the eyepiece will appear and this is a CCD camera which is being attached to this microscope and these are all some of the polarizing lenses and apertures I will talk about this little later is one of the variants as I mentioned that time we will use this I mean apertures and you see that now the elimination is coming from the bottom and then you keep your sample on this light and what now you are seeing is an another vertical simple type microscope is a standard microscope in any of the metallurgical laboratory you see that ocular and you see objectives usually you will have 3 to 5 objectives is there and this is again another microscope which is attached with the image analysis system or it is having come interfaced with the computer you can clearly see that the objective lenses now as I mentioned you can also you are also observing that you know some of the letters are written on the objective which is which they talk about the magnification some refractive index and whether it is a oil or a dry all those informations are given on this objectives usually it is with it comes with 5x 10x 20x and 40x so and then sometimes 50x and you can it goes up to 100x also depending upon the microscopic system so this is a tool which is called a leveling press to make the solid specimen in a same level using this plasticizer so I am just describing this assuming that we will be using only the solid metal piece to examine under the microscope not necessarily the case we will see the other materials how it is being viewed in the other type of microscope optical microscope and this is how the solid metal piece is leveled using this a leveling press and then it will it will be placed on this microscope as you can see that I will get into the details of all this preparations in a separate class just I am just introducing how the microscope will look like and how people use it and for those who have not come across this kind of an experience so you can see that now the specimen is being loaded in this stage specimen stage and then you choose the appropriate I mean objective lens you can start with a lowest magnification to highest magnification you can slowly move from lowest temperature to the highest temperature and the magnification is multiplication of these 2 for example you have about 5x here and then here it is 10 so it is 50 if you choose 50 here it is 500 something like that so here again for image grabbing you have the CCD camera attached to this and now what you are now seeing this is another type of microscope is called transmission optical microscope which is very different from what you have just seen before that is one is vertical another is you know inverted microscope you have here you have 2 type of illumination attached to it one is mercury lamp and another is halogen lamp on the top so I will just describe this microscopic parts so that you will get familiar with what are the important things you need to understand what is that being shown here is it is a polarizer and when you do not use that polarizing mode then it will be a slot for a bright field mode and then you also have a kind of a condenser aperture lenses in this which is having a different different I will talk about it in much more elaborately in the next class thank you.