 I welcome you all for the series of lecture. We will start module 9 on Interferometry. In this module, we will be learning about basics of interferometry, that is, what is the interference phenomena, how it happens, what are the theories of flight and how do we obtain the fringes, what are the different shapes of fringes depending upon the type of workpiece and then we will be studying about different types of interferometers and then what are the building blocks of interferometers, what are the different elements by which interferometers are made and what are the various applications of interferometers and what are the various light sources used in the interferometers and then we will move on to the discussion on different types of interferometers like NPL, flatness interferometer, pitter NPL engage interferometer, laser interferometer and then we will discuss about some of the commercial interferometers. Now let us start module number 9, lecture 1. In this lecture 1, our discussion will be focused on the basics of interferometry. We will study about theories of flight and then how the interference phenomena occurs, what are the conditions suitable for the occurrence of interference, what type of fringes we obtain depending upon whether the workpiece is flat or cylindrical or spherical and then we will list some of the available interferometers and then we will study on construction of interferometers, what are the various elements used to build the interferometers and what are the applications also we will see and what are the sources, light sources used in interferometer. These things we will discuss in this first lecture. Now let us start the introduction on the interferometry. Now we will study what is the interference phenomena and how it occurs when two light waves interact with each other that means we have to consider two light waves and when they interact with each other the wave effect leads to a phenomena called interference of light. Instruments designed to measure the interference are known as interferometers. Now what are the applications of the interferometry? Application of interference is of utmost interest in metrology. Interference makes it possible to accurately compare surface geometry with the master. So they are used to compare the surface geometry with the reference surface which is an optical flat is normally used as a reference surface. Microscopic magnification enables micron level resolution and for carrying out inspection or calibration of masters and gauges. Using the interference phenomena it can calibrate the masters and gauges. Lasers are also increasingly being used in interferometers for precision measurement. That means nowadays laser based interferometers are available commercially which are used for metallurgical purposes. Now what are the theories of light? Now light is a form of energy. It is transferred from the source of light to the eye either by motion of material particles or by means of wave disturbance traveling through a medium. Now we have two theories of light. One is emission theory of light proposed by Newton in the year 1975. According to this emission theory a light source continuously emits tiny light weight particles called corpuscles in all directions. You can see here this diagram we have a light source here which is emitting a tiny light weight particles in all directions. These tiny particles move with the light velocity when these particles fall on the retina they produce the sensation of vision. You can see here we have the eye on which these tiny particles fall and then we get the sensation of light. Now there is another theory called the Huygens wave theory proposed by Huygens in 1679. According to this theory each point in a source of light sends out waves. You can see here the light moves in the form of sinusoidal wave like this sends out waves in all directions in hypothetical medium called ether. So for the moment of these waves some medium is called and ether is assumed to be the medium. Ether was assumed to be continuous medium which pervades all space. The existence of ether was assumed since the propagation of a wave motion requires some sort of medium. Now you can see a light wave here which is moving in this direction. So the distance between this any two consecutive points on this wave is termed as wavelength and it is denoted by lambda and this height is the amplitude of light. Now very commonly we used a term called wave front in the interference phenomena. So let us understand what is the wave front. So there are different kinds of wave fronts spherical wave front cylindrical wave front plane wave front depending upon the shape. Now when the light spreads from a point source o we can see here we have a point source o here and light is spread in the wave form in all direction. The light waves travel with the same velocity in all directions. All the waves they move at the same speed in all directions and they arrive simultaneously at all points laying on the sphere having o as sector. If we assume a sphere here with center o with diameter ca then all these waves arrive at this circumference at the same point. So then this front is known as spherical wave front. Now let us assume that the source of light and a form of linear shape o o dash. If this is the case then in all isotropic medium wave front takes the cylindrical shape. So we get the waves from this source we get the wave from this source and they will be moving in all directions. Then this front of waves is known as cylindrical wave front. Similarly we can assume a point source at an infinite distance. If a point or a linear source is based at infinity then the portion of the spherical or cylindrical wave front in a limited region is simply a plane and it is termed as plane wave front. Now let us try to understand Eugene's principle of propagation of wave front. Now each point on the wave front you can see here we have a point source 4 and we are getting the waves they move like this in all directions at the same velocity. This is one wave front, this is another wave front and the radius of this wave front is getting changed with time and here we have a wave front a b. Now each point on a wave front acts as a center of new disturbance. Now if we keep a screen x y in this path of light with a small hole yes is the pin hole. Okay so now the light will pass through this pin hole so this becomes this pin hole becomes another source of light and again we get light from this point yes and again we get the spherical wave front. Each point on the wave front now we consider yes on this wave front a b. Each point on the wave front acts as a center of new disturbance and emits its own set of spherical waves. You can see here yes is the new source of light and we get spherical wave front with this as the center emits its own set of spherical waves called secondary wavelets. So this a b is the primary wavelet and this c d is the secondary wavelet. These secondary wavelets travel in all directions with the velocity of light so long as they move in the same medium. As long as the medium here and here remains same these light waves move in the same velocity. The radius of these wavelets increases with time which we can observe here. The radius is changing with time. Now let us try to understand the interference phenomena of light. Now when two light waves superimpose now we can see here in this diagram we have a source of light. Yes is the source of light and we are getting the primary spherical waves and at this point we have a screen say this is a a b. a b is the screen which is having two pinholes s 1 and s 2. Yes is the pinhole and this is the source of light. s 1, s 2 two sufficiently closed closed pinholes or narrow slits. This s 1, s 2 they can be pinholes or they can be narrow slits. So here from s 1 we get secondary wavelets and from s 2 also we get secondary wavelets and they are getting superimposed in this region. When two light waves superimpose then the resultant amplitude or intensity in the region of superposition. This is so this is the region of superposition. The intensity of the resultant wave is different than the amplitude or intensity of individual waves. This modification the distribution of intensity in the region of superimposition superposition is called interference. Now the primary wavelet from s 1 will have some intensity and the secondary secondary wavelet from s 1 and secondary wavelet from s 2 they will have certain intensity. When they get superposition the intensity level changes. So this phenomena is known as interference. When the resultant amplitude is the sum of amplitudes due to the two waves the interference is known as constructive interference and when the resultant amplitude is equal to the difference of two amplitudes then the interference is known as destructive interference. Now in this diagram we can observe here the light intensity is increasing you can see here we have placed the screen xx here in the path of light. So this is screen xx and we can observe intensity distribution of the resultant wave. So when the two waves intensity of two waves added we get constructive interference and we get a bright region here. When the intensity of two waves they get subtracted we get a destructive interference and we get a dark band. So like this we get a fringe pattern we get bright area followed by dark area followed by pretty like this. So we get a pattern of fringes. Now the constructive interference and the destructive interference are detailed here. So we have a source of light oh this is the origin oh from where we are getting the two waves A is one light wave B is another light wave since the source is same they have same wavelength but amplitudes are different. See YA is having an amplitude of oh yeah wave A is having an amplitude of YA and wave B is having an amplitude of YB. When they combine to increase the if they are face that means you can see here the starting point is same and they are in face they are moving on the same side of this reference line we say these two waves YA and B are in the face then the resultant wave R will have an amplitude of YR. So this is a constructive interference. Now we will see the another case varying the two waves A and B are out of face by 180 degree even though they start at the same point they are out of face by 180 degree which is nothing but of a wavelength. So we have the wave A with amplitude YA and we have wave B which is out of face with respect to wave A by 180 degree and B is having the intensity YB. Now when they are out of face then the intensity of the resultant wave R reduces and the intensity of the resultant wave is YR. If YA and YB values are same then amplitude becomes 0 that means complete interference occurs and hence we get darkness. So that is what we observed here. So this is the constructive interference wherein we get bright area and this is the destructive interference where we get dark area because of complete interference. Now let us learn some more things about the Fringe formation. Now you can see here we have a screen YAB and this is the light source and from here we are getting the light waves. So these are primary wavelengths from light source L. So here we have a pinhole A and pinhole B. So from A we are getting secondary wavelengths from B also we are getting the secondary wavelengths. At some distance there is a screen which is placed parallel to the screen YAB. Now rays YA and B from the same source they have the same wavelength. At 0.01 on the screen the two rays are converged. It means the ray from A and ray from B they travel in this media and they are getting combined at point O1. Since A O1 is equal to B O1 the distance A O1 is equal to B O1 the two rays will arrive at O1 in phase and at this point we receive the highest illumination and hence we get a brighter spot here. Now let us consider what happens at point O2. At O2 distance A O2 is less than distance B O2 and if B O2 minus A O2 which is nothing but the optical path difference if this optical path difference is equal to odd number of wavelength that means 2n plus 1 times lambda by 2 then the waves will be 180 degree out of phase and the complete interference occurs and hence we get a dark spot at O2. So here complete interference occurs and we get dark spot. Now let us study what happens at O3. If B O3 this distance B O3 minus A O3 is equal to even number of off wavelength then the rays are again in phase and point O3 receives a maximum illumination hence we get a bright spot at point O3. So like this we are getting alternate bright dark bright spot dark spot like this. So this happens on both sides of O1. The process repeats both above and below O1 and alternate dark and bright light areas that is fringes are formed on this screen. Now again the fringe formation is shown schematically here. We have a monochromatic light source and then we have a screen with two slits. Say this is a slit S1 and this is a slit S2 and at some distance we have a screen is placed here and we are getting light waves secondary wavelengths from S1 as well as from S2. Now we can observe here in this region the two secondary wavelengths from S2 and S1 they are constructive in nature hence they are getting a bright spot here whereas in this area the two wavelengths from S1 and S2 they are out of phase one by 180 degree. So destructive interference happens and we get a dark band here. So like this alternate dark and dark band and light band we are getting and hence we get a fringe pattern as shown here. This is the light source and the screen with the two slits S1 and S2 and on this screen we are getting the fringe pattern. Now let us study about the conditions which are suitable for the interference of light. So when do we get the fringe pattern what are the conditions are suitable for getting the fringes so that we will study now. Now the separation between the two sources should be small. Now from this diagram we can understand that we have a light source S from which we are getting the primary wavelengths and in the screen AB we have two pinholes S1 and S2 separated by a distance 2D. This 2D should be very small. When 2D is small the fringe width that is D lambda by 2D where D is the distance between the screen AB and screen XY and 2D is the distance between S1 and S2. So when the 2D is small the fringe width D lambda by 2D is large and the fringes are separately visible. On the other hand if 2D is large fringe width will be small and due to the limited resolving power of human height the fringes will not be separately visible. They will be very close and will not be able to identify the or will not be able to count the fringes. Second condition is the distance D between the two sources and the screen should be large that means the distance between the screen AB which contains two slips and the screen XY on which we get the fringe pattern should be large. When D is large fringe width is large and hence they are separately and clearly visible and the third conditions for the observation of interference is the background should be dark so that we can clearly observe the fringes. The typical values for small D and capital D are shown here for 2D should be 0.5 millimeter or 1 millimeter or 2 millimeter so like this the 2D should be very small whereas the capital D should be of the order of 1 meter or 1.5 meter so that we can clearly observe the fringes. Now we can see here the fringe pattern now we get the light from the monochromatic source so part of the light will be reflected from the surface and part of the light is passed through the medium and then again it is reflected from this surface. Now we can have an optical flag for this reference surface and this can be the surface devotees whose surface is to be inspected. Now we have to combine these two waves and then when we combine we get the interference pattern subjected to this condition that means the reflected light says reflected light L1 and this is reflected light L2. The path difference there is a path difference between the path length of L1 and L2. The L1 distance is this much whereas the reflected light L2 will have an additional length of this so this is the path difference. If the optical path difference is equal to even number of wave length that is 2 lambda by 2 or 4 lambda by 2 or 6 lambda by 2 like this then we get a bright band. So this is the constructive interference between the two wave frames or two waves is constructive in nature and the amplitude will be maximum and we get a very bright spot as shown here. Now at this place so again say this is the so we consider at this point this is the light from the source and then we get a reflected light. The light is reflected from this surface and then this is the transmitted transmitted light and then the light is reflected so we get two lights here one L1 and L2. If the optical path difference between these two waves is equal to odd number of of wave length that is destructive interference happens and then the the amplitudes of the two waves they get subtracted and we get a very minimum light intensity at this point and then we get a dark band here. So in between again we have a monochromatic light source and reflected lights. If the path difference between the two wave frames is equal to even number of of wave length then we get a bright spot maximum intensity and bright spot. If the optical path difference is equal to odd number of of wave length then we get a minimum intensity and dark band appears. So like this we get a fringe pattern. So this type of fringe pattern we obtain if the surface to be inspected is flat. Now how we can use this phenomena for meteorological application. So the interference of light using the interference of light we can always test the surfaces for flatness. Now you can see here this is the nominally flat surface and this surface we need to inspect whether it is flat or not. For this so this is the arrangement we use an optical flat. So the bottom surface of this optical flat is the reference. So this these optical flats they are discs of stress free glass or quartz and sometimes both the surface or sometimes only one surface which is indicated by the arrow. So these surface are ground, lap and polished and they are available in different sizes from 25 millimeter diameter up to 300 millimeter diameter. Now using this optical flat and monopromatic light source they can get the fringe pattern and the fringe pattern will tell us about the flatness of the surface which is under test. Now what we have to do is we have to keep the surface which is to be inspected and on the surface plate and then we have to keep an optical flat of suitable diameter over the surface to be inspected. So normally there will be a small gap between the optical flat and the workpiece under test. At one point there will be a contact, at another point there will not be a contact because of maybe the flatness variation there will be a small angle between these two surface which is indicated by theta. Now you can see here we have a light source monopromatic light source and we get the light wave so which is shown here this s is the light source. So now it will be in the wave form. Now this light will fall on the bottom surface of the optical flat and part of the light is reflected back as shown here and part of the light will be transmitted so this is the transmitted light. So this light transmitted will fall on the surface to be inspected and then again it is reflected back and it takes this path. Now we have two light waves these two are combined at the eye. Now if the optical path difference you can see here this light incident light ray it is falling at point here and from here we have a reflected light and we have another light which will which part of the light is transmitted and it takes this path A, B, C and then it will combine at the eye. Now between these two light waves there is an optical difference of A, B, C. Now if this optical path difference is equal to odd number of off wavelength that is 1 lambda by 2 or 3 lambda by 2 or 5 lambda by 2 like that then the complete interference occurs and then a dark band will appear which we can observe here a dark band appears here. Now we will consider as another point where in again we have a light from a monochromatic source and the light is passed through the optical flap it is reflected from the point D and the reflected light will move in this direction and part of the light is transmitted and it will take this path D, E and from E it is reflected and if you take the this path and these two waves are combined here and again if the optical path difference is equal to odd number of off wavelength again a dark band will appear here. Now in between again there will be light source and light is reflected from this point and light is reflected from this point. Now let us assume that the optical path difference here is equal to even number of off wavelength that is lambda 2 lambda by 2 or 4 lambda by 2 or 6 lambda by 2 like that then the intensity of the resultant wave will be maximum and then we get a bright light band here so like this they get a fringe pattern so this shows an optical flat and these optical flats are commercially available in different sizes. Now this shows the formation of dark fringe and bright fringe so this is the workpiece to be inspected and this is the surface which is to be inspected for flatness and this is the optical flat and there is a wedge shaped air cushion between the optical flat and the work to be inspected. Now you can see here this is the monochromatic light source and we are getting the incident light ray and then it is getting reflected from this point and it is transmitted and again reflected. So, here we can observe the optical path difference between these two, between these two waves if it is equal to odd number of wavelength then the dark complete interference happens and dark fringe appears and you can observe that in this region the two waves they are out of phase and hence a destructive interference happens and at this point again we have the light source reflected light a second reflected light and in this region you can see the two waves they are constructive the interference is constructive in nature and we get a bright fringe the reason is the optical path difference here is equal to even number of wavelength. Now we must understand that if angle theta increases that means we have the workpiece to be inspected and then we have the optical flat placed on the surface to be inspected and this is the angle theta. If the angle theta increases fringes are brought closer together say we have for this particular value of theta say we get the fringes like this so this is the fringe pattern if this theta increases say so this is theta 1 and now it is theta 2 which is greater than theta 1 then the fringes will move closer together like this. So here you can see here the distance between two fringes is more for this theta 1 when theta is increased we are when theta 2 is greater than theta 1 the distance between the fringe is reduced and if theta is reduced surfaces become nearly parallel and fringe spacing increases. Now let us consider another case wherein we have theta 3 theta 3 which is smaller than theta 1 that means they are almost parallel then the fringe distance will be large like this fringes move away. Now what happens if the surface to be inspected and the optical flat surface if they are parallel and there is no and the surface to be inspected is almost flat then we do not get any fringes so this is the ideal case. Now these optical flats are manufactured with great care so that we get a very fine and flat surface. These optical flats should be handled with care the work surface and optical flat surfaces should be cleaned with a soft cloth before they are used and never we should never ring two optical flats together or if we ring them together then the separation becomes very very difficult and the flatness of optical flats will be a fraction of a millimeter micrometer. Now let us see how we can check the slip gauge surface for flatness you can see the slip gauge is placed on the flat surface and an optical flat is placed over the surface of the slip gauge which is to be inspected and the complete set that is the slip gauge an optical flat is placed in a chamber where we get monochromatic light source. Now we can see the set of slip gauge and the optical flat from the top surface from the top you can see how when they rotate the optical flat how the fringes pattern changes by rotating the optical flat we can always make the fringes to be parallel to one edge and when they angle between the surface for surface and optical flat surface changes you can see how the number of fringes change or the pitch of fringes changes. Now we can see how the flatness of an anvil surface of a micrometer can be tested by using interferometry the micrometer is held vertically and on the anvil the optical flat is placed and when the complete set is placed under a source of monochromatic light we can observe the fringe pattern now we can see the fringes are almost parallel and they are straight which indicates that the surface of the anvil is flat. Now depending upon the workpiece surface we get different shapes of fringes so that is assumed that when the work surface is flat for example the flat surface of a slip gauge then we get the fringe pattern like this and if the dark band and white band they are parallel to each other straight fringes we get when the surface is spherical when the surface is spherical like this then we get the fringe pattern like this concentrated circles we get and when the surface of the workpiece is cylindrical in nature then we get the fringe pattern like this. Now let us start the discussion on various types of interferometers so commercially the following types of interferometers are available michelson interferometer, diamond green interferometer, fabricated interferometer and the interferometers developed by national physical laboratory that is npl flatness interferometer which is used to check the flatness of gauge blocks and then pitter npl gauge interferometers are available and recently laser based interferometers are also available some of these types we will discuss in the next lecture. Now let us study what are the various elements used in interferometers now we can see here a beam splitter which splits the beam into two parts I can see here we have a beam splitter here incident beam and then the incident beam is made to fall on the splitter part of the incident light is reflected and part of the incident incident light is passed through the beam splitter now here we can see a clear glass and the light will easily pass through that and this clear glass plate will not act as a beam splitter and here when the glass plate is coated with silver part of the light is or full full light is reflected now when the glass plate is partially silver part of the incident ray is reflected and part of it will pass through the glass plate now you can see some of the commercially available beam splitters a glass plate which is partially silver and glass cubes are also available so incident light is partly allowed to pass and partly reflected now different light sources are used see what happens if we use daylight which consists of the different colors you can see here each color will have a different or a range of wavelength so we will not be able to get a very clear fringe so monochromatic light source are developed which will have a sharp wavelength mercury 198 cadmium source krypton sodium helium gas lasers are developed and these like monochromatic light sources are used in making of interferometers and different optical lenses are used to manipulate the path of the light collimating lenses are used and these lenses are used to produce parallel rays of light we can see here we have a light source we get light in this fashion and we want to make them parallel we want to get a parallel beam of light in such cases we use collimating lens and sometimes we have to make the parallel beam of light to fall on a particular point in such cases we go for condensing lenses these lenses gather and concentrate the light in a specified direction now moving mirror is sometimes used in the fabrication of interferometers and workpiece compartment is very essential wherein we get the monochromatic light source and there is a arrangement to keep the workpieces and optical flats so that we can observe the fringe patterns and a detector is mounted at the appropriate place of the interferometer so that we can observe the fringe pattern and we can count the number of fringes computers are used to measure the signal and measure the signal is distanced and sent to the computer for processing of the information optical flats are used to have the interference phenomena and fixed mirrors are also used to deviate the light scales and readings are also used for measurement purpose we can see here an optical flat made out of glass or quartz and here you can see an optical bench and we can see the stands for keeping the various elements like mirrors and then light sources beam deflectors detectors etc etc we can see here a lot of arrangement is provided to adjust the orientation of light source or the mirrors or lenses screws are provided by operating these screws so we can tilt the mirrors or light sources and we can also adjust the height of mirrors or adjust adjust the height of light sources etc etc now let us conclude the lecture one in this lecture we discussed about the different theories of light and the phenomenon of interference of light and how do we get the fringe pattern and what is the shape of fringe pattern we get depending upon the type of workpiece and then the different we listed the different interferometers like APL interferometer laser based interferometers etc and we also discussed about the various building blocks like mirror light sources lenses etc which are used to build the interferometers and we also discussed about the application of interferometer for flatness testing and what are different light sources used in interferometers so with this we will conclude this lecture we will continue the discussion on interferometry in the next lecture thank you