 Welcome back to the lecture series on metrology, now we will start module number 12 lecture 7. In this lecture we will cover the following topics, limitations of atomic force microscopy, measurement challenges associated with AFM and large area AFM calibration of AFM and finally we will start the discussion on optical system design. Now in the previous lecture we discussed about the construction and working of atomic force microscopy. Also we discussed about the applications of AFM. Now let us study what are the limitations of atomic force microscopy. The major limitation is the scanning area. It can image a maximum height of the order of 10 to 20 micrometer and maximum scanning area that is x axis and y axis scanning size is 150 by 150 micro meter. The travel range of XY sample stage is 20 millimeter by 20 millimeter and z axis movement is limited to about 20 millimeter. The scanning speed of AFM is another important limitation of this device. A maximum scan range of 40 micron by 40 micron capable of scanning 5 microns by 5 micron area takes about 5 seconds to scan this much area. So the scanning speed is very slow. Also the functioning of AFM is very much dependent on the cantilever and probe design, the size of the probe tip, the material of the cantilever. So very precise cantilever and probe are needed to get meaningful measurement results. The sample size can go up to 50 millimeter by 50 millimeter and height 20 millimeter. If the workpiece size is greater than this, then it may not be possible with the regular AFM devices and currently large area AFMs are designed which we will discuss after a short while. Now what are the measurement challenges associated with AFM? The calibration, quantification and understanding of different modes of working of AFM is a big challenge. So we should properly understand the different modes of operation like force spectroscopy mode, multi-frequency modes, frequency modulation mode, lateral force and objective modulation mode. Properly we should select the mode depending upon the application and obtaining valid additional information from AFM is another challenge. And imaging soft samples at high resolution with a minimum damage to the surface is another challenge. The reason is we are using a very sharp probe tip with 20 to 800 millimeter tip radius. So there are chances that the tip may scratch the surface. So imaging the soft samples is another challenge associated with AFM. Another big challenge is the necessity of vibration free stage requirement. If there is a vibration of the stage then all the measurement results will not be meaningful. Now we can see an image obtained by AFM. This is the glass surface, clean glass surface. The scanned area is 6 micrometer by 6 micrometer and the roughness of this glass surface is 0.8 nanometer. Now we have another image, three-dimensional image of ultra high speed face milled stainless steel surface. You can see the scanned area is about 80 millimeter by 80 micrometer by 80 micrometer. Now the conventional AFM, they have very limited scanning range. So recently large area, atomic force, microscopes have been devised, where the area of scanning is as large as 10 millimeter by 10 millimeter. You can see the schematic arrangement of large area AFM. This is the cantilever with probe attached to the BZT, Z axis BZT. And this is the table X axis of the sample table and the specimen is placed on the table. D is the distance, that is the obey offset, the height of the workpiece surface from the reference axis and delta is the displacement of the Z axis. L is the length of the Z actuator and delta is the displacement of the Z actuator. And Z actuator stroke of 100 micrometer is possible in large area scanning AFM. So again you can see the errors in AFM. So the Z actuator may tilt as shown in this, the cantilever may also tilt and then the table also can tilt. You can see the tilting of X axis because of this the measurement results are affected. So we should compensate for these angular errors by using appropriate sensors. Now you can see here the capacitive sensors are used for compensation of the angular errors. So this is the Z actuator and two capacitive sensors are used for compensating the tilt of the Z actuator. And to compensate the tilt of the table surface, X angle sensor and Y angle sensors are used. And we can see the photographic view of the large area AFM. This is the PZT actuator and two capacitive sensors are used. And then we have the AFM cantilever and this is the stage, sample stage and the sample based on the sample stage. Now this picture shows a complete system of large area AFM. This is the manual jet stage depending upon the height of the workpiece. Initial adjustment of Z axis is made manually and this is for coarse adjustment of tip height. And then we have the specimen and this is the linear motor driven X stage and we have stepper motor driven Y stage. And the raster scanning is possible by moving its hand by stage. And the spiral scanning is also possible by using the rotary stage as shown here. And normally air bearings are used in these AFMs with linear encoders for feedback purpose. The resolution of such a system is about 0.2 nanometer. I can see the block diagram of large area AFM. We can see the X by stage with appropriate drivers. And then this is the stage table surface on which a specimen is mounted. And this is the cantilever with the probe and the measurement results are sent. There is a feedback system and this is the PZT driver and capacity sensor is used for compensation purpose. Now how do we calibrate the AFM? So there are different methods available. In the theoretical method, the cantilever force constant is calculated from the beam mechanics using elasticity theory. So this requires a very accurate knowledge of dimensions of the cantilever that is length width thickness of the cantilever and X modulus of material of the cantilever. Other method is dynamic method in nature. The cantilever force constant is obtained by analyzing the resonance frequency of cantilevers. So third method is the Wetsch method in which both normal and lateral force responses of the cantilever are studied during friction measurements on slope surfaces. So this way also we can calibrate the AFM. A very important method of calibration is by comparison. That means a known force is applied to the cantilever. They are defects and the measured force, the value given by the sensor is compared with the applied force. Thereby the calibration of the AFM is possible. Now for detailed discussion on atomic force microscopy, one can go through the NPETEL course by Professor Ormukherji from IIT Kharagpur. The topic of the course is instability and patterning of tin polymer films. Now with this we will close the discussion on AFM and we will start the discussion on optical system design. Under this we will discuss about the requirement of precision optical systems. What are the different types of optical lenses used in optical systems and then the lens design defects in lenses and then what are the mounting errors possible when we mount the lenses in the barrels and what are the different kinds of optical coatings used and how do we mount the lenses, what are the arrangements possible and then we will discuss about the lens assembly and cementing of lenses, the manual and automated aligning and bonding processes and then we will discuss about complex optomechanical assemblies. Now let us start the discussion on precision optical systems. Now we would understand that an optical system is basically a combination of different types of lenses, mirrors and prisms creating the optical part of an optical instrument such as a microscope or a camera or a telescope. Now there is an ever increasing demand for high performance lens assemblies as optical systems. The lens assemblies are becoming more and more complex and sophisticated, newly emerging life sciences and medical optics applications such as distal pathology, DNA sequencing and photolithography. They require high end objectives with highest levels of resolution and sensitivity. I can see here a part produced by photolithography, an array of micro holes has been made here with the whole diameter of about 25 microns. Now in order to make this, it is very essential that we need a very sophisticated optical system during the exposure process of photolithography so that we get a fine array of holes. Now the lens systems must provide an extremely high level of performance such as high numerical aperture, large field angles, broad spectral bandwidth and perfect wavelength correction. So this requires, this makes lenses highly sensitive to all sorts of manufacturing errors especially to lens alignment and ear spaces during assembly. So there is a challenge not only to create compatible lens designs but also to manufacture and assemble the lenses properly so that the desired level of performance is obtained. Now these pictures show the commonly used types of lenses, the bi-convex lens wherein it has two convex surfaces and the center it is bulged. Plano convex lens, one the surface is flat and other one is convex. Positive meniscus, negative meniscus and a plane of concave where in one the surface is plane and other one is concave and then we have bi-concave lenses. So these different types are not very used in optical systems. Now when we design an optical system we should understand some basic terminologies. So focal length is one basic terminology associated with the lens design. The focal length is a measure of how strongly the lens converges or diverges the light. For a lens working in the air medium it is the distance over which collimated rays are brought to focus. You can see here in this diagram we have a bi-convex lens, optical lens and one side we have incident light rays and these light rays are brought to focus at point F and the distance between the point F and the center of the lens is known as focal length. A lens with a shorter focal length has greater optical power than one with long focal length. That means the lens with shorter focal length bends the rays more sharply bringing them to focus in a shorter distance. So this diagram shows the focal length of a simple convex lens. Parallel rays of light entering the lens are brought to a point focus at F. So F is the focal length. A small focal length gives a wide angle view and a large focal length gives teleview and in case of microscopes lenses with a small focal length are used and in the case of telescope large focal length lenses are used. Now numerical aperture is another important terminology associated with optical system. It is numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept the light. The numerical aperture is calculated using the relationship n times sine mu where n is the index of refraction of the medium in which lens is used and the value of n for here is 1 and for pure water it is 1.33 and mu is half a cone angle. In the microscopy numerical aperture indicates the resolving power of a lens. The size of the finest detail that can be resolved is proportional to lambda divided by 2 times nA where lambda is the wavelength of the light. A lens with a larger radius will be able to visualize finer details. You can see here we have three lens systems. In the case of lens system A the half cone angle is 7 degree and numerical aperture is 0.12. As the numerical aperture value increases the half cone angle value also increases. That means a lens system with larger nA will accept more light and it gives a brighter image. Another important thing is as the value of nA increases the distance between the objective and the sample reduces. Now what are the defects in lenses? There are some constructional errors. So when the parallel ray of light impinged upon the lens perpendicular to the plane of the disc the lens bends the light rays so that the light rays come to focus. For example, this is the lens and this is the axis of the lens. The light ray will be bent and it is made to focus at a lens which effectively focus the light forms a clear image and appropriately fulfills its role in a telescope, microscope or a camera. However, the lens has defects of construction that is the curvature is not proper there are some improper curvature or the material of the lens is inhomogeneous then the images will proportionately suffer and a blur image will result. Now you can see here how the grinding of curvature on lenses is made. We have a spherical lens and this is a curvature is there on the lens and the light rays are falling on the curved surface of the lens and the light rays are made to focus. From this picture we can understand that this is the center of the lens. Light rays entering the lens at a greater distance or nearer to the edge of the lens are made to focus at a shorter distance from the lens surface whereas the light rays entering the lens very close to the center are made to focus at a larger distance from the lens. So because of this a focus shift happens and the image will not be clear. So in order to get a clear image we need to provide a spherical curvature on the lens and the details of the spherical curvature is shown here it has a special curvature as shown in this diagram. So because of this spherical nature all the light rays are made to focus at one point and we get a very sharp image. Now how these spherical curvature is provided on the lens as you can see here this is the lens blank holder this is the glass lens and this is the grinding stone which grinds the surface of the lens. This is the workpiece which is rotating and to provide the required curvature a template is used and there is a guide rule and the diamond cutter will move on the glass surface and it grinds the required curvature on the glass surface and hence we get the curvature on lens. When we use spherical lenses a focus shift occurs and this is known as spherical operation and due to this spherical operation a blurred image results. There are two ways in which we can eliminate this spherical operation. So first method is blocking the edges of lenses that means we can block the edge of the lens so that the focus shift is minimized and other method is a skillful combination of different lenses so by combining lenses skillfully we can eliminate spherical operation and we can get a clear image sharp image. Now the chromatic operation the lens bends some colors of light more sharply than others so in this diagram we can see the blue rays are more sharply bent we can see the focus point very close to the lens surface for the blue rays and for the red color rays the focusing is at a further distance. So this is known as chromatic aberration so this chromatic aberration occurs longitudinally as well as laterally. So by using a chromatic doublet that is a combination of two lenses of different glass materials this chromatic aberration can be correct. Now the chromatic aberration this occurs when light rays from a distance impinge upon the lens at an angle that means we have a point source here and the light rays from point source are falling on the lens surface. The result is a comet like figure with a tile appears as shown here so this is known as chromatic aberration so proper grinding of lens eliminates this problem. Now during the mounting of lenses in the barrel errors can occur these are known as mounting errors so different types of errors are listed here. So first one is translational displays under the lens that means the axis of the lens is not coinciding with the axis of the barrel so this is known as translational error or centration error. Another type of error is tilt of a lens so you can see here the lens is tilted so because this also the image quality is affected surface tilt error so if you see sometimes what happens the lens is seated properly but surface is tilted it's not manufactured properly that is surface tilt error and then the cementing error if you see here two lenses are cemented bonded together so when the two lenses are bonded the axis of these two lenses may not coincide that is known as cementing error and tilt of a spherical axis so we have a spherical lens here the axis of the lens is tilted and then there can be air gaps between two lenses because of these errors the image quality will be affected. Now the centration errors of lenses the precise centration and alignment of lens is essential to get the quality image the centration error occurs when the optical axis of lens do not coincide with the reference axis so you can see here this is the axis of the lens and this is the axis of the barrel in which the lenses are mounted so because of this shift this movement of the lens this gap is known as centration error so proper care should be taken to eliminate the centration error so the centration error occurs when cementing, aligning and fixing lenses in the barrel so precise centering can be met if all the manufacturing steps are designed and incorporated into one measurement and manufacturing system. Now here we have a set of pictures the photographic examples showing the high quality lens when we use high quality lens the image quality will be like this and if we use a lower quality lens the result will be like this we can see here a blurred image and a rainbow edge so a rainbow edge is appearing so such a blurred image will be the result if the quality of lens is not proper. Now this assembly of lens we can observe here by using a series of lens lenses assembled properly we can correct the operation error so this is a very compact assembly of a objective miniature objective with minimum operation the numerical aperture of this objective is 0.51 and the diameter of lenses is 5 millimeter diameter. Now let us discuss about optical coatings some layers of materials are applied on the lens surface to change the reflectivity of the surface and to change the transmittivity of the lens surface. Now the simplest optical coatings are thin layers of metals such as aluminum which are deposited on the glass substrates to make mirror surfaces so this process of applying material on lens surface to make it mirror is known as silvery. Aluminium is the cheapest and most common coating and yields a reflectivity of around 88 to 92 percent so other important material that is applied on glass surfaces to make to improve the reflectivity is the silver which has a reflectivity of 95 to 99 percent. Now in this picture I can see some of the lenses coated with some coating materials now here we can see a lens substrate glass lens and then a hard coating is provided to make it scratch proof and you can see multiple layers are applied on the hard coating surface and these are anti-reflective layers to increase the transmittivity of the lens and to reduce the loss of light rays in the form of reflection and finally you can see there is another coating hydrophobic layer is applied to make the surface water resistant. Now here we can see a bare lens no coating is applied and a light ray is impinging on the surface of the lens some portion of the light is reflected back and most of the light is refracted it is passed through the glass surface and when the refracted light reaches impinges the other surface again splitting that takes place and some portion of the light is reflected back and some portion leaves the glass and enters into the air. Now this reflected light reaches the right side surface of the lens that is this spot and again it undergoes splitting some light is reflected back and some light is refracted and enters into the air. Now this reflected light rays are lost light rays so due to the loss of these light rays the brightness of the image that is formed reduces. Now this reduction in the brightness of the image is known as pixel noise. Now to reduce the loss of light that is to reduce the reflecting reflection of the light rays from the lens surface anti-reflective coatings are applied on the lens surface normally magnesium fluoride with refractive index of 1.38 is applied on the lens surface other material is mesoporous silica nanocorticals with refractive index 1.12 can also be applied on the lens surface to increase the transmittivity. Now this picture shows a lens with anti-reflective layer applied on both the surfaces. Now again the light is impinging now when they apply this anti-reflective layer like this this is the bare lens glass surface and now coating is applied. Now when the light impinges the surface first it has to enter into the anti-reflective coating and then it will enter from anti-reflective coating to the glass surface into the glass. Now when the light falls on the anti-reflective coating surface some light is reflected back and remaining light will pass into the coating again it reaches the surface of the glass and again the splitting takes place some light will is reflected back and some light will pass into the glass. Now where the reflected light again it falls on the so this interface against splitting takes place some light will pass into the air and some light is reflected back. Now we can see this is the amount of light that is lost that is reflected light. Now some of these two reflected components will be less than the reflected component that would result from the bare glass alone so that the overall loss of light will be reduced. So by applying the anti-reflective coating the amount of light that is lost is reduced so most of the light will pass through the lens so image quality will improve. Now the layer thickness anti-reflective coating layer thickness is correct that is one-fourth of wavelength of incident light then the two reflected light rays will be out of phase with one another and they will cancel out each other. So this process decreases the total amount of reflected light and increases the amount of light that is transmitted through the lens so because of this the contrast increases. This reason is the there is reduction in the stray light from internal reflection since the reflected light amount decreases the internal reflection will reduce and the contrast of the image will increase and brightness of the image will also increase due to the increased light transmission through the glass surface and the improvement in the light transmission due to coating on a single lens surface may be very few percent but the total improvement resulting from coating of all lenses lens surfaces in a design of 10 to 20 lenses will be many times higher as high as 99.9 percent. Now let us start the discussion on lens mounting. This lens mounting is a major concern in getting a good quality picture. The lens barrel which is a mechanical part this barrel holds all the lens and lens assemblies. The lens barrel should be properly machined to ensure proper axial and radial position of all the optical elements. Now in this diagram we can see a barrel mechanical structure which holds the lenses a proper seating should be machined so that the lenses can be placed properly the tolerances should be maintained appropriate tolerances should be maintained so that the radial position positioning is obtained. The lenses must be mounted inside the barrel so that the centers of curvature of all the optical surfaces fall on a common line called optical axis. You can see here we have this common line which is known as optical axis. There are many elements many lenses are there. The center of curvature of all these elements should fall on this optical axis. If they do not fall if the center of curvature is not falling on the common axis then the image quality will be suffered. You can see here this particular assembly we have the axis of subassembly this is the axis and then we have the common axis that optical axis. Now there is a gap so this gap is known as centering error so because of this image quality suffers. Also the tilting of lens so we can see here when the lens tilts the center of curvature will not fall on the optical axis because of this the image quality suffers. Also the radial positioning of the lenses is very important the axial axis. Also the axial positioning of the lenses is very very important. Proper gap should be provided between the two lenses are just in lenses so that image quality is enhanced. Now this gap between two lenses is also known as the air spaces. Now the adjustment of air spaces between adjacent lenses there should be some provision for air space adjustment for that we can always use spaces and shim plates between two adjacent lenses so that proper gap is maintained. Also we can use balls and wedges you can see some mechanism here so we have a ball and then we have a conical screw here when the conical screw is driven inside it pushes the ball outside it the ball rises and here we can see a cantilevered wedge carrying half ball so when the screw is driven inside the wedge shape this wedge moves up along with the half ball that means when the ball moves up the lens will also move up so when the ball moves up the lens will move up and hence we can maintain the required air space between the two lenses so some mechanism like this should be provided for adjustment of the lenses in the axial direction. Now radial positioning of lenses is also very very important you can see the barrel here with the seat machine. Now you can see the optical axis of the lens and as the barrel axis that is reference axis now there is a shift one side the lens has displayed so this is known as radial positioning or centering error so some mechanism should be provided for example the centering screw should be provided here so here we can make a screw so by rotating these screws so one more screw can be provided here so by rotating these screws the lens can be centered here should be taken to see that the screws are not over tightened if they are over tightened then lenses are related to stresses which will affect the image quality. Now the straight barrels can be used for assembling the lenses if you use straight barrel all lenses will be of same diameter you can see here a straight barrel and many lenses are placed inside the barrel and spacers are provided here to maintain the proper air space between the two lenses now but this straight barrel is easy to mention and the cost is less and all the lenses can be easily mounted inside the straight barrel and the precision of positioning is limited to the precision of various elements including the stack up errors. Now normally the aluminum stylus steel titanium and aluminum are used to make the barrel we should select appropriate material with very low coefficient of thermal expansion so that thermal effects are minimized and the machining that you see is normally from 25 to 50 microns and centering adjustment based on rotation measurement can be provided and spacing adjustment by spacers can be provided. Now here we can see an assembly of lens in the barrel in the cell body this is the cell body and it has got internal threaded portion and then we have a lens pleno convex lens with the two lens capsule part so lens is placed in the the capsule and it is assembled and the complete lens capsule assembly can be inserted into the cell body and you can see here we have externally threaded retina and retina ring is pushed inside threaded inside to assemble the lens capsule into the body so this shows the lens capsule inside the cell body and by rotating the retina we can apply axial preload to the lens so that it sits properly in the seat we should not play over reload in that case the lens will be stressed and image quality suffers. Now there is a small clearance between the lens and the cell body which will be filled by the gun now steppard barrel also can be used for mounting of lenses in this case the lenses of varying sizes can be accommodated in the steppard barrel you can see a single piece steppard barrel so we have seats for placing the lenses and then we can also see spacers and retina rings and here we can see two part lens barrel this is the first part of the barrel having two lenses and this is the second part of the steppard barrel with single lens and then these two pieces are tight fitted to make a single assembly now lens proper lens the seat should be provided in the cell body of the barrel so that they are seated properly here we can see sharp corner seat and this is the concave surface of the lens and it is resting on sharp corner of the seat here we have a convex lens which is resting on the sharp corner of the seat appropriate radius should be provided to this corner so that the scratching of lens is minimized and here we can see tangential or conical seat the convex surface of the lens is in contact tangentially with this particular seat so proper geometrical tolerances should be provided on the barrel so that the seating of lens is proper now this picture shows the spherical seat the center of curvature the radius of curvature of the this portion of the seat and radius of curvature of lens should match each other so careful machining is required in order to get this spherical seat now in the barrel we can provide centering adjustment by providing screws centering screws or by using rotation and optical measurement technique we can center the lenses so but this process will be very labor intensive process and we can achieve 10 micrometer position very easily whereas one micrometer is possible so we should have an arrangement to rotate the lens system on an air bearing and adjust lens penetration and then we can apply gum to position to fix the lenses and there should be provision for spacing adjustment axial projection with shims so we can always select proper spacer and this method will be labor intensive assembly and we can achieve about micrometer precision very easily and 5 micrometer is also possible we can see some shims and the assembly process of shim in the barrel in the assembly here we can see the shim placed between the adjacent lenses now we can always mount the lenses in subcell and we can make subassemblies and the individual subassemblies can be put into the barrel to stack up the complete assembly but this process will be very labor intensive and expensive and in this the process we can achieve 10 micrometer positioning accuracy very easily and less than 10 less than 1 micrometer position accuracy is also possible now how do we hold the lens in a barrel how do we eliminate the falling of lens inside the barrel you can see here a C-shaped ring snapped into a groove so this is the cell or barrel and this is the lens and the C-shaped ring is snapped into the groove there is a groove here we can see the groove and this is the seat for lens lens is placed in the cell body and then the C-shaped ring is placed in the groove so that the lens will not fall and we can also use pristine continuous rings so here we have a continuous ring that is press fitted into the cell body which holds the lens in position now how do we statically seal the lens inside a cell now different methods are available so here we can see an o-ring around the lens so this is the lens and this is the edge of the lens and this is the mount that is the cell body and the o-ring is placed between the lens and the cell body it is pressed and pushed into the place and then retina threaded retina ring is positioned as shown here now here we can see the o-ring between retina cell and lens head so we have the cell body or the barrel body and we have the lens so o-ring is placed between the cell body and the lens edge and then the threaded retina is positioned and other method is injecting the elastomeric seal so the lens is placed inside the body cell body and then the retina ring is threaded into the cell body to hold the lens and then the elastomer seal is pulled into the body that means there should be a small hole in the cell body to pull the elastomeric seal and then the elastomer is allowed to solidify which holds the lens in position now let us see how we can achieve the dynamic sealing of moving lens assemblies if you observe this picture we can understand that this is the mount and we have the lens and there is a movable lens assembly so this will be moving parallel to the optical axis so in such cases how to seal the lenses so we can always use o-ring dynamic cell so that the lens is positioned properly or other method is with a quad ring we can use a quad ring as shown here to dynamically seal the moving lenses now in the previous cases the edge of the lens was used for mounting now let us understand the lens mounting using an optical surface we can see here we have an optical surface here we have another optical surface here using these optical surfaces we can mount the lenses that is mounting a lens by see if we use the edges these edges are poorly finished so if we use the edges then there are chances of de-centration tilt and the combination of tilt and de-centering to avoid that we can always use optical surface contact lens mounting so you can see here optical surface is used for mounting purpose so accurate lens edging is not needed with this type of mounting now with this we'll conclude the module 12 lecture number 7 in this lecture we discussed about some portion of atomic force microscopy that is limitations of AFM measurement challenges associated with AFM and then large area AFM calibration of AFM and then we started discussion on optical system design under this we have covered types of lenses defects in lenses and what are the different optical coatings and how to mount the lens in barrel this will conclude the lecture 7 in the next lecture we will continue the discussion on optical system design thank you