UNIT 9 INTERFEROMETRY

Transcription

1 UNIT 9 INTERFEROMETRY Structure 9.1 Introuction Objectives 9. Interference of Light 9.3 Light Sources for 9.4 Applie to Flatness Testing 9.5 in Testing of Surface Contour an Measurement of Height 9.6 Interferometers 9.7 Laser Interferometers 9.8 Summary 9.9 Key Wors 9.10 Answers to SAQs 9.1 INTRODUCTION Light is consiere as an electro-magnetic wave of sinusoial form. When two monochromatic light beams combine they unergo the phenomenon of interference. Therefore, the resultant light rays carry the characteristics of both the monochromatic light sources. The amplitue an hence the brightness of the resultant beam also becomes ifferent from the original ones. The rays of light, when allowe to fall on screen, form alternate ark an bright fringes from maximum intensity to complete minimum as the phase of the monochromatic beams changes from 0 to 180 egree. By analyzing ifferences in phase, which also correspon to ifference in wavelength (length), istance between the two lights sources can be calculate. This can be a tool to measure very small linear ifferences. Phenomenon of light use in this way has given rise to the branch of imension metrology calle. involves testing of flatness, surface contour, an etermination of the thickness of slip gauges, etc. Interferometers are commercially available instruments for calculating small ifferences, constructe on the basis of principles of interferometry. We will iscuss these instruments an the techniques use in them in the following sections. Objectives After stuying this unit, you shoul be able to familiarise yourself with the principle of interference, an unerstan the techniques an working of various evices base on the phenomenon of interference. 9. INTERFERENCE OF LIGHT To unerstan the phenomenon, let us consier two virtual sources S 1 an S erive from the same primary source. Since both are equiistant from the source S, the seconary wavelets emerging from S 1 an S are in same phase an have equal amplitue. Let the source slit S be illuminate with a monochromatic light of wavelength. The ientical light waves iverging from S 1 an S at an instant t may be represente by t c t E E0 sin E0 sin T... (9.1) 105

2 Metrology an Instrumentation where E 0 is the amplitue, T is the perio, an c is the velocity of light. In traveling from S 1 to P, the wave travels a path of x 1 = S 1 P. Hence, on reaching P, the wave that emerge looks like E1 E0 sin ct x1 E0 sin ( t 1)... (9.) c x1 where, is the angular frequency an 1 = the phase of the wave. T Similarly, on reaching P, the wave emerge from S is given by x where x = S P an = E E0 sin ( ct x) E0 sin ( t ) is the phase of the wave. Figure 9.1 The phase ifference between the two sources is 1 ( x x1 ) where the path ifference x x1 S P S1 P Now assuming that y D an D, i.e. the slits are very close together, we can consier electro-magnetic fiels E 1 an E at P very nearly in the same irection. In this conition, superposition of E 1 an E is simply the orinary sum of E 1 an E. The resultant wave is given by E E1 E E sin ( t ) E sin ( t ) E [(cos cos ) sin t (sin sin ) cos t]... (9.3) Let, E0 (cos 1 cos ) Rcos... (9.4) E (sin sin ) Rsin... (9.5) 0 1 Substituting Eqs. (9.4) an (9.5) in Eq. (9.3), we have E R sin ( t )... (9.6) 106 Thus, the resultant amplitue of the new ray is R an phase.

3 The intensity epens on the square of the resultant amplitue. Squaring an aing Eqs. (9.4) an (9.5) R E 0 1 [1 cos ( )] 0 E (1 cos ) As the value of cos varies between 1 an 1, intensity also varies from 0 to 4E 0. The resultant intensity I is maximum if R is maximum. R will be maximum if Hence, cos 1 or 0,, 4,... 0,, 4,... Hence, 0,,,... The maximum value of I is max 4 0 I K R K E where K is the proportionality constant. The interference in this conition is sai to be constructive interference. The resultant intensity is minimum if cos 1 or 0, 3, 5,... i.e. which means, 3, 5, ,,,... The minimum value is, I min = 0. The interference in this conition is sai to be estructive interference. Thus the conition for maximum an minimum of intensity is Maxima at SP S1 P m, m 0, 1,, 3,... 1 Minima at SP S1P m, m 0, 1,, 3,... This maxima an minima constitute the bright an ark fringes. From Figure 9.1, we can easily calculate position of the bright an ark fringes. ( S P) ( S B) ( BP) D y y S P D 1 D 1 Since we have assume that y < < D, < < D, we can expan the term binomially, Hence, 1 S P D y D 107

4 Metrology an Instrumentation Similarly, 1 S1 P D y D 1 Therefore, SP S1P 4y D Now for bright fringes : m y D Hence, which gives, y y m m m D m y D... (9.7) In the above relation, value of y m gives position of m th bright fringe. For the central fringe D at P 0, m = 0 an y 0 = 0 an the next bright fringe will be at y1 an so on. For the (m 1) th bright fringe, we have The fringe with y y m1 m ( m 1) D, where m = 1,, 3,... Similarly, the ark fringes satisfy the relation D ym1... (9.8) y m 1 D m The first ark fringe is at (m = 1) y 1 1 D The secon ark fringe is at (m = ) an so on. y 3 D... (9.9) The separation between two consecutive ark fringes is D. Thus, the fringes are equally space. There is a ark fringe between two bright fringes Fringe with is irectly proportional to D an inversely proportional to. Intensity of all the bright fringes is the same an the intensity of ark fringes is zero. Distribution of intensity of the fringes follow the following equation I K E0 (1 cos ) I0 cos From the equation it is seen that the maximum intensity is I0 4K E0 proportionality constant. In terms of y,, D, an, Eq. (9.5) can be written as... (9.10), where K is the 108 I I 0 cos yd... (9.11)

5 SAQ 1 (c) How is phase of light beam relate to the fringes forme ue to interference? Explain the formation of white an ark fringes ue to interference of light. What are the ifferences between constructive an estructive interference? 9.3 LIGHT SOURCES FOR INTERFEROMETRY As mentione earlier, it shoul be note that the light source use in interferometry shoul be a monochromatic in nature an their amplitue shoul be same or at least comparable with each other. Otherwise, interference will not be visible. Orinary light contains a mixture of light with a number of wavelengths. Hence, it cannot be consiere as a source light for interferometry. A variety of light sources are available for interferometry work but the selection of proper sources for any application epens on the requirements or results to be obtaine by the interferometer, cost an convenience. Characteristics for various light sources are summarize below. Mercury It is less expensive source having high intensity, an green line can be easily isolate with filters. Since natural mercury contains several isotopes, each isotope emits light whose wavelength is slightly ifferent from other. As a result, natural mercury light source raiates a mixture of slightly ifferent but close to each other wavelengths that can be treate as monochromatic light. Mercury 198 Camium Krypton It is pure isotope prouce by neutron bombarment of gol. It is consiere to be one of the best sources of very sharply efine wavelengths, an fringes are visible with path ifference upto 500 mm. Light is emitte when mercury 198 is excite by microwave prouce electric fiel. It is the international seconary stanar of wavelength. It is the only natural material proucing a spectral line (re) almost completely monochromatic. It can be conveniently use up to a path ifference of about 00 mm. Camium 114 is the official seconary international stanar of length. It is use in some instruments for its avantage of being easily excite. It is not as monochromatic as krypton-86 because krypton is a mixtures of isotopes. It can be use up to path ifference of 375 mm. Krypton 86 Krypton-86 lamp prouces spectral lines of ifferent wavelengths an, therefore, an elaborate monochromator is require to separate them. Further, its excitation takes place at very low temperature. So this lamp is use only in stanarizing laboratories. It enables the fringes to be observe with maximum path ifferences nearing up to 800 mm. 109

6 Metrology an Instrumentation Thallium Soium Helium Gas Lasers SAQ As 95% of its light is emitte at one green wavelength, it can be use over a reasonable path ifference without the use of filter. It is use only in applications where interference path ifference oes not excee a few hunre wavelengths. Usually yellow soium light is use which contains two separate but closely space lines of equal intensities. Orange line of helium is use where path ifference is not large. Lasers are highly monochromatic light that enable the interference fringes to be observe with enormous path ifferences, up to 100 million wavelengths. Why orinary light cannot be use as a source of light in interferometry? What are the various light sources commonly use in interferometry? 9.4 INTERFEROMETRY APPLIED TO FLATNESS TESTING 110 Flatness is efine as the geometrical concept of a perfect plane. It is an important function in construction of many technical components where accuracy is a require criterion. For example, controlle flatness is require to provie full contact with a mating part. Flatness is a preconition for the parallelism of nominally flat surface. It is a reliable bounary plan for linear imension. It also provies locating planes for epenable mounting or assembly of manufacture parts. Consiering the functional role of flatness, the measurement of that conition on the operating surface of manufacture parts is often an important operation of the imensional inspection process. There are various methos an instruments available for measuring the flatness of a plane. The choice of the best-suite metho is governe by various factors, such as size an shape of the part, the area to be inspecte, its accessibility an intersection with other surfaces an the esire egrees of measuring accuracy. is one of the precise methos for calculation of flatness. In this metho monochromatic light is allowe to fall on an optical flat which in turn is place on the surface at small angle whose flatness is to be calculate. Optical flats are transparent, flat, circular section of small thickness usually mae of clear fuse quartz or pyrex. The optical flat is place on the surface to be inspecte in such a way as to create interference bans observable uner monochromatic light. The resulting ban pattern permits the object s flatness conitions to be evaluate. The principle is explaine below. When optical flat is place on the surface plate, it makes a very small angle (say, ) to it. Monochromatic light of known wavelength is allowe to fall on it. This is shown in Figure 9.. Part of the beam passes through the glass, strikes the flat reflecting surface, an reflecte back. The other part of the beam is reflecte back to air at the lower

7 surface of the optical flat. These two beams again recombine an unergo the phenomenon of interference since they are of same wavelength. This results in formation of interference fringes as explaine in Section 9.. The position of the fringe with will epen on the separation between the surface an the lower surface of the optical flat. Consiering that the angle between the surface an the optical flat is very less, the extra istance that the reflecte light from the inspecte surface travels is more than the reflecte light from the optical surface, where is the separation between optical flat an the reflecting surface. Figure 9. For constructive interference, the path ifference between the rays shoul be even multiple of, where is the wavelength of light. i.e. n where n = 1,, 3,... i.e. n Thus, where there is a separation of integral multiple of, bright fringes will result. On the other han, for estructive interference, the path ifference between the rays shoul be o multiple of. i.e. (n 1) i.e. (n 1) 4 Thus, the separation giving o multiples of 4 will result ark fringes. By stuying the pattern of the fringe forme nature of the reflecting surface can be stuie. A perfectly flat surface will result exactly parallel fringes without any istortion. Deviation from the perfect flatness causes igression in parallelism of the fringes proportional to flatness error. SAQ 3 Calculate the ifference in height between a slip gauge pile an a block as shown in Figure 9.5. The number of fringes over the istance L is 18. The source of light is camium having wavelength of m. 111

8 Metrology an Instrumentation 9.5 INTERFEROMETERS Interferometers are optical instruments use for measuring flatness an etermining minute ifferences in length by irect reference to the wavelength of light. Basically, an interferometer is constructe using the same principle as of an optical flat. The isavantages of optical flats are overcome here by some refine arrangements. The fringes forme can be oriente to the best avantage in interferometers. Also there is an arrangement to view the fringes irectly from top, thus avoiing any istortion ue to incorrect viewing. This makes their uses easier an faster than the optical flats. Figure 9.3 : Interferometer There are a number of interferometers available. But most of them are esigne employing slightly ifferent methos to accomplish the same result. The arrangement of a typical interferometer is shown in Figure 9.3. The light sources from a single colour light source are collimate into parallel by a lens. When these rays reach the partially silvere surface of mirror A, about half of the light is reflecte towars mirror B, an the other half passes through the silvere surface towars the workpiece an table surface. Thus, the light rays are ivie an irecte along two ifferent paths. These ivie light rays fall on the surface an the mirror B an are then reflecte back to mirror A. Since they are of same wavelength an emerge from the same source, they will show the phenomenon of interference. Some light from the mirror B passes through the partially silvere surface towars the eye, an some light from the workpiece an table surfaces also are reflecte towars the eye. If the path ifference of these two rays are even multiple of the half of the wavelength of the light source, they unergo constructive interference an the light rays reinforce each other, an the workpiece an the table surface appear to be orinarily illuminate. However, if the path of the light reflecte from the workpiece surface iffers in length from that of the light reflecte from the mirror B by o multiples of half wavelength, the workpiece surface appears to be ark because of estructive interference. The surface of the table also appears to be ark if the same situation is applie to it. 11 Figure 9.4 : Fringes Appearing on the Table an the Surface

9 In orer that the operator can make measurement with an interferometer, the table is tilte slightly by a very small angle. This causes a series of interference fringes to appear on the surfaces of the workpiece an table as shown in Figure 9.3. If the workpiece is flat an parallel to the base plate, the fringe pattern will be straight, parallel an equally space. When the workpiece is flat but not parallel to the base plate, straight parallel fringes of ifferent thickness will be obtaine. In case, the surface of the workpiece is at certain angle with the base plate, fringe pattern will be as shown in Figure 9.5. Here the error is inicate by the amount by which the fringes are out of parallelism with those on the base plate. If the workpiece is concave or convex, fringe pattern will be as shown in Figure 9.5. If fringe pattern is same as shown in Figure 9.5(c), it can be euce that the surface is flat with slight rouning off at the corner. (c) Figure LASER INTERFEROMETERS The measuring capacity in interferometers of lamp of single wavelength as source of light is limite because of their low resolution an short measuring range. If the light source is replace by a laser source, measurement can be one over a long istance because it facilitates to maintain the quality of interference fringes over long istance. Since laser is highly monochromatic coherent light source that follows all the principles of light, the fringes forme ue to interference of laser are very sharp, accurate an precise. Figure

10 Metrology an Instrumentation Figure 9.6 explains the operation of an Interferometer. It uses two-frequency laser system with opposite circular polarization. These beams get split up by beam splitter B 1, one part travel towars B an the other towars external cube corner where the isplacement has to be measure. Unlike Michelson Interferometer, mirror is not use as a reflector. Instea cube corner reflector is use. It reflects light parallel to its angle of incience regarless of cube corner reflector s alignment accuracy. Beam splitter B optically separates the frequency f 1, which alone is sent to the movable cube corner reflector. The secon frequency f from B is sent to a fixe reflector. When these two light sources again meets once the cube corners reflect them to prouce alternate light an ark interference patterns. When the movable reflector moves, the returning beam frequency will be Dopplar shifte slightly up or own by f. Thus, the light beams moving towars the photo-etector P have frequencies f an f 1 f. P changes these frequencies into electrical signal. Photo etector P 1 receives signal from the beam splitter B 1 an changes the reference beam frequencies f 1 an f into electrical signal. An AC amplifier A 1 separates the frequency ifference signal f f 1 an A separates the frequency ifference signal f (f 1 f). The pulse converter extracts f, one cycle per half wavelength of motion. The up an own pulses from the converter are counte electronically an isplaye in analog or igital form on the inicator. From the value of f, the istance move by the moving cube corner can be etermine. The uses of a laser interferometer are as given below. (c) () (e) Since laser interferometer prouce very thin, straight beam, they are use for measurements an alignment in the prouction of large machines. They are also use to calibrate precision machine an measuring evices. They can also be use to check machine set ups. A laser beam is projecte against the work an measurements are mae by the beam an isplaye on a igital reaout panel. Because of their very thin, straight beam characteristics, lasers are use extensively in constructions an surveying. They are use to inicate the exact location for positioning girers on tall builing or establishing irectional lines for a tunnel being constructe uner a river. Laser interferometers can also be use in glass feature measurements. The main avantages of a laser interferometer are as given below. Laser interferometers have high repeatability an resolution of isplacement measurement. (c) () (e) SAQ 4 They give high accuracy (0.1 ) of measurement. It facilitates to maintain long range optical path (60 m). Laser interferometers are easy to install. There is no chance eterioration in performance ue to ageing or wear an tear. Describe the principle an operation of a Michelson Interferometer. What are the uses an the avantages of a laser interferometer? 114

11 9.7 SUMMARY In this unit, we have iscusse the phenomenon of interference an its applications in measurements of various parameters. The unit begins with the iscussion of conitions of interference an the light sources for this phenomenon to occur. Next, we have iscusse how interferometry can be use for testing of flatness an surface contour. A typical interferometer is escribe after that. The unit finishe with the iscussion of the principle an working of a laser interferometer. 9.8 KEY WORDS Interference Monochromatic Light Phase Optical Flat Flatness Cube Corner : It is the phenomenon of light ue to which light rays combines each other to give ifferent amplitue an brightness. : A light source, which has only one wavelength is calle a monochromatic light source. : Phase of a light is efine as the angular status of the electromagnetic wave of which it consists of. : An optical flat is a one-piece water white glass, generally use in measurement of flatness as a protector of camera lenses. : Flatness of a surface is efine as the minimum separation of a pair of parallel planes, which will contain all the point on the surface. : It is a reflecting evice which reflects light parallel to its angle of incience regarless of its alignment accuracy. 9.9 ANSWERS TO SAQs SAQ 1 (c) SAQ SAQ 3 SAQ 4 See preceing text for answer. See preceing text for answer. See preceing text for answer See preceing text for answer. See preceing text for answer Let x be the istance between the ajacent fringes The Number of fringes L 18 x The ifference between the height See preceing text for answer. See preceing text for answer L m x. 115