Optical System Design
For the upgrading of the hardware components used for flow visualization in the Virginia Tech supersonic wind tunnel lab, several optics pieces were procured. These pieces included optical components used solely for the interferometer and also pieces which can be used for general flow visualization. The requirements for general flow visualization and interferometry vary slightly. The discussion of procurement needs to begin with a general discussion of various optical hardware pieces. After the general discussion, the hardware chosen specifically for the interferometer is presented.
Because of the expense of optical components for flow visualization, it is important to look at what the requirements are for each of the optical components in the system. Although these devices are inherently expensive, one has to be careful not to set system design parameters too stringently. If system parameters are chosen carelessly, the cost of the system can easily increase by an order of magnitude. Further,it will take longer to build due to the use of non-standard parts.
Mirrors are required for every optical flow visualization experiment which is performed in the tunnel. Even the direct shadowgraph method, the simplest of all mentioned methods, requires at least one mirror. All mirrors in use need to be first surface mirrors. By this, we mean that the coating of the mirror needs to be on the surface facing the outside air. Mirror selection is based on two factors:
How the mirror is going to be used in the optical system
The type of coating needed on the mirror
Obviously, the usage of a mirror is an important factor in the selection of the type of mirror. There are two purposes for a mirror: to collect or distribute light and to deflect light. A flat mirror is used to deflect light without changing the magnification factor of the optical system. It is said that a flat mirror “folds” the light path. A flat mirror is frequently used when the optical path needs to be turned or when the optical path needs to be lengthened. Flat mirror geometry is strictly a function of the size of the flowfield that one wants to see. For example, if the flowfield in question is approximately four inches across, then a flat mirror larger than four inches is required. Care must be taken when selecting a flat mirror for an experiment, since flat mirrors are usually at a high angle relative to the oncoming light beam. For example, if one wants to turn the flow 45◦ , then the mirror will have a profile relative to the test section of an ellipse with a major axis equal to the diameter, and a semi-major axis equal to the diameter divided by √2. The situation gets worse as the angle increases. For this reason, one needs to know the incidence angle of the light beam relative to the flat mirror in use. Furthermore, the surface flatness of the mirror is important. Flat mirrors in an ideal sense do not change the amplification factor of the flow. However, commercial mirrors with no flatness specifications will have mild surface curvature. This will cause uneven changes in the amplification factor in the optical system. For this reason the surface flatness needs to be specified for these optical systems. Glass surface flatness is routinely measured relative to λ, where λ is the nominal wavelength of the light reflecting off the surface. For example,a surface flatness specification of “1-λ” is called one wave flatness. A surface flatness of “” is called quarter wave flatness. Selecting an adequate, though not overly stringent, flatness is key to purchasing a flat mirror. One problem which occurs in specifying mirror flatness is cost. As the flatness of a mirror becomes more and more stringent, the cost rises considerably. Table 3.1 shows a list of flat mirrors of the same diameter as the flatness increases. The flattest mirror costs over six times more than the poorest mirror. Part of this is due to a change in material which is required in order to grind the mirror to such a stringent specification. This has been minimized by selecting the cheapest material for each of the selections. In general, mirrors for flow visualization systems should have at least quarter-wave flatness.
The other type of mirror that is used is a mirror which does affect the magnification factor of the system. This can either be a concave or convex mirror, however in general the mirrors used here are all concave. Selection of the geometry of these mirrors is more difficult than in the case of the flat mirror. These mirrors all have different focal lengths and magnification factors. These factors heavily drive the selection process in this case. The object distance is the total distance from the object which needs to be in focus and the center of the mirror. For example, if there is one foot between a flat mirror and the test section followed by ten feet between the flat mirror and the parabolic mirror, then the total length will be eleven feet. The image distance is the total distance between the mirror and the imaging system image plane. This simple formulation works for a system containing a concave mirror. The formulae for dealing with compound optical systems, containing two or more components, is beyond the scope of this thesis. Obviously, for a single mirror system the required magnification is going to drive the focal length so that the system fits within a reasonable space. Unfortunately, there is a limited amount of freedom in selecting mirrors based on their focal length. In general, as a mirror’s focal length decreases, the maximum diameter available for stock mirrors decreases as well. A common measure of a mirror’s focal length is called its f-number. An f-number is defined as the ratio of the focal length to the diameter. As the f-number decreases, the manufacturing process becomes more difficult. Therefore, an f-number of no less than f4 is recommended. As the f-number decreases, the type of mirror surface shape must also be taken into consideration. There are two types of mirrors, parabolic and spherical. Spherical mirrors are much easier to manufacture and thus cost less. Unfortunately, there are some problems with spherical mirrors. As the edge of the mirror is approached, the effects of astigmatism increase. Therefore, if spherical mirrors are used, the light should not reflect off the outer surface of the mirror. Spherical mirrors should also be avoided in low f-number situations because this astigmatism effect is exaggerated. In general if the required f-number is smaller than f5 or f6, then a parabolic mirror. Parabolic mirrors do not suffer from astigmatism near their edges, because the surface is ground in the proper geometry for each point on its surface to have the same focal point. Near the center, both the spherical and parabolic mirrors have similar geometries. Near the edges however, rather than maintaining a constant curvature about the focal point, the edges follow a parabolic line. This reduces astigmatism. One final variation on these types of mirror is the off-axis parabolic mirror. This can be used to reduce the effects of coma in the optical setup. In the case of the off-axis parabolic mirror, the light source can be perfectly aligned with the primary axis of the entire optical system. Although this is a superior setup for the lighting system, it is rarely needed.
Besides the mirror geometry one has to take into consideration the coating used on the surface. A mirror coating is the reflective material applied to the surface. All mirrors for the currently used optical methods must be first-surface mirrors. This requirement creates a problem, since the coating is directly exposed to the elements. Although it is possible to have a coating applied without any protection, it is unwise and rarely done. Without the coating, not only will the coating be prone to coming off when touched, but the metal used will begin to oxidize. Various coatings are available under vendor specific names. In general, to minimize the deterioration due to periodic cleaning, the toughest available coating should be used. Regardless of the coating however, the surface should never be touched. Furthermore, cleaning should be done with a non-abrasive cloth and mild cleaning solution. Cleaning should be done as rarely as possible. To clean dust off the mirrors,clean compressed air should be used. The wavelength of the light being reflected is very important when selecting both the metallic and protective coatings. Silver and aluminum have a good reflectivity over a very broad range of wavelengths. Unprotected silver mirrors have very high reflectivity from wavelengths of 250nm to 20µm. These correspond to the entire visible spectrum, the ultraviolet spectrum and the near infrared spectrum. Different protective coatings can limit the band over which the mirror has high reflectivity. In general, if the light source for the system is in the visible spectrum, then standard coatings will not be a factor. If on the other hand, one is working outside or near the edge of the visible spectrum, it is important to check the manufacturer’s specifications on reflectivity. Furthermore, because silver is very susceptible to oxidation, aluminum is the coating of choice, despite the slightly lower reflectivity. In the case of infrared imaging, silver and aluminum do not have a high reflectivity. In this case it is advantageous to use a mirror with a gold coating. Gold coatings are very efficient at reflecting in the near-infrared and infrared range. Unfortunately, they are very poor at reflecting at the lower end of the visible spectrum.
Window design is a critical part of the optical system design for supersonic wind tunnels . The window must provide enough structural integrity to withstand the pressure field generated by the tunnel, and it must provide clear optical access for the system being used. Several factors must be considered when designing the tunnel windows. The first consideration is, of course, safety. The windows selected must withstand large pressure differences. A rudimentary calculation must be performed to determine whether the tunnel windows will have excessive deflection. Besides failure, it must be ensured that the flowfield is not adversely effected by distortions in the window. Excessive stresses in the window will most likely create distortions in any of the flow visualization systems. These distortions will hamper the use of these images for study. A second consideration that must be taken into account is manufacturing stresses. In the manufacturing process, it is possible to introduce surface distortions and residual stresses in the windows. In most cases, these will not be visible in a shadowgraph system, but will be readily apparent in a schlieren or interferometer system. These stresses can be minimized by carefully manufacturing the windows. For example, when drilling holes in plexiglas windows, the operator should continually cool the drill and drill the hole in steps, rather than in one pass. “Pumping” the drill will also reduce the distortions by allowing the surface to cool. Material selection for windows is governed by both the test section design and the optical system requirements. If the windows need to carry any load parallel to the surface, then Plexiglas needs to be used. Because glass is a ceramic, it performs poorly under tension. Therefore, it is very difficult to successfully mount a load bearing device directly in a glass window. Unfortunately, there are some cases where Plexiglas is inadequate for a good flow visualization system. If the window will be exposed to extreme pressure then Plexiglas will have larger material strains during a run than glass would. This is because the modulus of elasticity of plexiglas is lower than glass. These strains will become visible in both a schlieren system and an interferometer. For certain kinds of interferometry, the surface flatness is also critical. The required surface flatness for these optical systems is not possible with Plexiglas. In these instances, glass windows must be used.
2.1 General Theory of Interferometry
2.2 Mach-Zehnder Interferometer
2.3 Single Plate Interferometer
3. Optical System Design
3.3 Imaging Systems
3.4 Current Interferometer Hardware
4. Image Processing
4.2 Line Thinning
4.3 Manual Correction
4.4 Alternative Methods
5. Interferogram Processing
5.1 Line Following
5.2 Interferogram Object Structure
5.3 Stepping Routines
5.4 Initialization File Structure
5.5 Program Operation
6. Test Case
6.1 Testing Apparatus
6.2 Interferometer Program Initialization
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Upgrading and Automating the Virginia Tech Single-Plate Interferometer