Design, Assembly, and Calibration of a Focusing...

Design, Assembly, and Calibration of a Focusing Schlieren System 1

Design, Assembly, and Calibration of a Focusing Schlieren System Daniel Floryan,1 Jerrod Hofferth,2 and William Saric3 1Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, New York 14853, email: [email protected] 2Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77843, email: [email protected] 3 Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77843, email: [email protected]

Key Words

flow visualization, lens-and-grid Abstract

Density variations in transparent media can be studied by examining the attendant refraction of light. The schlieren technique is a non-intrusive optical technique which visualizes density gradients as light and dark areas in an otherwise monochromatic image; there are several variations and they are widely used in high speed wind tunnels. Among these variations is a lens-and-grid system, which adds a focusing ability to the technique. The design and implementation of such a system is described. The final system achieves a sharp depth of field of less than 10 mm, and equips the Texas A&M Mach 6 Quiet Tunnel with the capability to visualize second-mode instability waves in a Mach 6 boundary layer.


1. INTRODUCTION

A density variation in a gas changes the local refractive index which can be used as a flow diagnostic technique when the appropriate optics are used. These optical inhomogeneities can be measured using a number of techniques. A Mach-Zehnder interferometer measures levels of density, a schlieren system illustrates density gradients, and a shadowgraph illustrates the second spatial derivative of density. These are ranked in order of accuracy and complications with the interferometer being the most complex and the shadowgraph being the simplest to use. For flows exceeding the speed of sound, shock waves, and their attendant density gradients, are present offering the opportunity to use non-intrusive optical techniques. By using special optics associated with the schlieren system, deflections of the light path due to density gradients can be viewed as light and dark areas in the final image. A focusing schlieren system creates a narrow depth of field that concentrates on the detail in a special region of interest. For example, if there are other schlieren on the optical path besides the flow of interest, such as due to a scratched window, ambient convective currents in the room, or the shear layers surrounding the test article at the exit of an axisymmetric nozzle, they are out of focus and do not contribute to the final image.

The M6QT is currently equipped with a conventional z-type schlieren system. The z-type schlieren system sends collimated light through the flow field, resulting in a depth of field limited only by the length of the collimated beam. As such, all schlieren illuminated by the collimated beam are in-focus in the final image. Although some of the undesirable schlieren may be removed from the image by appropriate image processing, the undesirable schlieren also block internal flow structures from view. By using a focusing schlieren system with a sufficiently small depth of field, the internal flow structures can be viewed without interference from other schlieren. This allows for a detailed view of the flow from which new information can be extracted.

2. THEORY

Schlieren visualization has existed since the mid-17th century (Hooke 1665), and the first conventional schlieren system was made in the mid-19th century (Toepler 1864). Since then, many different types of schlieren systems have been developed and analyzed in-depth. Settles’ book (2001) provides a practical overview of a variety of schlieren techniques, and much of its information is repeated here.

2.1. Principle

Anyone looking down a long road on a hot day has experienced the principle behind schlieren visualization: the refraction of light caused by density gradients. The air closer to the road is hotter than the air further from the road, resulting in the air closer to the road being less dense than the air further from the road. Light travelling downward towards hotter air is bent upward. This results in the familiar pool of water being observed below a distant object.

The speed of light in a medium is described by the medium’s refractive index, n. When light exits one medium and enters another, its speed changes. The change in speed causes the light to bend. Using the Gladstone-Dale relation,

1 ,n k (1)


where n is the refractive index, k is the Gladstone-Dale coefficient, and ρ is the density, one can see that a change in density will result in a change in refractive index and thus bending of light. It can be shown (Settles 2001) that for schlieren of extent L along the optical axis, the angular deflection caused by a gradient of the refractive index, and therefore density, is given by

0 0x

L n L kn x n x

(2)

where 0n is the refractive index of the surrounding medium, and x is a direction perpendicular to the optical axis. By partially blocking the refracted light, the density gradients form light and dark areas in an image. 2.2. Conventional Schlieren System

A conventional schlieren system is one which passes a beam of collimated light through the schlieren. A schematic of a dual-field-lens schlieren system is shown in Figure 1. A point source emits light into a lens which forms a collimated beam from that light. The collimated beam travels through the schlieren and into another lens which refocuses the beam. At the point of focus there is a knife edge which, depending on its vertical position, either completely blocks or does not block the unrefracted light (darkfield and brightfield, respectively). When the light travels through the schlieren, it is refracted (represented by the solid blue line) and may or may not be blocked by the knife edge. It is important to note that the second lens focuses each refracted ray to a corresponding point in the image plane. This results in light and dark areas in the image plane corresponding to the density gradients of the schlieren. There is a limitation, however, to this system. Rays which are refracted onto the knife edge have no effect on the final image when the image plane is in darkfield. Similarly, rays which are refracted away from the knife edge have no effect on the final image when the image plane is in brightfield. Additionally, the collimated beam results in an infinite depth of field; any density gradients between the two lenses will be clear in the image plane. Ambient convection, for example, would appear in the final image in addition to the desired flow. Figure 1

Schematic of a dual-field-lens schlieren system with a point light source. Unrefracted light rays are represented by the dashed black lines, and light rays refracted by the schlieren are represented by the solid blue lines.

Point source

Lens 1 Lens 2 Knife edge

Image plane

Schlieren

ε


The limitations of the system are remedied by replacing the point source with an extended source, as well as a third focusing lens after the knife edge. The system with an extended light source can be thought of as a superposition of many point source systems offset from each other. This improves the system in two ways: firstly, the unrefracted light is partially blocked rather than fully blocked or fully unblocked; secondly, the finite size of the light source lends the system some focusing ability, however weak it may be. A larger light source gives the system a smaller depth of field. 2.3. Focusing Schlieren System

A focusing schlieren system is a schlieren system which is able to focus on a narrow plane of the flow of interest. This is desirable when working with three-dimensional flows, or to otherwise eliminate external density gradients from being imaged. Focusing schlieren systems were first conceived during the mid-20th century (Schardin 1942; Burton 1949; Kantrowitz & Trimpi 1950; Fish & Parnham 1950) and steadily improved until Weinstein wrote a guide to the modern lens-and-grid type focusing schlieren system (1993), schematically shown in Figure 2. There are several variations of focusing schlieren systems, but we will focus on the lens-and-grid type. Classically, the system consisted of an extended light source, two grids, and a lens. Boedeker (1959) added a Fresnel lens in front of the source grid in order to dramatically improve the image brightness. The source and cutoff grids are sets of alternating opaque and clear stripes, and are photographic negatives of each other. In this way, they function as the light source and knife edge of a conventional schlieren system. The system can be thought of as superposition of many conventional schlieren systems, with each clear stripe of the source grid and corresponding opaque stripe of the cutoff grid functioning as the light source and knife edge, respectively. This, along with the lens aperture, lends the system its focusing ability. Figure 2

Schematic of a lens-and-grid type focusing schlieren system and its cutoff grid.

Schlieren

Source grid

Cutoff grid

Image plane

ε

A

Lens

Fresnel lens

Extended source

l

L

L' l'

b

a Δa

Cutoff grid


Schlieren systems work best with 50% cutoff, i.e. with the knife edge set such that 50% of the incoming unrefracted light is blocked. This results in a medium grey image background with equal opportunity for light and dark spots. Focusing schlieren systems are no different, and so are set at 50% cutoff. Consider 2a to be the light source image height, set at 50% cutoff. When the light passes through the schlieren, it is refracted by a small angle ε which results in a change of the light source image height above the cutoff of Δa. By simple trigonometry,

( ) .l l Lal

(3)

If the smallest change in brightness that can be detected is 10%, the sensitivity of the system is

min

0.1 20626 arcsec.( ) ( )

al all l L l l L

(4)

Using the thin lens equation, an alternate form is obtained:

min

20626 arcsec.( )

aLL L l

(5)

The sensitivity is multiplied by a factor of L/(L – l) compared to the expression for conventional schlieren. Focusing schlieren systems thus require smaller values of a to obtain high sensitivity, which may be a limitation of the system.

If the grids are made too small, diffraction effects may become important. The resolution limit due to a slit is

2( - ) ,l Ldb

(6)

where λ is the wavelength of light used, and b is the height of the clear stripes on the cutoff grid. Including the magnification m of the image, the resolution limit of features in the flow is

2( - ) .l Lwmb

(7)

The major feature of the system is its ability to focus. Weinstein describes two ways to quantify the system’s focusing ability, a “sharp focus depth” and an “unsharp focus depth.” Although sharpness is based on perception and is thus subjective, Weinstein’s definitions are useful when comparing systems. The sharp focus depth is defined as the depth at which loss of resolution due to being out of focus exceeds the resolution of the optical system,

2 ,lDS w

A (8)

where A is the diameter of the lens aperture. The unsharp focus depth is defined as the depth at which the loss of resolution due to being out of focus exceeds some selected flow-related value, such as the smaller details required in the object field (Weinstein chose 2 mm),

4 mm.lDU

A (9)


The allowable field of view is determined by the lens. This is generally larger than the flow to be examined, and the actual field of view is determined by the sizes of the Fresnel lens and source grid.

The most important components of the system are the two grids; they are the light sources and knife edges, and thus give the system its functionality. If the cutoff grid lines are too widely spaced, they appear in the image background. To avoid this, a large number of pairs of cutoff grid lines must be used to form the image. Weinstein defines a parameter ϕ as the number of pairs of lines blended,

( ) ,2

An l Ll

(10)

where n = 1/(b + 2a) is the number of grid lines per millimeter at the cutoff grid. A value of ϕ > 8 is suggested for best results.

Although only unidirectional grid lines are considered here, two-dimensional patterns may also be used. By using two-dimensional grids, density gradients may be imaged in two dimensions rather than just imaging density gradients perpendicular to the grid lines. A cross-hatched pattern has been successfully used (Taghavi & Raman 1995), although Goulding (2006) gives some indication of the difficulties involved with two-dimensional grids. 3. DESIGN AND ASSEMBLY

Designing a lens-and-grid type focusing schlieren system involves making many compromises. The importance of each aspect of the system must be established. We will use our schlieren system to image second-mode instability waves in a hypersonic boundary layer, thus a narrow depth of field is required. However, other applications may require a large field of view, or high sensitivity. Acceptable values for the system’s characteristics must also be established. Using Equations 5-10 and considering the desired characteristics and available space, a system may be designed. Our design is guided by the spatial constraints of the M6QT, as well as by the design of the focusing schlieren system of the AEDC Hypervelocity Tunnel 9, which was used to image the second-mode instability waves of a Mach 10 boundary layer (VanDercreek 2010). The layout of our system is described by Table 1, and the two systems are compared in Table 2. The M6QT’s system’s design compares favorably with Tunnel 9’s. Table 1 Component description and spacing of M6QT focusing schlieren system

A (mm) f (mm) L (mm) l (mm) L' (mm) l' (mm) a (mm) b (mm)

155 195 1500 600 224 289 0.106 1.058 Table 2 Comparison between focusing schlieren systems of the M6QT and the AEDC Hypervelocity

Tunnel 9 Tunnel Field of view (mm) Sensitivity (arcsec) DS (mm) DU (mm) w (mm) ϕ M6QT 100 16 1.0 15 0.13 14 Tunnel 9 250 26 10 60 0.4 7


The system was built on an optical breadboard. The physical system can be divided into two parts all along the same optical axis: the first part comprises all of the components before the schlieren, and the second part comprises all of the components after the schlieren. The components of the first part are rigidly mounted to the breadboard. There should be around 100 mm between the Fresnel lens and the source grid so that the ridges of the Fresnel lens do not affect the source grid image. The light source is positioned such that its light fills the imaging lens; this can be quickly calculated using the focal length of the Fresnel lens and the thin lens equation. The light source has a coarse vertical position adjuster so that it can be aligned with the centers of the other components. The components of the second part should be placed on an optical rail. The lens requires a mount and a coarse vertical position adjuster. In our case, the image plane is the sensor of a digital camera. It requires a coarse vertical position adjuster and a fine position adjuster along the optical path so that the plane of sharp focus may be precisely chosen. The most complicated component is the cutoff grid. It should be able to be finely adjusted in the cutoff direction and along the optical path. It should have a fine roll adjuster to ease alignment with the cutoff grid. Fine yaw and pitch adjustment may be helpful as well, but are not necessary. Kinematic mounts should be used for fine adjustment, and sliding mounts and rails can be used for coarse adjustment.

Certain components can be made, while others must be bought. The most expensive component is the lens. The focal length must be picked to suit design constraints, however a smaller f-number is always better. A surplus low-f-number aerial camera lens was bought from an online retailer. The source and cutoff grids can be made in a variety of ways. Cutoff grids were traditionally made by focusing the source grid image onto high-contrast photolithographic paper and exposing the paper to create a photographic negative. This method, however, involved much trial and error because of the high sharpness and contrast required of the cutoff grid. A much quicker and reliable way of making the grids is to print them on clear transparencies using a desktop printer; high contrast and precision may be attained this way. The grids can be made in any photo-editing software, but must be made with the same resolution as the printer that will be used in order to avoid modulation. The grids can be printed with a set magnification, and the system can later be adjusted in order to match this magnification. The cutoff grid is much finer than the source grid, so it is recommended that the cutoff grid be made as an “original” in the photo-editing software, and the source grid be a magnified negative of the cutoff grid. Both grids should be placed against a flat piece of glass when added to the system so that their alignment remains exact. The light source used was a LED array capable of achieving a brightness of 12000 lumens. Care should be taken to block ambient light from entering the second part of the system, otherwise sensitivity is lost. There are several ways to capture the final image. In our case, the image plane was the sensor of a high-speed camera. This resulted in a smaller field of view, but this can easily be remedied with a relay lens (VanDercreek 2010). The final system is shown in Figure 3.

Before the system is used, it should be checked for alignment and cutoff. Using any small laser, the centers of all of the components may be aligned. To align and focus the grids, the system should be backlit; this way, the image of the fine cutoff grid appears where the source grid is. Half of the source grid should be covered in front with white paper, and the other half covered in the back by white paper. Now the image of the cutoff grid can be easily compared to the source grid, and the proper adjustments can be made. If the size of the cutoff grid image is different from the source grid, the cutoff grid and lens must both be moved. Once the proper size is attained, focus and angular alignment must be attained. Now the system is almost ready to use.


Figure 3

Layout of the focusing schlieren system. (a) Part 1: light source, Fresnel lens, and source grid. (b) Part two: aerial camera lens, cutoff grid, and camera. (c) View of the schlieren, a nozzle from a can of compressed air, along the optical axis. (d) View of the entire system. The last adjustment is the cutoff. The cutoff is subjective and should be set so that it gives the best possible image. To do this, create a schlieren in the proper position (e.g. by spraying a can of compressed air) and adjust the cutoff until the best image results are achieved. This will typically be when the background is a medium grey.


4. RESULTS

Images of a jet from a can of compressed air were taken using a high-speed camera at a rate of 10000 fps. The images showed good sensitivity and focusing ability. Figure 4a shows an in-focus jet. Different regions of the flow can clearly be discerned. The jet is laminar close to the nozzle, then begins to transition, and finally becomes turbulent. A large propagating helical structure is visible, along with many smaller turbulent structures. Figure 4b shows the same jet placed 25 mm away from the plane of sharp focus. At this distance from the plane of sharp focus, the flow is effectively blended into the background. Figure 5 shows two crossed jets from cans of compressed air separated by 13 mm. This separation blends any small-scale variations of the out-of-focus jet.

Figure 4

(a) Image of a jet from a can of compressed air. The jet is in the plane of sharp focus. (b) Image of a jet from a can of compressed air. The jet is 25 mm out of the plane of focus.

2.5 mm

2.5 mm


Figure 5

(a) Image of two jets from cans of compressed air separated by 13 mm. The horizontal jet is in the plane of sharp focus. (b) Image of two jets from cans of compressed air separated by 13 mm. The diagonal jet is in the plane of sharp focus.

5. FUTURE WORK

The focusing schlieren system described will primarily be utilized by the Mach 6 Quiet Tunnel in order to further analyze the second-mode instabilities present in hypersonic boundary layers. The system compares favorably with VanDercreek’s, which was used to analyze second-mode instabilities in hypersonic boundary layers. For current M6QT research conditions, these instabilities typically occur in the frequency range of 250-350 kHz. The focusing schlieren system will provide a diagnostic with high signal-to-noise ratio, enabling two key analyses of second-mode instabilities. Firstly, by using a continuous light source and a photomultiplier tube connected to a fiber optic, a high-bandwidth (O(MHz)) voltage signal proportional to light intensity (and thus density fluctuation) at a single point in the boundary layer may be compared with spectra obtained intrusively using hotwire anemometry. Secondly, a short-duration light source (via either a strobe or laser-induced spark system) may be employed in order to visualize a snapshot of the second-mode instability wave structure and directly extract the dominant spatial wavelength thereof. Schlieren image velocimetry (“ρIV”) is another possible avenue towards quantitative flow measurements (Hargather et al 2011). ACKNOWLEDGEMENTS

The support of the AFOSR/NASA National Science Center for Hypersonic Laminar-Turbulent Transition Research at Texas A&M University is gratefully acknowledged. The authors also would like to acknowledge the useful discussions with Dr. Raymond Humble.

2.5 mm 2.5 mm


LITERATURE CITED

Boedeker LR. 1959. Analysis and Construction of a Sharp Focussing Schlieren System. M.S. thesis. Massachusetts Institute of Technology.

Burton RA. 1949. A modified schlieren apparatus for large areas of field. JOSA 39(11):907-908. Fish RW, Parnham K. 1950. Focussing schlieren systems. Report CP-54, British Aeronautical Research Council. Goulding JS. 2006. A Study of Large-Scale Focusing Schlieren Systems. M.S. thesis, University of the

Witwatersrand. Hargather MJ, Lawson MJ, Settles GS, Weinstein LM. 2011. Seedless Velocimetry Measurements by Schlieren

Image Velocimetry. AIAA J. 49(3):611-620. Hooke R. 1665. Micrographia. London: J. Martyn & J. Allestry. Kantrowitz A, Trimpi RL. 1950. A sharp-focusing schlieren system. J. Aero. Sci. 17:311-319. Schardin H. 1942. Die Schlierenverfahren une ihre Anwendungen. Ergebnisse der Exakten Naturwissenschaften,

20:303-439. English translation available as NASA TT F-12731, April 1970 (N70-25586). Settles GS. 2001. Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media. Berlin:

Springer-Verlag. Taghavi R, Raman G. 1996. Visualization of supersonic screeching jets using a phase conditioned focusing schlieren

system. Expts. Fluids 20(6):472-475. Toepler A. 1864. Beobachtungen nach einer neuen optischen Methode – Ein Beitrag zur Experimentalphysik. Bonn:

M. Cohen & Son. VanDercreek CP. 2010. Hypersonic Application of Focused Schlieren and Deflectometry. M.S. thesis. University of

Maryland, College Park. Weinstein LM. 1993. Large-Field High-Brightness Focusing Schlieren System. AIAA J. 31(7):1250-1255.

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