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Schlieren-Based Flow Imaging Schlieren-Based Flow Imaging by Bradley Atcheson B.Sc., University of the Witwatersrand, 2004 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate Studies (Computer Science) The University Of British Columbia July, 2007 c Bradley Atcheson 2007 ii Abstract A transparent medium of inhomogenous refractive index will cause light rays to bend as they pass through it, resulting in a visible distortion of the background. We present a simple 2D imaging method for measuring this distortion and then show how it can be used to visualise gas and liquid flows. Improvements to the existing Background Oriented Schlieren method for acquiring projected density gradients are made by plac- ing a multi-scale wavelet noise pattern behind the flow and measuring distortions using a more reliable optical flow algorithm. Dynamic environment mattes can also be ac- quired, allowing us to render the flow into novel scenes. Capturing from multiple viewpoints then allows us to tomographically reconstruct 3D models of the tempera- ture distribution of the fluid. iii Contents Abstract ...................................... ii Contents ..................................... iii List of Tables ................................... v List of Figures .................................. vi Acknowledgements ............................... viii 1 Introduction ................................. 1 1.1 Motivation and Applications ...................... 3 1.2 Overview of the Method ........................ 6 1.3 Contribution ............................... 8 2 Schlieren Imaging .............................. 10 2.1 Optical Principle ............................ 10 2.1.1 Lens-Based Systems ...................... 11 2.2 Other Schlieren Configurations ..................... 14 2.2.1 Rainbow Schlieren ....................... 14 2.2.2 Grid-Based Systems ...................... 15 2.2.3 Background Oriented Schlieren ................ 16 2.3 BOS and Shadowgraphy ........................ 20 3 Optical Flow ................................. 22 3.1 Basic Concepts ............................. 23 Contents iv 3.2 Block-Matching Methods ........................ 24 3.2.1 Spatial Correlation ....................... 25 3.3 Gradient-Based Methods ........................ 28 3.3.1 Lucas-Kanade ......................... 28 3.3.2 Horn-Schunck ......................... 29 3.4 Variational Methods ........................... 30 3.5 Schlieren-Specific Optical Flow .................... 31 3.6 Wavelet Noise Background ....................... 32 3.7 Conclusion ............................... 34 4 Physical Setup ................................ 35 4.1 Acquisition Setups ........................... 35 4.1.1 Standard Setup ......................... 35 4.1.2 Camera Array .......................... 36 4.1.3 Lens Array ........................... 36 4.2 Angle Measurement ........................... 38 4.3 Implementation Notes .......................... 38 5 Results and Applications .......................... 40 5.1 Optical Flow Performance ....................... 40 5.2 Flow Visualisation ........................... 42 5.3 Environment Matting .......................... 46 5.4 Shadowgraphs .............................. 46 5.5 Tomographic Reconstruction ...................... 47 5.6 Conclusions ............................... 49 Bibliography ................................... 51 v List of Tables 5.1 Mean squared error of reconstructed fields. .............. 41 5.2 Mean squared error after autocorrelation subtraction. ......... 42 vi List of Figures 1.1 A vapour plume rises from burning alcohol. .............. 3 1.2 Particle image velocimetry setup. .................... 5 1.3 Interaction of candle plume with compressed air jet. .......... 7 2.1 Standard high-level configuration of any Schlieren system. ...... 11 2.2 A simple (idealised) lens-based Schlieren configuration. ........ 11 2.3 Example Schlieren photographs. .................... 13 2.4 Rainbow Schlieren filter. ........................ 15 2.5 Grid-based Schlieren system. ...................... 16 2.6 Virtual displacement caused by ray deflection. ............. 17 2.7 Shadowgraph example. ......................... 20 3.1 Deformation applied to block-matching windows. ........... 24 3.2 Cross-correlation matrix. ........................ 26 3.3 Fixed-pattern noise. ........................... 27 3.4 Horn-Schunck optical flow field for candle plume. ........... 30 3.5 Random noise patterns. ......................... 33 3.6 Wavelet noise patterns. ......................... 34 4.1 Standard single camera setup and small candle. ............ 36 4.2 Camera array setup and gas burner. ................... 37 4.3 Lens array setup and water tank. .................... 38 5.1 Synthetic optical flow tests. ....................... 41 5.2 Optical flow scaling test. ........................ 43 List of Figures vii 5.3 Candle plume results. .......................... 44 5.4 Captured images from plume interaction test. ............. 44 5.5 Optical flow vectors from plume interaction test. ............ 45 5.6 Corn syrup solution being injected into water. ............. 45 5.7 Candle lantern environment matting example. ............. 47 5.8 Synthetic shadowgraph example. .................... 48 5.9 Tomography results. ........................... 50 viii Acknowledgements Firstly, I’d like to thank everybody involved with this project for their comments, sug- gestions and proofreading. In particular, Wolfgang Heidrich, Ivo Ihrke, Derek Bradley and Marcus Magnor provided invaluable support and assistance. To my colleagues in the Imager and PSM labs, my friends, new and old, my family back home, and Whistler, thank you for always being there and for helping me along the way. I am also grateful to the Canadian Commonwealth Scholarship Programme for funding my studies, and to Kasi Metcalfe and Andrew Davidhazy for allowing me to use their images. 1 Chapter 1 Introduction Humans have a natural tendency to want to understand the world around us. This clas- sically involves making observations, devising theories and testing to see if predicted outcomes align with measured results. Physical phenomena and natural processes such as fire, cloud formation, plant growth, human behaviour etc. have all been studied in this way. In these cases, the subject is directly observable. Sometimes, however, we are only able to infer the existence of a process by its effects. Gravity itself is not visible, but through our observations of its interaction with objects of mass we know that it exists. The air around us, though at first glance stable, uninteresting, and in- visible, is actually host to an extremely complex flow of gas. All around us, slight temperature and pressure variations in air and liquid currents, as well as slight imper- fections in transparent solid materials create inhomogeneities in the refractive index of the medium. These are points at which the speed of light changes ever so slightly, causing rays to bend fractionally. Since they do not emit, absorb or reflect light, at a casual glance these inhomogeneities are entirely invisible, but to a careful observer they manifest themselves as a slight warping of the background seen through the me- dia. Through their effects on the environment (i.e., how they refract the light passing through them) we can learn their structure. With the right instruments, this invisible world can be observed, recorded, and subsequently illustrated for all to see in whatever manner we choose to render the information. The aim of this thesis is to present one such instrument and demonstrate its applications. The deflection of light is commonly exploited by scanning and acquisition devices. Structured light range scanners project sheets of light onto solid, opaque objects, and measure the resultant large-scale deformations to the projected stripe(s) in order to Chapter 1. Introduction 2 estimate scene depth [35]. At the other extreme, interferometry can be used to mea- sure surface profiles at the nanometre scale by illuminating a target with coherent laser light and observing the resultant patterns of constructive and destructive wave interfer- ence [19]. We shall restrict ourselves to the class of media producing light deflections on a scale that is just barely visible to the naked eye. In this case the refractive indices of the medium and its surroundings differ by as little as 10−4, resulting in a small yet still noticeable amount of refraction. Examples of this are the rising plume of heated air above a candle flame, the mixing of water and alcohol, and imperfectly formed panes of glass. This scale is large enough to be easily measured, yet small enough to have escaped much research interest in the past, and is useful in studying fluid flow. It is also large enough to be modelled using only geometric optics, allowing for a conceptually simple system. The Schlieren1 method has for centuries enabled scientists to observe the way in which light refracts when passing through these media. Although the presence of an inhomogeneity in the refractive index of the medium is often detectable without any aids, a cleverly-designed optical setup can be employed to produce a far superior view of it. Figure 1.1 shows the type of results that can be obtained. In this case, the flame itself is very small and no smoke is produced. In an ordinary photograph the only hint of the plume would be a slight distortion of the background, but even then we would not be able to discern nearly as much detail about its shape as is
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