Sally Bane Explosion Dynamics Laboratory Directed by Professor Joseph Shepherd Graduate Aerospace Laboratories (GALCIT) Ae104b Lecture February 9, 2010 Shadowgraph and Schlieren Techniques

2 Schlieren Visualization optical techniques have been used for decades to study inhomogeneous media Robert Hooke ( ) – “Father of the optics of inhomogeneous media”, invented the schlieren method many different optical techniques for studying fluid flow will focus on the classic schlieren technique Schlieren image of explosion in hydrogen-air

3 Basic Concepts: Light Propagation Through Inhomogeneous Media Schlieren and Shadowgraph Techniques allow us to see the phase differences in light Q: Why do stars “twinkle”? A: atmosphere is inhomogeneous – disturbances due to turbulence etc. change the air density → change in the refractive index → rays of starlight bend, wave front of the light is wrinkled → star not a point, but fluctuates (“twinkles”) on the time scale of the atmospheric disturbances

4 Basic Concepts: Light Propagation Through Inhomogeneous Media Refractive Index: describes how the speed of light changes upon interacting with matter Gases: linear relationship between n and the gas density

5 Basic Concepts: Light Propagation Through Inhomogeneous Media Increase air density by two orders of magnitue → 2.3% increase in n ! Refractive index only very weakly dependent on density → k = 0.23 cm 3 /g = 2.3 x m 3 /kg Require very sensitive optics!

6 Basic Concepts: Light Propagation Through Inhomogeneous Media What does “schlieren” mean? Schliere (singular of schlieren):  German for “streak,” “striation,” or “cord”  gradient disturbance of inhomogeneous transparent media  object that has a gradient in the index of refraction, i.e.

7 Basic Concepts: Light Propagation Through Inhomogeneous Media Example schliere: Laminar Candle Plume y x 22 11 11 The gas in the plume is hotter and less dense than the surrounding gas, so and therefore producing a gradient in the x- direction

8 Basic Concepts: Light Propagation Through Inhomogeneous Media Increasing n Negative vertical refractive-index gradient dn/dy < 0 y z x t = 0 t =  t y1y1 y2y2  z 1 = (c 0 /n 1 )  t z1z1 z2z2  z 2 = (c 0 /n 2 )  t and Planar wave front Rays (normal to wave front)  z = c  t = (c 0 /n)  t Since n 2 > n 1, c 2 < c 1 so  z 2 <  z 1

9 Basic Concepts: Light Propagation Through Inhomogeneous Media Increasing n Negative vertical refractive-index gradient dn/dy < 0 y z x t =  t RESULT: Refracted wave front Huygen’s Principle: Light rays, always normal to the local speed of light, are bent toward the zone of higher refractive index (zones of higher density in gases).

10 Basic Concepts: Light Propagation Through Inhomogeneous Media y z x yy y1y1 y y2y2 (c 0 /n 2 )  t z1z1 z2z2  Distance wave front moves in time  t: dn/dy < 0 Refraction angle: zz  Also:

11 Basic Concepts: Light Propagation Through Inhomogeneous Media y z x y1y1 y y2y2 (c 0 /n 1 )  t z1z1 z2z2  dn/dy < 0 zz Because  is a very small angle, it is approximately equivalent to dy/dz, the slope of the refracted ray. and Curvature of refracted ray yy

12 Basic Concepts: Light Propagation Through Inhomogeneous Media y z x y1y1 y y2y2 (c 0 /n 1 )  t z1z1 z2z2  dn/dy < 0 zz For a 2D schliere of length L along the optical axis (z): and So the angular ray deflection in the x and y directions are: and Refraction caused by gradients of n, not overall level of n ! yy

13 Shadowgraphy Only need a light source, a schlieren object, and screen on which the shadow is cast * point light source schliere  extra illumination less illumination * point light source Denser sphere (i.e. a bubble)  lens screen Screen

14 Shadowgraphy Screen Dark circle due to light refracted from outline of sphere Light circle due to refracted light from the outline illuminating this part of the screen Gradient back to background illumination due to non-uniform refraction of rays as the light wave travels down the optical axis (x)

15 Shadowgraphy Uniform shift of illumination z y z y Nonuniform illumination  see some shadow, but don’t get outline of the schliere  as move down optical path (z-direction), so all rays shift the same!  as move down optical path (z-direction), so rays shift non- uniformly Variation of gradients critical!

16 Example Shadowgraphs Shock wave diffraction around wedge (Settles 2001) Oil globs in water (Settles 2001) Sphere flying at M=1.7 (Merzkirch 1987) He/N 2 mixing layer (Settles 2001)

17 Shadowgraphy vs. Schlieren Imaging Less sensitive except for special cases (e.g. shock waves) More sensitive in general Schlieren ImagingShadowgraphy Focused optical image formed by a lens Requires cutoff of the refracted light Illuminance level responds to ∂n/∂x and ∂n/∂y Schlieren image displays the deflection angle  Not an image but a shadow No cutoff of refracted light Responds to second spatial derivative, ∂ 2 n/∂x 2 and ∂ 2 n/∂y 2 Shadowgraph displays ray displacement More difficult to set up – use lamps, mirrors, lenses Extremely easy to setup, occurs naturally

18 Schlieren System – Point Light Source * point light source lens schliere in test section screen merely a projector, imaging opaque objects in the test section deflected rays miss the focus focused back to same point on screen

19 Schlieren System – Point Light Source * point light source lens schliere in test section screen knife- edge translating phase difference causing a vertical gradient ∂n/∂y to amplitude of light on the screen refracts many rays in many directions – all downward deflected rays get blocked, painting at least a partial picture gives black and white image Brighter point on screen

20 Schlieren System – Extended Light Source extended light source lens knife- edge the light source is first collimated by a lens then refocused by the second lens an inverted image of the light source is formed at the knife-edge the extended light source can be considered as an array of point sources – each “point source” forms a schlieren beam that focuses to a corresponding point in the light source image (extreme rays shown in cartoon above) knife-edge blocks a portion of the image of the extended light source another lens focuses an inverted image of the test area on the screen screen

21 Schlieren System – Extended Light Source extended light source lens knife- edge each “point source” in the extended light sources illuminates every point in the test section → each point in test section is illuminated by rays from the entire extended source when focused to knife-edge, each point in test section produces an entire “elemental” source image to the “composite” image at the knife-edge e.g. if insert a pinhole in the test section, would still see an image of the extended source, but much weaker in intensity than the “composite” image screen

22 Schlieren System – Extended Light Source extended light source lens knife- edge IMPORTANT POINT: with no schliere present, if we advance the knife-edge to block more the “composite” image of the extended light source → block each “elemental” source image equally screen therefore blocking equal amount of light from every point in the test area Screen darkens uniformly! This is how you know your alignment is good and that you are at the true focus!

23 Schlieren System – Extended Light Source extended light source lens knife- edge consider one point in the test area to be subject to refraction by the schliere since all of the “point sources” on the extended light source contribute a ray to this point, a group of rays from all “point sources” is deflected (dashed lines in cartoon) this group of rays are focused to produce an “elemental” image of the light source at the knife-edge but the image is displaced due to the refraction the group of rays is returned to the same relative position on the screen by the third lens → true image of the schliere at the screen screen NOW PLACE A SCHLIERE IN THE TEST AREA

24 Schlieren System – Extended Light Source the displacement of the “elemental” source image separates the rays refracted by the schliere from the rays that provide the background illuminance because the refracted light is separated, can have a different amount of cut-off by the knife edge → recombined in the schlieren image at the screen → variations in the illumination with respect to the background Many points of varying illuminance schlieren image that shows the shape and strength of the schliere Note: using an extended light sources gives continuous gray- scale schlieren images! Knife- edge Undisturbed composite source image Weak source image displaced by schlieren object

25 Schlieren System – Extended Light Source Knife- edge Undisturbed composite source image Weak source image displaced by schlieren object Sensitivity: Constrast: differential illuminance at an image point background illuminance focal length of the schlieren lens refraction angle Sensitivity: Larger focal length = better sensitivity More obstruction of source image = better sensitity

26 Z-Type Schlieren Arrangement camera knife-edge parabolic mirror light source condenser lens pinhole or slit test area Most common arrangement: easy to set-up, allows for a schlieren mirror with long focal length (high sensitivity) and large field-of-views

27 Cool Schlieren Images Bullet and candle flame (Settles 2001) Glass fibers (Settles 2001) Projectile fired at Mach 4.75 in reactive H2/air mixture – cyclic detonation behind the shock (Settles 2001)

28 Cool Schlieren Images Removing frozen pizza from case (Settles 2001) Blackjack dealer and players (Settles 2001) Space heater (Settles 2001)

29 Cool Schlieren Images Image of a T-38 at Mach 1.1 (Leonard M. Weinstein, NASA Langley Research Center) – taken using a telescope, the sun, and a cutoff, field of view of 80 m!

30 Cool Schlieren Images 3D schlieren of a glass figurine (Settles 2001) Color schlieren of the space shuttle orbiter in supersonic wind tunnel test (Settles 2001) Color schlieren of a gun firing 0.22 caliber bullet (Settles 2001)

31 Important Equations Equations: Gaussian Lens Equation: Constraints: For Real Image: Table Size: where L is limited by the size of the optics table Magnification: Total Magnification x1x1 f1f1 x2x2 x3x3 x4x4 f2f2 y0y0 y I1 y I2 Lens 1Lens 2 Knife- edge Object (FOV) Inverted object image Object image

32 Important Equations Must Satisfy:Under the Constraints: SUMMARY x1x1 f1f1 x2x2 x3x3 x4x4 f2f2 y0y0 y I1 y I2 Lens 1Lens 2 Knife- edge Object (FOV) Inverted object image Object image

33 How My Schlieren Setup Works Light source (Xe arc lamp) Optical assembly Vertical slit (razor blades) Achromatic lens (to collimate the light) f = 200 mm Aperture (to make 1” Ø beam) Baffle (to block stray light) Flat mirror Test section (1” Ø field-of-view) Concave mirror (schlieren lens) f = 1000 mm Flat mirrors Flat mirror Knife-edges (razor blades) High-speed camera (no additional focusing lens used)

34 How My Schlieren Setup Works Camera Side: x1x1 f x2x2 yOyO yIyI Schlieren “Lens” (concave mirror) Knife- edges Object (1” Ø field-of-view) Inverted object image on camera CCD f Equations:Knowns: 1 2 Unknowns:

35 How My Schlieren Setup Works into 3 3Invert Solve for x 1 : Then from : 2 Remember: Sensitivity is proportional to the focal length so f should be as large as possible!

36 Setting Up a Schlieren System: Step-by-Step (1) Step 1: Calculate the required distances between he object, schlieren lens, focusing lens, and camera based on the equations on the previous slide and the focal lengths of your lenses Step 2: Set up the light source, any flat mirrors, and test section with windows in place if applicable Step 3: Set up a laser in the place where the camera will go Step 4: Turn on the laser and ensure that the beam is straight in both the vertical and horizontal directions along the optical axis (line to next mirror) Side ViewTop View y laser ruler or height gauge optical axis (z) z x laser right angle ruler optical axis (z)

37 Setting Up a Schlieren System: Step-by-Step (2) Step 5: Adjust any mirrors on this side of the set-up to direct the laser to the test section, ensuring that the beam stays the same height the whole way (use a ruler or a height gauge to test this at every mirror) Step 6: If there are windows on the test section, check for reflections to ensure the laser is perpendicular to the windows Tip 1: Try to keep the laser dot as close to the center of the mirrors as possible Tip 2: The laser light corresponds to approximately the center of the ultimate light beam, so locate the laser beam through the test section where you want the center of the light beam Incident laser beam reflection window piece of paper Tip 1: Use a piece of paper to probe all around the incident beam – any reflections will show up on the paper Tip 2: When it is properly aligned, when you look through the windows all the laser dots will appear in a straight line through the glass

38 Setting Up a Schlieren System: Step-by-Step (3) Step 7: Adjust any mirrors on the light-source side to direct the laser beam to the light source, ensuring the beam stays the same height and is centered on the mirrors Step 8: Adjust the height of the light source so that it is at the same height as the laser beam Step 9: Remove the cover of the light source (make sure it is unplugged and cold!) so you can see the filament or arc bulb. Step 10: Use the controls on the light source to move the filament or bulb until the laser light hits the center of the filament or bulb. Check for reflections. Tip 1: The two most common types of light sources are filament and arc light sources, and there are often lenses mounted on the front Tip 2: First, adjust the height of the light source so that the laser beam is centered on the lens on front of light source if present Tip 3: Check for reflections from the lens using the method described before – adjust light source orientation to minimize relfections

39 Setting Up a Schlieren System: Step-by-Step (4) Step 11: Once alignment of the laser, mirrors, and light source is complete, be sure to secure all the optics in place. Step 12: One-by-one, add the lenses to the setup. Step 13: Once the alignment is complete, secure well all of the optical components. Step 14: Replace the laser with the camera, place the knife-edge at the approximate location of the focus of the schlieren lens, and turn on the light source. Tip 1: The laser light should go through the center of the lens. Tip 2: Check for reflections using the method described before (probe around the beam with a piece of paper between the incident laser beam and the lens). Get rid of reflections by adjusting the height of the lens and angle of the lens with respect to the laser. Now the REAL work begins! Remember, the best tool for setting up a good schlieren system is PATIENCE!

40 Setting Up a Schlieren System: Step-by-Step (5) Step 15: Starting at the light source, very carefully make slight changes to the focusing lens (if one is not included on the light source) to focus the light source down onto the pin-hole or slit. Step 16: Using a precision translation stage, adjust the distance between the pin-hole or slit and the collimating lens until the beam is collimated. Use an aperture if desired to define the size of the beam Tip 1: Position the collimating lens (lens 2) one focal length (f 2 ) from the pin-hole or slit first. Tip 2: Put up a piece of paper a good distance from the lens, then carefully adjust the distance between lens 2 and the pin-hole/slit until the beam on the paper is the same size as at the aperture – then the light is collimated! f1f1 f2f2 light source lens 1lens 2 aperture

41 Setting Up a Schlieren System: Step-by-Step (5) Step 17: After the beam has been collimated, if it is not in the location where you want it in the test area, make adjustments to move the beam. Step 18: Follow the same procedure to position the image correctly on the camera, heeding the Tips 1 and 2. Step 19: Find the approximate location of the focus of the schlieren lens, and place the knife-edge there on translation stages. Step 20: Step the knife-edge in/up to block part of the light – if you are at the focus, the background will become dimmer uniformly. Adjust the location of the knife-edge using the translation stages until you find the focus. Tip 1: Make horizontal adjustments by moving the mirrors – NOT tilting the mirrors, but actually moving them horizontally. It is a good idea to mount the mirrors on translation stages to allow for this. Tip 2: Make vertical adjustments by changing the aperture (if you are using one) if possible; if not, change the height of both the lenses and the light source.

42 References & Where to Buy Optics Reference Books on Schlieren Methods: G. S. Settles. Schlieren and Shadowgraph Techniques. Springer-Verlag, W. Merzkirch. Flow Visualization. 2 nd Ed. Academic Press, Inc., Where to purchase optical components: Thorlabs, Inchttp:// Newport Edmund Optics CVI Melles Griot