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Sally Bane
Explosion Dynamics Laboratory
Directed by Professor Joseph Shepherd
Graduate Aerospace Laboratories (GALCIT)
Ae104b LectureFebruary 9, 2010
Shadowgraph and Schlieren Techniques
2
Schlieren Visualization
• optical techniques have been used for decades to study inhomogeneous media
• Robert Hooke (1635-1703) – “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
c
cn 0
medium in thelight of speed :
m/s 103 vacuumain light of speed :
000292.1 e.g.
1 index refractive :
80
c
xc
n
n
air
Gases: linear relationship between n and the gas density
kn 1
/gcm 23.0 e.g.
tcoefficien Dale-Gladstone :
density gas :
tyrefractivi :1
3
airk
k
n
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 cm3/g = 2.3 x 10-4 m3/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.
y
n
x
n
or
7
Basic Concepts: Light Propagation Through Inhomogeneous Media
Example schliere: Laminar Candle Plume
y
x
2
11
x
n
x
n
12
The gas in the plume is hotter and less dense than the surrounding gas, so
and therefore
12 nn
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
y1
y2
z1 = (c0/n1)t
z1
z2
z2 = (c0/n2)tand
Planar wave front
Rays (normal to wave front)
z = ct = (c0/n)t
Since n2 > n1, c2 < c1 so
z2 < z1
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
y1
y
y2 (c0/n2)t
z1
z2
Distance wave front moves in time t:
tn
ctc 0
dn/dy < 0
Refraction angle:
y
tnctnc
)/(/
tan 1020
z
Also:
0c
nzt
z
y
nn
nn
n
21
21
11
Basic Concepts: Light Propagation Through Inhomogeneous Media
y
z
x
y1
y
y2 (c0/n1)t
z1
z2
0 , 0 zydn/dy < 0
z
dy
dn
ndz
d 1
Because is a very small angle, it is approximately equivalent to dy/dz, the slope of the refracted ray.
y
n
nz
y
1
2
2
x
n
nz
x
1
2
2
and
Curvature of refracted ray
y
12
Basic Concepts: Light Propagation Through Inhomogeneous Media
y
z
x
y1
y
y2 (c0/n1)t
z1
z2
dn/dy < 0
z
For a 2D schliere of length L along the optical axis (z):
dzy
n
ny
1 dz
x
n
nx
1and
So the angular ray deflection in the x and y directions are:
y
n
n
Ly
0
x
n
n
Lx
0
and
Refraction caused by gradients of n, not overall level of n!
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
screenScreen
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!
constant yn
as move down optical path (z-direction),
so rays shift non-uniformly
constant 22 yn
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/N2 mixing layer (Settles 2001)
17
Shadowgraphy vs. Schlieren Imaging
Less sensitive except for special cases (e.g. shock waves)
More sensitive in general
Schlieren Imaging Shadowgraphy
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, ∂2n/∂x2 and ∂2n/∂y2
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 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 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 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 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 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 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
a
a
Undisturbed composite source image
Weak source image
displaced by schlieren
object
25
Schlieren System – Extended Light Source
Knife-edge
a
a
Undisturbed composite source image
Weak source image displaced
by schlieren object
Sensitivity:
Constrast:a
f
E
EC ys
differential illuminance at an image point
background illuminance
focal length of the schlieren lens
refraction angle
:E
:E
:sf
:ySensitivity: d
dC
d
dS
input
output
a
fS s
Larger focal length = better sensitivity
More obstruction of source image = better sensitity
26
Z-Type Schlieren Arrangement
camera
knife-edge
parabolic mirrorparabolic mirror
light sourcecondenser
lenspinhole 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:
243121
111 and
111
fxxfxx
Constraints:
For Real Image: 0, 32 xx
2311 and fxfx
Table Size:
Lxxxx 4321
where L is limited by the size of the optics table
Magnification:3
4
1
2
1
2
0
1 and x
x
y
y
x
x
y
y
I
II
13
24
0
2
xx
xx
y
yM I Total
Magnification
x1 f1
x2 x3 x4
f2
y0
yI1
yI2
Lens 1 Lens 2Knife-edge
Object (FOV)
Inverted object image
Object image
32
Important Equations
Must Satisfy:
13
24
243
121
111
111
xx
xxM
fxx
fxx
Under the Constraints:
Lx
fx
fx
ii
4
1
23
11
SUMMARY
x1 f1
x2 x3 x4
f2
y0
yI1
yI2
Lens 1 Lens 2Knife-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
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:
x1
f
x2
yOyI
Schlieren “Lens” (concave mirror)
Knife-edges
Object (1” Ø field-of-view)
Inverted object image on
camera CCD
f
Equations:
fxx
111
21
1
2
x
x
y
yM
O
I
Knowns: mm 1000f
Diameter Beam
CCD Camera of SizeM
625.0in. 1
in. 8/5
1
2
Unknowns: 21 , xx
35
How My Schlieren Setup Works
fxx
xx 1
21
12
12 Mxx
1
2 fMx
M
Mxx
xMx 11
111
11
12 into
3
3Invert fM
Mx
11
Solve for x1:
mm 1000625.0
625.0111
fM
Mx mm 26001 x
Then from :2 mm 2600625.012 Mxx mm 16252 x
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 View Top View
ylaser
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 frontTip 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 presentTip 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 (f2) 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!
f1 f2
light source
lens 1 lens 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, 2001.
W. Merzkirch. Flow Visualization. 2nd Ed. Academic Press, Inc., 1987.
Where to purchase optical components:
Thorlabs, Inc http://www.thorlabs.com Newport http://www.newport.com Edmund Optics http://www.edmundoptics.com CVI Melles Griot http://www.cvimellesgriot.com