Femtosecond Photography
Transcript of Femtosecond Photography
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Femtophotography(Trillion frames per second):
Capturing echoes of light around a
corner
Ashar A Z
CPMU Seminar
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Theme
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Plan of talk
Fast photography
Streak camera: Principle and operation
Imaging around a corner : Steps involved
Experimental setup
Geometric reconstruction using streak camera
5D Light propagation, model and surface reconstruction
3D Reconstruction process
Applications
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Fast photography
nanosecond exposuremagneto optic shutter
Raptronic camera used for collecting nuclear explosion after 2 msDr. Harold Edgerton, Germeshausen and Grier
BVd Eadweard Muybridge,Source: wikipedia
4Source: http://webmuseum.mit.edu
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Femtosecond laser Kerr lens mode locked Ti: Sapphire laser=795 nmRepetitions rate = 75 MHz, ie pulse repeats in every 13.3 ns
Streak cameraExposure time =100 ms , ie 7.5 million reading
Computation for reconstruction of image
Components of femtophotographyLooking around a corner to see a hidden object
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Pico10-12 sec
Velocity of light = 3 10 8 m/sDistance travelled by light in 2 ps ~ 610 -4 meter ~ 0.6 mm
Femtophotography
6Source: http://web.media.mit.edu/~raskar/cornar/
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Streak camera: Working principle
Source: Photonic Device Dynamics Group website,Tyndall National institute.7
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(a)
(b)
=888 nm
Time =0.5 ns
A streak camera will stretch information
in time.
Ultrafast, femtosecond time resolution
3D
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Time resolved photoluminescence
Pulsedlaser
Spectrograph
Streak camera
Sample
Source: Photonic Device Dynamics Group website,Tyndall National institute.
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Streak camera: Image formation
s
Point source of light
Spherical wavefront contribute tohyperbola in space time streakimage.
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Why streak camera ?
100 cm
1 cm
P1
P2
Velocity of light , c 3x10 10 cm/s
3x10 10 cm 1 second
0.05 cm 1.6 x 10 -12 seconds,
PICO SECONDS
Traditional cameras are limited by temporal resolution
Detector
Materials transport limitations
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Imaging around a corner
Phase I : Data acquisition 60 laser position on wall with 100 images for each position images taken at one position are overlayed to reduce the noise.
Optical imaging + Computational reconstruction
Phase II : Data processing Streak images are loaded, and corrected for intensity andspatiotemporal jitter.
Phase III: 3D reconstruction Corrected streak images are used in back projection algorithmto reconstruct the image
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Phase I:Experimental setup
Calibrationspot
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Source : Nature video
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Foci of ellipse
Back projection of points
Location on the hidden surfacepatch which contributed to pixelsp,q and r.
No correspondenceWe dont know whether or notlight detected at two pixels camefrom the same point on hidden
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Phase II: Geometric reconstruction usingstreak camera
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22 cm2
Occluder
Diffuserwall
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Scale bar 2 cm
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Phase III: Modeling light pulse propagation
5D light transport.
4 segments for optical path
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4 Segments 1 and 4 directed segments.
data received bycamera Cat time tat pointp
),( tpIC
)),((),( wCBLtwHItwI CR
Primary scattering problem.
data received surfaceat time tat pointp
),( twIR
H(w) is the projective transformation (homography) mapping coordinates
onR to camera co-ordinates 15
Time compensation for segment (1) and (4)
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Measuring distance in time units, setting c=1
SSc
c
R sddsItrr
twI
2
2),()(1),(
S lclc
R sdrrtrr
ItwI 222
)(11
),(
)/()(),( 2llS rrIsI sLrl
Generating streak image
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emitter sending pulses at time),( sIS
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Hyperbolic contribution
For fixedL and w at time t, t= rc + rl
In (w,t) space
222 ),()()( yxzvyuxrrt cl , a prolate spheroid
Each point of surfaceSwill contribute a hyperboloid to the imageIR(u , v , t).
Hyperboloid shape depends on depthz(x , y) and will be shifted along t axis
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Back projection: Principle of ComputedTomography
Each sample acquired in a CTsystem is equal to the sum of theimage values along a ray pointing tothat sample
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Absorption
http://www.dnatube.com
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Backprojection is formed bysmearing eachview back through the image in the
direction it was originally acquired
Filtered back projection
Digital Signal Processing: A Practical Guide for Engineers and Scientist By Steven W. Smith 19
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Voxel Grid setup
Down sampling(optional)
Filtering and threshold
Back projection
Using time of flight(ToF) method
3D Reconstruction
A voxel v can contribute to streakcamera pixel only if it satisfy ToF criteria.
Heat mapsum is overall contributing
pixelsp, andIPis the intensitymeasured at that pixel.
PP
ILvwvvH
)()(
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Applications
23Source: http://web.media.mit.edu/~raskar/cornar/
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Thank you
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