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Shape-from-Polarimetry:Recovering Sea Surface Topography
Shape-from-Polarimetry:Recovering Sea Surface Topography
Howard Schultz Department of Computer Science
University of Massachusetts140 governors Dr
Amherst, MA [email protected]>
Howard Schultz Department of Computer Science
University of Massachusetts140 governors Dr
Amherst, MA [email protected]>
October 2011
Outline
• Why recover the spatial-temporal structure of ocean waves?• Requirements• What is polarimetry?• What is the Shape-from-Polarimetry?• Build and Test an Imaging Polarimeter for Ocean Apps. • Recent Experiment and Results• Optical Flattening• Seeing Through Waves
• Why recover the structure of the ocean surface?– Characterize small small-scale wave dynamics and microscale breaking– Air-sea interactions occur at short wavelengths– Non-linear interaction studies require phase-resolved surface topography– Enable through-the-wave imaging– Detect anomalies in surface slope statistics
• Why use a passive optical technique– Probes disturb the air-sea interaction– Radar do not produce phase-resolved surfaces– Active techniques are complex and expensive
• Requirements– Spatial resolution (resolve capillary waves) ~ 1mm– Temporal resolution ~60Hz sampling rate– Shutter speed < 1 msec
What is polarimetry?
• Light has 3 basic qualities• Color, intensity and polarization• Humans do not see polarization
Linear Polarization
http://www.enzim.hu/~szia/cddemo/edemo0.htm
Circular Polarization
• A bundle of light rays is characterized by intensity, a frequency distribution (color), and a polarization distribution
• Polarization distribution is characterized by Stokes parametersS = (S0, S1, S2, S3)
• The change in polarization on scattering is described by Muller Calculus
SOUT = M SIN
• Where M contains information about the shape and material properties of the scattering media
• The goal: Measure SOUT and SIN and infer the parameters of M
What is polarimetry?
Amount of circular polarizationOrientation and degree of linear polarizationIntensity
Incident LightMuller MatrixScattered Light
What is Shape-from-Polarimetry (SFP)?
• Use the change in polarization of reflected skylight to infer the 2D surface slope, , for every pixel in the imaging polarimeter’s field-of-view
€
∂z /∂x and ∂z /∂y
What is Shape-from-Polarimetry (SFP)?
What is Shape-from-Polarimetry (SFP)?
€
RAW =
α +η α −η 0 0
α −η α +η 0 0
0 0 γ Re 0
0 0 0 γ Re
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
and TWA =
′ α + ′ η ′ α − ′ η 0 0
′ α − ′ η ′ α + ′ η 0 0
0 0 ′ γ Re 0
0 0 0 ′ γ Re
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
€
α =1
2
tan θ i −θ t( )
tan θ i +θ t( )
⎡
⎣ ⎢
⎤
⎦ ⎥
2
η =1
2
sin θ i −θ t( )
sin θ i +θ t( )
⎡
⎣ ⎢
⎤
⎦ ⎥
2
γRe =tan θ i −θ t( ) sin θ i −θ t( )
tan θ i +θ t( ) sin θ i +θ t( )
€
′ α =1
2
2sin ′ θ i( ) sin ′ θ t( )
sin ′ θ i + ′ θ t( ) cos ′ θ i + ′ θ t( )
⎡
⎣ ⎢
⎤
⎦ ⎥
2
′ η =1
2
2sin ′ θ i( ) sin ′ θ t( )
sin ′ θ i + ′ θ t( )
⎡
⎣ ⎢
⎤
⎦ ⎥
2
′ γ Re =4 sin2 ′ θ i( ) sin2 ′ θ t( )
sin2 ′ θ i + ′ θ t( ) cos2 ′ θ i + ′ θ t( )
SAW = RAWSSKY and SWA = TAWSUP
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sin θ i( ) = n sin θ t( ) and sin ′ θ i( ) =1
nsin ′ θ t( )
What is Shape-from-Polarimetry (SFP)?
• For RaDyO we incorporated 3 simplifying assumptions– Skylight is unpolarized SSKY = SSKY(1,0,0,0)
good for overcast days– In deep, clear water upwelling light can be neglected
SWA = (0,0,0,0).
– The surface is smooth within the pixel field-of-view
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DOLP θ( ) =S1
2 + S22
S02 and φ =
1
2tan−1 S2
S1
⎛
⎝ ⎜
⎞
⎠ ⎟+ 90°
What is Shape-from-Polarimetry (SFP)?
How well does the SFP technique work?
• Conduct a feasibility study– Rented a linear imaging polarimeter– Laboratory experiment
• setup a small 1m x 1m wavetank• Used unpolarized light• Used wire gauge to simultaneously measure wave profile
– Field experiment• Collected data from a boat dock• Overcast sky (unpolarized)• Used a laser slope gauge
Looking at 90 to the waves
Looking at 45 to the waves
Looking at 0 to the waves
Slope in Degrees
X-Component
Y-Component
X-Component Y-Component
Slope in Degrees
Build and Test an Imaging Polarimeter for Oceanographic Applications
–Funded by an ONR DURIP–Frame rate 60 Hz–Shutter speed as short as 10 μsec–Measure all Stokes parameters–Rugged and light weight–Deploy in the Radiance in a Dynamic
Ocean (RaDyO) research initiativehttp://www.opl.ucsb.edu/radyo/
Motorized Stage12mm travel5mm/sec max speed
ObjectiveAssembly
Polarizing beamsplitterassembly
Camera 1(fixed)
Camera 2
Camera 3Camera 4
FLIP INSTRUMENTATION SETUP
Scanning Altimeters
Infrared Camera
Air-Sea Flux Package
Polarimeter
Visible Camera
Sample Results
• A sample dataset from the Santa Barbara Channel experiment was analyzed
• Video 1 shows the x- and y-slope arrays for 1100 frames• Video 2 shows the recovered surface (made by
integrating the slopes) for the first 500 frames
Sample Results
X and Y slope field
Convert slope arrays to a height array
Use the Fourier derivative theorem
€
sX =∂h
∂x, sY =
∂h
∂y
ˆ s X = F sX( ), ˆ s Y = F sY( )
ikXˆ h = ˆ s X , iky
ˆ h = ˆ s Y
ˆ h =−ikX
ˆ s X − ikYˆ s Y
k 2
h = F −1 ˆ h ( )
Reconstructed Surface Video
Seeing Through Waves
• Sub-surface to surface imaging• Surface to sub-surface imaging
Optical Flattening
Optical Flattening
• Remove the optic distortion caused by surface waves to make it appear as if the ocean surface was flat– Use the 2D surface slope field to find the
refracted direction for each image pixel– Refraction provides sufficient information to
compensate for surface wave distortion– Real-time processing
Image FormationSubsurface-to-surface
Imaging Array
Exposure Center
Observation RaysAir
Water
Image Formationsurface-to-subsurface
Imaging Array
Exposure Center
Air
Water
Imaging Array
Exposure Center
Seeing Through Waves
0 20 40 60 80 0 10 20 30 40
Seeing Through Waves
Optical Flattening
• Remove the optic distortion caused by surface waves to make it appear as if the ocean surface was flat– Use the 2D surface slope field to find the
refracted direction for each image pixel– Refraction provides sufficient information to
compensate for surface wave distortion– Real-time processing
Un-distortionA lens maps incidence angle θ to image position X
Lens
Imaging Array
X
θ
X
θ
Lens
Imaging Array
Un-distortionA lens maps incidence angle θ to image position X
X
Lens
Imaging Array
Un-distortionA lens maps incidence angle θ to image position X
X
θ
Lens
Imaging Array
Un-distortionA lens maps incidence angle θ to image position X
X
θ
Lens
Imaging Array
Un-distortionA lens maps incidence angle θ to image position X
Distorted Image Point
Image array
Un-distortionUse the refraction angle to “straighten out” light
rays
Air
Water
Un-distorted Image Point
Image array
Un-distortionUse the refraction angle to “straighten out” light
rays
Air
Water
Real-time Un-Distortion
• The following steps are taken Real-time Capable– Collect Polarimetric Images ✔– Convert to Stokes Parameters ✔– Compute Slopes (Muller Calculus) ✔– Refract Rays (Lookup Table) ✔– Remap Rays to Correct Pixel ✔
Image Formationsurface-to-subsurface
Imaging Array
Exposure Center
Air
Water
Imaging Array
Exposure Center
Detecting Submerged Objects“Lucky Imaging”
• Use refraction information to keep track of where each pixel (in each video frame) was looking in the water column
• Build up a unified view of the underwater environment over several video frames
• Save rays that refract toward the target area• Reject rays that refract away from the target
area
Questions?
For more information contactHoward SchultzUniversity of MassachusettsDepartment of Computer Science140 Governors DriveAmherst, MA 01003Phone: 413-545-3482Email: [email protected]
