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Shape-from-Polarimetry: Recovering Sea Surface Topography. Howard Schultz Department of Computer Science University of Massachusetts 140 governors Dr Amherst, MA 01003 hschultz @cs.umass.edu >. October 2011. Outline. Why recover the spatial -temporal structure of ocean waves?

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Shape-from-Polarimetry:

Recovering Sea Surface Topography

Howard Schultz

Department of Computer Science

University of Massachusetts

140 governors Dr

Amherst, MA 01003

hschultz@cs.umass.edu>

October 2011


Outline
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
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



What is polarimetry1

Amount of circular polarization

Orientation and degree of linear polarization

Intensity

What is polarimetry?

  • A bundle of light rays is characterized by intensity, a frequency distribution (color), and a polarization distribution

  • Polarization distribution is characterized by Stokes parameters

    S = (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

Incident Light

Muller Matrix

Scattered Light


What is shape from polarimetry sfp
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



What is shape from polarimetry sfp2
What is Shape-from-Polarimetry (SFP)?

SAW = RAWSSKYand SWA = TAWSUP


What is shape from polarimetry sfp3
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



How well does the sfp technique work
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


X-Component

Y-Component

Slope in Degrees


X-Component

Y-Component

Slope in Degrees


Build and test an imaging polarimeter for oceanographic applications
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 initiative

    http://www.opl.ucsb.edu/radyo/


Camera 3 Applications

Camera 4

Camera 1

(fixed)

Polarizing

beamsplitter

assembly

Objective

Assembly

Camera 2

Motorized Stage

12mm travel

5mm/sec max speed


FLIP INSTRUMENTATION SETUP Applications

Scanning Altimeters

Visible Camera

Air-Sea Flux Package

Infrared Camera

Polarimeter


Sample results
Sample Results Applications

  • 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 results1
Sample Results Applications


X and Y slope field Applications


Convert slope arrays to a height array
Convert slope arrays to a height array Applications

Use the Fourier derivative theorem



Seeing through waves
Seeing Through Waves Applications

  • Sub-surface to surface imaging

  • Surface to sub-surface imaging


Optical flattening
Optical Flattening Applications


Optical flattening1
Optical Flattening Applications

  • 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 formation subsurface to surface
Image Formation ApplicationsSubsurface-to-surface

Observation Rays

Air

Water

Imaging Array

Exposure Center


Image formation surface to subsurface
Image Formation Applicationssurface-to-subsurface

Exposure Center

Imaging Array

Air

Imaging Array

Water

Exposure Center


Seeing Through Waves Applications


Seeing through waves1
Seeing Through Waves Applications

0 20 40 60 80

0 10 20 30 40


Optical flattening2
Optical Flattening Applications

  • 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 distortion a lens maps incidence angle to image position x
Un-distortion ApplicationsA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un distortion a lens maps incidence angle to image position x1
Un-distortion ApplicationsA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un distortion a lens maps incidence angle to image position x2
Un-distortion ApplicationsA lens maps incidence angle θ to image position X

Lens

Imaging Array

X


Un distortion a lens maps incidence angle to image position x3
Un-distortion ApplicationsA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un distortion a lens maps incidence angle to image position x4
Un-distortion ApplicationsA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un distortion use the refraction angle to straighten out light rays
Un-distortion ApplicationsUse the refraction angle to “straighten out” light rays

Image array

Air

Water

Distorted Image Point


Un distortion use the refraction angle to straighten out light rays1
Un-distortion ApplicationsUse the refraction angle to “straighten out” light rays

Image array

Air

Water

Un-distorted Image Point


Real time un distortion
Real-time Un-Distortion Applications

  • 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 formation surface to subsurface1
Image Formation Applicationssurface-to-subsurface

Exposure Center

Imaging Array

Air

Imaging Array

Water

Exposure Center


Detecting submerged objects lucky imaging
Detecting Submerged Objects Applications“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? Applications


For more information contact Applications

Howard Schultz

University of Massachusetts

Department of Computer Science

140 Governors Drive

Amherst, MA 01003

Phone: 413-545-3482

Email: hschultz@cs.umass.edu


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