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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

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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

[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


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)?

  • 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 (SFP)?


What is Shape-from-Polarimetry (SFP)?

SAW = RAWSSKYand SWA = TAWSUP


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


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


X-Component

Y-Component

Slope in Degrees


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 initiative

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


Camera 3

Camera 4

Camera 1

(fixed)

Polarizing

beamsplitter

assembly

Objective

Assembly

Camera 2

Motorized Stage

12mm travel

5mm/sec max speed


FLIP INSTRUMENTATION SETUP

Scanning Altimeters

Visible Camera

Air-Sea Flux Package

Infrared Camera

Polarimeter


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


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

Observation Rays

Air

Water

Imaging Array

Exposure Center


Image Formationsurface-to-subsurface

Exposure Center

Imaging Array

Air

Imaging Array

Water

Exposure Center


Seeing Through Waves


Seeing Through Waves

0 20 40 60 80

0 10 20 30 40


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

θ

Lens

Imaging Array

X


Un-distortionA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un-distortionA lens maps incidence angle θ to image position X

Lens

Imaging Array

X


Un-distortionA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un-distortionA lens maps incidence angle θ to image position X

θ

Lens

Imaging Array

X


Un-distortionUse the refraction angle to “straighten out” light rays

Image array

Air

Water

Distorted Image Point


Un-distortionUse the refraction angle to “straighten out” light rays

Image array

Air

Water

Un-distorted Image Point


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

Exposure Center

Imaging Array

Air

Imaging Array

Water

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 contact

Howard Schultz

University of Massachusetts

Department of Computer Science

140 Governors Drive

Amherst, MA 01003

Phone: 413-545-3482

Email: [email protected]


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