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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

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

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


Shape from polarimetry recovering sea surface topography

  • 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


Shape from polarimetry recovering sea surface topography

Linear Polarization

http://www.enzim.hu/~szia/cddemo/edemo0.htm


Shape from polarimetry recovering sea surface topography

Circular Polarization


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 sfp1

What is Shape-from-Polarimetry (SFP)?


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


What is shape from polarimetry sfp4

What is Shape-from-Polarimetry (SFP)?


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


Shape from polarimetry recovering sea surface topography

Looking at 90 to the waves

Looking at 45 to the waves

Looking at 0 to the waves


Shape from polarimetry recovering sea surface topography

X-Component

Y-Component

Slope in Degrees


Shape from polarimetry recovering sea surface topography

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/


Shape from polarimetry recovering sea surface topography

Camera 3

Camera 4

Camera 1

(fixed)

Polarizing

beamsplitter

assembly

Objective

Assembly

Camera 2

Motorized Stage

12mm travel

5mm/sec max speed


Shape from polarimetry recovering sea surface topography

FLIP INSTRUMENTATION SETUP

Scanning Altimeters

Visible Camera

Air-Sea Flux Package

Infrared Camera

Polarimeter


Sample results

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 results1

Sample Results


Shape from polarimetry recovering sea surface topography

X and Y slope field


Convert slope arrays to a height array

Convert slope arrays to a height array

Use the Fourier derivative theorem


Reconstructed surface video

Reconstructed Surface Video


Seeing through waves

Seeing Through Waves

  • Sub-surface to surface imaging

  • Surface to sub-surface imaging


Optical flattening

Optical Flattening


Optical flattening1

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 formation subsurface to surface

Image FormationSubsurface-to-surface

Observation Rays

Air

Water

Imaging Array

Exposure Center


Image formation surface to subsurface

Image Formationsurface-to-subsurface

Exposure Center

Imaging Array

Air

Imaging Array

Water

Exposure Center


Shape from polarimetry recovering sea surface topography

Seeing Through Waves


Seeing through waves1

Seeing Through Waves

0 20 40 60 80

0 10 20 30 40


Optical flattening2

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 distortion a lens maps incidence angle to image position x

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

Image array

Air

Water

Un-distorted Image Point


Real time un distortion

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 formation surface to subsurface1

Image Formationsurface-to-subsurface

Exposure Center

Imaging Array

Air

Imaging Array

Water

Exposure Center


Detecting submerged objects lucky imaging

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


Shape from polarimetry recovering sea surface topography

Questions?


Shape from polarimetry recovering sea surface topography

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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