Shape-from-Polarimetry: Recovering Sea Surface Topography Shape-from-Polarimetry: Howard Schultz Department of Computer Science University of Massachusetts 140 governors Dr Amherst, MA Howard Schultz Department of Computer Science University of Massachusetts 140 governors Dr Amherst, MA 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

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 parameters S = (S0, S1, S2, S3) The change in polarization on scattering is described by Muller Calculus S OUT = M S IN Where M contains information about the shape and material properties of the scattering media The goal: Measure S OUT and S IN and infer the parameters of M What is polarimetry? Amount of circular polarization Orientation and degree of linear polarization Intensity 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)?

S AW = R AW  S SKY and S WA = T AW  S UP

What is Shape-from-Polarimetry (SFP)? For RaDyO we incorporated 3 simplifying assumptions –Skylight is unpolarized S SKY = S SKY (1,0,0,0) good for overcast days –In deep, clear water upwelling light can be neglected S WA = (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

Slope in Degrees X-Component Y-Component

X-ComponentY-Component

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

Motorized Stage 12mm travel 5mm/sec max speed Objective Assembly Polarizing beamsplitter assembly Camera 1 (fixed) Camera 2 Camera 3 Camera 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

Reconstructed Surface Video

Seeing Through Waves Sub-surface to surface imaging Surface to sub-surface imaging

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 Imaging Array Exposure Center Observation Rays Air Water

Image Formation surface-to-subsurface Imaging Array Exposure Center Air Water Imaging Array Exposure Center

Seeing Through Waves

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-distortion A lens maps incidence angle θ to image position X Lens Imaging Array X θ

X θ Lens Imaging Array Un-distortion A lens maps incidence angle θ to image position X

X Lens Imaging Array Un-distortion A lens maps incidence angle θ to image position X

X θ Lens Imaging Array Un-distortion A lens maps incidence angle θ to image position X

X θ Lens Imaging Array Un-distortion A lens maps incidence angle θ to image position X

Distorted Image Point Image array Un-distortion Use the refraction angle to “straighten out” light rays Air Water

Un-distorted Image Point Image array Un-distortion Use 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 Formation surface-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 contact Howard Schultz University of Massachusetts Department of Computer Science 140 Governors Drive Amherst, MA Phone: