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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 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) Amount of circular polarization Orientation and degree of linear polarization Intensity • The change in polarization on scattering is described by Muller Calculus SOUT = M SIN Incident Light Muller Matrix Scattered Light 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 Shape-from-Polarimetry (SFP)? • Use the change in polarization of reflected skylight to infer the 2D surface slope, , for every pixel the/y imaging z /x andin z polarimeter’s field-of-view What is Shape-from-Polarimetry (SFP)? What is Shape-from-Polarimetry (SFP)? SAW = RAWSSKY and SWA = TAWSUP RAW 0 0 0 0 and T WA 0 0 0 Re 0 0 0 0 Re 0 0 0 2 1 tan i t 2 tan i t 2 1 sin i t 2 sin i t Re 0 0 Re 0 0 0 0 Re tan i t sin i t tan i t sin i t 2 2 2 2 2sin sin 2sin sin 4 sin sin t 1 1 i t i t i Re 2 sin i t cosi t 2 sin i t sin 2 i t cos2 i t sin i n sin t 1 and sin i sin t n 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 S12 S22 DOLP S02 1 1 S2 and tan 90 2 S1 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 Infrared Camera Polarimeter Air-Sea Flux Package 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 h h sX , sY x y sˆX F sX , sˆY F sY ik X hˆ sˆX , ik y hˆ sˆY ˆh ik X sˆX ikY sˆY k2 h F 1 hˆ 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 Formation Subsurface-to-surface Air Observation Rays Water Imaging Array Exposure Center Image Formation surface-to-subsurface Exposure Center Imaging Array Air Water Imaging Array 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-distortion A lens maps incidence angle θ to image position X θ Lens Imaging Array X Un-distortion A lens maps incidence angle θ to image position X θ Lens Imaging Array X Un-distortion A lens maps incidence angle θ to image position X Lens Imaging Array X Un-distortion A lens maps incidence angle θ to image position X θ Lens Imaging Array X Un-distortion A 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 Air Water Image array Distorted Image Point Un-distortion Use the refraction angle to “straighten out” light rays Air Water Image array 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 Formation surface-to-subsurface Exposure Center Imaging Array 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 01003 Phone: 413-545-3482 Email: [email protected]