Transcript SPIE2012x - UMass Amherst

Shape-from-Polarimetry:
A New Tool for Studying the Air-Sea Interface
Howard Schultz, UMass Amherst, Dept of Computer Science
Chris J. Zappa, Michael L. Banner, Russel Morison, Larry Pezzaniti
Introduction
Introduction
• 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
Muller Calculus
•
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
Shape-from-Polarimetry (SFP)
• Use the change in polarization of reflected or
refracted skylight to infer the 2D surface
slope, z /x and z /y, for every pixel in
the imaging polarimeter’s field-of-view

Shape-from-Polarimetry
S = SAW + SWA
SAW = RAWSSKY and SWA = TAWSUP
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
4 sin 2 i sin 2 t
1  2sin i sin t
1 2sin i sin t 
  
   
 Re
 
2 sin i t cosi t 
2  sin i t 
sin 2 i t cos2 i t

sin  i   n sin  t 
1
and sin i   sin t 
n
Kattawar, G. W., and C. N. Adams (1989), “Stokes vector calculations of the submarine light-field in an
atmosphere-ocean with scattering according to a Rayleigh phase matrix - Effect of interface
refractive-index on radiance and polarization,” Limnol. Oceanogr., 34(8),1453-1472.

Shape-from-Polarimetry
• For simplicity 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 
Shape-from-Polarimetry
Sensitivity =  (DOLP) / θ
Experiments
• 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 an Imaging Polarimeter for Oceanographic
Applications – Polaris Sensor Technologies
– 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
Deployed during the ONR experiment
Radiance in a Dynamic Ocean (RaDyO)
Scanning Altimeters and Visible Camera
~36°
Imaging Polarimeter
Air-Sea Flux Package
Analysis & Conclusion
• 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
Time series comparison
Convert slope arrays to a height array
Convert slope arrays to a height array
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
Analysis & Conclusion
• The shape-from-polarimetry method works well for
small waves in the 1mm to 10cm range.
• Need to improve the theory by removing the three
simplifying assumptions
– Skylight is unpolarized SSKY = SSKY(1,0,0,0)
– Upwelling light can be neglected SWA = (0,0,0,0).
– The surface is smooth within the pixel field-of-view
• Needs to have an independent estimate of lower
frequency waves.
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
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]