SALSA: Full Stokes Polarization camera - Spatial
inhomogeneity and field calibration
Mathieu Vedel* – Nick Lechocinski – Sebastien Breungot
Bossa Nova Technologies
11922 Jefferson Blvd
Culver City, CA 90230,USA
www.bossanovatech.com
[email protected]
Mathieu Vedel – Bossa Nova Technologies – March 2014
I)
Bossa Nova Technologies overview
II)
SALSA Technology
A.
B.
C.
III)
Division of time polarimeter
Calibration
Need for “field” calibration
Full Stokes polarization imager
A.
B.
C.
Software
Specifications
Potential applications - Examples
Mathieu Vedel – Bossa Nova Technologies – March 2014
Company Overview
 Located in Los Angeles (Culver City), CA, USA
 Founded in 2002
 Small business of 7 people specialized in optics, electronics, imaging and
software development
 Manufacturer of scientific and testing equipment : laser ultrasonic inspection
equipment, polarization cameras and systems for the cosmetic testing
 Provides research for NASA, NSF, DoD and corporate clients
Mathieu Vedel – Bossa Nova Technologies – March 2014
Polarization imaging products
Bossa Nova Technologies provides products and services
for non-destructive testing.
3 lines of products:
• Polarization Imaging
SAMBA, SALSA, RUMBA & POLKA
• Cosmetic Testing Equipment (Hair & Face)
• Laser Ultrasonics
TEMPO, QUARTET
LU Systems
Mathieu Vedel – Bossa Nova Technologies – March 2014
Our Objective was to develop a camera that is:
• COMPACT!
Mathieu Vedel – Bossa Nova Technologies – March 2014
Our Objective was to develop a camera that is:
• COMPACT!
• Uses off the shelf components
Mathieu Vedel – Bossa Nova Technologies – March 2014
Our Objective was to develop a camera that is:
• COMPACT!
• Uses off the shelf components
• Turn-key system
Mathieu Vedel – Bossa Nova Technologies – March 2014
Our Objective was to develop a camera that is:
• COMPACT!
• Uses off the shelf components
• Turn-key system
• At reasonable cost AND profitable!
Mathieu Vedel – Bossa Nova Technologies – March 2014
Full Stokes Polarization Imager
SALSA: Full Stokes Polarization camera
Complete turn-key system:
 Camera
 C-mount lens ready
 Controller
 Laptop
 Software
 SDK (LabVIEW)
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Technology: 2 FLCs, 1 Analyser
Iraw1
PSA: State 1
Raw images
time
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Technology: 2 FLCs, 1 Analyser
PSA: State 1
Iraw1
PSA: State 2
Iraw2
time
Mathieu Vedel – Bossa Nova Technologies – March 2014
Raw images
SALSA Technology
Technology: 2 FLCs, 1 Analyser
PSA: State 1
Iraw1
PSA: State 2
Iraw2
PSA: State 3
Iraw3
time
Mathieu Vedel – Bossa Nova Technologies – March 2014
Raw images
SALSA Technology
Technology: 2 FLCs, 1 Analyser
PSA: State 1
Iraw1
PSA: State 2
Iraw2
Processing
PSA: State 3
Iraw3
PSA: State 4
Iraw3
time
Mathieu Vedel – Bossa Nova Technologies – March 2014
Raw images
SALSA Technology
Technology -2
𝑰𝒓𝒂𝒘𝟏
𝑰
𝐗 = 𝒓𝒂𝒘𝟐 = 𝐂 ∙
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
Images
acquired
𝑺𝟎,𝒊𝒏
𝑺𝟏,𝒊𝒏
𝑺𝟐,𝒊𝒏
𝑺𝟑,𝒊𝒏
Incident
Stokes vector
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Technology -2
𝑰𝒓𝒂𝒘𝟏
𝑰
𝐗 = 𝒓𝒂𝒘𝟐 = 𝐂 ∙
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
Images
acquired
𝑺𝟎,𝒊𝒏
𝑺𝟏,𝒊𝒏
𝑺𝟐,𝒊𝒏
𝑺𝟑,𝒊𝒏
Incident
Stokes vector
Mathieu Vedel – Bossa Nova Technologies – March 2014
𝑺𝒊𝒏
Incident Stokes vector
estimate
𝑰𝒓𝒂𝒘𝟏
𝑰
= 𝑪−𝟏 ∙ 𝒓𝒂𝒘𝟐
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
Calibration
SALSA Technology
Technology -2
𝑰𝒓𝒂𝒘𝟏
𝑰
𝐗 = 𝒓𝒂𝒘𝟐 = 𝐂 ∙
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
Images
acquired
S0
𝑺𝟎,𝒊𝒏
𝑺𝟏,𝒊𝒏
𝑺𝟐,𝒊𝒏
𝑺𝟑,𝒊𝒏
𝑺𝒊𝒏
𝑰𝒓𝒂𝒘𝟏
𝑰
= 𝑪−𝟏 ∙ 𝒓𝒂𝒘𝟐
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
Incident
Stokes vector
Incident Stokes vector
estimate
Calibration
S1
S2
S3
Deduction of the 4 Stokes parameters!
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Mathematical model
Data Reduction Matrix (DRM) *
𝑰𝒓𝒂𝒘𝟏
𝑰
𝐗 = 𝒓𝒂𝒘𝟐 = 𝐂 ∙
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
Images
acquired
𝑺𝟎,𝒊𝒏
𝑺𝟏,𝒊𝒏
𝑺𝟐,𝒊𝒏
𝑺𝟑,𝒊𝒏
Incident
Stokes vector
𝑺𝒊𝒏
Incident Stokes vector
estimate
𝑰𝒓𝒂𝒘𝟏
𝑰
= 𝑪−𝟏 ∙ 𝒓𝒂𝒘𝟐
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
DRM
 Experimental determination of the DRM
*R. A. Chipman, “Polarimetry,” in Handbook of Optics, Vol. 2, Chap. 22.
Schott Tyo J. et al, "Review of passive imaging polarimetry for remote sensing applications", Applied Optics, Vol. 45, N22.
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Mathematical model
PSA Mueller matrices
𝑺𝒊𝟎,𝒐𝒖𝒕
𝒊
𝑺𝒔𝒕𝒂𝒕𝒆
𝒐𝒖𝒕
=
𝑺𝒊𝟏,𝒐𝒖𝒕
𝑺𝒊𝟐,𝒐𝒖𝒕
𝑺𝒊𝟑,𝒐𝒖𝒕
Polarization State Analyzer in
position i, i={0;1;2;3}
Mathieu Vedel – Bossa Nova Technologies – March 2014
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟎
=
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝑺𝟎,𝒊𝒏
𝟎𝟑
𝒊
𝑺𝟏,𝒊𝒏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟑
∙
𝒊
𝑺𝟐,𝒊𝒏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟑
𝒊
𝑺𝟑,𝒊𝒏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟑
Mueller matrix for the ith
state of the PSA
SALSA Technology
Mathematical model
PSA Mueller matrices
𝑺𝒊𝟎,𝒐𝒖𝒕
𝒊
𝑺𝒔𝒕𝒂𝒕𝒆
𝒐𝒖𝒕
=
𝑺𝒊𝟏,𝒐𝒖𝒕
𝑺𝒊𝟐,𝒐𝒖𝒕
𝑺𝒊𝟑,𝒐𝒖𝒕
Polarization State Analyzer in
position i, i={0;1;2;3}
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟎
=
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟏
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟐
Mueller matrix for the ith
state of the PSA
Detectors are only sensitive to the intensity of light
𝒊
𝒊
𝒊
𝒊
𝑺𝑷𝑺𝑨𝒊
𝟎,𝒐𝒖𝒕 = 𝒎𝟎𝟎 . 𝑆0,𝑖𝑛 + 𝒎𝟎𝟏 . 𝑆1,𝑖𝑛 + 𝒎𝟎𝟐 . 𝑆2,𝑖𝑛 + 𝒎𝟎𝟑 . 𝑆3,𝑖𝑛
Mathieu Vedel – Bossa Nova Technologies – March 2014
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝑺𝟎,𝒊𝒏
𝟎𝟑
𝒊
𝑺𝟏,𝒊𝒏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟏𝟑
∙
𝒊
𝑺𝟐,𝒊𝒏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟐𝟑
𝒊
𝑺𝟑,𝒊𝒏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟑𝟑
SALSA Technology
Experimental setup
𝜗𝑝𝑜𝑙
𝜗𝜆/4
CCD
Unpolarized
light
PSG: Linear polarizer + 𝜆/4
Known polarization
state 𝑺𝒊𝒏
𝑺𝟎𝟎,𝒊𝒏
𝑺𝟎𝟏,𝒊𝒏
𝑺𝟎𝟐,𝒊𝒏
𝑺𝟎𝟑,𝒊𝒏
𝑺𝟏𝟎,𝒐𝒖𝒕 = 𝑺𝟏𝟎,𝒊𝒏
⋮
⋮
𝑵
𝑵
𝑺𝟎,𝒐𝒖𝒕 𝑖
𝑺𝟎,𝒊𝒏
𝑺𝟏𝟏,𝒊𝒏
⋮
𝑵
𝑺𝟏,𝒊𝒏
𝑺𝟏𝟐,𝒊𝒏
⋮
𝑵
𝑺𝟐,𝒊𝒏
𝑺𝟏𝟑,𝒊𝒏
⋮
𝑵
𝑺𝟑,𝒊𝒏
𝑺𝟎𝟎,𝒐𝒖𝒕
PSA
Lens
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
∙ 𝒔𝒕𝒂𝒕𝒆 𝒊
𝒎𝟎𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
N Linear equations: possible estimation of the 𝒎𝒊𝟎,𝒍 parameters
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Data Reduction Matrix
State i={0;1;2;3}
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
=
𝒔𝒕𝒂𝒕𝒆 𝒊
𝒎𝟎𝟐
𝒊
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
𝑺𝟎𝟎,𝒐𝒖𝒕
𝑺𝒊𝒏
𝑻 +
𝟏
∙ 𝑺𝟎,𝒐𝒖𝒕
⋮
𝑵
𝑺𝟎,𝒐𝒖𝒕
Pseudo inversion
Global
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝑰𝒓𝒂𝒘𝟏
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝑰𝒓𝒂𝒘𝟐
𝟎𝟎
=
𝟑
𝑰𝒓𝒂𝒘𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝑰𝒓𝒂𝒘𝟒
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
∙ 𝑺𝒊𝒏
𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
PSA matrix
Mathieu Vedel – Bossa Nova Technologies – March 2014
12
SALSA Technology
Data Reduction Matrix
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝑰𝒓𝒂𝒘𝟏
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝑰𝒓𝒂𝒘𝟐
𝟎𝟎
=
𝟑
𝑰𝒓𝒂𝒘𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝑰𝒓𝒂𝒘𝟒
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟎
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟏
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟐
𝟏
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
𝟐
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
∙ 𝑺𝒊𝒏
𝟑
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
𝟒
𝒎𝒔𝒕𝒂𝒕𝒆
𝟎𝟑
Numerical inversion
𝑺𝒊𝒏
Incident Stokes vector
estimate
Mathieu Vedel – Bossa Nova Technologies – March 2014
𝑰𝒓𝒂𝒘𝟏
𝑰
= 𝑪−𝟏 ∙ 𝒓𝒂𝒘𝟐
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
DRM
Measured
intensities
13
SALSA Technology
Optimization of Condition Number?
𝑺𝒊𝒏
𝑰𝒓𝒂𝒘𝟏
𝑰
= 𝑪−𝟏 ∙ 𝒓𝒂𝒘𝟐
𝑰𝒓𝒂𝒘𝟑
𝑰𝒓𝒂𝒘𝟒
FLC1 FLC2
Linear
polarizer
CN needs to be minimal
• Fixed Retardance
• Fixed Orientations
Adjustable
orientation!
Optimization possible by adjusting the polarizer’s orientation => α
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Optimization of Condition Number?
FLC1 FLC2
Linear polarizer
Calibration
Mathieu Vedel – Bossa Nova Technologies – March 2014
CNα ≤ 2
SALSA Technology
Optimization of Condition Number?
FLC1 FLC2
Linear polarizer
Calibration
λ1
Mathieu Vedel – Bossa Nova Technologies – March 2014
CNα ≤ 2
SALSA Technology
Other wavelengths?
FLC1 FLC2
Linear polarizer
Calibration
CNα>50!
Calibration
CNα >50!
λ2
λ3
α is not optimum for all wavelengths
Mathieu Vedel – Bossa Nova Technologies – March 2014
SALSA Technology
Multi-Optimization of Condition Number?
1. Characterization/model of our FLCs for each wavelength
2. Simulation of calibration procedure for each wavelength of
interest
3. Optimization of polarizer orientation for each wavelength
4. Compromise angle αλ1, λ2, …!
5. Actual calibration at αλ1, λ2, …
6. Testing
7…
λ=[450nm…650nm]
Mathieu Vedel – Bossa Nova Technologies – March 2014
CN ≤ 6
SALSA Technology
Typical Calibration accuracy
S1  S 2
DOLP 
S0
2
2
Mathieu Vedel – Bossa Nova Technologies – March 2014
Error peak-to-valley (PV): 3%
FLCs spatial inhomogeneity
FLC between crossed polarizers
Mathieu Vedel – Bossa Nova Technologies – March 2014
Contrast +50%
FLCs spatial inhomogeneity
• Very little data from manufacturers
• Variations up to 2% from one area
to another accounts for up to +/5% variation of DOP
• Pixel/pixel calibration not realistic
for live measurement/display of
polarization parameters
• Need to develop a field calibration
of the FLCs
Contrast +50%
Mathieu Vedel – Bossa Nova Technologies – March 2014
• Several approaches are being
considered from basic grid
decomposition to “smarter”
segmentation
Full Stokes Polarization Imager
Example -1
Mechanical Stress on a plastic CD case
Stress
S0
Mathieu Vedel – Bossa Nova Technologies – March 2014
DOLP
DOCP
Full Stokes Polarization Imager
Example -1
Mechanical Stress on a plastic CD case
Stress
ZOOM
S0
Mathieu Vedel – Bossa Nova Technologies – March 2014
ZOOM
DOLP
ZOOM
DOCP
Full Stokes Polarization Imager
Example -1
Mechanical Stress on a plastic CD case
HSL Fusion Images
90°
45°
0°
-45°
-90°
Linear polarization
DOLP=0%
DOLP=100%
Circular polarization
Possible to perform retardance/stress mapping!
Mathieu Vedel – Bossa Nova Technologies – March 2014
Full Stokes Polarization Imager
Potential applications – Example -2
Biology measurements
Circular polarization reflected on a beetle scarab’s carapace
Non polarized illumination (integrated sphere)
S0
S1
S2
ALMOST NO LINEAR POLARIZATION REFLECTED
Mathieu Vedel – Bossa Nova Technologies – March 2014
Full Stokes Polarization Imager
Potential applications – Example -2
Biology measurements
Circular polarization reflected on a beetle scarab’s carapace
Non polarized illumination (integrated sphere)
S0
S3
Ellipticity
The specular reflection is elliptically polarized – left handed, DOCP≈40%, ε≈20°
Mathieu Vedel – Bossa Nova Technologies – March 2014
Thank you!
Mathieu Vedel – Bossa Nova Technologies – March 2014