Transcript Development of a clinical Fourier

Two-wavelength unwrapping for
transmission-geometry quantitative
phase microscopy
Duke University, Fitzpatrick Institute for Photonics
BIOS Lab, Department of Biomedical Engineering
Matthew Rinehart, Natan T. Shaked, Adam Wax
Phase Microscopy
• Phase microscopy measures relative optical
path delays
• Samples that are optically thicker than λ cause
2π rollovers in phase maps
absolute  measured  m  2
m=?
Δϕ
Transmission Phase Microscopy
• Modified Mach Zehnder interferometer
with an off-axis reference arm
N.T. Shaked, M.T. Rinehart, and A. Wax, "Dual-interference-channel quantitative-phase
microscopy of live cell dynamics," Opt. Lett. 34, 767-769 (2009)
Off-axis Quadrature Projections
• Wollaston prism splits images by
polarization
• interfering 45° light with circularly polarized
light creates a 90° phase delay
Color CCD channels
• Bayer mosaic filter splits 532nm light to G channel and
633nm light to R channel
• Predicted crosstalk:
~ 5% per channel
Measured
Crosstalk
Sony® ICX205AK
R Channel
7.0 %
G Channel
2.3 %
Acquisition & phase mapping
• Acquire 2 simultaneous interferograms,
90° out of phase, subtract to remove DC
I1 – I2
Acquisition & phase mapping
• Fit to find fringe pattern frequency, ϕc, and the phase, α
exp( jC )
I1  I 2  j  HTI1  I 2 
F
1  exp( j )
• Hilbert transform to remove complex conjugate
• Demodulate spatial image information
OBJ
 Im F 
 arctan

 Re F 
• Take angle to find wrapped phase map
2π rollover
absolute  measured  m  2
• 2π rollover can be removed using unwrapping algorithms
• Sharp changes in phase cannot be accurately resolved
• Algorithms are complex & computationally intensive
• Imaging at 2 wavelengths extends measurement range
12
12 
1  2
633nm & 532nm  3.33μm
Two-wavelength unwrapping
• Subtract wrapped phase maps & add 2π where <0
12  1  2  2 (1  2 )  0
ΟPD 
12 12
2π
• Amplifies phase noise
Use beat wavelength phase map as guide to add
correct multiple of 2π
Optical adhesive microstructures
• UV cure optical adhesive
• n = 1.53
• Steep edges at structure boundaries
• 3-6μm predicted height from exposure
Optical adhesive microstructures
• Extract phase from interferograms at 633nm and 532nm
Optical adhesive microstructures
• Compute coarse phase map
• Convert phase maps to optical path delay (OPD) profiles
• Low-pass filter
Optical adhesive microstructures
• Use beat wavelength phase map as a guide for adding
multiples of 2π to 532nm phase image
Optical adhesive microstructures
Image
σ*
532nm unwrapped
8.9 nm
Coarse map
50.2 nm
532nm adjusted
8.9 nm
*σ from 10x10-px area from background
•
Unwrapping algorithm did not accurately
reconstruct phase map
•
2 wavelength map extends measurement
range, but adds noise
•
Noise is reduced when beat wavelength
map is used to refine original phase map
Results, human skin cancer cells
532nm wrapped phase
532nm OPD map, with 2
wavelength unwrapping
Beat wavelength phase map
532nm OPD surface plot
Results, human skin cancer cells
532nm OPD map, with 2
wavelength unwrapping
532nm OPD map, with
computational unwrapping
Background Noise: σ = 8.2nm
Background Noise: σ = 8.2nm
2 wavelength refinement removes 2π ambiguities as
well as quality-map guided algorithm
Conclusions
• Color channels of a CCD can be used to
separate 633nm and 532nm interferograms
• 2 wavelength unwrapping extends measurement
range  3.33μm
• 2 wavelength unwrapping removes 2π rollover
with comparable accuracy to standard
unwrapping algorithms
Acknowledgments
• Duke BIOS Lab
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PI: Adam Wax, Ph.D
Natan Shaked, Ph.D.
Yizheng Zhu, Ph.D.
Matthew Crow
• Duke Materials Sciences
– Nathan Jenness
• Funding
– NSF Bioengineering and
Environmental Systems
grant BES 03-48204