1. Duke University, Fitzpatrick Institute for Photonics BIOS Lab, Department of Biomedical Engineering Two-wavelength unwrapping for transmission-geometry quantitative phase microscopy Matthew Rinehart, Natan T. Shaked, Adam Wax

2. Phase Microscopy Phase microscopy measures relative optical path delays Samples that are optically thicker than λ cause 2 π rollovers in phase maps ΔϕΔϕ m = ?

3. 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)

4. Off-axis Quadrature Projections Wollaston prism splits images by polarization interfering 45° light with circularly polarized light creates a 90° phase delay

5. Bayer mosaic filter splits 532nm light to G channel and 633nm light to R channel Color CCD channels Predicted crosstalk: ~ 5% per channel Sony® ICX205AK

6. Acquisition & phase mapping Acquire 2 simultaneous interferograms, 90° out of phase, subtract to remove DC I1 – I2

7. Acquisition & phase mapping Fit to find fringe pattern frequency, ϕ c, and the phase, α Hilbert transform to remove complex conjugate Demodulate spatial image information Take angle to find wrapped phase map

8. 2 π rollover 2 π 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 633nm & 532nm  3.33 μ m

9. Subtract wrapped phase maps & add 2π where <0 Amplifies phase noise Use beat wavelength phase map as guide to add correct multiple of 2 π Two-wavelength unwrapping

10. UV cure optical adhesive n = 1.53 Steep edges at structure boundaries 3-6 μ m predicted height from exposure Optical adhesive microstructures

11. Extract phase from interferograms at 633nm and 532nm Optical adhesive microstructures

12. Compute coarse phase map Convert phase maps to optical path delay (OPD) profiles Low-pass filter

13. Optical adhesive microstructures Use beat wavelength phase map as a guide for adding multiples of 2 π to 532nm phase image

14. Optical adhesive microstructures 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 * σ from 10x10-px area from background

15. Results, human skin cancer cells 532nm wrapped phase Beat wavelength phase map 532nm OPD map, with 2 wavelength unwrapping 532nm OPD surface plot

16. Results, human skin cancer cells 2 wavelength refinement removes 2 π ambiguities as well as quality-map guided algorithm Background Noise: σ = 8.2nm 532nm OPD map, with 2 wavelength unwrapping 532nm OPD map, with computational unwrapping Background Noise: σ = 8.2nm

17. Conclusions Color channels of a CCD can be used to separate 633nm and 532nm interferograms 2 wavelength unwrapping extends measurement range  3.33 μ m 2 wavelength unwrapping removes 2 π rollover with comparable accuracy to standard unwrapping algorithms

18. Acknowledgments Duke BIOS Lab –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