Quantitative phase estimation with a bright field microscope

1. Quantitative phase estimation with a bright field microscope Sri Rama Prasanna Pavani, Ariel Libertun, Sharon King, and Carol Cogswell Micro Optical – Imaging Systems Laboratory, ECE, University of Colorado at Boulder http://moisl.colorado.edu Pavani et al - Univ. of Colorado, Boulder Frontiers in Optics 9/18/2007

2. Bright field Phase contrast DIC Digital Holography Phase imaging – What? How? • Transparent (phase) objects modulate only the phase of light • Convert phase modulations into detectable intensity modulations • Quantitative phase for weak phase objects • No phase wrapping • Halo and shading-off • Only for thin objects • Quantitative phase after reconstruction • No phase wrapping • Polarization sensitive • Only for thin objects • Multiple images • Quantitative phase after reconstruction • Thick phase objects • Single image • Vibration sensitive • Phase wrapping • No quantitative phase Pavani et al - Univ. of Colorado, Boulder

3. Our method • Amplitude mask in the field diaphragm • Pattern is imaged on the sample • Phase object distorts the pattern • Record the distorted pattern • Analytical formula calculates phase Vs 0.2 0.1 (mm) 0.4 0.2 0 0.2 0.4 (mm) (mm) Pavani et al - Univ. of Colorado, Boulder

4. Our method – 1D • Analytically relate deformation to the optical path length • Consider a 1D phase object p(x) • Ray R from point A, after refraction, appears as if it originated from B • Deformation t(x) is the distance between A and B Normal Tangent n2 p(x) n1 A B t(x) Pavani et al, “Quantitative structured-illumination phase microscopy”, submitted to Applied Optics, June 07 Pavani et al, “Structured-illumination quantitative phase microscopy”, CMB4, COSI 2007 Pavani et al - Univ. of Colorado, Boulder

5. Our method – 2D 1D deformations After 1D integrations C1 C2 . . CN Quantitative Phase 2D deformation K1 K2 ………… KN Pavani et al, “Quantitative structured-illumination phase microscopy”, submitted to Applied Optics, June 07 Pavani et al - Univ. of Colorado, Boulder

6. Simulation X 100 18 9 0 5 0 -5 Calculated Phase Quadratic phase 50 25 0 50 25 0 200 100 200 100 After 1D integrations 1D deformations X 100 18 9 0 5 0 -5 0 100 200 0 100 200 Error 8 4 0 -4 -8 (nm) Error Peak error is 5 orders less than peak phase 0 100 200 Pavani et al - Univ. of Colorado, Boulder

7. Experimental Results Dot shift X,Y Deformations Original pattern 3 0 -3 360 180 0 240 480 Deformed pattern 3 0 -4 360 180 16.54 0 240 480 Quantitative phase 40 30 20 10 0 Profilometer Our method Object: Drop of optical cement 360 180 Pavani et al - Univ. of Colorado, Boulder 480 240 0

8. Spatial Resolution • Size and the spacing between dots • Dots sampling the object; must obey Nyquist • Resolution enhancement by shifting d s M M shift right shift down shift diagonally + + + = N N = + + + • If dot size = diffraction limited spot size, quantitative phase imaging with the same resolution as a bright field image is possible Pavani et al - Univ. of Colorado, Boulder

9. Spatial Resolution • Size and the spacing between dots • Dots sampling the object; must obey Nyquist • Resolution enhancement by shifting d s M M shift right shift down shift diagonally + + + = N N = + + + • If dot size = diffraction limited spot size, quantitative phase imaging with the same resolution as a bright field image is possible • Full resolution single image phase imaging with multi-colored dots Pavani et al - Univ. of Colorado, Boulder

10. t = Dot shift Phase resolution • Smallest detectable change in path length • Minimum deformation w = detector pixel width M = magnification • Trapezoidal numerical integration s x x Example < M = 100x NA = 0.9 w = 7µm s = 1µm n1 = 1.5 n2 = 1 Pavani et al - Univ. of Colorado, Boulder Depth of field = 753nm

11. Conclusion • Described wide field, full resolution quantitative phase imaging in a bright field microscope • Phase is calculated from deformation using an analytical formula • Conservative calculations with a 100x objective predict a phase resolution of 155nm Pavani et al - Univ. of Colorado, Boulder

12. Acknowledgements • Prof. Rafael Piestun • Prof. Gregory Beylkin • Vaibhav Khire CDMOptics PhD Fellowship National Science Foundation Grant No. 0455408 Pavani et al - Univ. of Colorado, Boulder

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14. Applications and Future work • Industrial inspection, biological imaging • Extracting information from axial deformation • Extending the depth of field of the system • Fabrication of an amplitude mask with higher spatial resolution Pavani et al - Univ. of Colorado, Boulder

15. Our method – How? 1 Dimensional analysis (from geometry) (Snell’s law, ) (Taylor expansion) C = 2 (C2 – C1) Pavani et al - Univ. of Colorado, Boulder

16. Our method – How? M 2 Dimensional analysis N and Apply 1D solution along x and y to obtain P2 Pavani et al - Univ. of Colorado, Boulder

17. Metrology - Cubic phase mask 120 80 40 0 360 180 480 240 0 Deformation Quantitative OPL profile 140 70 0 Cubic phase mask 360 180 480 240 0 Deformation Quantitative OPL profile Pavani et al - Univ. of Colorado, Boulder