Transcript Document
Structured-Illumination Quantitative Phase Microscopy Sri Rama Prasanna Pavani, Ariel Libertun, Sharon King, and Carol Cogswell Micro Optical – Imaging Systems Laboratory University of Colorado at Boulder http://moisl.colorado.edu Pavani et al - Univ. of Colorado, Boulder 1 Phase Imaging - What? Transparent objects (phase objects) modulate only the phase of light Square law detectors do not detect phase modulations Convert phase modulations into “detectable” intensity modulations Pavani et al - Univ. of Colorado, Boulder Bright field 2 Phase imaging - How? Convert phase modulations into “detectable” intensity modulations. Digital Holography Phase contrast Diff. Interference Contrast Quantitative phase for weak phase objects Quantitative phase after reconstruction Quantitative phase after reconstruction No phase wrapping No phase wrapping Thick phase objects X Halo and shading-off X Polarization sensitive Single image X Only for thin objects X Only for thin objects X Vibration sensitive X Multiple images X Phase wrapping Pavani et al - Univ. of Colorado, Boulder 3 Our method - Why? Purpose: Applicability: Quantitative phase imaging Thick, partially absorbing samples Polarization insensitive Single image Speed: Non-scanning (wide field) Non-Iterative Incoherent source Miscellaneous: Inexpensive Pavani et al - Univ. of Colorado, Boulder 4 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 (mm) 0.1 Pavani et al - Univ. of Colorado, Boulder 5 Our method – 1D 2D dot shift 1D dot shift Pavani et al - Univ. of Colorado, Boulder 6 Our method – 1D o Analytically relate deformation to the optical path length 2 n 1n 2 p( x ) (n1 n 2 ) t ( x ) dx C 1 2 r i n2 o Consider a 1D phase object p(x) p(x) o Ray R from point A, after refraction, appears as if it originated from B o Deformation t(x) is the distance between A and B n1 A t(x) B Pavani et al, “Quantitative bright field phase microscopy”, to be sent to Applied Optics Pavani et al - Univ. of Colorado, Boulder 7 Our method – 2D 1D deformations 2 n1n2 p( x) (n1 n2 ) t ( x) dx C 1 2 After 1D integrations Quantitative Phase 2D deformation Cm1 Cm Px 2 (m 1, d ) Px 2 (m, d ) Py 2 (m 1, d ) Py 2 (m, d ) Pavani et al, “Quantitative bright field phase microscopy”, to be sent to Applied Optics Pavani et al - Univ. of Colorado, Boulder 8 Simulation X 100 Quadratic phase 50 200 5 18 0 9 -5 0 25 200 25 X 100 100 5 18 0 100 0 200 0 9 -5 0 100 0 200 Error 8 (nm) 100 50 After 1D integrations 1D deformations 0 Calculated Phase 4 0 Peak error is 5 orders less than peak phase -4 -8 0 100 200 Pavani et al - Univ. of Colorado, Boulder 9 Experimental Results Original pattern Dot shift X,Y Deformations 360 0 180 0 Deformed pattern 3 240 480 -3 3 360 0 180 16.54 0 Quantitative phase Object: Drop of optical cement 240 480 -4 40 30 20 10 Pavani et al - Univ. of Colorado, Boulder 0 10 Experiment - Accuracy Profilometer Our method Pavani et al - Univ. of Colorado, Boulder 11 Conclusion Quantitative phase imaging in a brightfield microscope. Phase is calculated from deformation using an analytical formula. Inexpensive non-scanning, non-iterative, single-image technique. 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 13 References J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company, 2005) M Pluta, Advanced Light Microscopy, vol 2: Specialised Methods, (Elsevier, 1989) M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy” Journal of Microscopy 214 (1), 7–12 (2004) C. Preza, "Rotational-diversity phase estimation from differential-interference-contrast microscopy images," J. Opt. Soc. Am. A 17, 415-424 (2000) Sharon V. King, Ariel R. Libertun, Chrysanthe Preza, and Carol J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007) E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291-293 (1999) P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468-470 (2005) M. Born and E. Wolf, Principles of Optics, ed. 7, (Cambridge University Press, Cambridge, U.K., 1999). A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, (IEEE Press, New York, NY, 1988) A. C. Sullivan, Department of Physics, University of Colorado, Campus Box 390, Boulder, CO 80309, USA and R. McLeod are preparing a manuscript to be called “Tomographic reconstruction of weak index structures in volume photopolymers.” Huang D, Swanson EA, Lin CP, Schuman JS, Stinson WG, Chang W, Hee MR, Flotte T, Gregory K, Puliafito CA, et al., “Optical coherence tomography,” Science1991 Nov 22;254(5035):1178-81. A. F. Fercher, C. K. Hitzenberger, “Optical coherence tomography,” Chapter 4 in Progress in Optics 44, Elsevier Science B.V. (2002) A. F. Fercher, W. Drexler, C. K. Hitzenberger and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66 239–303 (2003) M. R. Ayres and R. R. McLeod, "Scanning transmission microscopy using a position-sensitive detector," Appl. Opt. 45, 8410-8418 (2006) Barone-Nugent, E., Barty, A. & Nugent, K. “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206, 194–203 (2002). J. Hartmann, "Bemerkungen uber den Bau und die Justirung von Spektrographen," Z. Instrumentenkd. 20, 47 (1900). I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, second edition Wiley, New York, 1992, pp. 367–396. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971). V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105- (1984) M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” Journal of Microscopy 198 (2), 82–87 (2000) M. D. Feit and J. A. , J. Fleck, "Light propagation in graded-index optical fibers (T)," Appl. Opt. 17, 3990- (1978) Haralick, Robert M., and Linda G. Shapiro. Computer and Robot Vision, Volume I. Addison-Wesley, 1992. pp. 28-48. Pavani et al - Univ. of Colorado, Boulder 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 p( x ) p( x ) n1 t ( x ) tan( r i ) x A (from geometry) n1 t ( x ) n dp ( x ) dp ( x ) tan sin 1 1 sin tan1 tan1 dx dx n2 (Snell’s law, tan( i ) dp ( x ) ) dx x A 1 1 1 3n n 3 (n 1) 3 3 6 3 2 2 1 n 1 dp( x ) higherorder terms p( x ) n 1 t ( x ) (n 1) 2 (n 1) dp ( x ) 2 dx dx p( x ) dp( x ) n1 n 2 t ( x ) dx ( n1 n 2 ) p( x ) 2I( x ) C 1 2 (Taylor expansion) n n 1 n2 n1 n 2 (n1 n 2 ) t(x) dx I(x) C 2 C = 2 (C2 – C1) Pavani et al - Univ. of Colorado, Boulder 16 Our method – How? M 2 Dimensional analysis N 2 Apply 1D solution along x and y to obtain Px and Py 2 Py 2 Px 2 Px 2 (m, 1 : N) P 2 (m,1 : N) Cm Py 2 (1 : M, n ) P (1 : M, n ) K n C m 1 C m Px 2 (m 1, d) Px 2 (m, d) P 2 (m 1, d) P 2 (m, d) , 2 2 2 P2 2 Py (m 1, d) Py (m, d) P (m 1, d) P (m, d) C m 1 C m Px 2 (m 1, d) Px 2 (m, d) Py 2 (m 1, d) Py 2 (m, d) . Pavani et al - Univ. of Colorado, Boulder 17