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High-Aperture Optical Microscopy Methods for Super-Resolution Deep Imaging and Quantitative Phase Imaging by Jeongmin Kim a Diss

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High-Aperture Optical Microscopy Methods for Super-Resolution Deep Imaging and Quantitative Phase Imaging by Jeongmin Kim a Diss High-Aperture Optical Microscopy Methods for Super-Resolution Deep Imaging and Quantitative Phase Imaging by Jeongmin Kim A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering { Mechanical Engineering and the Designated Emphasis in Nanoscale Science and Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Xiang Zhang, Chair Professor Liwei Lin Professor Laura Waller Summer 2016 High-Aperture Optical Microscopy Methods for Super-Resolution Deep Imaging and Quantitative Phase Imaging Copyright 2016 by Jeongmin Kim 1 Abstract High-Aperture Optical Microscopy Methods for Super-Resolution Deep Imaging and Quantitative Phase Imaging by Jeongmin Kim Doctor of Philosophy in Engineering { Mechanical Engineering and the Designated Emphasis in Nanoscale Science and Engineering University of California, Berkeley Professor Xiang Zhang, Chair Optical microscopy, thanks to the noninvasive nature of its measurement, takes a crucial role across science and engineering, and is particularly important in biological and medical fields. To meet ever increasing needs on its capability for advanced scientific research, even more diverse microscopic imaging techniques and their upgraded versions have been inten- sively developed over the past two decades. However, advanced microscopy development faces major challenges including super-resolution (beating the diffraction limit), imaging penetration depth, imaging speed, and label-free imaging. This dissertation aims to study high numerical aperture (NA) imaging methods proposed to tackle these imaging challenges. The dissertation first details advanced optical imaging theory needed to analyze the proposed high NA imaging methods. Starting from the classical scalar theory of optical diffraction and (partially coherent) image formation, the rigorous vectorial theory that han- dles the vector nature of light, i.e., polarization, is introduced. New sign conventions for polarization ray tracing based on a generalized Jones matrix formalism are established to facilitate the vectorial light propagation with physically consistent outcomes. The first high NA microscopic imaging of interest is wide-field oblique plane microscopy (OPM) for high-speed deep imaging. It is a simple, real-time imaging technique recently developed to access any inclined cross-section of a thick sample. Despite its experimental demonstration implemented by tilted remote focusing, the optical resolution of the method has not been fully understood. The anisotropic resolving power in high NA OPM is rigor- ously investigated and interpreted by deriving the vectorial point spread function (PSF) and vectorial optical transfer function (OTF). Next, OPM is combined with stochastic optical reconstruction microscopy (STORM) to achieve super-resolution deep imaging. The pro- posed method, termed obliqueSTORM, together with oblique lightsheet illumination paves the way for deeper penetration readily available in localization-based super-resolution mi- croscopy. The key performance metrics of obliqueSTORM, quantitative super-resolution and 2 axial depth of field, are studied. obliqueSTORM could achieve sub-50-nm resolution with a penetration depth of tens of microns for biological samples. The last part of the thesis covers the development of nonparaxial imaging theory of high NA differential phase contrast (DPC) microscopy for high resolution quantitative phase imaging. The phase retrieval in conventional optical DPC microscopy relies on the paraxial transmission cross-coefficient (TCC) model. However, this paraxial model becomes invalid in high NA DPC imaging. Formulated here is a more advanced nonparaxial TCC model that considers the nonparaxial nature of light propagation, apodization in high NA imaging systems, and illumination source properties. The derived nonparaxial TCC is numerically compared with the paraxial TCC to demonstrate its added features. The practical forms of the TCC for high resolution phase reconstruction are discussed for two special types of objects, weak objects and slowly varying phase objects. The theoretical studies conducted here can help to bring such high NA microscopy tech- niques into the real world to solve imaging challenges. i To My Family ii Contents Contents ii List of Figures iv 1 Introduction 1 1.1 Optical Imaging: Microscopy . 1 1.2 Challenges in optical microscopy . 2 1.3 Motivation and objective . 5 2 Advanced Imaging Theory 7 2.1 Optical diffraction theory . 7 2.2 Two-dimensional scalar image formation theory . 11 2.3 Partially coherent image formation theory . 14 2.4 Three-dimensional scalar image formation theory . 19 2.5 Vectorial image formation theory . 22 2.6 Polarization ray tracing . 23 2.7 Numerical comparison: vector vs. scalar theory . 27 3 Oblique Plane Microscopy 30 3.1 Introduction to wide-field OPM . 30 3.2 Schematic of direct oblique plane microscopy . 31 3.3 Formulation of vectorial PSF . 32 3.4 Numerical PSF and OTF in OPM . 36 3.5 Axial depth of field in remote focusing . 41 3.6 Experimental demonstration . 43 4 Super-Resolution Oblique Plane Microscopy 45 4.1 Schematic of obliqueSTORM . 46 4.2 PSF formulation in XY imaging mode . 47 4.3 PSF formulation in oblique imaging mode . 51 4.4 Analysis on super-resolution . 60 4.5 Penetration depth in obliqueSTORM . 63 iii 4.6 Preliminary super-resolution experiment . 65 5 Nonparaxial DPC Microscopy 69 5.1 Wide-field DPC system . 70 5.2 Nonparaxial DPC image formation with a planar detector . 73 5.3 Nonparaxial DPC image formation with a spherical detector . 76 5.4 Simplification of DPC image formation . 78 5.5 Numerical study: paraxial vs. nonparaxial TCC . 80 5.6 Further discussion . 83 6 Conclusion 86 6.1 Conclusion and Outlook . 86 6.2 Future work . 87 Bibliography 89 iv List of Figures 1.1 Coverage of various microscopy techniques for biological entities at different scales. Super-resolution optical microscopy methods can access sub-cellular features. 1 2.1 Diffraction geometry. O: geometrical focus, P : an observation point (~x), Q: a point (~x0) on the wavefront where the diffraction integral is evaluated, R~ =~x−~x0. 9 2.2 Image formation by a thin lens (focal length: f, aperture radius: a). A monochro- matic object field Eo forms an image field Ei in the image space with a lens law of 1=do + 1=di = 1=f.................................. 11 2.3 Schematic of a general partially coherent imaging system. gc(~xo; ~xs): amplitude spread function for a point source at ~xs into the object plane ~xo, g(~xi; ~xo): am- ~ plitude spread function between the object and the final image plane. Pc(ξc) and P (ξ~) are effective pupil functions of illumination and imaging optics respectively. 14 2.4 Geometrical interpretation of TCC (transmission cross-coefficient) in partial co- herent imaging as an overlap of three scaled pupils in spatial frequency domain. ¯ ¯ The scaled pupil radii of imaging and condenser optics are a=(λdo) and ac=(λzo), respectively. 18 2.5 Scalar 3D OTF for a circular aperture imaging system: (left) paraxial approxi- mation and (right) Debye approximation (α=71:8° for 0.95 NA, aplanatic). Here, ~ p 2 2 2 spatial frequencies are normalized as (l; s~)= fx + fy =(NA/λ); fz=(NA /λ) . An- alytical expressions of H(~l; s~) are available at [103], with doughnut-shaped pass- bands: (left) js~j ≤ j~lj(1 − j~lj=2), (right) ~l2 +s ~2 ≤ 2(j~lj sin α − js~j cos α). 21 2.6 Simple examples of polarization ray tracing: (left) light focusing and (right) light collimation cases. The fields refracts at a lens modeled as a spherical surface. 25 2.7 Example of polarization ray tracing for a simplified imaging system comprising an objective lens (left) and a tube lens (right) in air. 26 2.8 Comparison of intensity distribution at focus between scalar and vectorial diffrac- tion theory. A collimated, uniform, vertically polarized field (λ = 0:5 µm) is assumed to be focused by an aplanatic objective lens of 0.95 NA in air. 28 2.9 Comparison of axial intensity response among diffraction theories. 29 v 3.1 Conceptual arrangement of oblique plane imaging. OBJ: objective lens; BS: beam splitter; L: lens; M: mirror. The beam path for an on-axis point object is drawn in green, while the clipped beam at OBJ2 is shown in pink. Coordinates at (a) object space: an xαyα oblique plane tilted by α about the xy focal plane of OBJ1, 0 0 (b) remote space: the x1y1 intermediate image plane is rotated to the x1y1 plane (OBJ2's focal plane) by the α=2-tilted mirror, and (c) image space: the x2y2 lateral plane is conjugate with the xαyα object plane. 31 3.2 2D and 3D effective pupil function in direct oblique plane imaging in a normalized object space. 33 3.3 2D vectorial intensity PSF of oblique plane imaging at different oblique angles (α) and NAs. 36 3.4 FWHM of the vectorial PSF at different NA over the oblique angle. The FWHMs from the inclined 3D vectorial PSF in a circular aperture (the inset in the middle) are plotted for comparison, which fails to explain the anisotropic resolution in wide-field OPM. 37 3.5 Comparison between FFT-based OTF and analytical scalar Debye OTF. 38 3.6 2D vectorial OTF of oblique plane imaging over oblique angle (α) and NA (λ0 = 519 nm, n = 1:52) at frequencies normalized by n/λ0. Red contours are MTF cutoffs. 39 3.7 Vectorial OTF cross-sections along them ~ x andm ~ y directions for α = 0, 60, and 90°............................................ 40 3.8 Spatial cutoff frequency of the vectorial OTF over oblique angles. 40 3.9 A remote focusing geometry for an extended depth of field. The pupils of the two objectives are matched by a relay optics of jMRj = n2f2=(n1f1) to satisfy ~x2 = (n1=n2)~x1..................................... 41 3.10 Axial responses in the remote focusing from (left) scalar Debye theory (right) vectorial Debye theory. Objective NA: 1.4 (f =1:8 mm), n=1:52, λ0 =519 nm.
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