Quantitative bio-imaging in widefield microscopy: problems and - PowerPoint PPT Presentation

Faculty of Physics Optics Department Quantitative bio-imaging in widefield microscopy: problems and solutions Tatiana Alieva E-mail: talieva@ucm.es Wi t Winter College on Optics: Advanced Optical Techniques for C ll O ti Ad d O ti l T h i f Bio-imaging, ICTP, Trieste, 16 February 2017

What we can see with and without a microscope Light microscope with superresolution techniques � X X ray techniques t h i Image from Internet: unknown author 2 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

What we need to get a good image � Magnification of the image Same magnification but NA a >NA b Image from wcssamland.weebly.com/book-c-ch-1 � Large NA of the objective � Large NA of the objective � Correct illumination � Sufficient dynamic range of image detector � Good optics and alignment G d i d li 3 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Outline � Coherent versus partially coherent Illumination � Quantitative imaging (QI) � Phase retrieval methods for QI in microscopy � Different approaches for 3D QI � QI with partially coherent illumination � Illumination coherence engineering � Concluding remarks 4 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Partially coherent light � Approximation: scalar monochromatic field, pp Gaussian statistics Partially coherent field (4D) Coherent field (2D): mutual intensity (MI) y ( ) complex field amplitude complex field amplitude é ù * G = ( , ( , r r ) ) u ( ) ( ) r u ( ) ( ) r = i j j u ( ) ( ) r u ( ) ( ) exp r p ( ) ( ) r ë ë û û 1 1 2 2 1 1 2 2 � Only intensity can be measured directly O l i t it b d di tl 2 G G = = ( , ) ( r r r r ) u u ( ) ( ) r r 5 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Microscope illumination � August Köhler illumination proposal (1893) proposal (1893) � Coherence description: Van Cittert-Zernike theorem Van Cittert-Zernike theorem � � � � * ( , r r ) u ( ) r u ( r ) ( r r ) 1 2 s 1 s 2 il 1 2 MI in the sample plane after passing through the object � � � � � � � � � � � � � � � � ( , ( r r r r ) ) I I ( ')exp ( )exp r r ik ik r r r r r r '/ f / f d d r r ' � � � � il l 1 2 S 1 2 c MI of the illumination field I ( ) r S Intensity distribution of incoherent illumination source � Coherence parameter Coherence parameter Image from S=NA c /NA o http://www.olympusmicro.com/primer/anatomy/kohler.html 6 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Image depends on condenser aperture [J. A. Rodrigo & T. Alieva, Opt. Letters, 39 (2014)] 7 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Partially coherent versus coherent illumination � Speckle suppression Coherent Coherent Partially coherent Partially coherent [J R d i [J. Rodrigo and T. Alieva, Opt. Express 22 (2014)] d T Ali O t E 22 (2014)] 8 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Partially coherent versus coherent illumination � Optical sectioning: Diatom focusing Coherent S=0 3 Coherent S 0.3 Partially coherent Partially coherent S=0 7 S 0.7 [Courtesy J. Rodrigo and J. M. Soto , 2017] 9 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

What information we want to get from an image? � Object form + � Object size + � Object composition = � Quantitative imaging Movie: 4,7 � m polystyrene spheres focusing Movie: 4 7 � m polystyrene spheres focusing [J. A. Rodrigo & T. Alieva, Opt. Lett., 39 (2014)] � Does an image of biological object provide directly this g g j p y information? 10 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Quantitative phase imaging � Biomedical microscopic imaging: usually bad absorption contrast � Specimen may be often treated as a phase only object p y p y j � But only intensity distribution is detectable � How to recover the image phase? Using computational methods for its recovery! g p y � Application of image phase retrieval: pp g p � Digital refocusing � Information about specimen refractive index (thickness, optical potential, etc.) t ti l t ) 11 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Digital refocussing and object thickness g g j � Recovered phase of the image in one plane 3D image in one plane 3D Image is recovered calculating back/forward calculating back/forward field propagation � Thickness of object Thi k f bj t � � t ( ) r n ( , ) r z dz s is recovered from phase J. A. Rodrigo & T. Alieva, Opt. Express, 22 (2014) (optical path difference profile) (optical path difference profile) � using eikonal approximation � � � ( ) r k n ( ( , ) r z n ) dz s s m � the object size >> � � the object size >> � 12 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Phase retrieval methods Coherent light Measurements: intensity distributions 2 2 � 2 2 é ù = i j = u ( ) r u ( ) exp r ( ) r u ( ) , r u ( ) , r j 1,2,... N ë û j HOW TO RECOVER THE PHASE? � Gerchberg-Saxton type algorithms g yp g � Interferometry / Holography y g p y � Transport-of-intensity equation Transport of intensity equation � Phase-space tomography � Phase space tomography 13 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Iterative methods of phase retrieval p � Gerchberg - Saxton algorithm: 2 2 I Image intensity i t it g r ( ) + 2 2 Fourier power spectrum F r ( ) (= image intensity in conjugated plane) � The process converges when p g 2 2 � � � g g g g � n n 1 R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972); g p ( ) J. R. Fienup, Appl. Opt. 21, 2758 (1982) 14 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Generalized Gerchberg-Saxton methods g Other possible constraints provided phase diversity: � Fresnel diffraction patterns � Defocused images � Diffraction patterns in asymmetric systems � Object information (size, form, etc.) Z. Zalevsky et al, Opt. Lett. 21, 842 (1996); L. Camacho et al, Opt. Exp. 18, 6755 (2010); y ( ) ( ) J. A. Rodrigo, et al, Opt. Express 18,1510 (2010) 15 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Paraxial approximation of Helmholtz pp equation � Helmholtz equation: H l h lt ti � � � 2 E ( ) r k E ( ) r 0 � E E ( ) ( ) r u ( ) ( )exp( r ( ikz ik ) ) � z is a beam propagation direction � � � � 2 � � � � � � � � i k 2 u ( ) r u ( ) r 0 � � � � � 2 � z � z � � 2 � � � � � � u ( ) r � k u ( ) r i k 2 u ( ) r 0 � � � � � � � 2 � � z z z z � � z z � � � The angle between the wave vector k and z is small 16 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017

Generalized Fresnel transforms = Canonical integral transforms = ABCD transforms � Propagation through a paraxial system is described by � Propagation through a paraxial system is described by � � � � � � � � u r u r K r r , d r o o i i T i o i � � � � �� � � � * ( r , r ) ( r r , ) K r r , K r , r d r d r o 1 o 2 o i 1 i 2 i T 1 i 1 o T 2 i 2 o 1 i 2 i with kernel parameterized by real symplectic ray with kernel parameterized by real symplectic ray transformation matrix T � � � � � � 1 � � � � � � � � � � � � � � t t 1 1 t t 1 1 t t 1 1 exp i i r B Ar B A 2 2 r B r B r DB r DB , det d t B B 0 0 � � � i i i o o o det i B � � � � � K r r , 1 � � � � � � � � T i o � � i � � � � � � � � t 1 1 exp exp i r CA r r CA r r r A r A r , B B 0 0 o o i o � det A � S. A. Collins, J. Opt. Soc. Am. 60,1168 (1970); M. Moshinsky and C. Quesne, J. Math. Phys. 12, 1772 (1971). 17 Winter College on Optics: Advanced Optical Techniques for Bio-imaging, ICTP, Trieste, 16 February 2017