Optical Microscopy Principles and Applications Hari P. Paudel Wellman Center for Photomedicine 8/1/2018 Self Introduction China India BE in Electrical Engineering from Tribhuvan University Worked as a Telecom Engineer at Nepal Telecom M.Sc. in Electrical Engineering from South Dakota State University Ph.D. in Electrical Engineering from Boston University 2 Major Functions of the Microscope • Illuminate • Magnify • Resolve features • Generate Contrast • Capture and display image Pictures from MicroscopyU.com Lecture Outline • Propagation, diffraction, and polarization • Absorption, and scattering • Wide-field imaging techniques • Bright-field/dark-field imaging, • Phase-contrast imaging, and • Differential interference contrast imaging • Scanning imaging techniques • Confocal detection • Differential phase-gradient detection • Non-linear imaging techniques • Multi-photon, • Second harmonic, and • Raman scattering Light as photons, waves or rays Light is an electromagnetic (EM) field in space-time. Photon is the smallest, discrete quanta of EM field. Rays are the propagation direction of the EM field. 휕퐻 휕2퐸 푛2 훻 ∙ 퐸 = 0, 훻 × 퐸 = −휇 훻2퐸 − 휇휀 = 0 = 휇휀 Maxwell 휕푡 휕2푡 푐2 equations 휕퐸 훻 ∙ 퐻 = 0, 훻 × 퐻 = −휀 Wave equation in 휕푡 Linear medium Light as photons, waves or rays Light is an electromagnetic (EM) field in space-time. Photon is the smallest, discrete quanta of EM field. Rays are the propagation direction of the EM field. 휕퐻 휕2퐸 푛2 훻 ∙ 퐸 = 0, 훻 × 퐸 = −휇 훻2퐸 − 휇휀 = 0 = 휇휀 Maxwell 휕푡 휕2푡 푐2 equations 휕퐸 훻 ∙ 퐻 = 0, 훻 × 퐻 = −휀 Wave equation in 휕푡 Linear medium Ray Optics: Optical rays travelling between two points A and B B follow a path such that the time of travel (or optical path-length) between two points is minimal relative to the neighboring paths. A 퐵 Light travels along the 훿 푛 푟 푑푠 = 0 path of least time. 퐴 Light propagation 1 휕2퐸 Wave equation 훻2퐸 − = 0 Solution 퐸 푟, 푡 = 푎(푟)푒−푖풌.풓푒푖2휋휈푡 푐2 휕2푡 푖2휋휈푡 Helmholtz equation 훻2푈 + 푘2푈 = 0 퐸 푟, 푡 = 푈 푟 푒 Plane wave: Spherical wave: Fresnel Approx. of Paraxial wave: Spherical wave: 퐴 푥2+푦2 푈 푟 = 퐴푒−푖풌.풓 −푖푘푟 퐴 −푖푘 −푖푘푧 푈 푟 = 푒 푈 푟 ≈ 푒−푖푘푧푒 2푧 푈 푟 ≈ 퐴(푟)푒 푟 푟 z z z 훻2퐴 − 2푘 퐴 = 0 Light from stars Point source Point source at large distance Gaussian Beam Light travels more slowly in matter The speed ratio is the Index of Refraction (n=c/v) n = 1 n > 1 n = 1 Light travels more slowly in matter The speed ratio is the r Incident wave Reflected Index of Refraction wave (n=c/v) 1 n = 1 n > 1 n = 1 2 Refracted wave /n Snell’s law: Mirror law: n1 Sin(1) = n2 Sin(2) r = 1 Lenses work by refraction Incident light focus Focal length f Rays are perpendicular to wave fronts Single lens Imaging f Image Object d d1 2 L1 L2 1 1 1 d L The lens law: Magnification: M 2 2 L1 L2 f d1 L1 Finite vs. Infinite Conjugate Imaging Finite conjugate imaging Image f Object 0 Field-of-view (FOV) is determined by the size (optics diameter )of the >f0 f0 lenses. Infinite conjugate imaging f1 Need a tube lens Image f Object 0 Pupil f M 1 f f0 f0 (uncritical) f1 o The Compound Microscope Final image Eye Exit pupil Eyepiece Intermediate image plane Tube lens Back focal plane (pupil) Objective Object plane Sample Köhler Illumination Critical Illumination Sample Object plane Aperture iris (pupil plane) Field iris (image plane) Light source (pupil plane) • Each light source point produces a • The source is imaged onto the sample parallel beam of light at the sample • Usable only if the light source is perfectly • Uniform light intensity at the sample even uniform if the light source is not uniform Camera Eyepiece Imaging path Trans-illumination Tube lens Objective Object plane Condenser lens The aperture iris Aperture iris (pupil plane) controls the range of illumination angles Illumination Field lens path The field iris controls Field iris (image plane) the Illuminated field of view Collector Light source (pupil plane) Interference constructive interference In phase + = destructive interference Opposite phase + = Diffraction by a periodic structure (grating) Why is light diffract? Light is an EM field. Small aperture behaves like point source. Light from each point d source propagates in all directions. Only in-phase field can propagate. In phase if d Sin() = m for some integer m. Diffraction by an aperture Light spreads to The pure, “far-field” new angles diffraction pattern is formed at distance Larger aperture weaker diffraction It can be formed at a finite distance by a lens Any aperture produces a diffraction pattern Diffraction spot “Airy disk” diameter Point Spread function (PSF) on image plane ퟐ. ퟒퟒ 흀 풇 풅 = = Point Spread Function D D Sample 풇 풅 Image plane Objective Tube lens Sample Numerical Aperture and Resolution NA = n sin() FWHM Resolution ≈ 0.353 /NA ≈ 0.61 / NA D Axial Resolution ≈ 2 / NA2 풇 풅 Oil immersion: n 1.515 max NA 1.4 Water immersion: n 1.33 max NA 1.2 Source: MicroscopyU.com Polarization Light is a vector wave: it has not only field strength, but also field direction. −푖푘푧 푖2휋휈푡 푖(2휋휈푡−푘푧) 퐴 = 푎 푒푖휑푥 퐸 푧, 푡 = 푨푒 푒 퐸푥 푧, 푡 = 퐴푥푒 푥 푥 푖휑푦 푖(2휋휈푡−푘푧) 퐴푦 = 푎푦푒 푨 = 퐴푥풙 + 퐴푦풚 퐸푦 푧, 푡 = 퐴푦푒 z Polarizer Linear polarization Polarizer allows propagation of 휑푥 = 휑푦 only one component of electric field. z z Circular polarization 휑푥 − 휑푦 = 휋/2 Polarizer 푎푥 = 푎푦 Polarization Birefringent Crystal: Refractive index depends on the polarization and propagation direction of light. Calcite crystal 푥 푛푥 Quarter Waveplate 푛푧 훻푛 = 푛푦 − 푛푥 휆 훻푛 ∗ 훻푡 = 4 푛푦 푦 Uniaxial crystal: There is a single direction governing the optical anisotropy. All other Circular polarization directions perpendicular to it are optically 휑푥 − 휑푦 = 휋/2 equivalent. 푛표 Linear polarization 푎푥 = 푎푦 푛표 푛 is ordinary index 표 휑 = 휑 훻푛 = 푛푒 − 푛표 푛 is extra-ordinary index 푥 푦 푛 푒 푒 푎푥 = 푎푦 Light Scattering and Absorption Scattering of illumination light by the Cells 퐼푖 tissue limits our ability to image deeper. 10µm nuclei Mie Mitochondria 퐿 1µm − Beer − Lambert Law 퐿 푙푒 푙 Lysosomes, 퐼푏 = 퐼푖 푒 푒 attenuation length Vesicles 0.1µm Rayleigh Collagen fibrils 퐼푠 1 1 1 푙 scattering mean free path 10nm Membranes 푠 퐼푏 = + 푙 absorption length 푙푒 푙푠 푙푎 푎 1 = 휇푠 = 휌푠휎푠 푙푠 Mie Scattering 휇푠 scattering coefficient 휌푠 volume density 푄푠 scattering efficiency Rayleigh Scattering Wide-field imaging techniques Camera Sample Wide-field microscopy illuminates whole sample at all times and image is taken by camera.. ….. while in confocal microscopy, only a single focal spot is illuminated and recorded at a time. Illumination sources: halogen lamp, metal halide Sample lamps, or LED. Detection: directly by eyes, or with a digital camera. Scanner Collimated Contrast methods: Phase Contrast, Differential Light source Light source Interference Contrast (DIC), Fluorescence Dark-field microscopy • In Dark-field microscopy, any un-scattered beam is excluded from the image, as a result, the field around the specimen is dark Sample • It is well suited for uses involving live and unstained biological samples. Beam stop Bright-field Dark-field Phase-contrast microscopy • Phase contrast is an optical contrast technique for making unstained transparent objects visible under the optical microscope. Phase plate • An annulus aperture is placed in the front focal plane of the condenser and limits the angle of the penetrating light waves. • A phase plate is placed in the back focal plane of the objective Annulus aperture • The light waves which are not interacting with the specimen are focused as a bright ring in the back focal plane of the objective. Phase-contrast microscopy Phase plate • Phase plate changes the phase by λ/4 and dim the light. • Scattered light is phase shifted by -λ/4. • Phase shift in scattered light is caused by the differences in optical path length in the specimen. • Phase contrast is generated via interference. Annulus aperture Negative Phase shift Positive Phase shift Human Blood cells Source: MicroscopyU.com Differential interference contrast (DIC) DIC microscopy is a technique which uses gradients in the optical path length or phase shifts to make phase objects visible under the light microscope. In this way it is possible to observe living cells and organisms with adequate contrast and resolution. 45 polarized s-pol. p-pol. The polarized light is dispersed into two distinct light rays with an orthogonal plane of polarization using a Wollaston prism. These two light rays are extremely near to each other. Wollaston Prism Differential interference contrast (DIC) The two rays experience different phase shifts from the specimen. polarizer After recombination they interfere with each other producing interference contrast. Wollaston prism Images are relief-like, have a shadow cast, and no halo artifacts. Condenser Relatively thick specimens can be imaged due to the possibility of optical sectioning. Sample Objective Source: microscopyU.com Cheek Epithelial cells Human Blood cells micro.magnet.fsu.edu Fluorescence imaging Hoechst 33342 Oregon Green 488 Alexa Fluor 568 Fluorescence microscopy uses fluorescence and phosphorescence of biochemical compounds as a contrast mechanism. Fluorescent proteins and dyes have been powerful tools to visualize cellular components of cells. 300nm 400nm 500nm 600nm 700nm Rat Heart Tissue Labeled with Alexa Fluor 568 (for F-actin), Oregon Green 488 (for N-acetylglucosamine and N- acetylneuraminic), and Hoechst 342 (nucleus) Source: MicroscopyU.com Fluorescence imaging • Excitation filter selects specific wavelengths for illumination. • Fluorophore emits light of longer wavelengths. Excitation filter • Fluorescence light can be collected by the illumination objective lens (epifluorescence).