Lecture 3: Light Scattering F. Cichos http://www.uni-leipzig.de/~mona Dynamic Light Scattering - DLS speckle pattern Dynamic Light Scattering Dynamic Light Scattering - DLS speckle intensity fluctuations by Brownian motion 100 80 60 intensity 40 0 5 10 15 20 25 30 35 time [s] 3 150x10 ) 100 τ ( small q 2 g 50 for Brownian Motion 0 large q 4 6 8 2 4 6 8 2 4 6 8 0.1 1 10 time lag τ [s] Dynamic Light Scattering slow dynamics - small amplitude motion fast dynamics - large amplitude motion Lecture 4: Optical Microscopy F. Cichos http://www.uni-leipzig.de/~mona 2. Optical Microscopy, Computational Microscopy 2.1 Wide Field Microscopy Introduction 2.2 Confocal Microscopy 2.3 Fourier Optics Recapture 2.3.1 Fourier Transform in Optics 2.3.2 Fourier Optics and Imaging with a Lens 2.3.3 Imaging Bandwidth and Resolution 2.4 Phase and Darkfield Contrast 2.4.1 Phase Contrast Microscopy Detail 2.4.2 Darkfield Contrast Microscopy 2.5 Structured Illumination Microscopy 2.6 Photothermal Microscopy 2.7 Superresolution Microscopy 2.7.1 STED microscopy below the diffraction limit 2.7.2 PALM/STORM detection techniques for super-resolution Optical Microscopy direct imaging raster scanning bright field microscopy dark field microscopy differential interference contrast micr. confocal microscopy phase contrast microscopy near field microscopy fluorescence microscopy STED microscopy +++ spinning disc microscopy +++ advantages advantages illumination of the whole sample illumination of a small sample volume highly parallel detection from a small sample volume very fast imaging sectioning capability lower background drawbacks drawbacks illumination of the whole sample slow imaging no sectioning capabilities (usually) background fluorescence Near Field Raster Scanning Microscope Wide Field Microscopy Commercial Microscope key elements • illumination • imaging optics (objectiv) • tube lens • eye piece/camera http://www.microscopyu.com/articles/formulas/conjugatemicroscope.html Ray Path through Microscope Wide Field Microscope microscope intermediate objective image plane object image tube lens eye piece magnification tube lens focal distance (mm) • tube lens focal distance is typically fixed for Olympus 180 each microscope objective manufacturer Nikon 200 • varying tube lens focal distance leads to new Zeiss 165 magnification Microscope Objective Lens typical microscope objectives lenses are so called “infinity-corrected” image is created at infinite distance from the objective very useful, because we then have infinite space to place optical elements complex optical system replaced by simple lens picture microscope objective Immersion Fluid no immersion medium immersion medium Immersion Fluid Widewide fieldField microscope Microscopy CCD pro tube lens • larger excitation volume ø ~10 µm excitation lens filter Δz ~ depends (TIRF) • parallel acquisition excitation laser dichroic mirror con • large detection volume • larger background signal microscope • no sample sectioning objective sample Imaging Small Objects single PS particle with 600 nm emission 2.0 1.5 1.0 Bildgröße [µm] 0.5 diffraction limit 0.0 0.0 0.5 1.0 1.5 2.0 Partikelgröße [µm] microscopy image works down to 380 nm Optical Resolution • point like light source is not imaged into a point! the image of a point like light source corresponds to the optical impuls response function or point spread function (PSF) • Fraunhofer diffraction on the aperture of a lens the diffraction pattern is proportional to the square magnitude of the Fourier transform of the aperture function Fourier transform example: circular aperture of diameter D Diffraction Limit resolution = two or one object? the point spread function (psf) = intensity pattern in the focal area of a lens this is equivalent to the image of a point source (light path is reversible) light is diffracted on the aperture of the microscope objective lens lens aperture pattern is square magnitude of complex amplitude p(ξ, ρ) = a(ξ, ρ) 2 | | a(ξ, ρ) is Fourier transform of the aperture (Fraunhofer diffraction) dimensionless variables 2π 2π ξ(z) = NA2z ρ(r) = NA2r nλ λ the integrated intensity in every transverse plane is the same Diffraction Pattern ρresel 0.6 Intensity distribution in the focal plane 0.5 • only true for paraxial optics, but similar for high NA 0.4 0.3 intensity • usually termed resel (resolution element) 0.2 0.1 ρresel is the radius of the so called Airy disc 0.0 -10 -5 0 5 10 ρresel = 1.22π distance in focal plane 1.2 λ r = 0.61 resel NA 0.8 Intensity distribution along the optical axis intensity 0.4 0.0 -40 -20 0 20 40 distance along optical axis Point Spread Function in 3d the psf is a complicated pattern in 3d space often psf refers to the radial distribution in the focal plane diffraction changes with wavelength therefore psf too!!! optical axis focal plane radius R. H. Webb, Rep. Prog. Phys. 59 (1996) 427. Optical Resolution - Rayleigh Criterium two psf separated by one resel in plane ρresel 0.6 • dip between the maxima is resolved • dip is 26 % = Rayleigh criterion 26 % 0.4 Rayleigh: two objects can be resolved if λ intensity r = 0.61 0.2 resel NA 338 nm for wavelength 500 nm, NA=0.9 0.0 406 nm for wavelength 600 nm, NA=0.9 -10 -5 0 5 10 15 distance in focal plane • same can be done along the optical axis first minimum at this is the axial resolution 2nλ z = axis NA2 about 1.2 µm for 500 nm, NA=0.9 about 1.5 µm for 600 nm, NA=0.9 Diffraction Image -1000 -500 0 500 1000 x,y [nm] Optical Microscopy - Two Particles 490 nm PS Kugeln Beugungsminimum -1000 -500 0 500 1000 x,y [nm] 22 % -500 0 500 x [nm] Abbe Limit - Interference to find out if there are two light sources in the object plane, one needs to detect the first order interference of the two sources Resolution - Diffraction Limited Abbe Rayleigh Ein 1 nm kleines Objekt, dass Licht mit 600 nm emittiert sieht so aus, als wäre er 300 nm groß! Reality and Resolution same psf but different noise level 0.5 0.3 0.4 0.2 0.3 intensity 0.2 intensity 0.1 0.1 0.0 0.0 -10 0 10 -10 0 10 distance in focal plane distance in focal plane the resolution criterion is arbitrary, but can be at least exactly determined always hunt for the best signal to noise ratio! special techniques special techniques - dark field microscopy dark field image of a silicified cell special techniques - phase contrast microscopy Related Laureate: The Nobel Prize in Physics, 1953 - Frits (Frederik) Zernike » double 1/4 wavelength retardation of the source and the diffracted wave leads to destructive interference in the image plane special techniques - phase contrast microscopy special techniques - phase contrast microscopy special techniques - DIC microscopy DIC - differential interference contrast special techniques - DIC microscopy special techniques - DIC microscopy special techniques - DIC microscopy special techniques - DIC microscopy Ptychographic Imaging • high resolution • large field of view Ptychographic Imaging Research Article Vol. 2, No. 10 / October 2015 / Optica 906 (A) phase (0.7 NA) intensity (C) phase intensity 200µm ) × unstained 20µm 20µm conventional 20µm 40 NA, (0.65 20µm phase from defocus from phase rad 2 stained 20µm 20µm -0.6 20µm 20µm phase contrast (B) with DPC without DPC (D) simulated phase contrast (0.65 NA, 40×) 20µm 20µm FPMsequential FPM source-coded 20µm 20µm 20µm 20µm 20µm -1 2 rad 0 2 Fig. 2. Large-SBP reconstructions of quantitative phase and intensity. (A) Phase reconstruction across the full FOV of a 4× objective with 0.7 NA resolution (sample, U2OS). A zoom-in is shown to the right, with comparison with reconstructions of the same sample before and after staining. (B) Our improved FPM algorithm provides better reconstruction of low-frequency phase information. A zoom-in region shows comparisons between phase reconstructions with and without our DPC initialization scheme. (C) To validate our source-coded FPM results, we compare with images captured with a 40× objective having high resolution (0.65 NA) but a small FOV (sample, MCF10A), as well as with sequential FPM. (D) We simulate a phase- contrast image and compare with one captured by a high-resolution objective (0.65 NA, 40×). phase information is captured poorly, since it results only from contrast and is nearly invisible; however, the phase result clearly illumination angles that are close to the objective NA. Thus, low- captures the subcellular features. Due to the strong similarity be- spatial-frequency phase information is more difficult to recon- tween the stained intensity and unstained phase, it follows that a struct than high-spatial-frequency phase information, contrary quantitative phase may provide a valid alternative to staining. to the situation for intensity reconstructions. To improve our To demonstrate the importance of using a good initial guess to reconstruction, we use a linearly approximated phase solution initialize the phase recovery for unstained samples, we compare based on DPC deconvolution [25] as a close initial guess for spa- the FPM results both with and without our DPC initialization tial frequencies within the 2 NA bandwidth. We then run a non- scheme [Fig. 2(B)]. Both achieve the same 0.7 NA resolution, linear optimization algorithm to solve the full phase problem (see with high-spatial-frequency features (e.g., nucleus and filopodia) Section 4.B), resulting in high-quality phase reconstructions with being reconstructed clearly, as expected. However, without DPC high resolution [Fig. 2(A)] and good low-spatial-frequency phase initialization, the low-frequency components of the phase are not recovery [Fig. 2(B)]. well recovered, resulting in a high-pass-filtering effect on the re- We demonstrate our new source-coded FPM by reconstruct- constructed phase, much like Zernike phase contrast (PhC).