Point Spread Function and Modulation Transfer Function Engineering
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Single‑Molecule‑Based Super‑Resolution Imaging
Histochem Cell Biol (2014) 141:577–585 DOI 10.1007/s00418-014-1186-1 REVIEW The changing point‑spread function: single‑molecule‑based super‑resolution imaging Mathew H. Horrocks · Matthieu Palayret · David Klenerman · Steven F. Lee Accepted: 20 January 2014 / Published online: 11 February 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract Over the past decade, many techniques for limit, gaining over two orders of magnitude in precision imaging systems at a resolution greater than the diffraction (Szymborska et al. 2013), allowing direct observation of limit have been developed. These methods have allowed processes at spatial scales much more compatible with systems previously inaccessible to fluorescence micros- the regime that biomolecular interactions take place on. copy to be studied and biological problems to be solved in Radically, different approaches have so far been proposed, the condensed phase. This brief review explains the basic including limiting the illumination of the sample to regions principles of super-resolution imaging in both two and smaller than the diffraction limit (targeted switching and three dimensions, summarizes recent developments, and readout) or stochastically separating single fluorophores in gives examples of how these techniques have been used to time to gain resolution in space (stochastic switching and study complex biological systems. readout). The latter also described as follows: Single-mol- ecule active control microscopy (SMACM), or single-mol- Keywords Single-molecule microscopy · Super- ecule localization microscopy (SMLM), allows imaging of resolution imaging · PALM/(d)STORM imaging · single molecules which cannot only be precisely localized, Localization microscopy but also followed through time and quantified. This brief review will focus on this “pointillism-based” SR imaging and its application to biological imaging in both two and Fluorescence microscopy allows users to dynamically three dimensions. -
About Resolution
pco.knowledge base ABOUT RESOLUTION The resolution of an image sensor describes the total number of pixel which can be used to detect an image. From the standpoint of the image sensor it is sufficient to count the number and describe it usually as product of the horizontal number of pixel times the vertical number of pixel which give the total number of pixel, for example: 2 Image Sensor & Camera Starting with the image sensor in a camera system, then usually the so called modulation transfer func- Or take as an example tion (MTF) is used to describe the ability of the camera the sCMOS image sensor CIS2521: system to resolve fine structures. It is a variant of the optical transfer function1 (OTF) which mathematically 2560 describes how the system handles the optical infor- mation or the contrast of the scene and transfers it That is the usual information found in technical data onto the image sensor and then into a digital informa- sheets and camera advertisements, but the question tion in the computer. The resolution ability depends on arises on “what is the impact or benefit for a camera one side on the number and size of the pixel. user”? 1 Benefit For A Camera User It can be assumed that an image sensor or a camera system with an image sensor generally is applied to detect images, and therefore the question is about the influence of the resolution on the image quality. First, if the resolution is higher, more information is obtained, and larger data files are a consequence. -
Mapping the PSF Across Adaptive Optics Images
Mapping the PSF across Adaptive Optics images Laura Schreiber Osservatorio Astronomico di Bologna Email: [email protected] Abstract • Adaptive Optics (AO) has become a key technology for all the main existing telescopes (VLT, Keck, Gemini, Subaru, LBT..) and is considered a kind of enabling technology for future giant telescopes (E-ELT, TMT, GMT). • AO increases the energy concentration of the Point Spread Function (PSF) almost reaching the resolution imposed by the diffraction limit, but the PSF itself is characterized by complex shape, no longer easily representable with an analytical model, and by sometimes significant spatial variation across the image, depending on the AO flavour and configuration. • The aim of this lesson is to describe the AO PSF characteristics and variation in order to provide (together with some AO tips) basic elements that could be useful for AO images data reduction. Erice School 2015: Science and Technology with E-ELT What’s PSF • ‘The Point Spread Function (PSF) describes the response of an imaging system to a point source’ • Circular aperture of diameter D at a wavelenght λ (no aberrations) Airy diffraction disk 2 퐼휃 = 퐼0 퐽1(푥)/푥 Where 퐽1(푥) represents the Bessel function of order 1 푥 = 휋 퐷 휆 푠푛휗 휗 is the angular radius from the aperture center First goes to 0 when 휗 ~ 1.22 휆 퐷 Erice School 2015: Science and Technology with E-ELT Imaging of a point source through a general aperture Consider a plane wave propagating in the z direction and illuminating an aperture. The element ds = dudv becomes the a sourse of a secondary spherical wave. -
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. -
Topic 3: Operation of Simple Lens
V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Topic 3: Operation of Simple Lens Aim: Covers imaging of simple lens using Fresnel Diffraction, resolu- tion limits and basics of aberrations theory. Contents: 1. Phase and Pupil Functions of a lens 2. Image of Axial Point 3. Example of Round Lens 4. Diffraction limit of lens 5. Defocus 6. The Strehl Limit 7. Other Aberrations PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -1- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Ray Model Simple Ray Optics gives f Image Object u v Imaging properties of 1 1 1 + = u v f The focal length is given by 1 1 1 = (n − 1) + f R1 R2 For Infinite object Phase Shift Ray Optics gives Delta Fn f Lens introduces a path length difference, or PHASE SHIFT. PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -2- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Phase Function of a Lens δ1 δ2 h R2 R1 n P0 P ∆ 1 With NO lens, Phase Shift between , P0 ! P1 is 2p F = kD where k = l with lens in place, at distance h from optical, F = k0d1 + d2 +n(D − d1 − d2)1 Air Glass @ A which can be arranged to|giv{ze } | {z } F = knD − k(n − 1)(d1 + d2) where d1 and d2 depend on h, the ray height. -
Diffraction Optics
ECE 425 CLASS NOTES – 2000 DIFFRACTION OPTICS Physical basis • Considers the wave nature of light, unlike geometrical optics • Optical system apertures limit the extent of the wavefronts • Even a “perfect” system, from a geometrical optics viewpoint, will not form a point image of a point source • Such a system is called diffraction-limited Diffraction as a linear system • Without proof here, we state that the impulse response of diffraction is the Fourier transform (squared) of the exit pupil of the optical system (see Gaskill for derivation) 207 DR. ROBERT A. SCHOWENGERDT [email protected] 520 621-2706 (voice), 520 621-8076 (fax) ECE 425 CLASS NOTES – 2000 • impulse response called the Point Spread Function (PSF) • image of a point source • The transfer function of diffraction is the Fourier transform of the PSF • called the Optical Transfer Function (OTF) Diffraction-Limited PSF • Incoherent light, circular aperture ()2 J1 r' PSF() r' = 2-------------- r' where J1 is the Bessel function of the first kind and the normalized radius r’ is given by, 208 DR. ROBERT A. SCHOWENGERDT [email protected] 520 621-2706 (voice), 520 621-8076 (fax) ECE 425 CLASS NOTES – 2000 D = aperture diameter πD πr f = focal length r' ==------- r -------- where λf λN N = f-number λ = wavelength of light λf • The first zero occurs at r = 1.22 ------ = 1.22λN , or r'= 1.22π D Compare to the course notes on 2-D Fourier transforms 209 DR. ROBERT A. SCHOWENGERDT [email protected] 520 621-2706 (voice), 520 621-8076 (fax) ECE 425 CLASS NOTES – 2000 2-D view (contrast-enhanced) “Airy pattern” central bright region, to first- zero ring, is called the “Airy disk” 1 0.8 0.6 PSF 0.4 radial profile 0.2 0 0246810 normalized radius r' 210 DR. -
Improved Single-Molecule Localization Precision in Astigmatism-Based 3D Superresolution
bioRxiv preprint doi: https://doi.org/10.1101/304816; this version posted April 19, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. Improved single-molecule localization precision in astigmatism-based 3D superresolution imaging using weighted likelihood estimation Christopher H. Bohrer1Ϯ, Xinxing Yang1Ϯ, Zhixin Lyu1, Shih-Chin Wang1, Jie Xiao1* 1Department of Biophysics and Biophysical Chemistry, Johns Hopkins School of Medicine, Baltimore, Maryland, 21205, USA. Ϯ These authors contributed equally to this work. *Correspondence and requests for materials should be addressed J.X. (email: [email protected]). Abstract: Astigmatism-based superresolution microscopy is widely used to determine the position of individual fluorescent emitters in three-dimensions (3D) with subdiffraction-limited resolutions. This point spread function (PSF) engineering technique utilizes a cylindrical lens to modify the shape of the PSF and break its symmetry above and below the focal plane. The resulting asymmetric PSFs at different z-positions for single emitters are fit with an elliptical 2D-Gaussian function to extract the widths along two principle x- and y-axes, which are then compared with a pre-measured calibration function to determine its z-position. While conceptually simple and easy to implement, in practice, distorted PSFs due to an imperfect optical system often compromise the localization precision; and it is laborious to optimize a multi-purpose optical system. Here we present a methodology that is independent of obtaining a perfect PSF and enhances the localization precision along the z-axis. -
List of Abbreviations STEM Scanning Transmission Electron Microscopy
List of Abbreviations STEM Scanning Transmission Electron Microscopy PSF Point Spread Function HAADF High-Angle Annular Dark-Field Z-Contrast Atomic Number-Contrast ICM Iterative Constrained Methods RL Richardson-Lucy BD Blind Deconvolution ML Maximum Likelihood MBD Multichannel Blind Deconvolution SA Simulated Annealing SEM Scanning Electron Microscopy TEM Transmission Electron Microscopy MI Mutual Information PRF Point Response Function Registration and 3D Deconvolution of STEM Data M. MERCIMEK*, A. F. KOSCHAN*, A. Y. BORISEVICH‡, A.R. LUPINI‡, M. A. ABIDI*, & S. J. PENNYCOOK‡. *IRIS Laboratory, Electrical Engineering and Computer Science, The University of Tennessee, 1508 Middle Dr, Knoxville, TN 37996 ‡Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 Key words. 3D deconvolution, Depth sectioning, Electron microscope, 3D Reconstruction. Summary A common characteristic of many practical modalities is that imaging process distorts the signals or scene of interest. The principal data is veiled by noise and less important signals. We split the 3D enhancement process into two separate stages; deconvolution in general is referring to the improvement of fidelity in electronic signals through reversing the convolution process, and registration aims to overcome significant misalignment of the same structures in lateral planes along focal axis. The dataset acquired with VG HB603U STEM operated at 300 kV, producing a beam with a diameter of 0.6 A˚ equipped with a Nion aberration corrector has been studied. The initial experiments described how aberration corrected Z- Contrast Imaging in STEM can be combined with the enhancement process towards better visualization with a depth resolution of a few nanometers. I. INTRODUCTION 3D characterization of both biological samples and non-biological materials provides us nano-scale resolution in three dimensions permitting the study of complex relationships between structure and existing functions. -
Preview of “Olympus Microscopy Resou... in Confocal Microscopy”
12/17/12 Olympus Microscopy Resource Center | Confocal Microscopy - Resolution and Contrast in Confocal … Olympus America | Research | Imaging Software | Confocal | Clinical | FAQ’s Resolution and Contrast in Confocal Microscopy Home Page Interactive Tutorials All optical microscopes, including conventional widefield, confocal, and two-photon instruments are limited in the resolution that they can achieve by a series of fundamental physical factors. In a perfect optical Microscopy Primer system, resolution is restricted by the numerical aperture of optical components and by the wavelength of light, both incident (excitation) and detected (emission). The concept of resolution is inseparable from Physics of Light & Color contrast, and is defined as the minimum separation between two points that results in a certain level of contrast between them. In a typical fluorescence microscope, contrast is determined by the number of Microscopy Basic Concepts photons collected from the specimen, the dynamic range of the signal, optical aberrations of the imaging system, and the number of picture elements (pixels) per unit area in the final image. Special Techniques Fluorescence Microscopy Confocal Microscopy Confocal Applications Digital Imaging Digital Image Galleries Digital Video Galleries Virtual Microscopy The influence of noise on the image of two closely spaced small objects is further interconnected with the related factors mentioned above, and can readily affect the quality of resulting images. While the effects of many instrumental and experimental variables on image contrast, and consequently on resolution, are familiar and rather obvious, the limitation on effective resolution resulting from the division of the image into a finite number of picture elements (pixels) may be unfamiliar to those new to digital microscopy. -
Super-Resolution Optical Imaging Using Microsphere Nanoscopy
Super-resolution Optical Imaging Using Microsphere Nanoscopy A thesis submitted to The University of Manchester For the degree of Doctor of Philosophy (PhD) in the Faculty of Engineering and Physical Sciences 2013 Seoungjun Lee School of Mechanical, Aerospace and Civil Engineering Super-resolution optical imaging using microsphere nanoscopy Table of Contents Table of Contents ...................................................................................................... 2 List of Figures and Tables ....................................................................................... 7 List of Publications ................................................................................................. 18 Abstract .................................................................................................................... 19 Declaration ............................................................................................................... 21 Copyright Statement ............................................................................................... 22 Acknowledgements ................................................................................................. 23 Dedication ............................................................................................................... 24 1 Introduction ...................................................................................................25 1.1 Research motivation and rationale ........................................................25 1.2 -
Confocal Microscopes
Faculty of Science Debye Institute Measuring point spread functions and calibrating (STED) confocal microscopes Bachelor thesis Peter N.A. Speets Physics and Astronomy main supervisors Prof.dr. Alfons van Blaaderen Soft Condensed Matter Group Dr. Arnout Imhof Soft Condensed Matter Group daily supervisor Ernest B. van der Wee Soft Condensed Matter Group June 2016 Abstract In this thesis the point spread function (PSF) used to characterize a confocal microscope was determined for different configurations. The PSF was determined for a sample with a refractive index matched to the refractive index that the objective was designed for, which is in this case n = 1:518 and n = 1:451 [1], and it was investigated how a mismatch in refractive index affects the shape and size of the PSF. Also the PSF of stimulated emission depletion (STED) confocal microscopy was determined to investigate the advantages of STED over conventional confocal microscopy. The alignment of the STED and the excitation laser of the confocal microscope was checked by imaging the reflection of the STED and excitation laser with a gold core nanoparticle. For the calibration of the distance measurement in a sample with a mismatch in refractive index a colloidal crystal was grown to compare the interlayer distance determined by using FTIR spectroscopy and the interlayer distance determined by imaging the crystal with the confocal microscope. 2 1. INTRODUCTION 3 1 Introduction The purpose of confocal microscopy, compared to brightfield microscopy, is to increase resolution and contrast. The confocal microscope ensures that only light from the focus point in the sample is imaged. -
Overcoming the Diffraction-Limited Spatio-Angular Resolution Tradeoff
Variable Aperture Light Field Photography: Overcoming the Diffraction-limited Spatio-angular Resolution Tradeoff Julie Chang1 Isaac Kauvar1 Xuemei Hu1,2 Gordon Wetzstein1 1Stanford University 2 Tsinghua University Abstract Small-f-number Large-f-number Light fields have many applications in machine vision, consumer photography, robotics, and microscopy. How- ever, the prevalent resolution limits of existing light field imaging systems hinder widespread adoption. In this pa- per, we analyze fundamental resolution limits of light field cameras in the diffraction limit. We propose a sequen- Depth-of-Field 10 tial, coded-aperture-style acquisition scheme that optimizes f/2 f/5.6 the resolution of a light field reconstructed from multiple f/22 photographs captured from different perspectives and f- 5 Blur-size-[mm] number settings. We also show that the proposed acquisi- 0 100 200 300 400 tion scheme facilitates high dynamic range light field imag- Distance-from-Camera-Lens-[mm] ing and demonstrate a proof-of-concept prototype system. Figure 1. Photographs captured with different f-number settings With this work, we hope to advance our understanding of exhibit different depths of field and also diffraction-limited resolu- the resolution limits of light field photography and develop tion for in-focus objects (top row). This effect is most pronounced practical computational imaging systems to overcome them. for macro photography, such as illustrated for a 50 mm lens fo- cused at 200 mm (bottom plot). Using multiple photographs cap- tured from different perspectives and with different f-number set- tings, the proposed method seeks to recover a light field with the 1.