Resolution Enhancement Techniques in Microscopy
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Diffraction Interference Induced Superfocusing in Nonlinear Talbot Effect24,25, to Achieve Subdiffraction by Exploiting the Phases of The
OPEN Diffraction Interference Induced SUBJECT AREAS: Superfocusing in Nonlinear Talbot Effect NONLINEAR OPTICS Dongmei Liu1, Yong Zhang1, Jianming Wen2, Zhenhua Chen1, Dunzhao Wei1, Xiaopeng Hu1, Gang Zhao1, SUB-WAVELENGTH OPTICS S. N. Zhu1 & Min Xiao1,3 Received 1National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, School of Physics, Nanjing 12 May 2014 University, Nanjing 210093, China, 2Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA, 3Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA. Accepted 24 July 2014 We report a simple, novel subdiffraction method, i.e. diffraction interference induced superfocusing in Published second-harmonic (SH) Talbot effect, to achieve focusing size of less than lSH/4 (or lpump/8) without 20 August 2014 involving evanescent waves or subwavelength apertures. By tailoring point spread functions with Fresnel diffraction interference, we observe periodic SH subdiffracted spots over a hundred of micrometers away from the sample. Our demonstration is the first experimental realization of the Toraldo di Francia’s proposal pioneered 62 years ago for superresolution imaging. Correspondence and requests for materials should be addressed to ocusing of a light beam into an extremely small spot with a high energy density plays an important role in key technologies for miniaturized structures, such as lithography, optical data storage, laser material nanopro- Y.Z. (zhangyong@nju. cessing and nanophotonics in confocal microscopy and superresolution imaging. Because of the wave edu.cn); J.W. F 1 nature of light, however, Abbe discovered at the end of 19th century that diffraction prohibits the visualization (jianming.wen@yale. of features smaller than half of the wavelength of light (also known as the Rayleigh diffraction limit) with optical edu) or M.X. -
Phase Retrieval Without Prior Knowledge Via Single-Shot Fraunhofer Diffraction Pattern of Complex Object
Phase retrieval without prior knowledge via single-shot Fraunhofer diffraction pattern of complex object An-Dong Xiong1 , Xiao-Peng Jin1 , Wen-Kai Yu1 and Qing Zhao1* Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the lost phase part is indispensable for reverse transformation. Phase retrieval is usually conducted in two means: priori knowledge or multiple different measurements. However, priori knowledge works for certain type of object while multiple measurements are difficult for short wavelength. Here, by introducing non-orthogonal measurement via high density sampling scheme, we demonstrate that one single-shot Fraunhofer diffraction pattern of complex object is sufficient for phase retrieval. Both simulation and experimental results have demonstrated the feasibility of our scheme. Reconstruction of complex object reveals depth information or refraction index; and single-shot measurement can be achieved under most scenario. Their combination will broaden the application field of coherent diffraction imaging. Fraunhofer diffraction, also known as far-field diffraction, problem12-14. These matrix complement methods require 4N- does not necessarily need any extra optical devices except a 4 (N stands for the dimension) generic measurements such as beam source. The diffraction field is the Fourier transform of Gaussian random measurements for complex field15. the original light field. However, for visible light or X-ray Ptychography is another reliable method to achieve image diffraction, the phase part is hardly directly measurable1. with good resolution if the sample can endure scanning16-19. Therefore, phase retrieval from intensity measurement To achieve higher spatial resolution around the size of atom, becomes necessary for reconstructing the original field. -
Introduction to Optics Part I
Introduction to Optics part I Overview Lecture Space Systems Engineering presented by: Prof. David Miller prepared by: Olivier de Weck Revised and augmented by: Soon-Jo Chung Chart: 1 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Outline Goal: Give necessary optics background to tackle a space mission, which includes an optical payload •Light •Interaction of Light w/ environment •Optical design fundamentals •Optical performance considerations •Telescope types and CCD design •Interferometer types •Sparse aperture array •Beam combining and Control Chart: 2 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Examples - Motivation Spaceborne Astronomy Planetary nebulae NGC 6543 September 18, 1994 Hubble Space Telescope Chart: 3 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Properties of Light Wave Nature Duality Particle Nature HP w2 E 2 E 0 Energy of Detector c2 wt 2 a photon Q=hQ Solution: Photons are EAeikr( ZtI ) “packets of energy” E: Electric field vector c H: Magnetic field vector Poynting Vector: S E u H 4S 2S Spectral Bands (wavelength O): Wavelength: O Q QT Ultraviolet (UV) 300 Å -300 nm Z Visible Light 400 nm - 700 nm 2S Near IR (NIR) 700 nm - 2.5 Pm Wave Number: k O Chart: 4 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Reflection-Mirrors Mirrors (Reflective Devices) and Lenses (Refractive Devices) are both “Apertures” and are similar to each other. Law of reflection: Mirror Geometry given as Ti Ti=To a conic section rot surface: T 1 2 2 o z()U r r k 1 U Reflected wave is also k 1 in the plane of incidence Specular Circle: k=0 Ellipse -1<k<0 Reflection Parabola: k=-1 Hyperbola: k<-1 sun mirror Detectors resolve Images produced by (solar) energy reflected from detector a target scene* in Visual and NIR. -
Sub-Airy Disk Angular Resolution with High Dynamic Range in the Near-Infrared A
EPJ Web of Conferences 16, 03002 (2011) DOI: 10.1051/epjconf/20111603002 C Owned by the authors, published by EDP Sciences, 2011 Sub-Airy disk angular resolution with high dynamic range in the near-infrared A. Richichi European Southern Observatory,Karl-Schwarzschildstr. 2, 85748 Garching, Germany Abstract. Lunar occultations (LO) are a simple and effective high angular resolution method, with minimum requirements in instrumentation and telescope time. They rely on the analysis of the diffraction fringes created by the lunar limb. The diffraction phenomen occurs in space, and as a result LO are highly insensitive to most of the degrading effects that limit the performance of traditional single telescope and long-baseline interferometric techniques used for direct detection of faint, close companions to bright stars. We present very recent results obtained with the technique of lunar occultations in the near-IR, showing the detection of companions with very high dynamic range as close as few milliarcseconds to the primary star. We discuss the potential improvements that could be made, to increase further the current performance. Of course, LO are fixed-time events applicable only to sources which happen to lie on the Moon’s apparent orbit. However, with the continuously increasing numbers of potential exoplanets and brown dwarfs beign discovered, the frequency of such events is not negligible. I will list some of the most favorable potential LO in the near future, to be observed from major observatories. 1. THE METHOD The geometry of a lunar occultation (LO) event is sketched in Figure 1. The lunar limb acts as a straight diffracting edge, moving across the source with an angular speed that is the product of the lunar motion vector VM and the cosine of the contact angle CA. -
Ernst Abbe 1840-1905: a Social Reformer
We all do not belong to ourselves Ernst Abbe 1840-1905: a Social Reformer Fritz Schulze, Canada Linda Nguyen, The Canadian Press, Wednesday, January 2014: TORONTO – By the time you finish your lunch on Thursday, Canada’s top paid CEO will have already earned (my italics!) the equivalent of your annual salary.* It is not unusual these days to read such or similar headlines. Each time I am reminded of the co-founder of the company I worked for all my active life. Those who know me, know that I worked for the world-renowned German optical company Carl Zeiss. I also have a fine collection of optical instruments, predominantly microscopes, among them quite a few Zeiss instruments. Carl Zeiss founded his business as a “mechanical atelier” in Jena in 1846 and his mathematical consultant, Ernst Abbe, a poorly paid lecturer at the University Jena, became his partner in 1866. That was the beginning of a comet-like rise of the young company. Ernst Abbe was born in Eisenach, Thuringia, on January 23, 1840, as the first child of a spinnmaster of a local textile mill.Till the beginning of the 50s each and every day the Lord made my father stood at his machines, 14, 15, 16 hours, from 5 o’clock in the morning till 7 o’clock in the evening during quiet periods, 16 hours from 4 o’clock in the morning till 8 o’clock in the evening during busy times, without any interruption, not even a lunch break. I myself as a small boy of 5 – 9 years brought him his lunch, alternately with my younger sister, and watched him as he gulped it down leaning on his machine or sitting on a wooden box, then handing me back the empty pail and immediately again tending his machines." Ernst Abbe remembered later. -
The Most Important Equation in Astronomy! 50
The Most Important Equation in Astronomy! 50 There are many equations that astronomers use L to describe the physical world, but none is more R 1.22 important and fundamental to the research that we = conduct than the one to the left! You cannot design a D telescope, or a satellite sensor, without paying attention to the relationship that it describes. In optics, the best focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The diffraction pattern has a bright region in the center called the Airy Disk. The diameter of the Airy Disk is related to the wavelength of the illuminating light, L, and the size of the circular aperture (mirror, lens), given by D. When L and D are expressed in the same units (e.g. centimeters, meters), R will be in units of angular measure called radians ( 1 radian = 57.3 degrees). You cannot see details with your eye, with a camera, or with a telescope, that are smaller than the Airy Disk size for your particular optical system. The formula also says that larger telescopes (making D bigger) allow you to see much finer details. For example, compare the top image of the Apollo-15 landing area taken by the Japanese Kaguya Satellite (10 meters/pixel at 100 km orbit elevation: aperture = about 15cm ) with the lower image taken by the LRO satellite (0.5 meters/pixel at a 50km orbit elevation: aperture = ). The Apollo-15 Lunar Module (LM) can be seen by its 'horizontal shadow' near the center of the image. -
Bernhard Riemann 1826-1866
Modern Birkh~user Classics Many of the original research and survey monographs in pure and applied mathematics published by Birkh~iuser in recent decades have been groundbreaking and have come to be regarded as foun- dational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain ac- cessible to new generations of students, scholars, and researchers. BERNHARD RIEMANN (1826-1866) Bernhard R~emanno 1826 1866 Turning Points in the Conception of Mathematics Detlef Laugwitz Translated by Abe Shenitzer With the Editorial Assistance of the Author, Hardy Grant, and Sarah Shenitzer Reprint of the 1999 Edition Birkh~iuser Boston 9Basel 9Berlin Abe Shendtzer (translator) Detlef Laugwitz (Deceased) Department of Mathematics Department of Mathematics and Statistics Technische Hochschule York University Darmstadt D-64289 Toronto, Ontario M3J 1P3 Gernmany Canada Originally published as a monograph ISBN-13:978-0-8176-4776-6 e-ISBN-13:978-0-8176-4777-3 DOI: 10.1007/978-0-8176-4777-3 Library of Congress Control Number: 2007940671 Mathematics Subject Classification (2000): 01Axx, 00A30, 03A05, 51-03, 14C40 9 Birkh~iuser Boston All rights reserved. This work may not be translated or copied in whole or in part without the writ- ten permission of the publisher (Birkh~user Boston, c/o Springer Science+Business Media LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter de- veloped is forbidden. -
Optical Expert Named New Professor for History of Physics at University and Founding Director of German Optical Museum
URL: http://www.uni-jena.de/en/News/PM180618_Mappes_en.pdf Optical Expert Named New Professor for History of Physics at University and Founding Director of German Optical Museum Dr Timo Mappes to assume new role on 1 July 2018 / jointly appointed by University of Jena and German Optical Museum Dr Timo Mappes has been appointed Professor for the History of Physics with a focus on scientific communication at the Friedrich Schiller University Jena (Germany). He will also be the founding Director of the new German Optical Museum in Jena. Mappes will assume his new duties on 1 July 2018. Scientist, manager and scientific communicator "The highly complex job profile for this professorship meant the search committee faced a difficult task. We were very fortunate to find an applicant with so many of the necessary qualifications," says Prof. Dr Gerhard G. Paulus, Chairman of the search committee, adding: "If the committee had been asked to create its ideal candidate, it would have produced someone that resembled Dr Mappes." Mappes has a strong background in science and the industrial research and development of optical applications, and over the last twenty years has become very well-respected in the documentation and history of microscope construction from 1800 onwards. Last but not least, he has management skills and experience in sharing his knowledge with the general public, and with students in particular. All of this will be very beneficial for the German Optical Museum. The new concept and the extensive renovation of the traditional Optical Museum in Jena will make way for the new German Optical Museum, a research museum and forum for showcasing the history of optics and photonics. -
Fraunhofer Diffraction Effects on Total Power for a Planckian Source
Volume 106, Number 5, September–October 2001 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 106, 775–779 (2001)] Fraunhofer Diffraction Effects on Total Power for a Planckian Source Volume 106 Number 5 September–October 2001 Eric L. Shirley An algorithm for computing diffraction ef- Key words: diffraction; Fraunhofer; fects on total power in the case of Fraun- Planckian; power; radiometry. National Institute of Standards and hofer diffraction by a circular lens or aper- Technology, ture is derived. The result for Fraunhofer diffraction of monochromatic radiation is Gaithersburg, MD 20899-8441 Accepted: August 28, 2001 well known, and this work reports the re- sult for radiation from a Planckian source. [email protected] The result obtained is valid at all temper- atures. Available online: http://www.nist.gov/jres 1. Introduction Fraunhofer diffraction by a circular lens or aperture is tion, because the detector pupil is overfilled. However, a ubiquitous phenomenon in optics in general and ra- diffraction leads to losses in the total power reaching the diometry in particular. Figure 1 illustrates two practical detector. situations in which Fraunhofer diffraction occurs. In the All of the above diffraction losses have been a subject first example, diffraction limits the ability of a lens or of considerable interest, and they have been considered other focusing optic to focus light. According to geo- by Blevin [2], Boivin [3], Steel, De, and Bell [4], and metrical optics, it is possible to focus rays incident on a Shirley [5]. The formula for the relative diffraction loss lens to converge at a focal point. -
Rudi Mathematici
Rudi Mathematici Y2K Rudi Mathematici Gennaio 2000 52 1 S (1803) Guglielmo LIBRI Carucci dalla Somaja Olimpiadi Matematiche (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE P1 (1912) Boris GNEDENKO 2 D (1822) Rudolf Julius Emmanuel CLAUSIUS Due matematici "A" e "B" si sono inventati una (1905) Lev Genrichovich SHNIRELMAN versione particolarmente complessa del "testa o (1938) Anatoly SAMOILENKO croce": viene scritta alla lavagna una matrice 1 3 L (1917) Yuri Alexeievich MITROPOLSHY quadrata con elementi interi casuali; il gioco (1643) Isaac NEWTON consiste poi nel calcolare il determinante: 4 M (1838) Marie Ennemond Camille JORDAN 5 M Se il determinante e` pari, vince "A". (1871) Federigo ENRIQUES (1871) Gino FANO Se il determinante e` dispari, vince "B". (1807) Jozeph Mitza PETZVAL 6 G (1841) Rudolf STURM La probabilita` che un numero sia pari e` 0.5, (1871) Felix Edouard Justin Emile BOREL 7 V ma... Quali sono le probabilita` di vittoria di "A"? (1907) Raymond Edward Alan Christopher PALEY (1888) Richard COURANT P2 8 S (1924) Paul Moritz COHN (1942) Stephen William HAWKING Dimostrare che qualsiasi numero primo (con (1864) Vladimir Adreievich STELKOV l'eccezione di 2 e 5) ha un'infinita` di multipli 9 D nella forma 11....1 2 10 L (1875) Issai SCHUR (1905) Ruth MOUFANG "Die Energie der Welt ist konstant. Die Entroopie 11 M (1545) Guidobaldo DEL MONTE der Welt strebt einem Maximum zu" (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR Rudolph CLAUSIUS 12 M (1906) Kurt August HIRSCH " I know not what I appear to the world, -
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. -
Microscope Objectives, Part 2
Understanding the Microscope part 7 – Objectives: part 2 of 2 Objectives and Image formation In the second of this series of articles, it was stated that the chief role of the microscope is to present clearly- resolved detail to the eye; also the objective is the main optical element in the microscope. In the previous article on objectives (part 4), I wrote that diffraction was responsible not only for image formation but also limited the formation of the perfect image as a faithful representation of the object. There are three types of limiting factor that affect image quality: (a) optical aberrations (b) image noise and (c) diffraction. The previous article on objectives considered the various types of optical aberration found in the objective. Image noise, put simply, is merely the sum of all those factors aside of limitations due to diffraction which degrade the image as a true representation of the object. This can include the quality of the receptor or the quality of the illumination. If we assume that we are dealing with a perfect objective, we can ignore the effects of aberrations and optical noise. Let us assume that the specimen (as lit by the lamp and condenser) is self-luminous, then the more information from the spherical wavefront that is accepted by the lens, the greater the fidelity (or faithful representation) of the image (Figure 1). In other words, the angular aperture of the lens will determine the light gathering power of the lens and, as we might expect, the larger the angular aperture the greater the fidelity of the image.