Lab #7 Optical Aberrations
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Chapter 3 (Aberrations)
Chapter 3 Aberrations 3.1 Introduction In Chap. 2 we discussed the image-forming characteristics of optical systems, but we limited our consideration to an infinitesimal thread- like region about the optical axis called the paraxial region. In this chapter we will consider, in general terms, the behavior of lenses with finite apertures and fields of view. It has been pointed out that well- corrected optical systems behave nearly according to the rules of paraxial imagery given in Chap. 2. This is another way of stating that a lens without aberrations forms an image of the size and in the loca- tion given by the equations for the paraxial or first-order region. We shall measure the aberrations by the amount by which rays miss the paraxial image point. It can be seen that aberrations may be determined by calculating the location of the paraxial image of an object point and then tracing a large number of rays (by the exact trigonometrical ray-tracing equa- tions of Chap. 10) to determine the amounts by which the rays depart from the paraxial image point. Stated this baldly, the mathematical determination of the aberrations of a lens which covered any reason- able field at a real aperture would seem a formidable task, involving an almost infinite amount of labor. However, by classifying the various types of image faults and by understanding the behavior of each type, the work of determining the aberrations of a lens system can be sim- plified greatly, since only a few rays need be traced to evaluate each aberration; thus the problem assumes more manageable proportions. -
A N E W E R a I N O P T I
A NEW ERA IN OPTICS EXPERIENCE AN UNPRECEDENTED LEVEL OF PERFORMANCE NIKKOR Z Lens Category Map New-dimensional S-Line Other lenses optical performance realized NIKKOR Z NIKKOR Z NIKKOR Z Lenses other than the with the Z mount 14-30mm f/4 S 24-70mm f/2.8 S 24-70mm f/4 S S-Line series will be announced at a later date. NIKKOR Z 58mm f/0.95 S Noct The title of the S-Line is reserved only for NIKKOR Z lenses that have cleared newly NIKKOR Z NIKKOR Z established standards in design principles and quality control that are even stricter 35mm f/1.8 S 50mm f/1.8 S than Nikon’s conventional standards. The “S” can be read as representing words such as “Superior”, “Special” and “Sophisticated.” Top of the S-Line model: the culmination Versatile lenses offering a new dimension Well-balanced, of the NIKKOR quest for groundbreaking in optical performance high-performance lenses Whichever model you choose, every S-Line lens achieves richly detailed image expression optical performance These lenses bring a higher level of These lenses strike an optimum delivering a sense of reality in both still shooting and movie creation. It offers a new This lens has the ability to depict subjects imaging power, achieving superior balance between advanced in ways that have never been seen reproduction with high resolution even at functionality, compactness dimension in optical performance, including overwhelming resolution, bringing fresh before, including by rendering them with the periphery of the image, and utilizing and cost effectiveness, while an extremely shallow depth of field. -
Spherical Aberration ¥ Field Angle Effects (Off-Axis Aberrations) Ð Field Curvature Ð Coma Ð Astigmatism Ð Distortion
Astronomy 80 B: Light Lecture 9: curved mirrors, lenses, aberrations 29 April 2003 Jerry Nelson Sensitive Countries LLNL field trip 2003 April 29 80B-Light 2 Topics for Today • Optical illusion • Reflections from curved mirrors – Convex mirrors – anamorphic systems – Concave mirrors • Refraction from curved surfaces – Entering and exiting curved surfaces – Converging lenses – Diverging lenses • Aberrations 2003 April 29 80B-Light 3 2003 April 29 80B-Light 4 2003 April 29 80B-Light 8 2003 April 29 80B-Light 9 Images from convex mirror 2003 April 29 80B-Light 10 2003 April 29 80B-Light 11 Reflection from sphere • Escher drawing of images from convex sphere 2003 April 29 80B-Light 12 • Anamorphic mirror and image 2003 April 29 80B-Light 13 • Anamorphic mirror (conical) 2003 April 29 80B-Light 14 • The artist Hans Holbein made anamorphic paintings 2003 April 29 80B-Light 15 Ray rules for concave mirrors 2003 April 29 80B-Light 16 Image from concave mirror 2003 April 29 80B-Light 17 Reflections get complex 2003 April 29 80B-Light 18 Mirror eyes in a plankton 2003 April 29 80B-Light 19 Constructing images with rays and mirrors • Paraxial rays are used – These rays may only yield approximate results – The focal point for a spherical mirror is half way to the center of the sphere. – Rule 1: All rays incident parallel to the axis are reflected so that they appear to be coming from the focal point F. – Rule 2: All rays that (when extended) pass through C (the center of the sphere) are reflected back on themselves. -
Visual Effect of the Combined Correction of Spherical and Longitudinal Chromatic Aberrations
Visual effect of the combined correction of spherical and longitudinal chromatic aberrations Pablo Artal 1,* , Silvestre Manzanera 1, Patricia Piers 2 and Henk Weeber 2 1Laboratorio de Optica, Centro de Investigación en Optica y Nanofísica (CiOyN), Universidad de Murcia, Campus de Espinardo, 30071 Murcia, Spain 2AMO Groningen, Groningen, The Netherlands *[email protected] Abstract: An instrument permitting visual testing in white light following the correction of spherical aberration (SA) and longitudinal chromatic aberration (LCA) was used to explore the visual effect of the combined correction of SA and LCA in future new intraocular lenses (IOLs). The LCA of the eye was corrected using a diffractive element and SA was controlled by an adaptive optics instrument. A visual channel in the system allows for the measurement of visual acuity (VA) and contrast sensitivity (CS) at 6 c/deg in three subjects, for the four different conditions resulting from the combination of the presence or absence of LCA and SA. In the cases where SA is present, the average SA value found in pseudophakic patients is induced. Improvements in VA were found when SA alone or combined with LCA were corrected. For CS, only the combined correction of SA and LCA provided a significant improvement over the uncorrected case. The visual improvement provided by the correction of SA was higher than that from correcting LCA, while the combined correction of LCA and SA provided the best visual performance. This suggests that an aspheric achromatic IOL may provide some visual benefit when compared to standard IOLs. ©2010 Optical Society of America OCIS codes: (330.0330) Vision, color, and visual optics; (330.4460) Ophthalmic optics and devices; (330.5510) Psycophysics; (220.1080) Active or adaptive optics. -
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. -
An Instrument for Measuring Longitudinal Spherical Aberration of Lenses
U. S. Department of Commerce Research Paper RP20l5 National Bureau of Standards Volume 42, August 1949 Part of the Journal of Research of the National Bureau of Standards An Instrument for Measuring Longitudinal Spherical Aberration of Lenses By Francis E. Washer An instrument is described that permits the rapid determination of longitudinal spheri cal and longitudinal chromatic aberration of lenses. Specially constructed diaphragms isolate successive zones of a lens, and a movable reticle connected to a sensitive dial gage enables the operator to locate the successive focal planes for the different zones. Results of measurement are presented for several types of lenses. The instrument can also be used without modification to measure the mall refractive powers of goggle lenses. 1. Introduction The arrangement of these elements is shown diagrammatically in figui' e 1. To simplify the In the comse of a research project sponsored by description, the optical sy tem will be considered the Army Air Forces, an instrument was developed in three parts, each of which forms a definite to facilitate the inspection of len es used in the member of the whole system. The axis, A, is construction of reflector sights. This instrument common to the entire system; the axis is bent at enabled the inspection method to be based upon the mirror, lvI, to conserve space and simplify a rapid determination of the axial longitudinal operation by a single observer. spherical aberration of the lens. This measme Objective lens L j , mirror M, and viewing screen, ment was performed with the aid of a cries of S form the first part. -
Spherical Aberration
Spherical Aberration Lens Design OPTI 517 Prof. Jose Sasian Spherical aberration • 1) Wavefront shapes 8) Merte surface • 2) Fourth and sixth 9) Afocal doublet order coefficients 10) Aspheric plate • 3) Using an aspheric 11) Meniscus lens surface 12) Spaced doublet • 3) Lens splitting 13) Aplanatic points • 4) Lens bending 14) Fourth-order • 5) Index of refraction dependence dependence 16) Gaussian to flat top • 6) Critical air space • 7) Field lens Prof. Jose Sasian Review of key conceptual figures Prof. Jose Sasian Conceptual models F P N P’ N’ F’ First-order optics model provides a useful reference and provides graphical method to trace first-order rays Entrance and exit pupils provide a useful reference to describe the input and E E’ output optical fields Prof. Jose Sasian Object, image and pupil planes Prof. Jose Sasian Rays and waves geometry Geometrical ray model and wave model for light propagation. Both Ray Are consistent and are y 'I H different representations W/n of the same phenomena. Aperture Normal vector line Image plane Optical axis Reference sphere Wavefront Exit pupil plane Prof. Jose Sasian Spherical aberration Prof. Jose Sasian Spherical aberration is uniform over the field of view 2 W040 Wavefront Spots Prof. Jose Sasian Ray caustic Prof. Jose Sasian Two waves of spherical aberration through focus. From positive four waves to negative seven waves, at one wave steps of defocus. The first image in the middle row is at the Gaussian image plane. Prof. Jose Sasian Cases of zero spherical aberration from a spherical surface 2 1 2 u W040 WS040 I SI A y 8 n y 0 A 0 0 /un ' un un / /' y=0 the aperture is zero or the surface is at an image A=0 the surface is concentric with the Gaussian image point on axis u’/n’-u/n=0 the conjugates are at the aplanatic points Aplanatic means free from error; freedom from spherical aberration and coma Prof. -
Longitudinal Chromatic Aberration
Longitudinal Chromatic Aberration Red focus Blue focus LCA Transverse Chromatic Aberration Decentered pupil Transverse Chromatic Aberration Chromatic Difference of Refraction Atchison and Smith, JOSA A, 2005 Why is LCA not really a problem? Chromatic Aberration Halos (LCA) Fringes (TCA) www.starizona.com digitaldailydose.wordpress.com Red-Green Duochrome test • If the letters on the red side stand out more, add minus power; if the letters on the green side stand out more, add plus power. • Neutrality is reached when the letters on both backgrounds appear equally distinct. Colligon-Bradley P. J Ophthalmic Nurs Technol. 1992 11(5):220-2. Transverse Chromatic Aberration Lab #7 April 15th Look at a red and blue target through a 1 mm pinhole. Move the pinhole from one edge of the pupil to the other. What happens to the red and blue images? Chromatic Difference of Magnification Chief ray Aperture stop Off axis source Abbe Number • Also known as – Refractive efficiency – nu-value –V-value –constringence Refractive efficiencies for common materials water 55.6 alcohol 60.6 ophthalmic crown glass 58.6 polycarbonate 30.0 dense flint glass 36.6 Highlite glass 31.0 BK7 64.9 Example • Given the following indices of refraction for BK7 glass (nD = 1.519; nF = 1.522; nC = 1.514) what is the refractive efficiency? • What is the chromatic aberration of a 20D thin lens made of BK7 glass? Problem • Design a 10.00 D achromatic doublet using ophthalmic crown glass and dense flint glass Carl Friedrich Gauss 1777-1855 Heinrich Seidel 1842-1906 Approximations to -
Optical Performance Factors
1ch_FundamentalOptics_Final_a.qxd 6/15/2009 2:28 PM Page 1.11 Fundamental Optics www.cvimellesgriot.com Fundamental Optics Performance Factors After paraxial formulas have been used to select values for component focal length(s) and diameter(s), the final step is to select actual lenses. As in any engineering problem, this selection process involves a number of tradeoffs, wavelength l including performance, cost, weight, and environmental factors. The performance of real optical systems is limited by several factors, material 1 including lens aberrations and light diffraction. The magnitude of these index n 1 effects can be calculated with relative ease. Gaussian Beam Optics v Numerous other factors, such as lens manufacturing tolerances and 1 component alignment, impact the performance of an optical system. Although these are not considered explicitly in the following discussion, it should be kept in mind that if calculations indicate that a lens system only just meets the desired performance criteria, in practice it may fall short material 2 v2 of this performance as a result of other factors. In critical applications, index n 2 it is generally better to select a lens whose calculated performance is significantly better than needed. DIFFRACTION Figure 1.14 Refraction of light at a dielectric boundary Diffraction, a natural property of light arising from its wave nature, poses a fundamental limitation on any optical system. Diffraction is always Optical Specifications present, although its effects may be masked if the system has significant aberrations. When an optical system is essentially free from aberrations, its performance is limited solely by diffraction, and it is referred to as diffraction limited. -
Criminalistics & Forensic Physics MODULE No. 27
SUBJECT FORENSIC SCIENCE Paper No. and Title PAPER No.7: Criminalistics & Forensic Physics Module No. and Title MODULE No.27: Photographic Lenses, Filters and Artificial Light Module Tag FSC_P7_M27 FORENSIC SCIENCE PAPER No. 7: Criminalistics & Forensic Physics MODULE No. 27: Photographic Lenses, Filters and Artificial Light TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction- Camera Lenses i) Convex Lens ii) Concave Lens 3. Useful terms of the lens 4. Types of Photographic Lens 5. Defects of Lens 6. Filters for Photography 7. Film Sensitivity 8. Colour of Light 9. Summary FORENSIC SCIENCE PAPER No. 7: Criminalistics & Forensic Physics MODULE No. 27: Photographic Lenses, Filters and Artificial Light 1. Learning Outcomes After studying this module, you shall be able to know – What are Camera Lenses and their types Various terms of the Lens Various types of Filters used in Photography 2. Introduction – Camera Lenses Camera lens is a transparent medium (usually glass) bounded by one or more curved surfaces (spherical, cylindrical or parabolic) all of whose centers are on a common axis. For photographic lens the sides should be of spherical type. A simple or thin lens is a single piece of glass whose axial thickness is less compared to its diameter whereas a compound lens consists of several components or group of components, some of which may comprise of several elements cemented together. Lenses are mainly divided into two types, viz. i) Convex Lens ii) Concave Lens FORENSIC SCIENCE PAPER No. 7: Criminalistics & Forensic Physics MODULE No. 27: Photographic Lenses, Filters and Artificial Light i) Convex lens: This type of lens is thicker at the central portion and thinner at the peripheral portion. -
Wide Field Telescope Using Spherical Mirrors
Wide field telescope using spherical mirrors J. H. Burge and J. R. P. Angel Optical Sciences Center and Steward Observatory University of Arizona, Tucson, AZ 85721 ABSTRACT A new class of optical telescope is required to obtain high resolution spectra of many faint, dis- tant galaxies. These dim objects require apertures approaching 30 meters in addition to many hours of integration per object, and simultaneous observation of as many galaxies as possible. Several astronomical telescopes of 20, 30, 50, even 100 meters are being proposed for general purpose astronomy. We present a different concept here with a 30-m telescope optimized for wide field, multi-object spectroscopy. The optical design uses a fully steerable, quasi- Cassegrain telescope in which the primary and secondary mirrors are parts of concentric spheres, imaging a 3° field of view onto a spherical surface. The spherical aberration from the mirrors is large (about 2 arc minutes) but it is constant across the field. Our system design uses numerous correctors, placed at the Cassegrain focus, each of which corrects over a small field of a few arc seconds. These can be used for integral field spectroscopy or for direct imaging us- ing adaptive optics. Hundreds of these units could be placed on the focal surface during the day to allow all-night exposures of the desired regions. We believe that this design offers an economical system that can be dedicated for several important types of astronomical observa- tion. Keywords : telescope, optical design, astronomical optics 1. INTRODUCTION The optical design of the Schmidt telescope is well known to provide excellent images over a large field of view by using a spherical primary mirror and a corrector located at the stop of the telescope at the center of curvature of the primary mirror. -
Spherical Aberration Correction in a Scanning Transmission Electron Microscope Using a Sculpted Foil
Spherical aberration correction in a scanning transmission electron microscope using a sculpted foil Roy Shiloh1*†, Roei Remez1†, Peng-Han Lu2†, Lei Jin2, Yossi Lereah1, Amir H. Tavabi2, Rafal E. Dunin- Borkowski2, and Ady Arie1 1School of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel. 2Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, Jülich, Germany. *Correspondence to: [email protected] †These authors contributed equally to this work. Nearly twenty years ago, following a sixty year struggle, scientists succeeded in correcting the bane of electron lenses, spherical aberration, using electromagnetic aberration correction. However, such correctors necessitate re-engineering of the electron column, additional space, a power supply, water cooling, and other requirements. Here, we show how modern nanofabrication techniques can be used to surpass the resolution of an uncorrected scanning transmission electron microscope more simply by sculpting a foil of material into a refractive corrector that negates spherical aberration. This corrector can be fabricated at low cost using a simple process and installed on existing electron microscopes without changing their hardware, thereby providing an immediate upgrade to spatial resolution. Using our corrector, we reveal features of Si and Cu samples that cannot be resolved in the uncorrected microscope. Electron microscopy has been revolutionised by the introduction of aberration correction, which has allowed a vast range of new scientific questions to be addressed at the atomic scale. Although the first electron microscope was built 85 years ago [1], its rotationally-symmetric, static, charge-free lenses are fundamentally incapable of correcting the dominant spherical aberration [2].