Teaching Optics
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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. -
Sky & Telescope
S&T Test Report by Rod Mollise Meade’s 115-Millimeter ED Triplet This 4.5-inch apochromat packs a lot of bang for the buck. 115mm Series 6000 THIS IS A GREAT TIME to be in the ice and was eager to see how others market for a premium refracting tele- performed. So when I was approached ED Triplet APO scope. The price for high-quality refrac- about evaluating Meade’s 115mm Series U.S. Price: $1,899 tors has fallen dramatically in recent 6000 ED Triplet APO, I was certainly up meade.com years, and you can now purchase a for the task. 4- to-5-inch extra-low dispersion (ED) First impressions are important, and What We Like apochromatic (APO) telescope that’s when I unboxed the scope on the day Sharp, well-corrected optics almost entirely free of the false color it arrived, I lit up when I saw it. This is Color-free views that plagues achromats for a fraction of Attractive fi nish the cost commonly seen a decade ago. I’ve had a ball with my own recently q The Meade 115mm Series 6000 ED Triplet What We Don’t Like purchased apochromat after using APO ready for a night’s activity, shown with an optional 2-inch mirror diagonal. The scope Visual back locking almost nothing but Schmidt-Cassegrain also accepts fi nderscopes that attach using a system can be awkward telescopes for many years. However, I standardized dovetail system commonly found Focuser backlash still consider myself a refractor nov- on small refractors. -
Tessar and Dagor Lenses
Tessar and Dagor lenses Lens Design OPTI 517 Prof. Jose Sasian Important basic lens forms Petzval DB Gauss Cooke Triplet little stress Stressed with Stressed with Low high-order Prof. Jose Sasian high high-order aberrations aberrations Measuring lens sensitivity to surface tilts 1 u 1 2 u W131 AB y W222 B y 2 n 2 n 2 2 1 1 1 1 u 1 1 1 u as B y cs A y 1 m Bstop ystop n'u' n 1 m ystop n'u' n CS cs 2 AS as 2 j j Prof. Jose Sasian Lens sensitivity comparison Coma sensitivity 0.32 Astigmatism sensitivity 0.27 Coma sensitivity 2.87 Astigmatism sensitivity 0.92 Coma sensitivity 0.99 Astigmatism sensitivity 0.18 Prof. Jose Sasian Actual tough and easy to align designs Off-the-shelf relay at F/6 Coma sensitivity 0.54 Astigmatism sensitivity 0.78 Coma sensitivity 0.14 Astigmatism sensitivity 0.21 Improper opto-mechanics leads to tough alignment Prof. Jose Sasian Tessar lens • More degrees of freedom • Can be thought of as a re-optimization of the PROTAR • Sharper than Cooke triplet (low index) • Compactness • Tessar, greek, four • 1902, Paul Rudolph • New achromat reduces lens stress Prof. Jose Sasian Tessar • The front component has very little power and acts as a corrector of the rear component new achromat • The cemented interface of the new achromat: 1) reduces zonal spherical aberration, 2) reduces oblique spherical aberration, 3) reduces zonal astigmatism • It is a compact lens Prof. Jose Sasian Merte’s Patent of 1932 Faster Tessar lens F/5.6 Prof. -
Applied Physics I Subject Code: PHY-106 Set: a Section: …………………………
Test-1 Subject: Applied Physics I Subject Code: PHY-106 Set: A Section: ………………………….. Max. Marks: 30 Registration Number: ……………… Max. Time: 45min Roll Number: ………………………. Question 1. Define systematic and random errors. (5) Question 2. In an experiment in determining the density of a rectangular block, the dimensions of the block are measured with a vernier caliper with least count of 0.01 cm and its mass is measured with a beam balance of least count 0.1 g, l = 5.12 cm, b = 2.56 cm, t = 0.37 cm and m = 39.3 g. Report correctly the density of the block. (10) Question 3. Derive a relation to overcome chromatic aberration for an optical system consisting of two convex lenses. (5) Question 4. An achromatic doublet of focal length 20 cm is to be made by placing a convex lens of borosilicate crown glass in contact with a diverging lens of dense flint glass. Assuming nr = 1.51462, nb = ′ ′ 1.52264, 푛푟 = 1.61216, and 푛푏 = 1.62901, calculate the focal length of each lens; here the unprimed and the primed quantities refer to the borosilicate crown glass and dense flint glass, respectively. (10) Test-1 Subject: Applied Physics I Subject Code: PHY-106 Set: B Section: ………………………….. Max. Marks: 30 Registration Number: ……………… Max. Time: 45min Roll Number: ………………………. Question 1. Distinguish accuracy and precision with example. (5) Question 2. Obtain an expression for chromatic aberration in the image formed by paraxial rays. (5) Question 3. It is required to find the volume of a rectangular block. A vernier caliper is used to measure the length, width and height of the block. -
Carl Zeiss Oberkochen Large Format Lenses 1950-1972
Large format lenses from Carl Zeiss Oberkochen 1950-1972 © 2013-2019 Arne Cröll – All Rights Reserved (this version is from October 4, 2019) Carl Zeiss Jena and Carl Zeiss Oberkochen Before and during WWII, the Carl Zeiss company in Jena was one of the largest optics manufacturers in Germany. They produced a variety of lenses suitable for large format (LF) photography, including the well- known Tessars and Protars in several series, but also process lenses and aerial lenses. The Zeiss-Ikon sister company in Dresden manufactured a range of large format cameras, such as the Zeiss “Ideal”, “Maximar”, Tropen-Adoro”, and “Juwel” (Jewel); the latter camera, in the 3¼” x 4¼” size, was used by Ansel Adams for some time. At the end of World War II, the German state of Thuringia, where Jena is located, was under the control of British and American troops. However, the Yalta Conference agreement placed it under Soviet control shortly thereafter. Just before the US command handed the administration of Thuringia over to the Soviet Army, American troops moved a considerable part of the leading management and research staff of Carl Zeiss Jena and the sister company Schott glass to Heidenheim near Stuttgart, 126 people in all [1]. They immediately started to look for a suitable place for a new factory and found it in the small town of Oberkochen, just 20km from Heidenheim. This led to the foundation of the company “Opton Optische Werke” in Oberkochen, West Germany, on Oct. 30, 1946, initially as a full subsidiary of the original factory in Jena. -
The Plumbers Telescope-English
240.BLT KLAUS HÜNIG than 10mm. Use sandpaper to smooth the hole and then roughen the inside of the plug The Plumber’s Telescope to provide a good base for the glue. Remove Kit for an astronomical refracting telescope with Put a small amount of glue evenly all dust and loose plastic bits. 30x magnification, fromusing any 40mm local drain DIY pipes store around the inner side of the end with the Step 8: tags, again without drops or strings. Apply a generous amount of glue onto the Push the eyepiece into the holder from disk holding the eyepiece and fit it into the the tag side and slide it into place by socket plug so that the hole in the disk sits pushing it onto the work surface so it is centrally over the hole in the plug. Again flush with the six tags. take care that no glue gets onto the surface of the lens. After the glue has set, push the plug into the second push-fit coupling. This •Achromatic objective lens, finishes the construction of the eyepiece Ø 40mm, f +450mm holder. •Colour corrected Plössl eyepiece, 15mm, f +15mm Step 5: D. The final assembly Ø Open the 11mm central hole in Part C Step 9: •Tripod adapter (without tripod) Remove the rubber seal from the open end of (blind) using a sharp knife and then •Indestructible HT tubing Shopping list for the DIY store: remove the part from the cardboard. the eyepiece holder. Then fit the eyepiece Fold the six tags backwards and glue the holder on the open end of the objective lens •Shows Moon craters, phases tube. -
31 the Superachromat
Lesson 31: The Superachromat This lesson will explore a unique feature of SYNOPSYS that can be helpful when you need exceptional color correction, better even than an apochromat. Lesson 8 in this Online Tutorial showed how to select three glass types that make it possible to correct axial color at three wavelengths. For many tasks, that is as good as you will need. But not always. Suppose you are designing a lens to be used over the range 0.4 to 0.9 um. Can you do it with an apochromat? Let’s find out. Here is the RLE file for a starting system, where all surfaces are flat except for the last, which will give us an F/8 telescope objective of 6-inch aperture. (Copy these lines and paste them into the MACro editor.) RLE ID WIDE SPECTRAL RANGE EXAMPLE OBB 0 .25 3 UNITS INCH 1 GLM 1.6 50 3 GLM 1.6 50 5 GLM 1.6 50 6 UMC -0.0625 YMT 7 1 TH .6 2 TH .1 3 TH .6 4 TH .1 5 TH .6 END We did not specify the wavelengths yet, so we get the default CdF lines. We need to change this. Open the Spectrum Wizard (MSW), and change the points indicated. 1 After clicking the Get Spectrum button, click the Apply to lens button. Our lens now has a wider spectrum. Here is our starting lens, in the SketchPad display Uggh! Yes, it’s really awful. Let’s optimize it, varying the glass models. Make a MACro: LOG STO 9 PANT VLIST RAD 1 2 3 4 5 VLIST TH ALL AIR VLIST GLM ALL END AANT END SNAP SYNOPSYS 50 Now put the cursor on the blank line after the AANT command, and click the button . -
A New Refracting Telescope Optical Design in This Article
THE MELIOR A NePw ROefracCtingH TeleRscopOe OMptical ADesT ign By Joseph Bietry Refracting telescopes have de - veloped over centuries, from the humble beginnings of the Galilean telescope to the modern apochromats of today. Advances in astronomical refractors often came about through improvements to optical materials that offered better control of color er - rors (chromatic aberration). Occa - sionally, a different optical design offered improvements as well. This article will describe a new optical-de - sign form that offers improvements to chromatic aberration, as well as field of view beyond that of current refracting apochromatic telescopes. The name, the Melior Apochro - mat, was chosen for two reasons. First, the English translation for the Latin “melior” is “better” or “im - Figure 1: A simple lens with spherical aberration. proved,” and this is indeed a per - formance improvement over current apochromats. But of more impor - tance to me is that “Meliora” is the motto of my alma mater, the Univer - sity of Rochester. I was lucky enough to have studied lens design at the UR’s Institute of Optics under such greats as Rudolf Kingslake and Robert Hopkins. By using the root of the motto for the naming of this de - sign, I am honoring the University Figure 2: The upper half of a simple lens with spherical aberration. The plot at the right shows and the professors who gave me the the focus error with respect to the position of the ray within the aperture. Astronomy TECHNOLOGY TODAY 69 THE MELIOR APOCHROMAT parallel rays of light entering from the left of the lens represent an infinitely distant point of light (i.e. -
Engineering an Achromatic Bessel Beam Using a Phase-Only Spatial Light Modulator and an Iterative Fourier Transformation Algorithm
Optics Communications 383 (2017) 64–68 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/optcom Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm Marie Walde a, Aurélie Jost a, Kai Wicker a,b,c, Rainer Heintzmann a,c,n a Institut für Physikalische Chemie (IPC), Abbe Center of Photonics, Friedrich-Schiller-Universität, Jena, Germany b Carl Zeiss AG, Corporate Research and Technology, Jena, Germany c Leibniz Institute of Photonic Technology (IPHT), Jena, Germany article info abstract Article history: Bessel illumination is an established method in optical imaging and manipulation to achieve an extended Received 12 June 2016 depth of field without compromising the lateral resolution. When broadband or multicolour imaging is Received in revised form required, wavelength-dependent changes in the radial profile of the Bessel illumination can complicate 13 August 2016 further image processing and analysis. Accepted 21 August 2016 We present a solution for engineering a multicolour Bessel beam that is easy to implement and Available online 2 September 2016 promises to be particularly useful for broadband imaging applications. A phase-only spatial light mod- Keywords: ulator (SLM) in the image plane and an iterative Fourier Transformation algorithm (IFTA) are used to Bessel beam create an annular light distribution in the back focal plane of a lens. The 2D Fourier transformation of Spatial light modulator such a light ring yields a Bessel beam with a constant radial profile for different wavelength. Non-diffracting beams & 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND Iterative Fourier transform algorithm Frequency filtering license (http://creativecommons.org/licenses/by-nc-nd/4.0/). -
Lens/Mirrors
Refractive Optical Design Systems Any lens system is a tradeoff of many factors Add optical elements (lens/mirrors) to balance these Many different types of lens systems used Want to look at each from the following Performance Requirements Resolution of the lens – how good at seeing fine details Also compensation to reduce lens aberrations Field of View: How much of a object is seen in the image from the lens system F# - that is how fast is the lens i.e. how good is the lens at low light exposures Packaging requirements- can you make it rugged & portable Spectral Range – what wavelengths do you want to see Also how to prevent chromatic aberrations Single Element Poor image quality with spherical lens Creates significant aberrations especially for small f# Aspheric lens better but much more expensive (2-3x higher $) Very small field of view High Chromatic Aberrations – only use for a high f# Need to add additional optical element to get better images However fine for some applications eg Laser with single line Where just want a spot, not a full field of view Landscape Lens Single lens but with aperture stop added i.e restriction on lens separate from the lens Lens is “bent” around the stop Reduces angle of incidence – thus off axis aberrations Aperture either in front or back Simplest cameras use this Achromatic Doublet Typically brings red and blue into same focus Green usually slightly defocused Chromatic blur 25x less than singlet (for f#=5 lens) Cemented achromatic doublet poor at low f# Slight improvement -
CCAM Objectives.Pdf
CCAM’s Selection of Zeiss Microscope Objectives Things to consider when selecting an objective 1. Magnification Image scale 2. Resolution The minimum separation distance between two points that are clearly resolved. The resolution of an objective is limited due to diffraction and the nature of light Defined by Abbe’s formula d= l /2NA (l = wavelength of light used, NA = the numerical aperture of the objective) Things to consider when selecting an objective 3. Numerical Aperture (NA) Objective’s ability to collect light and resolve specimen detail at a fixed distance. n = refractive index of medium between front lens element and cover slip. m = ½ the angular aperture (A) (https://micro.magnet.fsu.edu/primer/anatomy/numaperture.html) Things to consider when selecting an objective 3. Numerical Aperture/Refractive index (cont.) • The refractive index is the limiting factor in achieving numerical apertures greater than 1.0. • To obtain a higher numerical aperture, a medium with a higher refractive index must be used. • Highly corrected lenses are designed with higher numerical apertures. Things to consider when selecting an objective 4. Working Distance Distance between the front lens of the objective and the cover glass of the specimen. Note the working distance is reduced with the increase in numerical aperture and magnification. Things to consider when selecting an objective 4. Flatness of Field Correction of field curvature Objectives provide a common focus through the field of view. Such objectives are traditionally named as “plan” Edges in focus Entire field in focus Center in focus https://micro.magnet.fsu.edu/primer/anatomy/fieldcurvature.html Things to consider when selecting an objective 6. -
Chapter 7 Lenses
Chapter 7 Lenses Chapter 7 Lenses © C. Robert Bagnell, Jr., Ph.D., 2012 Lenses are the microscope’s jewels. Understanding their properties is critical in understanding the microscope. Objective, condenser, and eyepiece lenses have information about their properties inscribed on their housings. Table 7.1 is an example from objective lenses. This chapter will unfold the meaning and significance of these symbols. The three main categories of information are Numerical Aperture, Magnification / Tube Length, and Aberration Corrections. Zeiss Leitz Plan-Apochromat 170/0.17 63X/1.40 Oil Pl 40 / 0.65 ∞/0.17 Nikon Olympus Fluor 20 Ph3 ULWD CDPlan 40PL 0.75 0.50 160/0.17 160/0-2 Table 7.1 – Common Objective Lens Inscriptions Numerical Aperture & Resolution Figure 7.1 Inscribed on every objective lens and most 3 X condenser lenses is a number that indicates the lenses N.A. 0.12 resolving power – its numerical aperture or NA. For the Zeiss lens in table 7.1 it is 1.40. The larger the NA the better the resolving power. Ernst Abbe invented the concept of numerical aperture in 1873. However, prior to Abbe’s quantitative formulation of resolving power other people, such as Charles Spencer, intuitively understood the underlying principles and had used them to produce 1 4˚ superior lenses. Spencer and Angular Aperture 95 X So, here is a bit about Charles Spencer. In the mid N.A. 1.25 1850's microscopists debated the relationship of angular aperture to resolution. Angular aperture is illustrated in 110˚ Pathology 464 Light Microscopy 1 Chapter 7 Lenses figure 7.1.