Instructor: Doc. Ivan Kassamakov, Assistant: Kalle Hanhijärvi, Doctoral student

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1 Instructor: Doc. Ivan Kassamakov, Assistant: Kalle Hanhijärvi, Doctoral student Course webpage:

2 Gaussian Optics Errors Taylor series 3 θ sin θ = θ θ cosθ = Aberration IA Transverse Aberration IB-Longitudinal Aberration Ideal Wavefront Ideal rays Optical System Actual Rays B I A Blur Actual Wavefront Paraxial Image Plane

3 Any deviation from perfection of an image not due to diffraction are known as aberrations There are six primary aberrations: Chromatic aberrations Longitudinal chr. Ab. Lateral chr. Ab Wavefront aberrations Spherical aberration Astigmatism Coma Optical Aberrations Curvature of field Distortion All, except the first one, affect both refractive and reflective components. Chromatic aberration affects only refractive components.

4 Wavefront Aberrations Aberrated Ideal wavefront in the pupil

5 Spherical Aberration D-aperture (Entrance Pupil) Size Longitudinal SA~D 2 LSA Transverse SA~D 3 TSA D Ideal (parabolic) surfaces Marginal Focal Plane Need to reduce D limit the amount of light Paraxial Focal Plane For lenses and mirrors made with spherical surfaces, rays which are parallel to the optic axis but at different distances from the center fail to converge to the same point. Effect is usually a 1%, or larger, difference in focal length For mirrors, effect can be totally removed if the mirror is parabolic instead of spherical (However, it is difficult to grind parabolic shape!)

6 Spherical Aberration Correction 1. Aspherical Optics 2. Combination of Lenses n 1 n 2 n 1 n 2 Aplanat Positive Lens Positive Spherical Aberration Negative Lens Negative Spherical Aberration

7 Spherical Aberration With SA SA free

Coma This aberration exists for the off-axis points Chief ray I O O Marginal Rays Chief Ray Focus I Marginal Rays Focus The optical powers are different for chief and

8 Coma This aberration exists for the off-axis points Chief ray I O O Marginal Rays Chief Ray Focus I Marginal Rays Focus The optical powers are different for chief and marginal rays Create trailing "comet-like" blur directed away from axis. May produce a sharp image in the center of the field, but become increasingly blurred toward the edges.

9 Demonstration of Coma Aberration Circular stars Comet-shaped stars

and Sagital Rays The lens corrected for spherical aberration and coma is

10 Astigmatism Tangential rays Tangential Focus Chief Ray Sagital Focus Sagital Rays Circle of Minimum Confusion Optical Powers are different for Tangential and Sagital Rays The lens corrected for spherical aberration and coma is called aplanat If it is also corrected for astigmatism it is called anastigmat

Distortion Unlike other aberrations the distortion changes the shape of image and not its sharpness O I s o Object Put Aperture Stop behind the lens AS For points far

11 Distortion Unlike other aberrations the distortion changes the shape of image and not its sharpness O I s o Object Put Aperture Stop behind the lens AS For points far from axis the AS lets through only the rays that have smaller distance from the lens hence these objects experience higher magnification Image Image Pin-Cushion Distortion

12 Distortion Consider another type of distortion O s o I Object AS Put Aperture Stop in front of the lens For points far from axis the AS lets through only the rays that have larger distance from the lens hence these objects experience lower magnification Image Image Barrel Distortion

13 Correcting Radial Lens Distortions Before After These distortions are fixed by an orthoscopic doublet or a Zeiss orthometer.

lens as having an effectively smaller diameter and an effectively

14 Field Curvature O O θ ' s 0 s 0 The focal plane is not a plane, but a curved surface of radius f ' s i s i f I I Rays at a large angle see the lens as having an effectively smaller diameter and an effectively smaller focal length, forming the image of the off axis points closer to the lens.

$Chromatic aberration Because the lens material has a different refractive index for each wavelength, the lens will have a different focal length for each$

15 Chromatic aberration Because the lens material has a different refractive index for each wavelength, the lens will have a different focal length for each wavelength. Recall the lens-maker s formula: 1/ f( λ) = ( n( λ) 1)(1/ R 1/ R ) 1 2 You can model spherical aberration using ray tracing, but only one color at a time.

16 Chromatic aberration

$Chromatic Aberration f λ The refractive index is larger for$

17 Chromatic Aberration f λ The refractive index is larger for blue than red, so the focal length is less for blue than red.

18 Chromatic Aberration Longitudinal Chromatic Aberration Lensmaker Equation F F F C = ( nc 1) + fc R R = ( nf 1) + > ff R1 R2 f C Lateral Chromatic Aberration

19 Chromatic Aberrations longitudinal chromatic aberration (axial) transverse chromatic aberration (lateral)

Usually, two lens have same curvature and are cemented together Note:

20 Chromatic aberration greatly reduced (~10 times) by multiple lens system, e.g. achromatic doublet Low dispersion glass High dispersion glass Usually, two lens have same curvature and are cemented together Note: Same focal length for two wavelengths so that they can be corrected simultaneously

21 Spherical Coma Astigmatism Distortion Summary of aberrations Mono-chromatic (affects single wavelength light), on- and off-axis Mono-chromatic, off-axis only Mono-chromatic, off-axis only Mono-chromatic, off-axis only Field Curvature Mono-chromatic, off-axis only Chromatic Hetero-chromatic (affect multiple wavelength light), on- and off- axis Corrections: Most of the aberrations can be reduced (but never totally removed) by using multi-lens system.

22 Telescopes

23 Optical Telescope Telescopes serves three main functions: (1) they are light collectors. The simplest telescopes simply focus light rays to a small area.; (2) Resolve light so that finer details can be seen; (3) Magnification: making objects look bigger (closer) As we are observing objects at very large distances, light can be assumed to come from infinity and can be represented as parallel rays Two main types: refractive and reflective

24 The Powers of a Telescope: Size Does Matter 1. Light-gathering power: Depends on the surface area A of the primary lens / mirror, proportional to diameter squared: D A = π (D/2) 2

that set a limit to the resolution of the telescope.

25 The Powers of a Telescope 2. Resolving power: Wave nature of light => The telescope aperture produces fringe rings that set a limit to the resolution of the telescope. Resolving power = minimum angular distance α min between two objects that can be separated. α min = 1.22 (λ/d) For optical wavelengths, this gives α min α min = 11.6 arcsec / D[cm]

26 The Powers of a Telescope 3. Magnifying Power = ability of the telescope to make the image appear bigger. The magnification depends on the ratio of focal lengths of the primary mirror/lens (F o ) and the eyepiece (F e ): M = F o /F e A larger magnification does not improve the resolving power of the telescope!

27 Telescope Optics One of the most important number that characterize a telescope is its focal ratio (or, f/ number) focal ratio = Focal Aperture length of diameter primary of primary E.g. Telescope s aperture diameter = 5 cm Focal length of primary = 25cm Focal ratio = 25cm/5cm = 5 (a f/5 telescope)

$Basic Refractor (Convex lens) f o$ image formed here Concave Basic

28 Basic Refractor (Convex lens) f o = focal length of objective real image formed here Concave Basic Reflector f o = focal length of primary

29 Telescope Configuration (Refractors) Aberration overcome by having achromatic objective lens and multi-lens eyepiece Biggest refractor built: >1 m diameter Limitations for building bigger refractors: 1. Light absorption and chromatic aberration 2. Objective lens has to be supported at the edges and they sag under their own weight (glass is a fluid!) 3. To achieve large f/ number, telescope should be long and requires massive support and domes

Kepler Telescope d 1571-1630 F α in α out f o f e Objective

30 Kepler Telescope d F α in α out f o f e Objective Intermediate Image Eyepiece d=f o +f e Angular Magnification m = α f f o e

31 Galileo s Telescope f o α in d f e F α out d=f o -f e Objective Eyepiece Intermediate Virtual Image Angular Magnification m α = f f o e More difficult to manufacture with the same quality image as with positive focal length lenses.

32 Largest optical refracting telescopes

$Great Paris Exhibition Telescope of 1900 Objective lens of 1.25 m (49.2 inches) in diameter - the largest refracting telescope ever constructed.$ When the year-long exposition was over, its builders were unable to sell it.

When the year-long exposition was over, its builders were unable to sell it.

33 Great Paris Exhibition Telescope of 1900 Objective lens of 1.25 m (49.2 inches) in diameter - the largest refracting telescope ever constructed. Since it was built for exhibit purposes within a large metropolis, and its design made it difficult to aim at astronomical objects, it was not suited for scientific use. When the year-long exposition was over, its builders were unable to sell it. It was ultimately broken up for scrap; the lenses are still stored away at the Paris Observatory The telescope was erected near the Eiffel Tower. The tube, oriented north-south, was made up of 24 cylinders 1.5 meters in diameter and rested on 7 concrete and steel pillars; its axis was 7 meters above the floor.

$refracting telescope$ Yerkes Observatory,

34 The world s largest refracting telescope Yerkes Observatory, Wisconsin 1 meter diameter Completed 1897

35 Telescope Configuration (Reflectors) The biggest optical telescopes (~10 m diameter) built in the world are reflectors Major advantages: 1. No chromatic aberration 2. No spherical aberration (parabolic mirrors) 3. Mirror can be supported at the back, no huge support structure needed 4. Improved technique on making big mirrors (Aluminium-on-glass, recoating needed)

36 Newtonian The first working reflector (1668, 1 inch diameter) Eyepiece moved to the side of the telescope

Gregorian telescope Gregorian telescope James Gregory's telescope design (1663) uses two concave mirrors a primary parabolic-shaped mirror and a secondary elliptic-shaped mirror to focus images in a

37 Gregorian telescope Gregorian telescope James Gregory's telescope design (1663) uses two concave mirrors a primary parabolic-shaped mirror and a secondary elliptic-shaped mirror to focus images in a short telescope tube. (1) light enters the open end of the telescope; (2) light rays travel to the primary mirror, where they are reflected and concentrated at the prime focus; (3) a secondary mirror slightly beyond the prime focus reflects and concentrates the rays near a small aperture in the primary mirror; (4) the image is viewed through an eyepiece.

38 The Cassegrain reflector. A contemporary of Newton, N. Cassegrain of France, invented another type of reflector. Called the Cassegrainian telescope, this instrument employs a small convex mirror to reflect the light back through a small hole in the primary mirror to a focus located behind the primary. Some large telescopes of this kind do not have a hole in the primary mirror but use a small plane mirror in front of the primary to reflect the light outside the main tube and provide another place for observation. The Cassegrain design usually permits short tubes relative to their mirror diameter

$Catadioptric - Schmidt telescope A catadioptric telescope design incorporates the best features of both the refractor and reflector i.e., it has both reflective and refractive optics.$

39 Catadioptric - Schmidt telescope A catadioptric telescope design incorporates the best features of both the refractor and reflector i.e., it has both reflective and refractive optics. The Schmidt telescope has a spherically shaped primary mirror. Since parallel light rays that are reflected by the centre of a spherical mirror are focused farther away than those reflected from the outer regions, Schmidt introduced a thin lens (called the correcting plate) at the radius of curvature of the primary mirror. Since this correcting plate is very thin, it introduces little chromatic aberration.

40 Maksutov-Cassegrain Spherical corrector lens Spherical primary mirror Spherical mirror Two spherical mirrors and a lens in front (spherical surfaces are easier to manufacture) Secondary mirror is formed by aluminizing a spot on the inside of the lens

41 Advances in Modern Telescope Design Modern computer technology has made possible significant advances in telescope design: 1. Lighter mirrors with lighter support structures, to be controlled dynamically by computers Floppy mirror Segmented mirror 2. Simpler, stronger mountings ( Alt-azimuth mountings ) to be controlled by computers

42 Adaptive Optics Computer-controlled mirror support adjusts the mirror surface (many times per second) to compensate for distortions by atmospheric turbulence

43 New developments of optical telescopes Segmented primary mirrors: Large equivalent light collecting area Adapted from: Telescope and Technique by C.R Kitchin 36 mirror segment (1.8m) equivalent of a single 10m mirror

mirror. Disadvantage: 1. Can only point straight up!

44 Large Zenith Telescope Primary mirror (6 m) Liquid Mirror: Spin up liquid Mercury on parabolic surface Advantage: ~10 times cheaper than conventional mirror. Disadvantage: 1. Can only point straight up! (that explains the name); 2. Mercury is toxic Rotate at period of ~8.5 second to get a thin (~2mm) layer of Mercury

45 Telescope Mount Function: Support the optical components, point them to a required position, and track the object as it moves Two components: telescope tube, support for the tube (mounting) Actually, most research telescopes contain no tube (open frame)

46 Very Large Telescope Secondary mirror Primary mirror Adapted from: Very Large Telescope project

47 Observatory and Observatory site All telescope can be benefited by placing in an observatory (sometimes known as the dome ) Classic design: a hemispherical roof with a open slot, rotating on a circular wall Choosing good sites means that majority of world s largest telescopes are located in a few places, e.g. Hawaii, Chile, Arizona, Canary Island Criteria: away from light pollution, clean atmosphere (low dust and water), height, accessibility, steady atmosphere,

48 Observatories Observatories Twin 10-meter Keck telescopes largest optical telescopes in the U.S. (in Hawaii) VLT (very large telescope) world s largest optical telescope (in Chile)

The diameter of the main mirror is 605 cm The

50 The telescope is located near Mt. Pastukhova at an altitude of 2070 m above sea level The main mirror is parabolic in shape and has a focal length of 24 meters. The diameter of the main mirror is 605 cm The Bolshoi Teleskop Azimutalnyi, or Big Alt-azimuth Telescope, largest in the world from 1976 to 1991.

51 Table of reflecting telescopes

52 Gases in our atmosphere such as ozone, carbon dioxide, and water vapor strongly absorb infrared, ultraviolet, and shorter wavelengths Some infrared radiation can penetrate the atmosphere through regions called atmospheric windows

atmosphere The blurring of the atmosphere creates scintillation, or the twinkling of stars

53 Observatories in Space Since our atmosphere absorbs much of the infrared, ultraviolet, and X-rays given off by objects, many telescopes are placed in orbit around Earth above the atmosphere The blurring of the atmosphere creates scintillation, or the twinkling of stars Slight variations in the atmosphere s temperature can cause the path of the light from the star to change slightly

54 The Great Observatories Space Program

55 The Hubble Space Telescope Launched in 1990; maintained and upgraded by several space shuttle service missions throughout the 1990s and early 2000 s Avoids turbulence in the Earth s atmosphere Extends imaging and spectroscopy to (invisible) infrared and ultraviolet

56 Hubble Space Telescope (launched 1990) Diameter of mirror = 2.4 meters Angular resolution = 0.05 arcseconds

57 The James Webb Space Telescope It s only a model Will have diameter 6.5 meters (vs. HST 2.5 meters) much higher resolution and sensitivity. Will also observe infrared, whereas Hubble is best at visible light. Expected launch 2013 (

58 NASA s Space Infrared Telescope Facility (Now Spitzer Space Telescope) Launched in 2003, uses a 0.85 meter mirror.

59 Other Space Telescopes HESSI: Gamma Rays Chandra: X-rays SIRTF: infrared

60 Space Observatories vs Ground-Based Observatories Ground-based telescopes will remain larger than orbiting telescopes Space telescopes can be expensive to build, put into place, and maintain Astronomers must find places free of light pollution for ground-based telescopes

61 Microscopes Objective Image plane #1 Eyepiece M 1 M 2 Microscopes work on the same principle as telescopes, except that the object is really close and we wish to magnify it. When two lenses are used, it s called a compound microscope.

62 Microscope Need a very small focal length! s o L d L-tube length f o f o f e Objective Intermediate Image Eyepiece L>>f e,f o f mic <<f e,f o So we have one big magnifier with short focal length 25 L mα = f = = m m 25/ mic α, eye obj fe fo Angular magnification of the microscope is a product of angular magnification of the eyepiece and transverse magnification of the objective

63 Microscope terminology

64 Finite and Infinity Optical Systems

65 Microscope Objectives Amici Objective Many creative designs exist for microscope objectives. Example: the Burch reflecting microscope objective: Object To eyepiece

66 Getting in Focus

Optical Systems: Pinhole Camera Pinhole camera: simple hole in a box: Called Camera Obscura Aristotle discussed, Al-Hazen analyzed in Book of Optics

Optical Systems: Pinhole Camera Pinhole camera: simple hole in a box: Called Camera Obscura Aristotle discussed, Al-Hazen analyzed in Book of Optics 1011CE Restricts rays: acts as a single lens: inverts