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Introduction to Optics Part I

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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. Target Scene *rather than self-emissions Chart: 5 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Transmission-Refraction Medium 1 Medium 2 n1 n2 Recall Snell’s Law Incident ray n1 sinT12 n2 sinT Refracted Ray c Light Intensity S H E 2 4S Dispersion if index of refraction is wavelength dependent n(O) Refractive devices not popular in space imaging , since we need different lenses for UV, visual and IR. Chart: 6 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Polarization Light can be represented as a transverse electromagnetic wave made up of mutually perpendicular, fluctuating electric and magnetic fields. Ordinary white light is made up of waves that fluctuate at all possible angles. Light is considered to be "linearly polarized" when it contains waves that only fluctuate in one specific plan (Polarizers are shown) In-phase=> 45 degrees linearly polarized 90 degree out of phase->circular Chart: 7 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Interference Interference: Interaction of two or more light waves yielding a resultant irradiance that deviates from the sum of the component irradiances If the high part of one wave (its crest) overlaps precisely with the high part of another wave, we get enhanced light. Crest + Crest = Strong Light (r1 r2 ) 2Sm / k mO If the high part of one wave overlaps precisely with the low part of another 1 wave (its trough), they cancel each other out. (r r ) Sm / k mO Crest + Trough = Darkness 1 2 2 Conditions of Interference: QuickTime™ and a Cinepak decompressor • need not be in phase with each source, but are needed to see this picture. the initial phase difference remains constant (coherent) • A stable fringe pattern must have nearly the same frequency. But,white light will produce less sharp, observable interference • should not be orthogonally polarized to each other Chart: 8 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Diffraction Diffraction occurs at the edges of optical elements and field stops, this limits the Field-of-View (FOV). This is THE limiting factor, 2 2 sin u which causes spreading of § · screen I E Io ¨¸ light and limits the “sharpness © u ¹ of an image” O T pinhole S u BsinT Incoming light B O B - aperture size Intensity T - angle of boresight pattern Fraunhofer Diffraction Thoery (very distant object) is applied. sine function is replaced by J1 for a circular aperture Chart: 9 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Derivation of Angular Resolution 2 2 § 2J (u)· 1 J1:Bessel function of I E Io ¨ ¸ © u ¹ the first kind(order 1) S S u 3.83 BsinT BT O O 3.83O 1.22O T B - aperture size SB B T - angle of boresight => Rayleigh Criterion Angular Resolution(Resolving Power) :the telescope's ability to clearly separate, or resolve, two star points (i.e., two Airy discs) Goal is to design optical system to be diffraction limited at the wavelength of interest. Chart: 10 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Angular Resolution Simulation 1.22O T B Effects of separation, diameter and wavelength on Resolving Power Chart: 11 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Absorption Electronic Detectors work by absorption, i.e. a photon is absorbed by a semiconductor surface and turned into a photo- electron -> photoelectric effect. - photon 4000Å<O<10,000Å ,e =1 E=hQ - - e- 1Å<O<1000Å, e = eV/3.65eV/e # of photoelectrons Epitaxial layer 30-50:cm generated. 20 Pm Substrate Absorption in an opaque non-silicon 500 Pm 0.01:cm opaque material + hole photons -> heat E.g. Germanium is opaque in visible but transmissive in the band from 1.8-25 Pm. Opaque surfaces absorb. Chart: 12 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Optical Design Fundamentals (1) Systems for gathering and transmitting RF (radio frequency) and optical signals are identical in theory. Hardware is different. Optical Focal length f determines overall Axis length of optical train and is related to the radius of curvature (ROC) of the primary mirror/lens surface. r1 n d Power of a lens/mirror: f Pf 1/ [diopters=m-1] r2 Lensmakers Formula: 2 § 11· n 1 d P n 1 Focal Length ¨ ¸ © r1 r2 ¹ n rr12 Focal Point In principle: Optical Mirror ~ RF Parabolic Dish Antenna Chart: 13 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Optical Design Fundamentals (2) Approach (I) for determining the focal length f Required Field of Plate Scale s View (FOV) s=f [m on focal plane/rad on sky] Size of Image E.g. “1cm on the focal plane Plane [m]* equals 2 km on the ground” Focal length f needed to record a scene of Radius R on the ground: Important Equation !!! f: focal length [m] h: altitude [m] f rd m magnification rd: radius detector array [m] hR R: Target radius [m] * can arrange several detectors (CCD’s) in a matrix to obtain a larger image on the focal plane Chart: 14 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Optical Design Fundamentals (3) Approach (II) for determining the focal length f Detect point targets at a fixed range: There is a central bright ring containing 83.9% of the total energy passing through the aperture. Angular dimension of this ring is: O d 2.44 AIRY D *D Required focal length f to give an image of f diameter * for a point target: 2.44O O : wavelength of light Diffraction spreads the light: D: aperture diameter * *: image diameter of a point target True Image of Point Source Point Source Chart: 15 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Telescope Key Variables Most important: f - Focal length f 1 F # D 2NA Infinity F-number* , e.g. F# or f/ * a.k.a. F-stop: synonyms: f/, F, F No., F# 1 D Numerical Aperture NA 2#F 2f Image brightness is proportional to 1/F2 11 1 Depth of focus Gf: f h f G f Best optical systems are DIFFRACTION-LIMITED. Chart: 16 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Space Based Imaging Pixel of ground-resolution Telescope Depth of element size: 'x/m Focal Length f focus Gf Image radius rd Field Stop for Aperture Ray from Orbital Aperture Diameter D Elements target edge Flat Earth Altitude h Approximation Tt Radius of Resolution element Tr nadir y R Ground Scene Oh 'x 1.22 x Caution: D cos Tt boresight Not to scale Chart: 17 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Ground Resolution Ground Resolution O (Rayleigh Diffraction Element defined by 1.22 Tr Criterion) (Angular Resolution): D Oh Length Normal to 'x 1.22 Relate this to the 0.3m ground resolution Boresight Axis: D cos Tt requirement given in the SOW Assumes a circular aperture For astronomical imaging, angular resolution is more relevant metric Since our target is faint distant Stars(point source). 1 arcsec=4.8 micro radians Chart: 18 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Field-of-View (FOV) Determines the scope of the image. Defined by angle on the sky/ground we can see in one single image. E.g. “Our FOV is 4x4 arcminutes”. 1 §·rd T FOV 2tan ¨¸ Angular diameter of FOV: ©¹f Large detector = Large FOV T A R 22(tanh §· ) Long Focal Length f = Small FOV SS ¨¸ ©¹2 R T FOV A S/C FOV Ground Target Chart: 19 16.684 Space Systems Product Development MIT Space Systems Laboratory February 13, 2001 Ray Tracing/Optical Train Ray-Tracing uses first term in paraxial approximation (first order theory).
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