Class Note for PA 699 at UA
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Date Created: 02/06/15
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ASA 8 0 Sellmeier Formula valid 036 to 15 um Fit equations to measured refractive index data In 1992 Schott adopted the Sellmeier six constant formula as their standard for expressing the dispersion curve of their materials 694 Secondary Color Reduction Selection of Glass to Reduce Secondary Color 7 Glasses must have different Abbe numbers but equal Partial Dispersion Recall plot of Partial Dispersion vs Abbe Number 7 Selected glasses will be on a horizontal line 7 At least one glass falls off of the preferred line 0 Resulm in increased cost and may be more difficult to manufacture LaSFN30 is 24 times more expensive than BK7 KZFSN4 is 7 times more expensive SFSE39 i SCH OTT ism 0 62 gm made nl Ideas 5751 osrs 050 055 NW 7Nuzsram 056 New o Nuns mm mm NPKJZA N PKM quot NUIKCm o i 054 quotmquot Mm ms NBK 052 90 80 70 60 50 40 30 20 695 Glass Selecti Optimization for glass type 7 Typically FK PSK SK LaK LaSF and SF glasses chosen during glass optimization 7 Very rarely KF LLF LF or F selected Located in the central region of the glass map Doesn t allow a large Abbe number difference amp secondary color not easily corrected 7 Exceptions KZFS amp TiF These are in the central region but have anomalous relative partial dispersions Allows easier correction of secondary spectrum Unfortunately KZFS is not a preferred Schott glass Escrow i95 cern glasses Hlinl glasses 39 LISP Ls 39 relractive index LES ma 355 15a PK 39 quot PK I45lt 900 mm 7nn am am win an mu 696 Parameters for Glass Selection Availability Preferred always available and in stock Standard generally in inventory Inquiry available only on special request and not kept in stock Transmittance Near UV absorbed by most glasses Use fused silica or fused quartz for UV A few SF glasses have reduced transmittance in the deep blue wavelengths Stress vs Refractive Index Mechanical or thermal stress isotropic glass can become anisotropic s amp p polarization components undergo refraction with different indices Dense ints large index change with a small stress birefringence Crowns small index change with a large stress birefringence If the optical system is designed for polarized light it must maintain the state of polarization SF glasses best for prisms to avoid temperature gradients producing stress birefringence Thermal Properties Positive coef cient of thermal expansion glass expands with increasing temperature Thermal expansion or contraction should not con ict with expansion or contraction of lens housing Optical system may need to be athermalized optical characteristics remain unchanged with temperature change metal structures compensate 697 Stress Optic Coefficient Stress induces a change in the optical path of the beam passing through the lens Stress Birefringence Stress Optic Coef cient determines the amount of stress birefringence OPD kho OPD stress bireringence or optical path difference k stress optic coefficient h distance light travels in the optical element 6 stress in the optical element Pa Material K 103912 P214 SF59 l 36 SF57 002 SF6 065 FKSl 071 BK7 277 F2 281 ZKN7 3 62 SKl4 200 BaF2 489 Germanium l 56 698 Glass DOpants Nickel Purple Cobalt Blue Chromium Green Uranium Greenish Yellow Ferrous Iron Green 1R absorber Gold R e d Selenium Red most common 699 Plastic Optical Materials Advantages Lowcost materials and fabrication Light weight impact resistance Molding exibility Aspherics Lenses integrated With mounts Disadvantages Low heat tolerances Less resistant to surface damage More difficult to coat coatings less durable Ionassisted deposition of coatings are more durable on plastics Temperatures required for the application of standard coatings are too high Material choices limited Plastics limited by a high thermal coef cient of expansion amp a large change in index With temperature Index decreases With temperature in plastics opposite of glasses Index change is 50 times larger than in glass 700 Commonly Used Plastic Materials Acrylic Most common amp important low cost Good clarity amp very good transmission in visible High Abbe number 553 Easy to machine and polish good for injection molding Polystyrene Cheaper than acrylic Higher absorption in deep blue region Index higher 159 but Abbe number lower 309 Lower resistance to UV amp scratches easier Acrylic and Polystyrene achromatic pair Polycarbonate More expensive than acrylic but very high impact strength Performs well over broad temperature range Poor scratch resistance COC cycloole n copolymer Similar to acrylic Water absorption much lower amp has a high heat distortion temperature HDT Brittle See Fischer Table 61 701 Infrared Glasses vs Visible Glasses IR glasses have significantly higher refractive indices Visible glass n ranges between 145 and 20 IR glasses n ranges between 138 to 40 Dispersion can be significantlyl lower depending on spectral band Visible glasses V ranges from 20 to 80 IR glasses V ranges from 20 to 1000 Many IR glasses are opaque in the visible And most visible glasses are opaque in the IR IR glasses are often heavier than visible glasses IR glasses have significantly higher 1de values factor of 10 or more higher IR glasses cost more than visible glasses by 2 or more orders of magnitude Significantly fewer number of practical glasses than visible glasses 702 Infrar l Gla ses The list of commonly used IR materials is unfOItunately pretty short V Value 3 5 Germanium AMTIR 13 Magnesium Fluoride Silicon Sapphire Gallium Arsenide Zinc Sulfide Zinc Selenide Calcium Fluoride 400 1500 Midwava IR glass Longwave IR glass map 85 115 microns map 3 5 mlcrons m 300 1200 3 KErI 3 Knss T n 200 a mo 2m 3 MZSEU cm E gt as 59A 100 Gal 400 AMHR l MD 7 u a GaAs can mm 9 M203 35quot 0 I l 0 I I Lo 21 a 0 u m 20 an 40 ndex Index 703 Transmittance of IR Glasses Maunumm 00 uor de N5 Inclu is sumc rlll39dioll IDESIS mm mum mum s so Zinc mm mum a g Camum 39 39 quotWm 6 r g Iquot E I I I E M 2m I a 5mm 39 Arael I sum 2a quotnonequot I 39 rq l 6mm I IH IIIHHI 01 02 0 was 1 z a 4 56 78910 1m wavelength um me Bub Fischer 704 Designing with IR Glasses Advantages Refractive index is usually higher so fewer lenses are needed to achieve diffractionlimited performance Dispersion is often low enough such that color correction may not be necessary Most IR materials can be diamond point machined so aspherics are commonly used in designs The Airy disk size and diffractionlimited depth of focus are larger for the IR than for the visible so achieving diffractionlimited performance is easier Disadvantages Small choice of glasses Materials are expensive l gram Oneinch diameter BK lens 5 Oneinch diameter germanium lens 500 Fiveinch diameter sapphire dome Priceless Some IR materials are difficult to fabricate andor antire ection coat Fragile soft chip easily low thermal conductivity etc Most IR materials have large dndT values so atherrnalizing can be difficult 705 Cautions on IR Glasses and Optics Software There is only one source of data on Schott glasses Schott Optical Glass However there is no source of data on IR glasses Most optical software programs depend on some literature source of data for IR materials then t the data to Sellmeier equations V Some programs do a better job of this than others Some IR glasses such as AMTIR are made by a speci c supplier who publishes index data on the material V Sometimes these data are not consistent some om different measurement sources and may not have suf cient signi cant digits V In these cases if your design is sensitive to the glass dispersion you may need to doublecheck the index data Thermal data such as thermal expansion coef cient and dndT data may vary widely for some materials depending on who measured it V Usually optical software do not include these data as there is no of cial source for these data 706 pllerical Aberr Refract m 2n2 z pat Km r2 4H ZH 16n71 n2 For germanium n4 3 02387 A Kl x4 x Kgtz Kwol P w A 1 ve 7 z Elmxm 4m IIIIumINIIIIIIIIIIIIIIHIIIImIIIIIIIHIIIII muun xl z xlrl39 KIn I xiquot 1 x2 39K a z x cl39acin 1 Cr 520 C 707 NBK7 vs Germanium Spherical Aberration m5 NBK7 j RMS WFE 1455 mus Germanium was i RMS WFE 011 40 inch EFL f2 39M 708 Exa ple Germanium Singlet 0 We want an F2 germanium singlet to be used at 10 microns 001 mm 0 Question 7 What is the longest focal length we can have and not need aspherics to correct spherical aberration 0 Answer Diffraction Airy disk angular size is Bdiff 244 MD Spherical aberration angular blur is 3 00087F3 Equating these gives D 244 7 F300087 224 mm For F2 this gives efl 45 mm Strehl 091 709 omatic Aberration Example Germanium Singlet I We Want to use anF2 germanium singlet over the 8 to 12 micron band I Question 7 What is the longest focal length We can have and not need to color correct Assume an aspheric to correct any spherical aberration I Answer Over the 812 micron band for germanian V 1000 The longitudinal defocus e V efl1000 The A Wave depth of focus is i 2 F11z Equating these and solving gives e 4 1000 20 F22 150 mm Waves 0 25 Field Height 0 000 Temperature Effects 0 An optical element has two properties which cause changes in optical performance with temperature The coef cient of thermal expansion CTE usually denoted by a with units of lengthlength C The change in refraction index with temperature dndT o The change in focal length of a lens with temperature is given by AFFa Ld AT n ldT 0 Since in most cases the focal length decreases with temperature the equation is usually stated as AF vFAT where V is often referred to as the thermooptic coef cient 0 The shift in focus relative to the image plane also includes the CTE of the lens mount so the shift in focus is given by Afocus v a mount FAT 711 v Values of Optical Materials x1 061 C Visible glasses 3K7 15 It is possible to find combinations of visible BaK4 03 glasses to make an athermal design with BaK50 114 common mounting materials SK16 34 SF4 38 infrared glasses G 127 Tf niglum 34 Most common IR materials have positive Zns 28 v so it is more difficult to make a passive ZnSe 35 athermal design Silicon 63 CTE of common mount materials x106 C Aluminum 6061 234 416 stainless 99 lnvar 35 06 Titanium 87 Beryllium 1 1 6 cache 4 2006 Infrared Opiia Seminar 28 712 Antirefection coatings Simplest Antire ection AR coating The index of refraction of the substrate is n2 the index of the coating is n1 and the input media is typically air 110 l The re ectivity R of a surface for incident angle 0 is 2 2 r1 r2 2r1r2 cos 8 R 2 2 lr1r2 2r1r2 cos8 where rlr2 lt amplitude re ectances 8 47t111t cos 9 L I R is minimized when cos 8 l or when nlt M4 713 Fresnel Re ectance 0 Re ectance is minimized when 0035 16 7 4nn1t 575 0039 9 if nlt Z G 0 lt This condition is met With quarter wave For normal incident 6 0 n n 1391 2 0 1 1392 110 n1 111 112 r2r2 2rr r r2 R 1 2 12 Z 1 2 2 2 2 1r1r2 2r1r2 1r1r2 To get no re ection R 0 2 rl rz 0 2 n n n n 0 1 1 2 0 n0n1 n1n2 2 2 non1 n1 n0n2 n1n2 non1 n1 n0n2 n1n2 R 0 nO n1n1n2 R 2n0n2 n120 n1 2 Jnonz lt Requirements for antire ection coating 2 ie Ge n2 2 4 n0 1 air n1 2 A coating of Z nlt 714 Infrared Optics Suppliers Elcan Optical Systems Richardson TX Corning NetOptiX Keene NH Exotic ElectroOptics Marietta CA Optimum Optical Systems Camarillo CA IIVI Incorporated Saxonburg PA Janos Technology Keene NH DRS Optronics Palm Bay FL Coherent Auburn CA Diversi ed Optical Products Salem NH Telic OSTI North Billerica MA References Handbook of Military Infrared Technology William Wolfe Of ce of Naval Research 1965 Thermal Imaging Systems J M Lloyd Plenum Press 1975 The In ared Handbook Wolfe and Zissis Of ce of Naval Research 1978 Handbook of Infrared Optical Materials Paul Klocek Marcel Dekker 1991 0 Infrared Design Examples William Wolfe SPIE Optical Engineering Press 1999 Optical System Design Fischer and TardicGaleb McGrawHill 2008 Optical Design Fundamentals for Infrared Systems MaX Riedl SPIE Press 2001 715 nts To eliminate frost formation on the detector need lt 10395 Torr 1 Torr lmm 7 No thermal loading at these pressures Minimize heat loss due to convection 7 increase the mean path of gas molecules large wall spacing Requires Window interface for detector 7 PPP in optical system abermtions proportional to thickness hug Material F PSI m i T ZnSe 8000 How 7239 ZnS 15000 I AP KRS75 5000 106 D F BaFZ 5500 AP Pressure Differential PSI Sapphire 100000 F Elastic Limit PSI BK 7 50000000 716 Cold Shield Ef ciency All IR systems with cooled detectors have a cold shield in the Dewar to minimize the background radiation The background radiation on the detector sets the sensitivity of the detectorDquotlt 717 Thermal interfaces 718
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