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Master thesis
Optical system for Auroral Diagnostics package onboard PoGO-Lite astrophysical balloon
CHRISTIAN JONSSON
Master of Science Thesis
Stockholm, Sweden 2010
XR-EE-SPP-2010:008
KTH School of Electrical EngineeringSE-100 44 Stockholm
SWEDEN
© Christian Jonsson, Oct 2010
Abstract
This thesis report describes the development of the optical system ALBERT (AlfvénLaboratory Baloon ExpeRimenT) that will fly from ESRange in 2011 as an auroraldiagnostic unit for the PoGO-Lite mission. ALBERT has been developed at KTH incollaboration with the University of Southampton.
ALBERT consists of two main systems. A support structure (mechanical system)and two spectrometers (optical system). The development started with a conceptualCAD assembly and the end objective was to have ALBERT manufactured.
The mechanical system has been developed and manufactured in house and theparts are mainly manufactured from aluminum. The mechanical system was co-developed with the thermal engineer to make sure the etalon temperature would bekept at a stable 20C to ensure the performance of the spectrometers.
The thesis also aimed to optimize the photometers for the use in the PoGO-Litemission. The photometers have been designed to detect auroral oxygen emissions at777.4nm and 844.6nm. The photometers consist of one interference filter, one Fabry-Pérot Etalon filter, two lenses, an aperture and one photomultiplier tube. The Fabry-Pérot Etalon filter is mounted on a tilting mechanism which enables the photometerto become a spectrometer.
Extensive testing has been performed throughout this project with the objective tooptimize the spectrometers. Knowhow about the system and its components enablesthe design of the aperture, a critical component that determines the performance of thespectrometer. After extensive testing of the Fabry-Pérot Etalon filters and the inter-ference filters with an Michelson interferometry spectrometer a final characterizationof the Fabry-Pérot Etalon could be done using an Argon lamp and a high-end EMCCDcamera. It could then be concluded that one of the etalons was not to specificationand was rendered useless for ALBERT.
The other etalon could be used and the optimization of the aperture for that spec-trometer concluded in that a banana shaped aperture was the optimal. The inner andouter radii of the aperture corresponded to the radii of the rings from the interestingspectrum in the characteristic ring pattern produced by an etalon.
Sammanfattning
Detta examensarbete har fokuserat på utvecklingen av ALBERT och dess optiskasystem. ALBERT är ett projekt som har utförts på Rymd- och plasmafysik på KTHdär ett diagnossystem för norrsken har utvecklats. ALBERT kommer att flyga medPoGO-Lite som är ett experiment utvecklat at partikelfysik på ALBANOVA, KTHfrån Esrange 2011.
ALBERT består av två huvudsystem. Ett optiskt system som innefattar av tvåspektrometrar samt ett mekaniskt system som håller det optiska systemet på plats ochser till så att det är rätt förutsättningar innuti tryckkärlet för det optiska systemetunder ballongexperimentet.
Det mekaniska systemet har utvecklats under detta examensarbete i samarbetemed en termoingenjör för att hålla luft- och bänktemperatur på stabila 20C för attinte påverka spektrometrarnas prestanda.
Examensarbetet ämnade också till att optimera det optiska systemet. PoGO-Litesmätningar blir störda av norrsken så det är viktigt att ALBERT kan mäta hur starktnorrskenet är under ballongexperimentet. Spektrometrarna har designats så att syree-missionerna vid 777.4nm och 844.6nm kan detekteras. Spektrometrarna består av ettinterferensfilter, ett Fabry-Perot Etalon samt två linser, en apertur och en PMT. Eta-lonet är monterat på en mekanism som kan vinkla filtret under ballongexperimentetmed hjälp av en stegmotor för att ändra vilken våglängd som spektrometern är mestkänslig för.
Utförliga tester har gjorts under detta examensarbete. Tester av sex stycken fil-ter gjordes på ALBANOVA för att mäta upp transmissionsspektrumet för varje filter.Transmissionspektrumet mättes upp med hjälp av en Michelson-interferometerbaseradspektrometer. Dels testades båda etalonen och båda interferensfiltren som skall använ-das vid ballongexperimentet samt två ytterligare filter som användes vid ett noggran-nare test av etalonen där en EMCCD kamera användes. Det testet visade att ettav etalonen var obrukbart för ALBERT men det andra etalonet kunde användas förballongexperimentet.
Därför optimerades aperturgeometrin för 777.4nm spektrometern där resultatetblev en apertur som ser ut som en banan. Bananens yttre och inre radier svarar motradierna på de interferensringar som etalonet ger upphov till vid den största och minstavåglängd i det intressanta spektrumet kring syreemissionerna.
Contents
1 Introduction 11.1 The PoGO-Lite Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 ALBERT - Alfvén Laboratory Balloon Experiment . . . . . . . . . . . . . . 21.3 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Theory 52.1 Geometrical optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Thin Lens formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Radiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 Surface Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 The unit Rayleigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Power/Photon counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Fabry-Pérot Etalon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5.1 General Fabry-Pérot Etalon . . . . . . . . . . . . . . . . . . . . . . . 82.5.2 Maximum transmittance condition . . . . . . . . . . . . . . . . . . . 8
2.6 Auroral Oxygen Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Design 113.1 Optical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 Bench Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.2 PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Mechanical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1 Optical Bench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.2 Support structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Beam calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.2 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Transmittance characterization of interference filters and Etalons 214.1 Transmittance measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Fabry-Pérot Etalon characterization . . . . . . . . . . . . . . . . . . . . . . 31
4.2.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2.2 Mathematical calculations and algorithm . . . . . . . . . . . . . . . 314.2.3 Results 777.4 nm Fabry-Pérot etalon filter . . . . . . . . . . . . . . . 334.2.4 Results 844.6 nm Fabry-Pérot etalon filter . . . . . . . . . . . . . . . 34
4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
title-5
5 Optimization of spectral resolution and throughput 375.1 Optimization objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Spectral resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3 Optimization calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3.2 Identifying potentially optimal aperture geometrics . . . . . . . . . . 41
5.4 Optimization results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.4.1 Banana aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.4.2 Rectangular aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6 Conclusions 51
Bibliography 53
Chapter 1
Introduction
The overall task of this master thesis has been to develop an optical system for an auroraldiagnostic device starting from an already set concept to implementation together with twoother master students. The other two master students focused on thermal engineering andelectrical engineering. The development has taken place at Alfvén Laboratory at the RoyalInstitute of Technology, Stockholm.
1.1 The PoGO-Lite Experiment
The PoGO (Polarized Gamma-ray Observer) experiment will measure polarization of softgamma rays in the energy range of 25keV-80keV. PoGO-Lite is a down-scaled instrumentflying a pathfinder mission from Esrange, Kiruna. PoGO has been developed by groups fromStanford University, University of Hawaii (US), Royal Institute of Technology, StockholmUniversity (Sweden), Tokyo Institute of Technology, Hiroshima University, ISAS, YamagataUniversity (Japan) and Ecole Polytechnique (France). Polarization of soft gamma-rays hasnever been measured. The non-thermal processes are likely to produce high degrees ofpolarization. The polarization will be derived from the azimuthal distribution of Comptonscattering angles in the sensitive volume of the instrument. The detectors on the PoGO-Liteconsist of a system of plastic scintillators, anticoincidence crystals and PMT detectors [1].
The PoGO-Lite (see figure 1.1) will in its initial balloon flights look at the Crab (Nebula& Pulsar), Cygnus X-1 and Hercules X-1. The observations of these three targets will helpunderstanding pulsar emission mechanisms, particle acceleration in the pulsar wind nebulae,the geometry of reprocessing material around the black hole and photon propagation nearthe strongly magnetized neutron star surface.
The first science flight is planned to take place shortly thereafter. On the pathfindermission, 61 phoswich detectors will be flown instead of 217 [2].
1
Figure 1.1: Overview of the PoGO-Lite Gondola
1.2 ALBERT - Alfvén Laboratory Balloon Experiment
ALBERT is an auroral diagnostic package that will provide support for the PoGO-Liteexperiment. Aurora produces emissions in the energy range of PoGO-Lite and to differen-tiate those from astrophysical sources, a characterization of the aurora in the field of viewis needed. ALBERT will be able to detect auroral emissions from atomic oxygen whichwill provide information about the background of the PoGO-Lite measurements. The di-agnostic package consists of two photometers and one state of the art three axial fluxgatemagnetometer called SMILE [3]. The photometers will measure auroral emissions and thesurrounding background. Each photometer scans a different wavelength spectrum by tiltingan etalon shifting the photometers operational wavelength. The photometer use an interfer-ence filter and an etalon because the continuum background can be too bright even with anarrow passband interference filter. Combining an etalon and an interference filter enablesthe measurement of narrow lines thanks to a good resolution.
An overview of ALBERT is shown in figure 1.2. One baffle, the front lid and theback lid are shown of the outer structure. Two poles are connected with the front lid andthey go through the instrument to the back where they are connected to a pole holder atthe back lid. On the poles two photometers are mounted. Each photometer consists ofone interference filter, one Fabry-Pérot etalon, one forelens, an aperture, a fieldlens and aPhotomultiplier tube (PMT) detector. Tilting of the etalon will be done by a step motor.The aperture is placed in the image plane of the fore lens and defines the field of view (fov)of the photometer.
Behind the PMTs is a thermal system (consisting of fans, a Peltier element and airflowdirectors) designed by the thermal engineer to heat or cool the air inside ALBERT to keepthe etalon temperature at 20 C. Bench heaters are also installed between the two benchesand on the back T there are air heaters. The heating system is controlled by the PCB
2
Figure 1.2: Overview of ALBERT
mounted next to the PMT detectors.ALBERT has been developed at the Alfvén Laboratory at the Royal Institute of Tech-
nology in Stockholm in collaboration with the University of Southampton, UK.
1.3 Thesis objectives
The objectives of this thesis is to
• finalize the mechanical design and manufacturing of componentsof ALBERT.
• verify the filters and etalons parameters.
• optimize the aperture in each photometer.
The content of this thesis report is divided into five chapters. The first chapter is theIntroduction where an overview of the ALBERT project is presented, followed by a Theorychapter for all the relevant physics and mechanics used to reach the thesis objectives. Inthe Design chapter the mechanical and optical design is presented. In chapter four theTransmittance characterization of interference filters and Etalons is presented with thepurpose of determine the filter parameters to be used in chapter five which is devoted tothe Optimization of spectral resolution and throughput of the photometers when calculatingthe optimal aperture geometry.
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Chapter 2
Theory
The basic concepts relevant to the design of ALBERT’s optical system are introduced inthis chapter.
2.1 Geometrical optics
A set of theoretical tools are needed to design the optical system and two very importanttools in this case are Snell’s law and the thin lens formula.
2.1.1 Refraction
Snell’s law describes the relationship between the angles of incidence when light passesthrough a boundary between two different media.
n1 sin α1 = n2 sin α2 (2.1)
where n1 and n2 are the refractive indices of respective media and α1 and α2 are the anglefrom the normal of the interface between the two media. The fundamental physics behindthe phenomenon is that a wave changes direction due to a change in its speed.
2.1.2 Thin Lens formula
The thin lens formula describes what distance from the lens with a certain focal length theimage of an object will be projected.
1
f=
1
do
+1
di
(2.2)
where f is the focal length of the lens, di and do are the distances from the lens to the objectand image.
2.2 Radiometry
Radiometry focuses on light energy emerging from a portion of a surface. This surface maybe fictitious or it may coincide with the surface of a source [4].
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2.2.1 Surface Brightness
Surface Brightness describes the amount of light that is emitted from a given surface ina certain direction. The unit is photons per meter squared per second per steradian asdescribed by
B =dnphotons
dAdtdΩ(2.3)
The surface brightness (B, equation 2.3) of an extended source is independent of thedistance of the observer from that source, provided that there is no extinction betweensource and observer [5, p. 36].
2.2.2 The unit Rayleigh
The auroral intensity is usually measured in the surface brightness unit Rayleigh (R) definedas the column emission rate of 1010 photons per square meter per second (photons/m2/s)).It is an apparent emission rate where neither scattering nor absorption are taken into ac-count. The column emission rate (4πB) is defined as the volume emission rate (ǫ) integratedalong a column with a unit cross-sectional area stretched in the line of sight of the imageras described by
B′ = 4πB =
∫
∞
0
ǫ(l)dl (2.4)
Column emission rate can be easily measured by imagers unlike volume emission rates [6,p. 57]. The key distinctions between B and B′ is that B is what is observed and B′ is whatis emitted from the source.
2.3 Throughput
The throughput S of a system imaging objects at infinity is the area of the entrance pupilof the system (which in ALBERT’s case is the etalon, 29.7mm) times the solid angleof field of view. The solid angle can be expanded evolving the expression for throughputwhich gives
S = Aetalon · Ω = Aetalon ·a
F 2=
Aetalon
F 2a = aω (2.5)
where a is the area of the aperture, Aetalon is the area of the etalon, F is the focal lengthof the forelens and ω is the solid angle of the cone that starts at the aperture and coversthe area of the etalon at the forelens. AetalonΩ = aω is a geometrical relationship betweenthe external solid angle of the instrument and the internal solid angle at the aperture.
2.4 Power/Photon counts
The number photon counts the PMTs will register is given by the surface brightness of theauroral emissions multiplied with the throughput of the instrument and the PMTs quantumefficiency according to
fpulses = QE · B · S (2.6)
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where fpulses is the number of photons detected per second, and QE is the quantum effi-ciency at the operating wavelength of the PMTs. The unit fpulses is suitable in ALBERT’scase since the PMTs will give a pulse for every photon that is detected.
Given that the useful information is the surface brightness of the emissions (equation2.4) results in
B′ =4πfpulses
QE · S(2.7)
which has unit Rayleigh. One must bear in mind though that there is a scale factor of 1010
in the definition of the Rayleigh.
2.5 Fabry-Pérot Etalon
A Fabry-Pérot etalon is a a thin filter with two parallel partially reflective surfaces. Onesuch filter is shown in figure 2.1.
When a plane wave of monochromatic light is incident with an angle α some of thelight will be reflected and the rest will be transmitted at the first mirror. How much isdetermined by the reflectivity of the surfaces. Refraction will determine the internal angleof incidence (θ). The light transmitted through the first surface will be partially reflectedmultiple times inside the etalon between the two surfaces. There will be a phase shiftbetween the rays after consecutive reflections inside the etalon. The phase shift depends onthe wavelength of the incoming light, refractive index of the etalon, thickness of the etalonand the incident angle. If the phase shift is 2πm (where m is an integer) the transmittedlight will be amplified due to constructive interference while if the phase shift is 2πm + π itwill dampen the transmittance due to destructive interference [7].
Two types of etalon are solid etalons and air spaced etalons. Solid etalons are often madeout of Fused Silica and the are in relatively robust but prone to temperature instability sinceboth the thickness of the etalon and its refractive index change with temperature.
Figure 2.1: 777 Etalon used in ALBERT
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Air spaced etalons use air as the etalon medium which reduces the temperature sen-sitivity. Air spaced etalons are however more complex since they have three components,two mirrors and one spacer. There are several ways to tune an etalon where tilting is thesimplest one. One can also move the mirrors or change the index of the medium (pressure,temperature, electrostatic) [8].
2.5.1 General Fabry-Pérot Etalon
The equation for the transmittance of the etalon is
T (λ, α) =1
1 + F sin2( δ2 )
(2.8)
where F is the coefficient of finesse, α is angle of incidence of the light and δ is the phasedifference between consecutive reflections inside the Etalon. The coefficient of finesse of theetalon depends on the reflectivity (R) of its mirrors and its given by F = 4R(1−R)−2. Thephase difference is given by
δ =4π
λvacuum
net cos θ (2.9)
where λvacuum is the wavelength in vacuum, ne is the refractive index of the Etalon, t isthe thickness of the Etalon and θ is the internal angle of incidence [4].
Given Snell’s law (equation 2.1) and the conversion to wavelength in air instead ofvacuum (nairλair = λvacuum) one can get the relationship between transmittance, theexternal angle of incidence on the Etalon and wavelength in air.
T (λair, α) =1
1 + F sin2( 2πnairλair
net cos(arcsin( nair
nesin α)))
(2.10)
2.5.2 Maximum transmittance condition
Maximum transmittance is achieved when the phase difference of the internal reflections hasa multiple of 2πm in phase difference (m is an integer). Derived from (2.9) and δ = 2πmresults in
mλvacuum = 2net cos θ → (2.11)
mλair = 2ne
nair
t cos θ (2.12)
which is the condition for maximum transmittance.
2.6 Auroral Oxygen Emissions
Auroral radiation is attributed to the consequences of energetic electron and proton bom-bardment of the atmosphere, usually confined to the auroral ovals [9]. The auroral ovals(example shown in figure 2.2) encircle the two polar regions of the earth and they pivotaround the earth’s geomagnetic poles. The diameter of the auroral oval depends on whetherthe conditions in the solar wind are quiet or active.
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Figure 2.2: NOAA/POES image of the northern auroral oval on the 23 of August 2010
Two of the strongest allowed oxygen emissions in the aurora are the OI(777.4nm) andOI(844.6nm) multiplets [10]. These two oxygen emissions are the interesting emissions forthe ALBERT instrument. They are interesting because both of the oxygen emissions atomiclines are in the near infrared and infrared spectrum which minimizes the effects of scatteringcompared to other emissions with shorter wavelengths. According to The National Instituteof Standards and Technology (NIST) database [11] oxygen has three emission lines around777.4nm and another three around 844.6nm.
Oxygen spectral lines [nm]777.194 777.417 777.539844.625 844.636 844.676
Table 2.1: Oxygen emission lines around 777nm & 844.6nm.
Direct electron impact excitation is the dominant cause of OI(844.6nm) and high altitudeOI(777.4nm) emissions in table 2.1 [10].
In 1957 Omholt reported a value of 2 for the I(8446)/I(7774) ratio and an intensity of8kR for OI (777.4 nm) in an IBC III aurora [12]. If only direct impact of electrons onoxygen is considered as the excitation mechanism, then the ratio should be between fourand eight acording to theory. In high altitude dayside aurora the ratio has been measuredto three and eleven while in the nightside aurora the ratio is less than three [10]. Both theOI(777.4nm) and OI(844.6nm) emissions have an excitation threshold above 10eV [13].
All six lines have about the same relative intensity according to [11]. OI emissionsaround 777nm and 844.6nm have a surface Brightness of 25kR (for IBC III aurora) [5, p.197].
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Chapter 3
Design
Two major areas of the ALBERT experiment had to be developed. One was the opticaldesign and the other one was the mechanical design. The optical design regarded thespecification of the positioning of the filters and the lenses in the photometer to achievethe best possible result. The mechanical structure did not only provide the support for thephotometers but it also was co-developed with the thermal engineer to enable the controlover the temperature of the air and benches in the instrument within acceptable limits thusnot effecting the optical performance of the etalon filters.
3.1 Optical design
Each photometer consists of one interference filter, one Fabry-Perot etalon, one etalon tiltingmechanism, one forelens, one aperture, one fieldlens and one PMT detector.
Figure 3.1: Overview of the optical system
A photometer bench is shown in figure 3.1. The incoming light first passes through aninterference filter and then through the Fabry-Pérot Etalon. A step motor is the actuator
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that tilts the etalon. The forelens then focuses the light in the aperture plane creating animage on the aperture. Tilting the etalon will result in that the image position will shift onthe aperture allowing different sections of the picture to be let through the aperture to becollected onto the PMT’s photocathode via the fieldlens.
The benches have different operating wavelengths around 777.4 nm and 844.6 nm sothe aperture and the filters differ between the two benches. However the rest of the opticalsystem of the benches are identical. They both consist of a front T, a bench plate and aback T for support of the optical components.
The interference filters are statically mounted inside the front Ts and can not be tilted.The etalon filter can be tilted in flight with a step motor around one axis but also tunedon the ground in the perpendicular axis. It is very important that the etalon can beperpendicular to the optical axis, else the operational wavelength of the photometer will beshifted since there will be a static tilt of the etalon.
Both the fieldlens’s and the forelens’s position can be tuned in the direction of theoptical axis. Aligning the forelens’s focal point on the aperture surface will affect thespectral resolution of the instrument. Positioning the fieldlens will determine if all the lightpassing through the aperture is collected on the photocathode surface which will affect thephotometers sensitivity.
3.1.1 Bench Parameters
The optical system is shown in figure 3.2 and the bench parameters were initially set beforemanufacturing began [14]. However the parameters needed to be changed and the newparameters are given in table 3.1.
Figure 3.2: Overview of the parameters in the optical system
D1 Dpmt F1 F2 L2 L3 L4 L5
(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm)30.0 4.5 200.0 30.00 230.05 34.50 30.05 64.55
Table 3.1: Optical layout quantities.
Lens specifications
The optical specifications for the forelens are given by table 3.2 and for the fieldlens in table3.3. Focal length in the tables 3.2 and 3.3 is abbreviated FL.
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Diameter Clear Aperture Effective FL Back FL FL Tolerance(mm) (mm) (mm) (mm) (%)40.0 39.0 200.0 194.21 ±2
Table 3.2: Forelens specifications
Diameter Clear Aperture Effective FL Back FL FL Tolerance(mm) (% of diameter) (mm) (mm) (%)
6.0 ≥ 90 30.0 29.23 ±1
Table 3.3: Fieldlens specifications
Calculations of bench parameters
The positioning of the fieldlens is important to create an image of the forelens on the PMTsurface of the right size. The forelens position is fixed in relation to the aperture, hence thepositioning of the fieldlens is what decides the image size on the PMT detector surface. Anequations system consisting of geometrical and optical equation can be set up and solvedto calculate the distances between the aperture and the fieldlens (L3), fieldlens and thephotocathode (L4) and the effective area used on the PMT (Dpmt).
L3 + L4 = L5 (3.1)
D1(L5 − L4) = Dpmt(F1 + L4) (3.2)
1
F2=
1
F1 + L4+
1
L5 − L4(3.3)
The equation system (3.1), (3.2) and (3.3) determines Dpmt, L3 & L4 with L5, F1 & F2
being bound inputs. Results are shown in table 3.1.Dpmt is 4.5 mm in diameter which is less than the 5.0 mm detector diameter of the
PMT which results in a 81% utilization rate of the photocathode area.
Filter specifications
The oxygen emissions that the photometers are built to detect are in a narrow spectrum.The three 844.6 nm emissions is within half an Angstrom from each other and the three777.4 nm emissions is within less than 4 Angstrom. The etalon’s operating wavelengthis the transmittance peak closest to its corresponding emission. To get a good spectralresolution it is essential that the etalons transmittance peaks have a very narrow FWHM(≤ 1 Angstrom). The etalon have transmittance peaks at every multiple of the free spectralrange (FSR). An interference filter is needed to single out one etalon transmittance peak.
An interference filter is needed with a narrow enough but not too narrow FWHM. If theFWHM would be too large in combination with additional etalon transmittance peaks twowavelengths would be scanned at the same time, corrupting the measurements. However,if the FWHM would be too narrow one or more emission lines would be constantly affectedby the low interference filter’s transmittance reducing the sensitivity of the photometer.
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Fabry-Pérot Etalons
The Etalons’ specification are presented in table 3.4.
Name Diameter Refractiveindex
CWL m0 Thickness FSR Finesse
(mm) (nm) (µm) (nm)777.4 30.0+0/-0.25 1.485 777.88 400 104.8 1.94 28.5844.6 30.0+0/-0.25 1.485 844.3 433 123.1 1.95 38.5
Table 3.4: Etalon specifications
where CWL is the center wavelength of closest peak next to the interesting wavelength bandand m0 the corresponding peak number.
Interference filters
On each bench there is one interference filter provided by Glen Spectra [15]. Fitted Speci-fications are shown in table 3.5.
Name CWL Maximum Transmittance FWHM(nm) [%] (nm)
777.4 777.58 83.49 1.78844.6 844.66 84.59 2.06
Table 3.5: Interference filters specifications
3.1.2 PMT
The PMT used is the H7421-50 from Hamamatsu. It has a sensitive spectral range from 380nm to 890 nm with a peak wavelength at 800 nm. The GaAs photocathode is circular and5.0 mm in diameter (). The quantum efficiency is 12% at peak wavelength however noquantum efficiency graph was avalible in the datasheet to find out the quantum efficiencyat the operating wavelengths. The PMT’s operatating ambient temperature is +5C to+35C. Albert will be flown with an air temperature stabilized at +20C [16].
14
3.2 Mechanical design
3.2.1 Optical Bench
The optical bench (shown in figure 3.1) consists of several components vital for the perfor-mance of the photometer. The positioning of the filters and the lenses are key to obtain awell performing system. The fieldlens and forelens assemblies are designed so that light inthe field of view from the aurora will hit the PMT detector surface. The filter assembliesare designed to hold the filters.
Forelens/fieldlens assemblies
Figure 3.3: Overview of fieldlens system
The fieldlens system (shown in figure 3.3) consists of an aperture holder (transparent),an aperture (red), an aperture lid (grey), two lens holders (khaki) and the fieldlens shownin figure 3.3. The aperture holder is mounted with four screws to the back T. Through theaperture holder is a circular cutout (12mm) where the lens holders are placed. A focustuning mechanism is present and consists of two screws inserted through the grooves in theaperture holder into the threaded holes in the front lens holder.
15
Figure 3.4: Detailed fieldlens mount
A front and a back lens holder are mounted together with two M1.2 screws. The screwsare inserted through the back holder and screwed into the threaded hole in the front holder.Two M1.2 threaded holes are also present in the front lens holder for the focus tuningmechanism as shown in figure 3.4.
Filter assemblies
The interference filters are mounted into the front T of the photometer bench (shown infigure 3.5). Due to a mistake in the communication between the designer and the man-ufacturer the slot in which the filter would be positioned was milled too deep. Thus thefilter lids have a deeper than necessary flange though the overall tradeoff in performancewas none.
The Fabry-Pérot Etalon was fitted into a filter holder that was specially designed to bemounted into the Edmund optics TECHSPEC® Kinematic Filter Mount, 2-Screw NT58-874[17].
16
Figure 3.5: Filter assembly of the ALBERT photometer
The filter lids are mounted in place by four screws into the filter holders.
3.2.2 Support structure
The support structure for ALBERT photometers consists of two hollow carbon fiber poles(outer 12.0mm, inner 9.0mm), two front Ts, two back Ts and two benches and a poleholder. All parts except the poles and the screws are made of aluminum. The screws arestainless steel.
Figure 3.6: Support structure for ALBERT photometers
17
The front and back Ts have precision milled out cutouts to encircle the poles. Theyare then joined together with two M5x25 stainless steal screws clamping on to the poles.The lower Ts holes are threaded through and the upper Ts holes are partially sunken tofit the screw head. The interface between the T’s and the benches consists of three M5x12screws and two alignment pins furthest towards the poles to reach the required alignmentstandards. At the back end of the poles, there is a pole holder. It is mounted to the outertube with six screws.
O-rings
Three different O-ring types are used in ALBERT which are all made from silicone becausethe material can withstand low temperatures and still have an sealing effect. They weresupplied by Teknikprodukter AB. The models where
• O-RING 19.2X3.0/MVQ 70
• O-RING 42.2X3.0/MVQ 70
• O-RING 174.3X5.7/MVQ 70
in which one 19.2X3.0 was used once to seal the Canon-contact, two 42.2X3.0 were usedto seal the windows and two 194.3X5.7 were used to seal the back and front lid. For easymounting of the lids high vacuum grease from DOW CORNING was used to reduce frictionbetween the 174.3X5.7 O-rings and the outer tube.
3.3 Beam calculations
When it was time to decide on the material and the geometry of the poles a lot of designconstraints were present. The poles geometry could not be oversize thus an analysis had tobe undertaken to investigate the deflection of the beams due to the benches weight.
3.3.1 Problem
The two optical benches are mounted onto two poles fastened in the front lid and in thepole holder. A requirement is that the deflection of the poles should be minimal so thebenches are symmetrically aligned in the tube. Two forces are affecting each beam.
L1(50.0 mm) is the distance from the front lid to the interference filter holder. L2
(202.56 mm) is the distance from the interference filter holder to the center of gravity ofthe hole bench. L3 (117.44 mm) is the the distance from the center of gravity of the benchto the back T and finally L4 (194.0 mm) is the distance form the back T to the pole holder.
18
Figure 3.7: Forces affecting the deflection of the beams
The forces F1 (3.38 N) and F2 (5.83 N) are different in magnitude because the center ofgravity is not in the middle of the two T’s. Both benches have a mass of 3 422g togetherand the gravity constant used in calculation is 9.82 m/s2.
The problem is to find the right material/composite and geometry of the poles that willkeep the deflection of the beams lower than the manufacturing tolerances of the opticalbenches which is estimated at 0.2 mm. Due to all ready manufactured parts a designconstraint on the diameter of the poles was present. The absolute maximum diameter ofthe poles would be 14 mm.
3.3.2 Solution
A solution was found using the Euler-Bernoulli equation for the quasistatic bending ofslender, isotropic, homogeneous beams of constant cross-section under an applied transverseload.
EId4w(x)
dx4= q(x) (3.4)
where E is the Young’s module of the material. I is the area moment of inertia forthe specific cross sectional geometry. w(x) is the deflection of the beam and q(x) is thetransverse load.
The boundary conditions for the problem were that at the front lid the deflection and
its first derivative is equal to zero (w(0) = dw(0)dx
= 0). The third boundary condition isthat at the pole holder the deflection would also be zero as well as that at Ltot there is no
counter-inertia (w(Ltot) = d2w(Ltot)dx2=0 ). Thanks to the superposition principle we can solve
the deflection on the beam from each of the two forces and then add the deflections togetherto reach the resulting deflection.
Solving equation (3.4) with the boundary conditions stated above we get
w(x) =
−(Lf −Ltot)F x2((3Ltot−x)L2
f +2Ltot(x−3Ltot)Lf +2L2
totx)
12EIL3 , if 0 ≤ x ≤ Lf
L2
f F (Ltot−x)(3Ltotx(x−2Ltot)+Lf (2L2
tot+2xLtot−x2))
12EIL3 , if Lf ≤ x ≤ Ltot
19
where F is the applied force and Lf is where the force is applied.The materials and composites investigated were fiberglass (70 fibers/30 resin), alu-
minum, copper, carbon fiber (50/50) and steel with the corresponding Young’s modulus(E) of 42.5, 69, 117, 137.5 and 200 GPa.
A hollow pole instead of a solid poles was used to minimize the thermal conductivity.The area moment of inertia for a hollow cylindrical cross section is
I0 =π
4(r4
O − r4I ) (3.5)
where rO is the outer radius and rI is the inner radius. The difference between the innerand outer radius was requested by the thermal engineer to be no greater than 1.5 mm.
0 0.1 0.2 0.3 0.4 0.5
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
Length of beam [m]
Def
lect
ion
[mm
]
10/12/14 mm beam diameter
Fiberglass (f70/m30)AluminumCopperCarbon fiber (f50/m50)Steel
Figure 3.8: Deflection of the poles with different diameters and materials/composites.
The results of the computation are shown in figure 3.8. A large steel pole would deflectthe least due to the benches weight, however after consultation with the thermal engineerin the ALBERT project to use either carbon fiber or fiberglass due to thermal conductivityreasons.
3.3.3 Conclusion
The carbon fiber pole with a outer diameter of 12 mm and an inner diameter of 9 mm issufficient for our purposes since it deflects a maximum of 0.2 mm. The calculation is aworst case calculation and it has not been taken into consideration that ALBERT can betilted with respect to the gravitational force which would only improve the results.
20
Chapter 4
Transmittance characterization ofinterference filters and Etalons
The characterization of the optical filters is essential for the performance of the photometersbecause the parameters determined will be used for the optimization of each photometersaperture. Two different types of tests where performed. One spectral transmittance andemission test and one for further Fabry-Pérot Etalon characterization. The transmittancetests where performed so that accurate data of the interference filters maximum transmit-tance, CWL and FWHM could be obtained.
An accurate enough transmittance spectrum of the etalon could not be obtained duringthe first test, so further etalon characterization had to be done, thus a second test wasperformed. The second test imaged the interference ring pattern produced by the Argonlamp emission through a broad passband interference filter and a Fabry-Pérot Etalon. Af-ter the second test the etalon parameters could be successfully identified and used in theoptimization of the aperture geometry.
4.1 Transmittance measuring
In collaboration with Dr. Olli Jokiaho from the University of Southampton in September2009 measurement of the transmittance spectra of four interference filters and two Fabry-Pérot Etalons was performed. The two narrow passband interference filters are going to beused in the photometers while the two broad passband interference filters have been usedfor further characterization of the Fabry-Pérot Etalons. The spectral emission lines from aspecific Argon lamp was also measured for the same purpose.
The test equipment used was an spectrometer based on Michelson Interferometer. Thetest equipment gave the measured results as transmittance as a function of wavenumber invacuum. The conversion from wavenumber (ν) to wavelength (λ) in spectroscopy is doneaccording to
λ =1
ν. (4.1)
The wavelengths measured needed to be converted from vacuum to air. The modifiedEdlén refractive index of air at 20C, 1 atm and 10% relative humidity is 1.000270 (nair)for both 777.4 and 844.6 nm wavelengths [18]. The conversion from wavelength in vacuumto air was then done by
21
λair =λvacuum
nair
. (4.2)
The spectrometer used in the transmittance test is shown in figure 4.1. The numbers inthe figure represents different parts of the spectrometer. The detector is (1), the variableoptical path length is (2), the light source is (3) and the semi transparent mirror is (4). Byvarying the optical path length by adjusting the position of the mirror inside (2) differentconstructive and and destructive interference of wavelength occur which is detected by (1).
Figure 4.1: Michelson interferometry based spectrometer
The test equipment could not provide a collimated beam anywhere between the semitransparent mirror and the photo cathode detector. Nominally one would place the filtersclose to the detector to get the most intense beam possible through the filter. The beamwas not collimated enough at the detector to detect the narrow etalon transmittance peaksnor give accurate transmittance levels hence a better position for the filter was needed. Themost collimated beam was close to the mirror although that position had a drawback as
22
well. The beam size close to the mirror was physically larger than the any of the filtersresulting that the measurements had to be taken with a less than optimal intensity leveleffecting primarily the noise level. The issue could be compensated with more measurementcycles and higher detector gain.
Results
The narrow passband interference filter plots (figures 4.3 and 4.4) show both a measuredand a fitted Gaussian function. The fitted Gaussian function is used for the optimizationof spectral resolution and throughput.
Argon lamp emission spectrum
An argon lamp was used in the further characterization of the etalon since Argon hademission lines relatively close the the operating wavelength of both photometers.
650 700 750 800 850 900 950 1000 1050 11000
0.5
1
1.5
2
2.5
3x 10
5
Inte
nsity
Wavelength [nm]
Argon lamp emission spectrum
Figure 4.2: Argon lamp emission spectrum
The tests verified that the argon lamp (spectrum shown in figure 4.2) would be a suitablelight source for the further etalon characterization, with a number of strong distinct spectrallines between 700nm and 950nm.
Narrow Passband Interference Filters
For the narrow passband interference filters it is important to have a CWL very near thecentral of the three emission lines, regardless of weather it is the 777.4 nm or the 844.6 nmspectrum. This is because the FHWM of the filters should be narrow enough to block outall other emissions but the three intended OI emissions but still have a high transmittancefor the emission lines. The free spectral range of both etalons is approximately 2.0 nm andthe etalon can be tilted so the operating wavelengths shifts approximately 1nm. A FWHMof 2.0 nm leads to that the operating transmittance peak and the next transmittance peakhave the same total transmittance hence that is the maximum allowed FWHM.
23
777.4 Interference filter transmittance data
The filter parameters identified in figure 4.3 are shown in table 4.1.
Figure 4.3: Measured and fitted IF 777.4 filter
CWL Tmax FWHMnm nm
777.56 ± 0.05 84.5 ± 0.5% 2.05 ± 0.01
Table 4.1: 777.4 Interference filter transmittance data
The CWL of the narrow passband 777.4 filter is near the OI(7774) emission lines. Arelatively high transmittance level at the CWL is also to specifications. The value of theFWHM is near acceptable tolerances.
844.6 Interference filter transmittance data
The filter parameters identified in figure 4.4 are shown in table 4.2.
CWL Tmax FWHMnm nm
844.69 ± 0.05 84 ± 0.5% 1.78 ± 0.01
Table 4.2: 844.6 nm Interference filter transmittance data
It is shown in figure 4.4 that the transmittance is at an acceptable level, CWL is nearthe OI(8446) emission lines and the FWHM is within the acceptable limits which makesthis filter useful in the photometer.
24
Figure 4.4: Measured and fitted IF 844 filter
Broad Passband Interference Filters
As stated above the broad passband interference filters are useful for further characterizationof the etalons as described in the introduction in this chapter. The filters were commercialoff the shelf interference filters (Edmund optics: NT43-093 and NT67-785) which meantthat they might not be optimal for their intended purpose. The main conclusions that willbe drawn from these measurements are not primarily the transmittance spectrum, but whatemissions from an argon lamp the filter would transmit. Preferably only one bright line ofthe argon spectrum should be singled out and thus lead to more accurate results whencharacterizing the etalons. This is because if only one emission line is transmitted duringthe further etalon characterization a clear ring pattern from one single bright emission willreduce the unknown parameters in the identification of the etalon parameters.
777.4 nm Interference filter transmittance data
The filter parameters identified in figure 4.5 are shown in table 4.5.
CWL Tmax FWHMnm nm
781.8 ± 0.1nm 42.0 ± 0.8% 10 ± 0.1
Table 4.3: Broad 777.4 nm Interference filter transmittance data
This filter misses four (772nm peak is a double) Ar peaks around its center wavelengthof 781 nm (shown in figure 4.5) which makes it unclear if only one emission peak will bedominant after the Ar light has passed through the filter. This filter shall be used in thesecond characterization of the etalons and for that purpose it would be better if the CWL
25
755 760 765 770 775 780 785 790 795 800−2
0
2
4
6
8
10
12
14
16x 10
4
Wavelength [nm]
Inte
nsity
/Tra
nsm
ittan
ce [N
ot to
sca
le]
Broad FWHM 844.6 interference filter & Ar spectrum
Filter transmittanceAr emission
Figure 4.5: Measured broad passband 777.4 nm interference filter
could be closer to 772nm and the FWHM of the filter could be narrower so that the 763.5nmAr peak would not affect the further testing.
Broad 844.6 nm Interference filter transmittance data
The filter parameters identified in figure 4.6 are shown in table 4.6.
CWL Tmax FWHMnm nm
849.5 ± 0.1nm 66.5 ± 2.5% 9 ± 0.1
Table 4.4: Broad 844.6 nm Interference filter transmittance data
This filter is good since a clear Ar emission peak around 852nm passes through thefilter with high transmittance (shown in figure 4.6). The large peak at 842.5 might alsohave some throughput over the filter but at least there will be one bright line available forfurther etalon characterization.
26
835 840 845 850 855 860 865−2
0
2
4
6
8
10
12
14x 10
4
Wavelength [nm]
Inte
nsity
/Tra
nsm
ittan
ce [N
ot to
sca
le]
Broad FWHM 844.6 interference filter & Ar spectrum
Filter transmittanceAr emission
Figure 4.6: Measured broad passband 844.6 nm interference filter
777.4 Fabry-Pérot etalon filter
A broader spectrum over the 777.4 nm etalon is shown in figure 4.7.
700 750 800 850 900 950 1000 1050 11000
10
20
30
40
50
60
70
80
90
Etalon 777nm filter
Wavelength [nm]
Tra
nsm
ittan
ce [T
%]
Figure 4.7: Measured broad transmittance spectrum of the 777.4 nm etalon
The etalon will have its characteristic peaks only when the reflective surfaces reflectthe light inside the etalon. Reflectance and transmittance added together is by definitionalways one. So when the etalon loses its reflectivity for a certain spectrum it is no longer
27
an effective etalon. The 777.4 nm etalon seems to work quite well in the interval 760nm to930nm (R > 90%).
A high resolution spectrum of the etalon was also measured and the results can be seenin figure 4.8.
777 777.2 777.4 777.6 777.8 7780
10
20
30
40
50
60
70
80
X: 777.6Y: 64.48
Wavelength [nm]
Tra
nsm
ittan
ce [T
%]
Etalon 777 nm filter
765 770 775 780 7850
10
20
30
40
50
60
70
80
X: 777.6Y: 64.48
Wavelength [nm]
Tra
nsm
ittan
ce [T
%]
Etalon 777 nm filter
Figure 4.8: Measured narrow transmittance spectrum of the 777.4 etalon
The CWL of the nearest peak to the OI(7774) emissions is higher than the longestspectral line’s wavelength which makes this etalon filter look promising for its application.
28
844 Fabry-Pérot etalon filter
This etalon has high reflection in the spectrum 760-930 nm shown in 4.9.
700 750 800 850 900 950 1000 1050 11000
10
20
30
40
50
60
70
80
90
Wavelength [nm]
Tra
nsm
ittan
ce [T
%]
Etalon 844.6 nm filter
Figure 4.9: Measured broad transmittance spectrum of the 844.6 nm etalon
29
843.8 844 844.2 844.4 844.60
10
20
30
40
50
60
70
80
90
100X: 844.3Y: 99.15
Etalon 844.6 nm filter
Wavelength [nm]
Tra
nsm
ittan
ce [T
%]
840 842 844 846 848 8500
10
20
30
40
50
60
70
80
90
100X: 844.3Y: 99.15
Etalon 844.6 nm filter
Wavelength [nm]
Tra
nsm
ittan
ce [T
%]
Figure 4.10: Measured narrow transmittance spectrum of the 844.6 nm etalon
Unfortunately the nearest CWL of the peak is shorter than 844.6 nm (shown in figure4.10) rising the suspicion of that the etalon might have a too low operating wavelength. Thetransmittance peaks however reach near 100% which means that for certain wavelengths,there will be no unnecessary losses resulting in a more sensitive instrument. This filter mustbe further investigated carefully when characterized.
30
4.2 Fabry-Pérot Etalon characterization
As described in the theory chapter the formula for maximum transmittance for an etalon is
mλ = 2net cos θ. (4.3)
The refractive index (ne) and the thickness (t) parameters were only specified from themanufacturer with quite high uncertainty. The parameters that you can have fairly goodcontrol over is λ and θ then you just need to find the integer m. Defining λ0 of the etalon asthe operating wavelength closest to the interesting spectral emissions and a correspondingm0, together with an incident angle (α) of 0 degrees (for maximum CWL of the operationtransmittance peak) then results in
m0λ0 = 2ne
nair
t cos(0) = 2ne
nairt (4.4)
The etalon thickness, refractive index and the CWL of the operating transmittance peakwere approximately known, with an uncertainty, giving a span of integer values m0 couldtake.
The test firstly imaged the ring pattern which an etalon interferometer generates inthe focal plane from the fore lens from the Argon lamp. That ring pattern was thenimported in MATLAB to be analyzed and compared to a theoretical model. The λ0 andm0 parameters where iterated over a span of possible values to fit the theoretical modelwith the measurements. The best fit was then concluded to be the right λ0 and m0.
4.2.1 Test setup
The test setup consisted of an Argon lamp, a small aperture close to the argon lamp, thebroad passband interference filters, a Fabry-Pérot etalon, the forelens and a high resolutionmegapixel EMCCD system called ALVIS (shown in figure 4.11). The forelens is placed so itsfocal point is on the ALVIS detector surface to get the imaged interference pattern as clearas possible. ALVIS is a system developed in-house at Alfvénlab where the detector is theAndor iXionEM +885. The sensitive area is 1004x1002 pixels and 8x8 mm large [19]. Thismeant that one measurement could not be done to get a complete picture of the interferencepattern. Several measurements could however with different tilts of the etalon be assembledinto a mosaique creating a complete picture.
Figure 4.11: Test setup for the etalon characterization
4.2.2 Mathematical calculations and algorithm
From the multiple pictures that were taken a mosaique was created (example shown infigure 4.12).
31
Figure 4.12: Mosaique of the 844.6 etalon images
After the mosaique image had been created, it was imported into MATLAB and therelationship between intensity and the radius of the ring pattern was investigated. This wasdone by averaging the intensity over the angle in the image for every radius.
I(r) =1
θr
∫
Irdθ (4.5)
where θr is the sweep angle for that radius from the center of the pattern. Ir is the intensityat a radius r. Generating the I(r) data and localizing the intensity peaks with the respect tothe radius will result in identifications of r1, r2, ..., rj (with j being the number of identifiablepeaks and ri any of the radii in the set) for comparison to the theoretically calculated radialpositions of the intensity peaks corresponding to Ar emission lines.
0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
3
3.5
4
radius [mm]
Inte
nsi
tyI(r
)
Figure 4.13: Analyzed and averaged intensity of the 844.6 nm etalon mosaique
Calculations of the theoretical radial positions of the peaks is done by combining Snell’slaw, equations (4.3), (4.4) and the fact that the focal point of the forelens is on the detectorsurface (r = f sin α) according to
ri = fnetalon
nair
sin(cos−1(mλArgon
m0λ0)) (4.6)
where f is the focal length of the fore lens and λArgon being one of Argon’s emission lines.
32
Equation (4.3) also helps couple m, λArgon, m0 and λ0 with the simple fact that
mλArgon
m0λ0= m
λArgon
m0λ0= mΛ = cos θ ≤ 1 (4.7)
Λ is fixed for a specific emission line (λArgon) hence there will be a maximum value ofm according to
mmax =
⌊
λArgon
m0λ0
⌋
(4.8)
which tells us what transmittance peak is the operating wavelength creating the smallestring in the ring pattern that has been imaged. Outer rings will then be visible when theright conditions are met (when the internal angle of incidence inside the etalon correspondsto previous interference order ). The same is true for the third order of ring patterns andis used to generate the outer ring patterns in the model.
In the mosaique images created three repetitive (with respect to the radius) circularpatters could be identified for both the 777.4 nm etalon and the 845nm etalon. This isbecause the order of the transmittance peaks shifting over the emitted λArgon changes withthe angle of incidence of the etalon. There were three repetitions of the ring pattern in bothmeasurements hence for the emission line λArgon the visible peaks were mmax,mmax − 1and mmax − 2.
(mmax − 2)λArgon
m0λ0= cos θm−2 ≤
(mmax − 1)λArgon
m0λ0= cos θm−1 ≤ cos θ =
mmaxλArgon
m0λ0(4.9)
All the tools to calculate the ri are given by (4.6), (4.8) and (4.9). Values of m0 and λ0
are bounded by definition (λ0) and the manufacturer’s specification (equation (4.4)) to afinite set of possible combinations thus making it possible to iterate over all of the scenarios.
4.2.3 Results 777.4 nm Fabry-Pérot etalon filter
Since no strong Argon emission lines were within the FWHM of the broad passband 777.4nm interference filter resulted in that several Argon emission lines were visible in the ringpattern. The results are shown in figure 4.14 and table 4.5.
ne λ0 m0
nm1.485 777.88nm 400
Table 4.5: 777.4 nm etalon parameters
There are still unidentified peaks, i.e. at r=18.28 mm thats still unidentified. A broadbandinterference filter with an CWL near the 772 nm Argon emission line would be better suitedfor this task.
Emission spectrum lines used
Several emission lines were visible in the mosaique. The argon emission lines 750.38, 751.46,763.51, 800.61, 801.47, 810.36, 811.53 and 842.46 nm as well as the krypton spectral line760.15 nm was used as ri [11].
33
0 5 10 15 20 25 30 35 400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
radius [mm]
777.4nm etalon filter ring pattern radial identification
I(r)m
max
mmax
−1
mmax
−2
Figure 4.14: Modeled peaks positions compared to measured peaks
4.2.4 Results 844.6 nm Fabry-Pérot etalon filter
Three strong Argon emission lines were close to the broad passband interference filter (figure4.6) giving a clear ring pattern reducing the complexity of the analysis compared to the777.4 nm filter.
The results are shown in figure 4.15 and table 4.6.
0 5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
radius [mm]
844.6nm etalon filter ring pattern radial identification
I(r)m
max
mmax
−1
mmax
−2
Figure 4.15: Modeled peaks fitted with measurement peaks
34
ne λ0 m0
nm1.485 844.29nm 433
Table 4.6: 844.6 nm etalon parameters
In the calculations the value of the refractive index of air (nair) was 1.00027. The strong852.14 nm argon emission line is clearly visible at 1.84 mm and repeated at 20.35 mm and28.77 mm.
Emission spectrum lines used
From the mosaique pictures of the 844.6 tests there where three clear spectral lines visible.Three argon spectral lines where close to the interference filters CWL. Those three spectrallines were 840.82, 842.46 and 852.14 nm (ri) [11].
4.3 Conclusions
The transmittance measuring showed that both of the narrow filters would be suitable inflight given their filter properties. The broad 844.6 nm passband interference filter showedto have great potential for the etalon characterization while the 777.4 nm broad passbandinterference filter could have been better suited for the application ahead. The 777.4 nmetalon showed to have a suitable operating wavelength but it would have to be confirmed ina second test. The 844.6 nm etalon however showed to have an operating wavelength thatwas less than the OI(8446) emissions thus causing a huge problem.
The further characterization of the etalons confirmed the suspicion with the 844.6 nmetalon and for sure determined that is was not to specifications which rendered it uselessfor it is application. The 777.4 nm nm etalon was confirmed to be suitable for ALBERT.
35
Chapter 5
Optimization of spectral resolutionand throughput
In the Theory chapter equation (2.5) describes the throughput of a photometer without anyoptical filters. However since an interference filter and an Fabry-Pérot etalon is present inALBERT’s photometers, the a term have to be revised to
a =x
Aperture
Tλ(α)dxdy (5.1)
Without any filters, the transmittance for all wavelength on the aperture is one, hencethe term would be equal to the surface integral over the area of the aperture hole in theimage plane. This results in that the effective throughput for a wavelength at one specificetalon tilt angle will be
Sλ(α) =Aetalon
F 2
x
Aperture
Tλ(α)dxdy (5.2)
Since the area of the etalon (Aetalon) and the focal length of the lens (F ) is geometri-cal properties hence the solid angle subtended by the etalon as viewed from the aperture( Aetalon
F 2 ) is constant.
5.1 Optimization objectives
To ensure that the optical system has the best possible precision over the narrow wave-length band ALBERT will scan an optimization of the aperture geometry for both benches(operating at different wavelength bands) has to be performed.
The optimization parameters for the aperture is
• Maximize the peak effective aperture (Sλ) for all etalon tilting angles (∀α)
• Minimize the passband of the effective aperture (∆λ) for all etalon tilting angles (∀α)
• Keep peak Sλ constant for all Etalon tilting angles (∀α)
• Keep ∆λ constant for all Etalon tilting angles (∀α)
• Keep the total effective aperture Stotal constant for all Etalon tilting angles (∀α)
37
Where the total effective aperture is the integral of the effective aperture over all wave-lengths
Stotal(α) =
∫
Sλ(α)dλ (5.3)
The objective to keep Stotal constant would be equivalent to having a spectral instrumentwith a known passband and tunable CWL.
5.2 Spectral resolution
The optimization objectives can be conflicting. Just by inspection of equation (5.2) tomaximize the effective throughput for a specific wavelength for a specific tilting angle is tohave high either high transmittance and/or a large area. To minimize the passband at onespecific tilting angle of the of the effective throughput a small area and a transmittancespectrum looking like a the Dirac function would be desirable. To illustrate this, andexample is shown below with a circular aperture of different sizes.
The circular apertures range from 0.1 mm in radius to 2.8 mm in radius. The aperturescan bee seen in figure 5.1.
Figure 5.1: Overview of the circular apertures
CWL
When tilting the etalon, the CWL of Sλ changes as seen in figure 5.2. There is a slightlylesser CWL shift with a large aperture than a small, however no significant behavior changeis observed.
38
0
0.5
1
1.5
2
0
1
2
776.6
776.8
777
777.2
777.4
777.6
777.8
Etalon tilting angle [o]
Center wavelength of effective apperture for circular apertures
Radius [mm]
CW
L of
S [n
m]
776.7
776.8
776.9
777
777.1
777.2
777.3
777.4
777.5
777.6
Figure 5.2: CWL of the effective aperture as a function of the tilting angle
Maximization of the effective aperture
Generally for a circular aperture, the larger the aperture, the higher the effective aperturefor all tilting angles as seen in figure 5.2. This is natural since the transmittance is alwayspositive in the interval zero to one. Since the aperture area is larger with a higher radius,it is only natural that the effective aperture is also greater.
00.5
11.5
2
0
1
2
0
1
2
3
4
x 10−7
Etalon tilting angle [o]
Maximum effective throughput for circular apertures
Radius [mm]
Sm
ax [m
2 ]
Figure 5.3: Maximum of the effective aperture as a function of the tilting angle
39
Passband of the effective aperture
Since one of the goals is to minimize the passband of the effective aperture and keep itconstant for all tilting angles one can clearly see in figure 5.4 that a small circular apertureis preferable.
00.5
11.5
2
0
1
2
0
0.5
1
1.5
Etalon tilting angle [o]
FWHM of S [nm]
Radius [mm]
FW
HM
of S
(α)
Figure 5.4: Passband of the effective aperture as a function of the tilting angle
The peak at (α = 2,radius = 2.8) is probably because multiple orders of interferencestarts to affect the calculation.
Total effective aperture
The total effective aperture varies more from the mean if the aperture is larger but it is atthe same time higher for a larger aperture as seen in figure 5.5.
40
00.5
11.5
2
0
1
2
0
2
4
6
8
x 10−17
Etalon tilting angle [o]Radius [mm]
Sto
t [m3 ]
Figure 5.5: Total effective aperture
5.3 Optimization calculation
5.3.1 Algorithm
The computation was done by firstly generating a mesh of the aperture. A 6x6 mm meshdivided into 14 400 pixels (50x50 µm large each). Each pixel was assigned a transmittancevalue of either one or zero representing whether light would pass through that specific pixelon the aperture surface. A set of apertures was then generated to be iterated through thecalculation loop.
To calculate the effective throughput (equation 5.2) a trapezoidal integration of thetransmittance in each pixel was done over the aperture surface . The transmittance of thepixels was numerically calculated according to
Tx,y = TIF (λ) · Tetalon(λ, α, x, y) · Taperture(x, y) (5.4)
where x and y is the coordinates on the aperture, λ is the wavelength in air for the incominglight and α is the etalon tilting angle.
This was then repeated for for etalon tilt angles from 0 to 2 and a 1.5 nm spectrumwith the highest wavelength being the operating wavelength for the photometer (λ0).
5.3.2 Identifying potentially optimal aperture geometrics
An investigation was needed to show what geometry shapes of the apertures had the mostpotential to fulfill the optimization objectives. Eight different apertures geometries wereinvestigated and all the apertures had the almost same area not to wrongfully influence thelevel of effective throughput by enhancing the aperture hole size.
41
Aperture geometries
The eight different apertures were not chosen at random. Aperture number one has abanana shape which is designed to have the same radius as the ring’s in the ring patterncorresponding to the longest and shortest wavelength of an interesting ring pattern. Thesecond aperture is a circular aperture with a radius of 0.33 mm. The third aperture is ahalf circle with cutout in the center of the circle to limit the upper scanning boundary. Thefourth is a half circle. Apertures five to eight are various kinds of rectangular apertures todetermine a behavior of the effective throughput for rectangular aperture geometries sincethis can results in conclusions how apertures could be aligned with respect to the image.The apertures are shown in figure 5.6 where the red area is the aperture and the blue areahas a transmittance of 0 because it represents the metal in which the aperture is cut. Thered areas has a transmittance of 1.
Figure 5.6: Apertures used in the optimization
Results
The results from the calculation are shown in figure 5.7. One can directly conclude thatthe shape of the aperture does not greatly affect the CWL of the effective aperture nordoes it greatly influence the behavior of the total effective throughput of the aperture. Thegeometry of the aperture greatly influences the passband of the effective throughput and tosome extent the peak value and its behavior when tilting.
Conclutions
The results from figure 5.7 conclude that aperture eight is not preferable in any way whileaperture 5 performs well. Since the ring pattern moves up or down (with respect to theapertures in figure 5.6) on the apertures it is natural that the aperture eight has a lot ofthroughput from different wavelengths and less of it from any specific wavelength while thefifth aperture singles out fewer wavelengths much better and gets more of those wavelengthssince its wider. The only aperture that matches aperture five is aperture one which is alsosimilar to aperture five.
Aperture five can be differentiated in two ways, height and width of the aperture, wherewidth is larger than height. Aperture one can be differentiated in several ways, howevergiven a certain spectrum that interesting, only the width between the circles intersecting
42
0 0.5 1 1.5 20.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5x 10
−9
Etalon tilting angle [o]
Sm
ax [m
2 ]
Peak effective throughput forsignificantly different aperture geometries
Apertur 1Apertur 2Apertur 3Apertur 4Apertur 5Apertur 6Apertur 7Apertur 8
0 0.5 1 1.5 20.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
FW
HM
[nm
]
Etalon tilting angle [o]
FWHM for significantly different aperture geometries
Apertur 1Apertur 2Apertur 3Apertur 4Apertur 5Apertur 6Apertur 7Apertur 8
0 0.5 1 1.5 2
776.6
776.8
777
777.2
777.4
777.6
777.8
SC
WL [n
m]
Etalon tilting angle [o]
CWL for significantly different aperture geometries
Apertur 1Apertur 2Apertur 3Apertur 4Apertur 5Apertur 6Apertur 7Apertur 8
0 0.5 1 1.5 22.5
3
3.5
4
4.5
5
5.5
6
6.5x 10
−19
Etalon tilting angle [o]
Sto
t [m3 ]
Total effective throughput forsignificantly different aperture geometries
Apertur 1Apertur 2Apertur 3Apertur 4Apertur 5Apertur 6Apertur 7Apertur 8
Figure 5.7: Results from the calculations
points of the aperture banana is needed to be changed since the radius of the rings isdetermined by what wavelength spectrum is interesting. Aperture one and five will befocused on for further analysis.
5.4 Optimization results
Since only the 777.4nm etalon has the right specifications to be used in ALBERT theaperture optimization is going to be concluded only for the 777.4 nm photometer.
5.4.1 Banana aperture
A total of 210 different apertures were investigated. They differed in radii and the widthof the separation distance in the middle of the aperture. The radii depended on whatwavelength span was going to be important. The upper boundary of the wavelength spanwas the photo meters operating wavelength (λ0) and the span was at maximum 1.5 nm.The circle radii were calculated according to
rcircle = fnetalon
nair
sin cos−1(λ
λ0) (5.5)
43
with the help of Snell’s law (equation 2.1) and the formula for etalons maximum transmit-tance (equation 2.12).
The computation gave the results shown in figure 5.8 and it must be noted that theapertures are sorted with respect the their total area even though they do not necessarilyhave the same proportions.
00.5
11.5
2
050
100150
200250
0
1
2
3
4
x 10−8
Etalon tilting angle [o]
Maximum effective aperture for banana apertures
Aperture number
Sm
ax [m
2 ]
00.5
11.5
2
050
100150
2002500.05
0.1
0.15
0.2
0.25
Etalon tilting angle [o]
Passband of the effective aperture
Aperture number
FW
HM
of S
(α)
[nm
]
00.5
11.5
2
050
100150
200250
776.6
776.8
777
777.2
777.4
777.6
777.8
778
Etalon tilt [°]
Center wavelength of the effective aperture for banana apertures
Aperture number
CW
L of
S [n
m]
00.5
11.5
2
050
100150
200250
0
1
2
3
4
5
6
x 10−18
Etalon tilting angle [o]
Total effective aperture for banana apertures
Aperture number
Sto
t [m3 ]
Figure 5.8: Results from the calculations of the banana aperture
As stated before, it is the maximum effective aperture and its passband that we cangreatly affect with the aperture geometry. A statistical analysis of the two parameters wasdone as seen in figure 5.9.
The plots in figure 5.9 shows the ratio between the standard deviation and the meanof the the maximum effective throughput and the ratio between standard deviation of theeffective throughput’s passband and the mean of the effective throughput’s passband. Thestandard deviation and mean of both the peak value of the effective throughput and theeffective throughputs passband is calculated over the etalon tilting angle. Both of thereshould preferably be as close to zero as possible to reach the optimization objectives ofkeeping the peak value of the effective aperture and the passband of the effective apertureconstant.
The larger apertures do not seem to keep the passband constant at higher tilting anglesthus affecting the ratio between the standard deviation of the passband and the mean of thepassband. The noisiness of the maximum effective throughput disappears with the largerapertures. One of the lowest ratios of the passband dataset is as aperture number 171 and
44
0 50 100 150 200
0
0.2
X: 171Y: 0.03577
Aperture number
Pas
sban
d ra
tio
0 50 100 150 200
0
2
Sm
ax r
atio
std(Passband)/mean(Passband)std(S
max)/mean(S
max)
Figure 5.9: Statistical analysis of results
that aperture is also among the best in the effective aperture ratio. Thus that aperture isconcluded to be the optimal aperture if the banana aperture is the best and it can be seenin figure 5.10 and it is geometrical data in table 5.1.
The geometrical data is
rmin rmax dintersection center height(mm) (mm) (mm) (µm)6.85 18.43 5.4 356
Table 5.1: Optimal banana aperture parameters
where rmin is the radius of the smaller circle, rmax is the radius of the larger circle,dintersection is the distance between the two points the circle intercepts and the centerheight is the height of the aperture hole in the middle of the aperture.
45
Figure 5.10: Optimal banana aperture
5.4.2 Rectangular aperture
The aperture calculation for the rectangular aperture consisted of generating 42 differentapertures where the ratio between width and height is higher than eight. All apertureswhere sorted by area size in the same way as for the banana apertures. The maximumvalue for height was 1.8mm and 5.4mm for height.
The calculation for the rectangular aperture generated results shown in figure 5.11.
46
00.5
11.5
2
0
20
40
600
0.5
1
1.5
2
2.5
x 10−8
Etalon tilting angle [o]
Maximum effective aperture for rectangular apertures
Aperture number
Sm
ax [m
2 ]
00.5
11.5
2
0
20
40
600.05
0.1
0.15
0.2
0.25
Etalon tilting angle [o]
Passband of the effective aperture
Aperture number
FW
HM
of S
(α)
[nm
]
0
0.5
1
1.5
2 010
2030
4050
776.5
777
777.5
778
Aperture number
Center wavelength of the effective aperture for rectangular apertures
Etalon tilt [°]
CW
L of
S [n
m]
00.5
11.5
2
0
20
40
600
1
2
3
4
5
6
x 10−18
Etalon tilting angle [o]
Total effective aperture for square apertures
Aperture number
Sto
t [m3 ]
Figure 5.11: Results from the calculations of the rectangular aperture
The Smax ratio behaved in the same way as for the banana aperture and a sweet spotwas found in aperture 36 as seen in figure 5.12.
47
0 5 10 15 20 25 30 35 40 450
0.05
0.1
0.15
X: 36Y: 0.02269
Smax
and FWHM for Comparison
Aperture number
Pas
sban
d ra
tio
0 5 10 15 20 25 30 35 40 450
2
4
6
Sm
ax r
atio
std(Passband)/mean(Passband)std(S
max)/mean(S
max)
Figure 5.12: Statistical analysis of results
The best aperture is shown in figure 5.13 and the geometrical data are presented in table5.2.
Figure 5.13: Optimal rectangular aperture
48
width height(mm) (µm)4.98 313
Table 5.2: Optimal rectangular aperture parameters
5.4.3 Conclusion
Both the optimal rectangular and the optimal banana aperture has similar levels of effec-tive aperture, CWL of the effective aperture and total effective aperture. The thing thatdistinguish them is how the effective aperture’s passband behaves as shown in figure 5.14.
0 0.5 1 1.5 20.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Etalon tilting angle [o]
FW
HM
[nm
]
Comparison between optimal square and banana aperture
Banana apertureSquare aperture
Figure 5.14: Comparison between the rectangular aperture’s and the banana aperture’spassband behavior when tilted
The banana aperture behaves better than the rectangular aperture and in regard tothe optimization requirement of minimizing the passband and keeping it stable thus its thebetter aperture for ALBERT. The effective aperture and total effective aperture is shownin figure 5.15 of the optimal solution.
49
0 0.5 1 1.5 21.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1x 10
−18
Etalon tilt angle [°]
Tot
al e
ffect
ive
aper
ture
[m3 ]
Optimal Total Effective aperture
Aperture 171
Figure 5.15: Optimal effective aperture and optimal total effective aperture
50
Chapter 6
Conclusions
The three thesis objectives were presented in chapter one and they were to finalize thedesign and manufacture ALBERT, verify the optical filters and optimize the aperture forthe spectrometers.
The design of ALBERT was done gradually as manufacturing progressed. An importantfactor in being able to produce a spectrometer with only two degrees of tuning freedom postassembly is to make sure the manufactured parts are manufactured with high precision andthat the interface between the parts enables proper alignment. Therefore to have had thehelp of the technicians at Alfvén laboratory, not only in the manufacturing of the parts butalso in the design of the parts has facilitated the assembly with proper alignment of thephotometers.
Sometimes compromises had to be done in the mechanical design between the opticalsystem and the thermal system to make sure both systems would perform as necessaryand a middle ground was always found. An advantage of the design and manufacturingof ALBERT is that the system was built in house which spawned great solution with highquality manufacturing where the technicians could understand the purpose of a part andthen manufacture it with suitable tolerances. The overall conclusion with the design ofALBERT is that its a well built system.
The Michelson-interferometry based spectrometer at ALBANOVA gave clear and usefulresults on the interference filter parameters for the interference filters, although it was notoptimal for the etalon characterization due to the non-collimated beam path.
The second test with the EMCCD imaging is however good enough to characterize theetalon and the system is available at Alfvén laboratory when a new 844.6 nm etalon arrivesfrom the manufacturer. It could also be useful at the same time to recharacterize the 777.4nm etalon with a 770 nm CWL interference filter with the Argon lamp since there is astrong argon emission line around 772 nm.
An optimization procedure has been developed and can be reused further on. Theoptimization procedure is written in such a way that to characterize the new etalon oneonly needs to change the parameters m0 and λ0 which will facilitate the optimization of the844.6 nm aperture. The optimization algorithm is quite consuming on computer processingpower even though it is fairly optimized. More through calculations with a finer meshand additional aperture geometries are also parameters that will improve the optimizationresult.
51
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