Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2 Techniques Discussions Atmospheric Measurement , and N. D. Lloyd 2 , A. E. Bourassa 2 3694 3693 (McClintock et al., 2009). However, vertical infor- [email protected]) ff 1 , D. A. Degenstein use horizontal picture due to a long line of sight and long 1 ff , J. Gumbel 1 Also denoted as Noctilucent Clouds (NLC) when viewed from the ground. 1 This discussion paper is/has been under review for the journal Atmospheric Measurement Techniques (AMT). Please refer to the corresponding final paper in AMT if available. Department of Meteorology, Stockholm University, Stockholm,Department Sweden of Physics and Engineering Physics, University of Saskatchewan, mation cannot be derived fromon nadir pointing the instruments. Limb-scanning other satellitesPMCs hand are but able give to ascan provide very duration. global When di information investigatingto about atmospheric obtain phenomena the local like structures vertical PMCs, tovertical/horizontal structure it understand information, the a is of technique global essential that picture.inhomogeneity can To retrieve handle is two-dimensional both needed. vertical and Tomographicments horizontal methods are such applied techniques. to limb-scanning measure- 1 Introduction Downward imaging can providePolar detailed Mesospheric information Clouds about (PMCs) the horizontal structure of ern Hemisphere summer 2011/2012, thespecial Swedish-led mesospheric Odin mode satellite with wasMesospheric short operated in limb Clouds. a scans For limited Odin’s(OSIRIS) to Optical this the provides Spectrograph altitude multiple and range viewsfor of through InfraRed tomographic a Polar analysis Imager given of System cloud thegorithms volume vertical/horizontal for and, tomographic cloud thus, analysis structure. a of Here basis mesosphericity we clouds techniques. based present We on also al- maximum present probabil- resultscloud of structures simulating from OSIRIS the tomography special and tomographic retrieved periods. Limb-scanning satellites can providePolar global Mesospheric information about Clouds. the However,remains vertical information limited. structure about This of horizontal iseighteen due structures days to usually during both the a Northern long Hemisphere line summers of 2010–2011 sight and and the a South- long scan duration. On Abstract Application of tomographic algorithms to Polar Mesospheric Cloud observations by Odin/OSIRIS K. Hultgren Atmos. Meas. Tech. Discuss., 5, 3693–3716,www.atmos-meas-tech-discuss.net/5/3693/2012/ 2012 doi:10.5194/amtd-5-3693-2012 © Author(s) 2012. CC Attribution 3.0 License. 1 2 Saskatoon, Canada Received: 23 April 2012 – Accepted: 7Correspondence May to: 2012 K. – Hultgren Published: (kristo 25 May 2012 Published by Copernicus Publications on behalf of the European Geosciences Union. 5 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ective- ff ) it is possible to y , x ( f 3696 3695 erent lines of sight through the analyzed volume. Observations from a satellite platform, however, have certain limitations compared Compared to a limb-imaging technique where several lines of sight are collected si- This paper is divided into three main parts: first, we discuss the tomographic tech- The ideal application of tomography is within the medical field where the term usually The history of tomography related to satellite measurements is limited and has so Forward directed satellite-based limb observations of PMC scattering from consec- ff the atmosphere, only a verythrough limited a interval given of point. viewing Figure angles 2 can shows this provide scenario. line The integrals paths shown are tangent to the reduce a tomographic problemFig. 1 to make the up solution acan set of be of this calculated. discrete If field pathsfield, it through by and is a inversion. the given possible The point to anglescan along lines determine between be which in reduced line successive line to integrals lines integrals the atthe are Radon every solution transform infinitesimal, for point (Herman, then this 1980). within field. The these the inverse integrals transform is then to the method shown in Fig. 1. The solid Earth limits the look directions so that, for 2 The tomographic technique 2.1 Atmospheric model From the knowledge of a set of line integrals trough a field nique and a modelwe present for model the simulations atmospheremographic of recoveries OSIRIS to and measurements which to to theuploaded test optimize algorithm to the settings possibilities OSIRIS. applied is of Then, to applied.ment to- special thirdly, Secondly, modes we tomographic and present modes retrieve datatomographic algorithm. results collected We conclude from during with these running aparisons discussion measure- the and with an OSIRIS other outlook satellite observations on instruments. ongoing through com- the multaneously, OSIRIS is a limb-scanningable instrument. to This capture means oneolution that line of OSIRIS of the is sight measurements. only perrecovery We read-out, of show PMC leading that structures to the despite a tomographic the technique very sparse data allows coarse sampling. for temporal the res- representative of the atmosphere. veloped. The possibility ofwas first recovering demonstrated airglow by structures usingand Llewellyn an from (1993). iterative limb In maximum the emission probabilitya current method tomographic profiles work, algorithm by we that McDade use assumesness an no of atmospheric a satellite model priori limb together information tomography. The with by to technique examine the is the OSIRIS applied e to instrument PMCintegral onboard radiance of the measured Odin the satellite, volumeto where emission a each taken tomographic measurement along technique is alocation that an line involves of of the volume sight. discretization emission of This rates the is to integrals fundamental points and input the in al- a discrete two-dimensional grid that is and Vardi, 1982). far focused on airglownightglow emissions. in The the use F ofsciences region satellite (Thomas initiated limb and the measurements Donahue, use 1972). of of Since tropical tomographic then, techniques various methods in have atmospheric been de- di refers to Magnetic Resonance Imagingboth (MRI) or cases, X-ray an Computed Tomography imagingery (CT). In angle. device In is contrast, discrete rotateda limb around limited observations angular a from a range. patient,imum moving The collecting likelihood spacecraft method cover expectation data only used maximization fromtwo-dimensional in positron technique, ev- emission the fields developed in current originally medical work imaging to of is the recover human similar brain to (Shepp the max- utive positions along the satellitetechniques orbit invert provide the input observed to brightness intoand tomographic an techniques. hence estimate These of provide the information volumea emission about measurement rate plane both that theresulting coincides reconstruction vertical is with and strongly the horizontal dependent satellite on dimensions orbit the in plane. number of The measurements quality along of the 5 5 20 25 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (1) (2) cient ffi . Now, each ij L . The possible lines of sight inter- ◦ , increasing with atmospheric layer : j 20 j . An extended maximum probability V j ≈ V θ , this implies that the time interval between 1 3698 3697 − 7kms 0: ∼ = s along the line of sight and the intercept lengths s ), to find the source distribution s j 2 V )d ) is the unknown source distribution. ij is the geometric path length through each element. Hence, the summation s s ( L ( ij V V j L ∞ Z 0 X = = The overall goal with the tomographic inversions is to solve the set of linear equa- In the two-dimensional discrete case, the observation plane created by the limb As can be seen in Fig. 3, the atmosphere can be divided into a discrete emission grid. is also, in a geocentric system, determining the movement of the satellite between i i method, the Multiplicative Algebraic ReconstructionLloyd and Technique Llewellyn (MART), (1989) developed and by modified to its current state by Degenstein et al. (2003, grid cell at any distance relevant line of sight intersects at leastsatellite two to grid all cell boundaries. of If thesetwo the distances consecutive intersections from intersections with the defines boundaries the arethese geometric known, path intersections the length and through distance path a between we cell. lengths have Finding is applied the a method straight described forward in geometrical Degenstein problem. (1999, Here, Appendixtions, B). Eq. ( O Here represents a forward model of the measurement and requires knowledge of the relevant O where scans and the satelliterepresenting movement the is mean divided of into the source grid distribution cells with the value in each cell so to apply ahave to tomographic be technique developed. to Forobservations limb-scanning are satellite determined measurements borne by from instruments, an afrom integral new the satellite of satellite platform, techniques the position the volume at emission along lines of sight inverse Radon transform is however extremely unstable with respect to noisy data, one-dimensional projections of an objectperfectly taken reconstruct at an the infinite original number of object angles, by we finding can the inverse Radon transform. The Also, the retrieval gridthe must power be of optimized thesolution. with available The computing size respect parameters equipment to used to the are provide discussed satellite an further geometry below. 2.2 accurate and and e Tomographic algorithm The mathematical basisduring for the tomographic beginning imaging oftransform” the was (Radon, 20th laid century 1917). down when This by he paper published Johann the tells Radon basis us for that the if “Radon we have an infinite number of rate profile for the simulatedto observations store – OSIRIS the observations emission – grid.retrieved the Secondly, profile a observation from grid grid. the is Thirdly, tomographic a used however, inversions grid do – is not the used have retrieval the to grid. same store Thesein resolution the three general since grids, needs the a atmospheric finer volume emission structure rate than is possible to obtain for the resulting retrievals. a set of boundary pathstime for interval a is given consequently point alsospace in the at the temporal 85 mesopause km. scale region for is sampling about a 5 min. specific This volume in The grid cells are definedcentre by of the the angle Earth. along Theyand are the labeled angular orbit with division. and an The the index type radialtomographic of algorithms; distance grid first, from a shown the grid in is Fig. used 3 to is contain used an atmospheric for volume three emission purposes in the these limiting paths are separated bysecting an the angle given point areθ then all paths betweenpositions these 1 boundaries. and The 2 same andpaper. angle thereby For defines a the satellite “angle speed along the of orbit” used throughout this solid Earth and therefore represent limiting paths. For an observational point at 85 km, 5 5 20 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (4) (3) ), is then 2 . The choice (1) j V 3700 3699 1) indicate the current and previous iterations, − k   ) and ( ij k β 1) i − ! k est O ( i 1) ij − O β k ( j ij   V i L ij i i O L X , as shown in Fig. 3. The measured brightness, defined by Eq. ( P j ◦ 1) ect of each observation on the convergence of the tomographic inversion. ij

− ff L ij k X 0.1 ( i i j L = V X × P 1) = = mode = − ) The first step of the modeling process is the creation of an arbitrary emission grid, The algorithm starts with an initial estimate of the source distribution k k est ( i (1) ( ij j j rameters of Odin. Theserepresent simulations the are measured performed for set successive provided lines by of the sight that satellite limb scans. This data is then The OSIRIS measurements are, as alreadyThis mentioned, integrations means along that lines the of sight. measurementssphere. are functions For of test the optical purposesessary path to and through apply the optimization atmo- aretrieval. of forward the model that tomographic describes algorithm, the it observations is and100m to nec- simulate the simulated by using various vertical scan speeds as well as orbital and attitude pa- used with the OSIRIS observations. 3 Simulation results used to configure Odin and OSIRIS for the tomographic and maximum radial shellalso distances shows and (in red radialprocess or and is grey, angular depending implemented grid on tothe cell online produce “compare” sizes. or the step Figure printed final isemissions 4 reading) volume skipped from how each emission. and the cell. For Eq. For iterative timated the the (4) observations next first is which iteration are, the iteration, used in first turn, asprocess estimate compared is is a with repeated used the first until as actual the estimate input observationsof output to and for the converges, es- the the usually present around work volume 30 is iterations. on The the focus practical evaluation of the technique described above as Figure 4 shows athe block radiance diagram measurements of (the the observations)put tomographic made is process. by a OSIRIS. The set Alsoand primary of required ancillary orientation inputs as data are in- of containing the various spacecraft satellite parameters, as such well as as position the grid parameters defining minimum 2.3 Overall retrieval scheme is of primary importanceations. for the In applicability our of case,process. the The the method initial and observations estimate for is provide the given an number by of the initial iter- MART value technique as thatV starts the iterative and is thus theprofile weighted is average uniform over along all each observations line using of the sight. assumption that the β is an observation weightingrelative filter e acting as an averaging kernel which determines the where the superscriptsrespectively. ( O represents an estimatedmodel observation outlined of above together a with single the previous line estimate of of the sight volume emission based and on the forward a ray by ray basis until the algorithm converges. The expression is givenV by 2004), solves the problem in an iterative fashion where the iteration is performed on 5 5 20 25 15 10 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , which then ◦ 380 km), also 250 m still re- ∼ ∼ ( 0.5 ◦ × 3.5 set of ∼ ff . 1 − and, finally, the tomographic inversion ◦ 0.1 × 3702 3701 1 km. ∼ Simulations including noise have also been performed. The result showed that the The input emission includes a wave structure with wavelength Figure 6 shows the integrated vertical (black lines) and horizontal (grey lines) cross The result of a retrieval simulation is presented in Fig. 5. The top panel shows an Important parameters characterizing the simulations are the vertical scan speed and OSIRIS sweep over selected altitude ranges. 96 min (Murtagh etare al., installed: 2002; the Llewellyn Sub-Millimeter et RadiometerInfraRed al., (SMR) Imager and 2004). System the Onboard (OSIRIS). Optical Odin, Thesion Spectrograph Odin two for and mission both instruments was astronomers designedwhen and performing as atmospheric astronomy a scientists measurements shared and by mis- vations. down looking For to out Earth the into for latter atmosphericusually deep purpose, obser- space in the the satellite directionments is the pointed of towards entire the the satellite satellite limb is track. of nodded When the so performing Earth, that these the limb co-aligned measure- optical axes of SMR and 4 Odin and OSIRIS The Odin satelliteSiberia. was The launched satellite was on600 km placed 20 with into the February ascending an node almost 2001 at circular 18:00 from local Sun-synchronous time Svobodny orbit and in with near a Eastern period of approximately scales are unlikely to bespeed captured. and The the possible retrieval vertical gridthus scales cell resolved size, are at which limited both by are the set scan to 0.5 km fortomographic this work algorithm and is are capableduced of noise successfully levels of reproducea up input large to uncertainty emissions on 4 with %. the in- output. Noise levels larger than this limit will however have sembles the input emissions verycloud well. is It reproduced. is also noticeable that the peak altitude ofresolved the in the recovered emission.able to This be shows retrieved that with waves the of tomographic algorithm. these On scales the should contrary, be smaller horizontal vertical resolution of OSIRIS observations is about 1 km, this o of a horizontal plane, are verysions, well measurements captured. However, of the horizontally a integrated vertical emis- plane, are slightly misplaced in altitude. Since the put. In the ideal case,see that the this second is and not the entirelyas bottom true. shown However, panels the below, should structures very of thuswork. similar the be Important and input identical. to and thus We note the considered output hereto are, satisfactory is the that for result the the – second purpose the panel data of is in only this the included top as panelsections a is comparison of what the is simulation being results,of sampled corresponding Fig. by to the 5. the forward It second model. is and apparent the that bottom the panels vertically integrated emissions, i.e. the measurements arbitrarily created inputsimulated. emission, The a second “test panelreduced shows PMC”, to the the on same same which asulated input the the emission OSIRIS tomographic but retrieval measurements measurements, grid. with were andi.e. The the the third the resolution panel result bottom shows of panel the the sim- shows tomographic the algorithm using retrieved the emission, simulated measurements as in- when observing the limbmade shorter from than a two seconds satellite forbe OSIRIS. platform, able The to the vertical draw scan conclusions read-out speed aboutserved is which frequency more scan as cannot speed flexible. input To to to be use, the the tomographiceasily simulated retrieval observations algorithm. be In changed this and way, the finallyemission parameters could tweaked profile. to As match a thevertical result, best resolution recovery were the of obtained best for the retrievals a input scan in volume speed terms of of 0.5 kms combined horizontal and is performed onto the observation gridis creating containing a retrieval the grid, recovered 500mbased cloud on the structure. observation The geometry. grid cell sizesthe have read-out been frequency optimized of the limb spectra. Since there is a limit on the exposure times interpolated to an observation grid, 125m 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . A dotted ◦ 0.01 × e scattering (Llewellyn et al., ffl 3704 3703 ects result, e.g. from sensitivity of the instrument optics to radi- ff ects. Instrumental e The tomographic mode was uploaded to Odin/OSIRIS to be used during a total There are two primary scan modes for the atmospheric mission: the stratospheric In order to extract PMC properties, the pure cloud radiance needs to be separated OSIRIS is designed to retrieve altitude profiles of atmospheric minor species by ob- ff tude pair. The result has been interpolated to a resolution of 100m 5 Data and retrieval Figure 7 showssponding an tomographic example recovery. The of datatechnique an in discussed the OSIRIS above to top observation make panel aume set was two-dimensional emission tomographic used together as retrieval together of a with with the functionmiddle vol- the of the panel altitude corre- and of angle Fig. along 7, the where satellite each track, shown angle in corresponds the to a unique latitude and longi- radial distance from the centre of the Earth andof angle along 270 the orbits satellite (these track. AIM/CIPS, orbits further were discussed chosen below).the as In PMC to this altitudes provide and way, Odin coincident maximize the could measurements number focus with of more lines intensely of sight on through the cloud. of 2010–2011 and thewas southern incorporated summer of for 2011/2012 thethe a orbit simulations special presented numbers above “tomographic shown and mode” first concentrated in period on Table (2010) the 1. and altitudes 77 Thisscans, 73 to to mode the 88 88 km horizontal was km for for distance based theThis the between on rest strongly subsequent of increased the scans the orbits. numbersequently, was By of allowed significantly performing lines for reduced. these of a short sightmake tomographic through a analysis a two-dimensional given using retrieval volume the of and, technique the con- volume outlined emission above rate to profile as a function of peak OSIRIS PMC radiances shown in Sect. 5. mode where theand lines the of stratospheric/mesospheric sight modeOdin cover where usually altitudes the operates between altitudes in 7–67 7–107 one km km of are of these covered. the two atmosphere modes, but during the northern summers these uncertainties in the PMC limb data can be estimated to be less than 1 % of the altitude ranges above andscattering below background is the calculated PMCtering in are by terms an not of atmospheric available. thebackground density Instead, altitude-dependent is profile taken Rayleigh the as from scat- molecular the thescans mean MSIS during value the climatology. of days The the before background instrumental then and obtained subtracted after from from the ordinary the tomography limb measured scans.signal These total as backgrounds limb are radiance input in to order theinstrumental to tomographic background obtain retrieval. the introduces This pure uncertainties use PMC ability as of of “climatological” it these molecular ignores parameters. and Based the on scan-to-scan ordinary vari- non-tomographic PMC measurements, ranges below and abovethen the PMC readily layer. be Molecular(Karlsson and discriminated and instrumental by Gumbel, background fitting 2005). can centrated This the tomography procedure data scans is in applied notare in these possible restricted the in cloud-free to the present the altitude case work. narrow ranges of As altitude the the region con- tomographic of scans the PMC, background fits to cloud-free free from perturbing airglowthe and current work auroral we emissions have (Karlsson averaged over and the Gumbel, wavelength interval 2005).from 302.8–305.9 In nm. the background radiatione due to molecular Rayleighation scattering from and below the instrumental nominal2004). field-of-view Odin’s in ordinary terms PMC of analysis ba the uses lower limb thermosphere. scans This provides ranging limb from radiance the profiles troposphere covering to extensive height serving limb-radiance profiles. Thesunlight optical over spectrograph the range obtainsFor 275–810 spectra nm the of with analysis scattered a of spectralabsorption PMCs, resolution by stratospheric of mainly ozone approximately ultraviolet at 1upwelling wavelengths these nm. radiation. wavelengths below Below prevents 310 310 complications nm nm due several to are wavelength intervals used can be as chosen that are 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | krhu6073/ ∼ erent lines of sight ff http://people.su.se/ 3706 3705 ects. ff ected by gravity waves with periods less than 5 min (Witt, ff erent. Also, the relative magnitudes of the retrieved features ff .) . Odin is placed in an orbit perpendicular to the AIM strips. In addition, the two 2 erent from the features seen in the measurements. (A complete collection of the ff The altitude region under examination in this paper is also the transition region be- Work is currently also conducted to compare the retrieved PMC structures to images As noted earlier, only OSIRIS UV data around 304.3 nm are analyzed in this paper. To check the consistency of the algorithm, the recovered emissions have also been As noted earlier, the temporal scale for sampling a specific cloud volume at 85 km A comparison of the two top panels shows that the clouds have been localized in with limb imaging would be essential. In this scenario, the algorithm presented in this above, are currently being comparedThe and used tomographic in retrievals are a co-analysis providingplement of good the the sources very two for detailed instruments. vertical horizontal information structures to provided com- by CIPS. tween the middlecontrolled and by upper wave dynamics atmosphere. fromin The below, the while state thermosphere and waves and ionosphere. actingof The variability upward PMC information cause region of for variability is research this therefore that anorder region important aims to source at is address merging the the entire middle wave and spectrum upper of atmosphere. this In region, tomography in combination of 25 m satellites have very similarin orbital common periods, volume hence during providing overlappingThe parts coincident coincident of measurements about measurements 30 during sequentialmographic the modes orbits per in total 30 the of days. northern the hemispheric 270 summers of events 2010 provided and by 2011, the discussed to- By utilizing a broader wavelength range,PMC spectral particle analysis can sizes. reveal information Ongoinggraphic about work analysis to thus the concernswavelength spatial intervals the distribution in possibility of the to particle ultraviolet. extend sizes by the using tomo- datacollected from by several the CIPS instrumentager aboard providing the 900 AIM km satellite. wide CIPS orbit is strips a that nadir contains pointing albedo im- of PMCs with a resolution a higher speed andfocusing thus on obtain tomographic a methods, is much toa better be two-dimensional horizontal planned, imager resolution. the to ideal Ifview produce scenario a would three-dimensional would new be retrievals. also mission, to Including enhance use theaccommodate the nadir for measurements. the albedo However, one e would then also need to simultaneously. This would provide the possibility to sample the region of interest at mized for tomographic applications. A futureneed instrument dedicated an to tomography would imaging device that could sample brightness along di 6 Discussion and conclusions With this work wegations have of demonstrated middle the atmosphericsatellite. possibility phenomena The using to motivation the perform for OSIRIS tomographicysis this instrument of investi- work on has PMCs. the been Thereforethe Odin the to Odin conduct settings platform the of and first the the tomographic algorithm OSIRIS anal- presented instrument. here However, are the Odin specific mission for is not opti- and hence that the algorithm is consistent. is about 5 min. PMCs1961), are but a at the horizontalered scales not to resolved provide by any the complications. algorithm this time scale is consid- tomoOS/ used as a base tocoveries predict of OSIRIS OSIRIS measurements. observations In aregrid. other used words, as Simulated the the measurements tomographic emissions re- predictions contained are of in then the the observations. emission performed Theseof using predictions Fig. are these 7 exemplified and recoveries, in it the yielding bottom can panel be seen that the predictions agree well with the real observations plots from the orbits listed in Table 1 can be found on ments. the retrievals. As compared tosimilar the but original noticeably limb di data,are the di retrieved PMC structures are saw-tooth shaped pattern is showing the tangent positions of the original measure- 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , doi:10.1139/p01-157 ´ eele, F., and Nordh, L.: 100 km horizontally and ´ e, L., Smith, K., Warshaw, ´ egie, G., Hauchecorne, A., ∼ doi:10.1016/j.jastp.2008.10.011 oen, E., Kaminski, J., Evans, W. F. J., Puckrin, ¨ a, E., Auvinen, H., and Oikarinen, L.: Review: ffi ¨ ol 3708 3707 ¨ e, J., Ricaud, P., Baron, P., Pardo, J. R., Hauchcorne, A., , 1986. ¨ oe, J., Ricaud, P., Frisk, U., Sjoberg, F., von Sch We would like to thank SSC for making tomographic scans with ¨ a, E., Oikarinen, L., Leppelmeier, G. W., Auvinen, H., M ¨ ol ´ enez, C., Megie, G., de la No ` evre, F., de La N nightglow, J. Geophys. 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Space Res., 36, 935–942, 2005. Wiensz, J. T., Ivanov, E. V., McDade,Savigny, C., I. Sioris, C., C. Solheim, E., B. McLinden, C. H.,E., A., McConnell, Gri Strong, J. C., K., Haley, C.Brohede, S., Wehrle, S., von V., Stegman, Hum, J., Witt,G., R. G., Deslauniers, H., Barnes, D.-L., G., Kendall, Marchand, Payne, D. W. P., Richardson, F., Pich J. E. W., H., Matsushita, King, R. J., A., Murtagh, Wevers, D. I., McCreath, P., and maximum probability, Can. J. Phys., 67, 89–94, 1989. 2009. 630 nm emission, J. Geophys. Res., 106, 21367–21380, 2001. thesis, University of Saskatchewan, Saskatoon, 1999. a satellite platform, Appl. Opt., 42, 1441–1450, 2003. atmospheric band with the OSIRIS infrared imager, Can. J. Phys., 82, 501–515, 2004. Witt, G.: Height, structure and displacements of noctilucent clouds, Tellus, 14, 1–18, 1962. Thomas, R. J. and Donahue, T. M.: Analysis of Ogo 6 observations of the OI 5577 – a tropical Shepp, L. A. and Vardi, Y.: Maximum likelihood reconsruction for positron emission tomography, Radon, J. and Parks, P. C. (Translator): On the determination of functions from Murtagh, D., Frisk, U., Merino, F., Ridal, M., Jonsson, A., Stegman, J., Witt, G., Eriksson, P., McDade, I. C. and Llewellyn, E. J.: Satellite airglow limb tomography: methods for recovering McClintock, W. E., Rusch, D. W., Thomas, G. E., Merkel, A. W., Lankton, M. R., Drake, V. A., Llewellyn, E. J., Lloyd, N. D., Degenstein, D. A., Gattinger, R. L., Petelina, S. V., Bourassa, A. E., Karlsson, B. and Gumbel, J.: Challenges in the limb retrieval of noctilucent cloud properties Lloyd, N. and Llewellyn, E. J.: Deconvolution of blurred images using photon counting statistics Herman, G. T.: Fundamentals of Computerized Tomography: Image Reconstruction From Pro- Frey, S., Mende, S. B., and Frey, H. U.: Satellite limb tomography applied to airglow of the Degenstein, D. A., Llewellyn, E. J., and Lloyd, N. D.: Tomographic retrieval of the oxygen infrared Degenstein, D. A., Llewellyn, E. J., and Lloyd, N. D.: Volume emission rate tomography from Degenstein, D. A.: Atmospheric volume emission tomography from a satellite platform, PhD Acknowledgements. Odin/OSIRIS possible. OSIRISthank is the funded Climate Research in Schoolproject. (CRS) part within by the Bert the Bolin Canadian Centre for Space partially funding Agency. the We also References 1 km vertically. Using athree two dimensional dimensional tomographic imager retrieval. would also provide a base for a future paper would be able to reproduce wave signatures of down to 5 5 25 20 15 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) along which line integrals y , x ( f 3710 3709 15–17 Jun 201014–16 Jul 2010 50775–50804 12–14 Aug 2010 51209–51238 15–17 Jun 2011 51642–51671 17–19 Jul 2011 56233–56261 18–20 Aug 2011 56711–56740 29–30 Nov 57190–57219 20117–9 Jan 2012 58729–58757 14–16 Feb 2012 59911–59925 59313–59343 Days Orbit numbers Orbit numbers and days covered by the tomographic mode of Odin. A set of discrete paths through a given point in a field can be calculated. If thecan angles be between solved successive for lines by of the this inverse type Radon are transform. infinitesimal, the field Fig. 1. Table 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3712 3711 A two-dimensional emission grid used for multiple purposes, explained in the text (not The viewing interval for tangent lines through a point at 85 km over which line integrals to scale). Fig. 3. Fig. 2. can be calculated. Thepoint points can 1 be and seen 2 (to represent scale). the limiting satellite positions from where this Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3714 3713 The steps through a simulated OSIRIS tomography retrieval; the top panel shows an A block diagram of the tomographic algorithm. Fig. 5. arbitrarily created emission profile,file a but “test with PMC”, a andOSIRIS resolution the observations corresponding second using to panel thethe shows the test tangent the retrieval PMC point) same grid. as and pro- Thesurements input the third through (with bottom the panel both tomography panel shows algorithm. axes shows simulated referring the to retrieved the structure position after running of the mea- Fig. 4. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3716 3715 An example of the tomographic retrieval using real OSIRIS data. The top panel shows Integrated vertical and horizontal cross sections of simulated OSIRIS observations. The the OSIRIS observations plotted asshows tangent altitude the vs. angle resulting alongshows structure the predictions orbit. from of The OSIRIS middle running measurements panel using the recovered retrieval emissions, for on consistency. the top data. The bottom panel Fig. 7. dashed lines shows emissions fromresult the from second the panel bottom of panel. Fig. 5 and the solid lines the retrieved Fig. 6.