Author Institution: National Security Technologies, LLCSlides presented at the 3nd Annual Photonic Doppler Velocimetry (PDV) Conference and Workshop held at Sandia National Laboratories, Albuquerque, New Mexico, September 3-4, 2008

Berninger, Michael

Diaz, Abel B.

Gallegos, Cenobio H.

Sanders, Fred

Teel, Matthew G.

Tunnell, Thomas W.

KnowledgeBank at OSU

Page 1Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008SUBNANOSECOND ANALYSIS OF COMPLEXVELOCITY PROFILESAbel Diaz, Thomas W. Tunnell, Cenobio Gallegos, Michael Berninger, Matthew Teel, Fred SandersNational Security Technologies, LLC, Los Alamos Operations,Los Alamos, NM 87544This work describes progress at the Los Alamos Operations (LAO) of National Securities Technology (NSTec) in developing sub-nanosecond analysis capability for Photon Doppler Velocimetry (PDV)/triature data. We are developing analysis techniques that will ultimately provide fine time resolution for PDV/triature data. The application of these techniques to simulated data and laser-driven shock data are presented. The simulated data were generated with a “complex” velocity profile provided by Los Alamos National Laboratory to help determine uncertainties on expected velocity profiles of interest. The simulated triature data include gain and phase discrepancies that might be expected in actual data. The triature analysis flow applies a forward modeling technique to resolve these gain and phase discrepancies. Using the resolved gain and phase discrepancies, the fine time resolution techniques successfully extract rise times of a few hundred picoseconds (and less) for the simulated data. Pre- and post-experiment characterization techniques to resolve gain and phase discrepancies are also described here, although the analysis has the capability to extract such information from data. In addition, NSTec applied these analysis capabilities to laser-driven shock data to extract velocities of 2,500 m/s with subnanosecond rise times. Comparisons of these analysis results are made with corresponding VISAR diagnostic results.This work was done by National Security Technologies, LLC, under Contract No. DE-AC52-06NA25946 with the U.S. Department of Energy.Page 2Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Outline• Adaptive Down Conversion• VISAR – Like analysis• Omega filter analysis• Simulation with Results• Triature• Forward Modeling• Lissajous• Triature Results (with Single PDV)• VISAR Results• ConclusionPage 3Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Single Channel Analysis: Adaptive Down Conversion1. Interpolate data with FFT approach to double sample frequency 2. Compute FFT power spectrum at greatest overlap as possible. 3. Extract velocity and bandwidth as function of time4. Convert to frequency5. Integrate to obtain phase, Ɏ(t)6. Compute mixing functions cos(Ɏ(t)) and sin(Ɏ(t))7. Multiply each mixing function by the data, D(t)8. Low pass filter the products, PC(t) and PS(t)9. Regenerate data using sin(Ɏ(t)) and cos(Ɏ(t)) mixing functionIn phase, Out of Phase, Compute phase as Refined velocity asWe use polynomial fit to calculate time derivative( ) ( ) 2)()(sin)()(cos)()( tDttPSttPCtI ≈Φ−Φ=( ) ( )degrees 90by  phase ofout  2)()(sin)()(cos)()(tDttPCttPStQ≈Φ+Φ=( ))()(tan)( tItQat =φ( ) ( )dttdtv )(22)( Φ=piλPage 4Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Single Channel Analysis: VISAR Like( ) ( ) ( )( )( ) ( ) ( )( )( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )( )( ) ( ) ( )( )n)calculatio slopepoint   twot to(equivalen VISARin  Astan4asVelocity  Unfold2tan/ :Note2sin                and ,2cos Generatesin phase, ofOut and ,cos phase,In :sets data Begin with1¸¸¹·¨¨©§′+′′−′¸¹·¨©§∆=∆=′+′′−′∆+=+=′∆+=+=′==−QQIIQIIQttvtfQQIIQIIQtfttAdttQtQtfttAdttItIttAtQttAtIpiλpipiφpiφφφPage 5Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Single Channel Analysis: Omega FilterFrom Wikipedia, the free encyclopediaPage 6Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Single Channel Analysis: Omega Filter, cntd( ) ( ) ( )( ) ( ) ( ) ( )( )( ) ( ) ( )( ) ( )( ) ( )( ) ( )( )( ) ( )( )( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( )ttvtitqtqtittitqtqtitqtittAtQtqttAtItitQtItAttAtQttAtIωpiλωωωφφφφωωωω¸¹·¨©§=−==−=====+===4 as velocity Compute, that Notely.respective , and ,as  and  of sderivative  timecompute filter to Omega Usesin and cos  :Normalizesin phase, ofOut  and ,cos phase,In :sets data Begin with22Page 7Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Simulation provided by Michael Furlanetto.ADC at 800MHz bandwidthPage 8Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008ADC at 800MHz bandwidthPage 9Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Triature: Phase/Gain CharacterizationsPage 10Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Triature: Issuesdelays  timeduncorrecte    resolvedgains    detectorsin   Response           resolved120 be shouldsplitter     phasesin  iesUncertaint•→•→• $Page 11Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Triature: Forward Modeling( ) ( ) ,stationary is 03 Channel assume and 4cos4sin :1 Channel Begin with       Results) (ADC 3 Channel with 1 Channel Model :Example       another.by  channel one modelingby  channels Triaturebetween  gains and phases relative Finding11 pipi QI +( ) ( )( ) ( ).sin            cossin                       cos13113133φφφφφφ∆−=∆−===QIQI, and  of in terms  Find 331 QII ( )( ) ( ) ( ) ( )( ) ( )( )( ) ( ) ( ) ( )( ) ( ).sincossincoscossinsinsincossinsincoscoscos1331331313131133133131311φφφφφφφφφφφφφφφφ∆−∆=∆−∆=∆−=∆+∆=∆+∆=∆−=IQQQII1, Channelfit   tousedFunction ( ) ( )$120 and initialy  where4cos4sin132121232313113113=∆++=+=¦¦¦¦ φpipiQIQIgQgIgFPage 12Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Triature: Forward Modeling, continued. and  findcan  weSimilarly  . and  parameters get the fit webest   theFrom 12121313 φφ ∆∆ gg( )( ) ( ) ( )( ) ( ) ( )1311311312112112sincosIcos03sincosI cos02cos01φφφφφφφφφ∆+∆=∆−=∆−∆=∆+==QChQChCh can write,  wedata Triature  theFrom( ) ( )( ) ( ) ( ) ( )( ) ( )( ) ( ) ( ) ( )121313121212121313121213cossincossincos02cos03sincossincossin03sin02φφφφφφφφφφφφ∆∆+∆∆∆+∆=∆∆+∆∆∆+∆=ChChQChChIcompositecompositeget,  wealgebra some DoingPage 13Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Triature: Lissajous (as suggested by Will Hemsing)Powder Gun Shot  OctoberInterval 1c h0 1/ ch 02120.63o± 13.15c h0 2/ ch 03125.33o± 17.88c h0 3/ ch 01124.98o± 22.45(1.63 - 1.68)µsInterval 2120.69o± 1.94118.64o± 2.18120.40o± 1.76(1.68 - 1.72)µsInterval 3118.92o± 1.72118.51o± 1.78122.60o± 2.08(1.72 - 1.77)µsInterval 4117.11o± 1.86117.89o± 1.86125.06o± 2.28(1.77 - 1.81)µsInterval 5116.82o± 2.02114.93o± 2.82128.27o± 2.19(1.81 - 1.86)µsInterval 6116.42o± 3.36107.33o± 2.65135.99o± 3.54(1.86 - 1.90)µsInterval 7103.28o± 5.21113.44o± 2.31144.11o± 4.36(1.90 - 1.95)µsInterval 893.50o± 3.46121.70o± 3.48144.94o± 6.80(1.95 - 1.99)µsInterval 9102.02o± 2.85125.05o± 2.00132.31o± 2.60(1.99 - 2.04)µsInterval 10108.09o± 2.57123.05o± 1.68129.39o± 1.99(2.04 - 2.08)µsInterval 11112.70o± 2.67124.63o± 2.25123.02o± 2.52(2.08 - 2.13)µsInterval 12113.93o± 2.49122.65o± 2.45123.08o± 3.16(2.13 - 2.17)µsInterval 13115.52o± 3.35118.38o± 2.34125.74o± 1.79(2.17 - 2.22)µsInterval 14121.21o± 9.44113.49o± 18.32124.60o± 9.00(2.22 - 2.26)µsInterval 15125.40o± 5.45115.00o± 6.28119.77o± 8.42(2.26 - 2.31)µsInterval 16122.97o± 3.05113.52o± 5.24123.48o± 4.14(2.31 - 2.35)µsInterval 17121.73o± 4.51122.78o± 2.59116.03o± 5.35(2.35 - 2.40)µsInterval 18122.80o± 5.01124.91o± 2.95112.05o± 6.62(2.40 - 2.44)µsInterval 19121.41o± 2.99123.24o± 1.81115.44o± 2.39(2.44 - 2.49)µsInterval 20121.95o± 2.99125.63o± 2.77112.58o± 4.36(2.49 - 2.53)µs1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.60200400600800100012001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20µsm/ sSHOT_DET1_S200_000.dig.txt~Velocity(BP6.00MHz I).txt  VelocityTime rangesPage 14Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Data vs. Model-9 -8 -7 -6 -5 -4 -3x 10-9-0.4-0.3-0.2-0.100.10.20.3Break OutTime (s)Vo lt s ( V)  Channel 1 (filtered data)I composite (model)Page 15Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008-8.6 -8.4 -8.2 -8 -7.8 -7.6x 10-95001000150020002500Laser Driven Shot Data 07.16.08 [Shot 10]Time (s)Ve lo ci t y ( m/ s)  VISAR-Like [ADCVL]Triature [300ps smoothing]1 nsPage 16Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 20082008-20-08 shot 2SaturatedFringes not added past this point in time.Page 17Vision – Service - PartnershipPDV Workshop, Albuquerque, NM, September 3-4, 2008Conclusions• Sub-nanosecond time resolution in single PDV and Triature analysis.• Need to finalize tools for ADC processing.• Forward modeling recovers phase shifts and gains of Triature data. Need technique to resolve time delays. • Lissajous methods support Triature results.• Resolve “ringing” in Triature (possibly due to baseline or uncorrected time delays).

Sub-nanosecond Analysis of Complex Velocities

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Sub-nanosecond Analysis of Complex Velocities

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