Simultaneous broadband laser ranging and photonic Doppler velocimetry for

Transcription

1 DOE/NV/ Simultaneous broadband laser ranging and photonic Doppler velocimetry for dynamic compression experiments B. M. La Lone, 1,a) B. R. Marshall, 1 E. K. Miller, 1 G. D. Stevens, 1 W. D. Turley, 1 L. R. Veeser 2 1 National Security Technologies, LLC, Special Technologies Laboratory, Santa Barbara, California 93111, USA 2 National Security Technologies, LLC, Los Alamos Operations, Los Alamos, New Mexico 87544, USA A diagnostic was developed to simultaneously measure both the distance and velocity of rapidly moving surfaces in dynamic compression experiments, specifically non-planar experiments where integrating the velocity in one direction does not always give the material position accurately. The diagnostic is constructed mainly from fiber-optic telecommunications components. The distance measurement is based on a technique described by Xia and Zhang [Opt. Express 18, 4118 (2010)], which determines the target distance every 20 ns and is independent of the target speed. We have extended the full range of the diagnostic to several centimeters to allow its use in dynamic experiments, and we multiplexed it with a photonic Doppler velocimetry (PDV) system so that distance and velocity histories can be measured simultaneously using one fiber-optic probe. The diagnostic was demonstrated on a spinning square cylinder to show how integrating a PDV record can give an incorrect surface position and how the ranging diagnostic described here obtains it directly. The diagnostic was also tested on an explosive experiment where copper fragments and surface ejecta were identified in both the distance and velocity signals. We show how the distance measurements complement the velocity data. Potential applications are discussed. a) Author to whom correspondence should be addressed: Electronic mail: lalonebm@nv.doe.gov. 1

2 I. INTRODUCTION Optical velocimetry measurements are central to nearly all dynamic experiments, from wave profile measurements in simple 1-D plate impact experiments to assessing the drive shape for imploding capsules at the National Ignition Facility. In many non-planar experiments, time-resolved surface position is also desired for comparison with hydrodynamic models and other diagnostics, such as radiography, but the position cannot always be obtained from the velocity data. In general, the surface distance cannot be found by integrating the measured surface velocity because velocimetry techniques such as VISAR 1 or PDV 2 measure only one component (parallel to the probe axis) of the surface velocity, and the direction of motion can be unknown or changing. Examples of dynamic events with significant off-normal motion are imploding (or expanding) cylindrical liners, 3 explosively driven frangible joints, 4 shaped charge liners, imploding hemispheres, 5 and expanding cylinder tests. 6, 7 Another problem with integrating the velocity is that sometimes new material, such as ejecta or target fragments, enters the field of view of the probe, and there is no reference position for this material. These limitations of velocity measurements have been discussed previously. 6,8,9 To obtain position information directly in dynamic experiments, researchers have relied on x-ray and optical imaging techniques or on arrival time measurements, such as with piezoelectric and electrical shorting pins. However, these are limited to a few snapshots in time in the case of imaging or a few discrete position points in the case of impact fiducial times. Therefore, a continuous time history of the surface position is still desired. Optical distance measurements in dynamic compression experiments are challenging because surfaces can be moving at many kilometers per second, and experiments occur on relatively small length (~1 mm) and time (~1 µs) scales. Therefore, a ranging diagnostic for dynamic experiments should have time resolution << 1 µs and position accuracy << 1 mm. Recently, Briggs et al. have demonstrated a frequency swept LIDAR technique on a moving projectile, 10 but the relatively low sampling rates and sensitivity to the Doppler shift are limitations for dynamic applications. 11 They are also exploring a technique based on the phase detection of a modulated light source. 6 This technique may be used in future dynamic experiments, but it will be limited to experiments with a single, well defined surface, and 2

3 obtaining accuracy to better than 100 µm may be a challenge. Weng et al. 12 recently demonstrated a fast ranging diagnostic with distance precision of < 1 µm; it records a white light interference spectrum with a high-speed streak camera and relays the light source to the target and from the target to the streak camera over a photonic crystal fiber. This approach may be useful for some dynamic applications. An alternative optical ranging technique that operates on a similar principle was developed earlier by Xia and Zhang. 13,14 They constructed an interferometric optical ranging method based mainly on fiber telecommunications components. A wide-spectrum, mode-locked fiber laser was used as the light source, and the interference spectrum was converted into the time domain with a dispersive element so that the entire spectrum could be recorded on a single photoreceiver. Their ranging technique is insensitive to the Doppler shift, is sampled every 20 ns, and was demonstrated in quasi-static applications with a measurement precision of 1.5 µm. In this work we adapted the Xia and Zhang technique to dynamic experiments by extending the full range to several centimeters. To obtain a simultaneous velocity measurement along a single probe s optical axis we added a PDV system. 2,15 We demonstrated the combined distance and velocimetry diagnostic on a spinning square cylinder and on an explosively driven copper surface. Both experiments demonstrate that the added distance measurement provides information that cannot be obtained from velocity data alone. II. TECHNIQUE FOR SIMULTANEOUS DISTANCE AND VELOCITY MEASUREMENT A diagram of the diagnostic is shown in Fig. 1. It is constructed almost entirely from fiber-optic telecommunications components. A mode-locked fiber laser made by either PolarOnyx 16 or Menlo, 17 with a short temporal pulse of < 1 ps and a wide spectral width of ~ 80 nm (10 THz), sends pulses of laser light through a fiber-based Mach-Zehnder interferometer. The target leg of the interferometer contains a circulator that sends and receives signals from the target via a collimating probe. The path length in the target leg is dependent on the target distance along the probe axis. The other leg of the interferometer is a fixed reference. The reference leg contains a variable delay to adjust the relative path lengths and a 3

4 polarization controller for fine tuning of the polarization, but these have been omitted in the figure for clarity. After the light in the target and reference legs recombines and interferes, a dispersive element converts the interference spectrum into the time domain for high-speed recording. We used either 35.3 or 70.6 km of Corning single-mode optical fiber 18 for chromatic dispersion of the signals. After dispersion, the signals are detected with a fast photoreceiver and digitizing oscilloscope with a combined 18 GHz bandwidth. Experiments using the PolarOnyx laser have a laser repetition rate of 50 MHz. When using the Menlo laser, a pulse picker divides the repetition rate down from 100 MHz to 25 MHz to prevent the pulses from overlapping during detection. Erbium-doped fiber amplifiers (EDFA) 19 are placed before and after the interferometer to increase signal levels. The amplifiers cause the spectral width to be narrower than the laser output so that the actual spectral width used is about 35 nm (4.5 THz). A single ITU 20 channel add/drop filter is inserted into the probe leg of the interferometer to multiplex a PDV system with the ranging measurement. Our PDV system operates at a wavelength of nm and this wavelength takes a different path through the add/drop filter than other wavelengths as indicated in Fig. 1. The PDV shares the probe optics, but otherwise it is a separate system that is recorded with a separate photoreceiver and digitizer channel. A recorded ranging signal for a single pulse leaving the fiber spool is shown in Fig. 2. Such pulses arrive either every 20 or 40 ns, depending on the repetition rate of the laser and pulse picker. The difference in path lengths between the target and reference legs sets up an interference pattern in the recorded spectral time history. The interference pattern in Fig. 2 was recorded with a target distance of 1.6 mm from the balance point of the interferometer and 35 km of dispersion fiber for converting the spectrum into the time domain. The missing interference near 5.5 ns is caused by the add/drop filter removing light with optical frequencies near the THz PDV-laser frequency. During analysis of the experimental data, the spacing between constructively interfering optical frequencies (Δν) determines the target s distance (d) from the balance point of the interferometer d = c/2δν, where c is the velocity of 4

5 light. Since the spectrum is recorded in the time-domain, the optical frequency spacing is detected as a beat frequency (F) on the photoreceiver, F = (dν/dt) / Δν, (1) where dν/dt is the optical frequency vs. time slope determined by the amount of dispersion in the spool of optical fiber. Therefore, d is proportional to the measured beat frequency, d = F c/[2(dν/dt)]. (2) Because the pulses have undergone negligible dispersion (<1/1000 of the total pulse dispersion) before reflecting from the target, the beat frequency in the recorded signal is independent of the Doppler shift and is a function of only the target distance. 13 It is assumed in deriving Eqs. (1) and (2) that the chromatic dispersion in the fiber is linear so that dν/dt is a constant. However, the chromatic dispersion in the optical fiber used here is slightly nonlinear. Fig. 3 shows measured optical frequencies and their divergence from linear as a function of time for 35.3 km of fiber. As discuss by Xia and Zhang, 12 this nonlinearity can be compensated for in the analysis; otherwise there will be a slight chirp in the beat frequency across a single pulse. We removed the nonlinear chromatic dispersion of the fiber by remapping time for each pulse to the adjusted variable t* = t + a t 2, where the variable a is chosen to compensate for the third-order fiber dispersion. Fig. 3 also shows the fiber dispersion data plotted as a function of t*. A linear fit to the optical frequency versus t* is an excellent match. We also tried using a higher order polynomial for remapping time, and this change resulted in only a slight improvement over the second order polynomial fit. It is important to note that since this is a correction for the nonlinear dispersion in the fiber spool, the time remap is independent of the target distance. For analysis of the experimental range data, we transform each recorded pulse to the t* domain and then perform a Fast Fourier Transform (FFT) to obtain the beat frequency. The beat frequencies are converted to positions using a calibration that was done prior to the experiment. This procedure generates a position spectrogram. For 35 km of fiber for dispersion, the distance-beat frequency calibration slope is about 0.6 mm/ghz; for 70 km of fiber it is about 1.2 mm/ghz. With 70 km of fiber for dispersion, the 5

6 maximum detectable target distance (d) is 22 mm with a recorded beat frequency of 18 GHz. Since a target can be tracked from d to +d, the diagnostic can track the position over a range of 44 mm if the balance point is centered initially in the target range. The PDV data are analyzed using a sliding window FFT. 2 We named the diagnostic simultaneous broadband laser ranging (BLR) and PDV. III. EXPERIMENTS We performed two kinds of experiments with the BLR-PDV diagnostic. First we measured the distance to the surface of a spinning square cylinder and the surface velocity in the probe direction. As was pointed out by Dolan, 8,9 a PDV or VISAR system measures only one component of the velocity and does not give the derivative of the distance-time curve for a spinning object. First, we performed the spinning square cylinder measurement to illustrate how the BLR technique records the true distance and how this differs from an integrated velocity measurement. The second experiment measured the distance and velocity of a copper target in an explosive experiment. It demonstrates that the BLR-PDV diagnostic can be fielded on dynamic experiments and shows how it can provide complementary information to the velocimetry data. The explosive experiment also verifies the Doppler insensitivity of the BLR technique. We operated the BLR-PDV diagnostic with a stronger reference signal than the signal returning from the target to increase the heterodyne gain. Heterodyne gain provides high dynamic range and enables experiments with large (and time-varying) fluctuations in return light levels. For the BLR technique, we typically launched about +15 dbm of optical power toward the target and about 10 dbm of optical power into the reference leg of the interferometer. Target reflection and scattering losses ranged from 40 to 60 db so that 25 to 45 dbm of power was returned from the target and mixed with the reference. The second EDFA amplified the mixed signal to about +0 dbm before it entered the fiber spools. The PDV system was operated with approximately +20 dbm of optical power launched toward the target and 2 dbm or reference local oscillator power. A. Spinning square cylinder 6

7 For the spinning square cylinder experiment, we used the BLR-PDV diagnostic to measure both the distance and velocity of the surface as the target rotates. The square cylinder in the experimental setup is shown in Fig. 4a. The square cylinder was made from an 11 mm diameter aluminum rod with its sides partially cut away, leaving rounded corners. It was mounted in a high-speed drill press and spun at a constant angular rate of about 12,000 rpm. The surface finish was diffuse so that it returned some of the reflected light to the probe at all surface angles. A collimating probe, used to send and receive signals between the BLR/PDV optical fibers and the surface, had its axis offset from the rotation axis by 2.2 mm. When the probe was viewing one of the rounded corners, the distance remained fixed, but when a flat side came into view, the distance would first decrease and then increase as shown by the calculation in Fig. 4b. The distance calculation is detailed in Appendix A. The measured velocity spectrogram from the spinning square experiment is shown in Fig. 5a. The square rotates about 90 in the times shown; two of the corners and one of the flat faces are viewed in this time window. Regardless of which portion of the square is being viewed, the velocity measured with PDV is a constant value of about 2.6 m/s and gives no indication of the shape of the object. A constant velocity was observed in previous work for a spinning cam shaft, and will always be observed 8,9 for an arbitrarily shaped object rotating about a fixed axis at a constant angular velocity (Appendix A). The distance spectrogram for the spinning square experiment is shown in Fig. 5b in the same time window as the velocity spectrogram. The signal intensity varies by more than 20 db, requiring us to display a large dynamic range in the spectrogram to show data at all times. This variation is responsible for the noise and artifacts between about 0.5 and 0.8 milliseconds when the signal return is the strongest. The distance spectrogram gives the true distance of the intersection between the square object and the probe axis. The distance calculated from geometry (Appendix A) is also shown in Fig. 5b and is an excellent fit to the data, deviating from the measurement by less than 40 µm. We believe that this small difference results from an imprecise angular velocity used in the calculation, not from a distance measurement error. It is clear that for the spinning object, the measured velocity is not the derivative of the distance-time history and could not be used to determine the position of the object. Similarly, the time derivative of the BLR 7

8 distance will not give the erroneous constant velocity component seen by the PDV. The BLR technique overcomes a limitation of traditional velocity measurements by directly measuring the dynamic distance to the intersection of the probe light with the material surface, regardless of the surface motion. B. Explosive experiment on copper A diagram of the copper experiment is shown in Fig. 6. An exploding bridge-wire detonator 21 was used as the explosive charge. The copper target was a 2 mm thick by 40 mm diameter copper disk with a diffusely scattering, bead-blasted surface. A small fiber-optic probe was placed about 25 mm from the rear surface of the disk and viewed a spot about 3 mm from the center axis of the detonator. Upon detonation, copper fragments were sent toward the probe at high speeds. Placing the probe off-axis allowed us to observe the effects of the dynamically sweeping point of intersection of the probe light with the spalled and damaged surface. Note that, as in most off-axis dynamic experiments, our sensor does not follow the position of a single object, but instead it responds to whatever reflecting material comes into its line of sight. The PDV velocity spectrogram from the explosive experiment is shown in Fig. 7a. The discontinuous jump in velocity at about 5 µs corresponds to the shock wave breakout at the rear surface. The strongest signal return is from the primary copper surface moving at about 850 m/s. A fainter signal is also observed and is caused by a cloud of ejected material (ejecta), which initially travels faster than the primary surface. Since the surface is still observed through the ejecta, it is somewhat transparent and likely of relatively low density. This experiment was performed in open air so that the ejecta decelerate with time due to air resistance and eventually recollect onto the surface. The recollection occurs at about 20 µs as evidenced by the disappearance of the ejecta signal. It is important to note that the distance between the ejecta and the copper surface cannot be determined from the velocity data prior to the recollection. Just after 30 µs, a second velocity appears at about 600 m/s. At this time the viewing spot of the probe moved off of the primary surface and onto a different copper fragment moving at a lower speed. This is labeled second fragment in Fig.7a. For a few microseconds, both the primary surface and the 8

9 second fragment are viewed simultaneously because of the finite spot size of the laser on the target. Because all of the signals are from material not moving parallel to the probe axis and have uncertain directions of motion, we cannot accurately determine their positions from the velocity data. The distance spectrogram for the explosive experiment is shown in Fig. 7b. The balance point of the interferometer was positioned about 12 mm ahead of the surface, resulting in low-frequency noise centered at 0 mm in the spectrogram. Each signal in the spectrogram appears as both positive and negative values because we cannot distinguish between positive and negative frequencies in the analysis. In Fig. 7b, the upper-left and lower-right portions of the spectrogram are removed to avoid displaying the distances with the wrong sign. All of the same qualitative features are observed in the distance spectrogram as are observed in the velocity spectrogram. Surface motion begins at 5 µs and is observed as an abrupt change in slope of the signal. If the distance measurement were sensitive to the Doppler shift there would have been a step in the distance spectrogram when the velocity changes discontinuously at shock breakout (see Fig. 7a). Ejecta appear as a cloud of material initially separating from the copper surface. The ejecta slow down relative to the free surface because of air resistance, reaching a maximum excursion of about 1.5 mm from the surface, and are eventually recollected. The recollection of ejecta by the surface occurs at near 20 µs and 0 mm in the spectrogram and is somewhat obscured by the low-frequency noise near the zero crossing. After the recollection, the surface is well defined. Measurement precision for each pulse is better than 10 µm for the surface after recollection. After 30 µs, the second fragment that was seen in the velocity is also observed in the distance spectrogram as another signal 4.5 mm behind the primary surface. Similar to the velocity data, both surfaces are viewed simultaneously for a few microseconds because of the finite laser spot size. Unlike in the velocity spectrogram, where the positions of the ejecta and surfaces were ambiguous, the BLR technique obtains the distances directly. IV. SUMMARY AND CONCLUSIONS 9

10 We have developed and successfully demonstrated a diagnostic for recording both the distance and velocity of rapidly moving surfaces in dynamic compression experiments. The diagnostic overcomes the limitation of velocity measurements in determining material distance in non-planar experiments. The diagnostic is an extension of that described by Xia and Zhang 13,14 and is built mainly from telecommunications components. It is compatible with probes typically used for PDV experiments, has high dynamic range, and can record multiple targets simultaneously (including clouds of ejecta). The distance measurement is insensitive to the Doppler shift. The target distance is recorded every 20 or 40 ns with a measurement precision of better than 10 µm. Currently, the diagnostic can track a target for a total distance of 44 mm, but we plan to extend this range in the future. The simultaneous ranging and velocity diagnostic was demonstrated on a spinning square cylinder experiment, in which the velocity measurement gave a constant speed, whereas the ranging measurement showed the true time-varying distance of the cylinder s surface. The diagnostic was also tested on an explosive experiment where the distance and velocity of copper fragments and ejecta were measured. Because of the non-planar geometry of the copper experiment, the positions of these features could not have been obtained from a velocity measurement alone. This BLR-PDV diagnostic has several potential uses in the dynamic compression community. In experiments where the direction of motion is unknown or changing with time, measurements that record only one component of the velocity result in position ambiguity. Our technique overcomes this ambiguity by recording material distance along the probe s optical axis directly. The diagnostic has potential uses in imploding and exploding cylinder or hemisphere experiments, explosive shape charge liner experiments, explosive frangible joint experiments, and perhaps others. The measurement sampling frequency of <100 MHz is probably not high enough for imploding capsule experiments at laser facilities such as Omega or NIF, but future developments may enable experiments at these facilities as well. ACKNOWLEDGMENTS 10

11 We would like to thank Matt Briggs, George Rodriguez, Richard Sandberg, and Joseph Stone of Los Alamos National Laboratory for numerous useful discussions and experimental assistance. We would also like to thank Ed Daykin, Carlos Perez, and Mike Grover of National Security Technologies, LLC, for their experimental assistance. This manuscript has been authored by National Security Technologies, LLC, under Contract No. DE-AC52-06NA25946 with the U.S. Department of Energy and supported by the Site-Directed Research and Development Program. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The U.S. Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( APPENDIX A: VELOCITY AND DISTANCE TO THE SURFACE OF A SPINNING SQUARE CYLINDER This appendix details the calculation of the distance to, and the velocity of, the surface of a spinning square cylinder as measured by a fixed optical probe. A schematic diagram of the experiment is shown in Fig. 8. When the probe views a flat side, the distance from the midpoint of the square cylinder to the intersection between the probe axis and the surface is given by d = b/cosφ + h tanφ, where φ is the angle of rotation of the square. The square cylinder used in our experiments had rounded corners where the radius of the corner was also the radial distance from the center axis to the corners. When the probe is viewing one of the corners, the distance is constant and is given by d = (R 2 h 2 ) 0.5. The velocity of the intersection point between the probe axis and the surface is given by V = ω r, where r is the time varying distance from the center of the square to the contact point, and ω is the angular frequency (ω = dφ/dt) of the spinning square cylinder. The laser-based velocity system (PDV) 11

12 measures only the component of the velocity parallel to the probe axis. Therefore, the PDV records a velocity given by V y = ω r cosθ, where θ is the time varying angle between the probe axis and the velocity vector of the surface at the contact point (as shown in Fig. 8). However, r cosθ = h so that V y = ω h, which is a constant for constant spin rate. This result is independent of the shape of the object as r will always vary with θ in such a way as to keep r cosθ = h for any spinning object rotating about a fixed axis. Therefore, the velocity measured by the PDV system is constant, which is a somewhat surprising result given the complexity of the distance-time history. The apparent discrepancy between the time-varying distance and the constant speed measured by the PDV is a consequence of the probe spot moving across the surface instead of remaining on a single element on the target. References 1 L. M. Barker and R. E. Hollenbach, J. Appl. Phys. 43, 4669 (1972). 2 O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, Rev. Sci. Instrum. 77, (2006). 3 D. H. Dolan, R. W. Lemke, R. D. McBride, M. R. Martin, E. Harding, D. G. Dalton, B. E. Blue, and S. S. Walker, Rev. Sci. Instrum. 84, (2013). 4 D. Wentzel, NASA Johnson Space Center White Sands Test Facility, Private communication (2014). 5 J. R. Danielson, E. P. Daykin, A. B. Diaz, D. L. Doty, B. C. Frogget, M. R. Furlanetto, C. H. Gallegos, M. Gibo, A. Garza, D. B. Holtkamp, M. S. Hutchins, C. Perez, M. Pena, V. T. Romero, M. A. Shinas, M. G. Teel, and L. J. Tabaka, J. Phys.: Conf. Series 500, (2014). 6 M. E. Briggs, E. A. Moro, M. A. Shinas, S. McGrane, and D. Knierim, J. Phys.: Conf. Series 500, (2014). 7 J. W. Ferguson and P. Taylor, J. Phys.: Conf. Series 500, (2014). 8 D. H. Dolan, AIP Conf. Proc. 505, 589 (2000). 9 D. H. Dolan, Rev. Sci. Instrum. 81, (2010). 12

13 10 M. E. Briggs, L. Hull, E. A. Moro, P. W. Younk, and D. Knierim, Proc. 15th Inter. Detonation Symp., (in press, to be published). 11 Most interferometric-based ranging techniques, such as frequency-swept LIDAR, are sensitive to the Doppler shift and have beat frequency contributions from both velocity and position. These contributions can sometimes be difficult to distinguish. For dynamic applications, where surfaces are moving at high velocities, the ideal ranging measurement is insensitive to the Doppler shift. 12 J. Weng, S. Liu, H. Ma, T. Tao, X. Wang, and C. Liu, Rev. Sci. Instrum. 85, (2014). 13 H. Xia and C. Zhang, Opt. Lett. 34, (2009). 14 H. Xia and C. Zhang, Opt. Express 18, 4118 (2010). 15 The configuration of our PDV system is such that the local oscillator is mixed in after the circulator, as in E. A. Moro, J. Phys.: Conf. Series 500, (2014). 16 PolarOnyx, San Jose, CA, model Mercury INS-PM (modified to broaden and flatten the spectrum). 17 Menlo Systems, Munich, Germany, model T-Light FC Femtosecond Fiber Laser. 18 Corning Optical Fiber, Corning, NY, optical fiber type SMF Amonics Limited, Hong Kong, models AEDFA-PA-25 and AEDFA-LP. 20 International Telecommunication Union, Geneva, Switzerland. 21 Teledyne-RISI, Tracy, CA, detonator model RP80. 13

14 FIG. 1. (Color online) Schematic diagram of the simultaneous broadband laser ranging and velocity diagnostic. PDV: photonic Doppler velocimetry system with a photoreceiver and digitizer channel that is separate from the rest of the diagnostic shown; A/D: single-channel optical add/drop filter; CP: collimating probe to relay the light to/from the optical fiber to the target surface; LASER: mode-locked fiber laser and pulse picker; EDFA: erbium-doped fiber amplifiers; FS: fiber spool that is either 35 or 70 km in length; P/D: photoreceiver and digitizer for recording the ranging signals. Arrows indicate the path for a laser pulse as it traverses the fiber interferometer. 14

15 FIG. 2. (Color online) Recorded time-resolved intensity for a single pulse from the broadband laser ranging measurement. The optical frequency spacing Δν is used to calculate the target distance. The missing spectrum at 5.5 ns (193.4 THz) is due to an add/drop filter, which removes reflected PDV light from the target leg of the fiber interferometer. 15

16 Fig. 3. (Color online) Measured dispersion in 35.3 km of optical fiber plotted as optical frequency vs. time (blue dots) and optical frequency vs. adjusted time, t* (red squares). Adjusted time t* is a quadratic function of real time that cancels out the effect of third-order dispersion. The black line is a linear function with a slope of THz/ns. Optical wavelengths are listed on the right axis. 16

17 FIG. 4. (Color online) (a) Photograph of the spinning square experiment. A collimating probe is used to send and receive light from the BLR-PDV diagnostic to and from the surface of the square. Here, the probe was backlit with red light for ease of viewing. A green arrow indicates the rotation direction. (b) A calculation of d as a function of time; see Appendix A. 17

18 FIG. 5. (Color) (a) Velocity spectrogram from the spinning square cylinder measured with the PDV portion of the BLR/PDV diagnostic. Signal strengths are color coded according to the db scale to the right. (b) Distance spectrogram measured simultaneously using the ranging portion of the BLR/PDV diagnostic. The red line in the distance spectrogram is a geometrical calculation. 18

19 FIG. 6. (Color online) Schematic diagram of the measurement on explosively driven copper. The copper is backed by an RP80 detonator. A single probe placed 3 mm off-axis sends and receives laser light between the copper surface and the BLR-PDV diagnostic for recording both the distance and velocity of the surface. After detonation, the copper surface travels at high speeds. A component of the surface velocity is toward the probe. 19

20 FIG. 7. (Color) (a) Velocity spectrogram from the copper surface in the explosive experiment measured with the PDV portion of the BLR/PDV diagnostic. (b) Distance spectrogram of the copper surface measured with the BLR diagnostic. Signal strengths for both figures are color coded according to the db scale in (b). 20

21 FIG. 8 (color online). Schematic drawing of the spinning square cylinder measurement. The green arrow indicates the direction of rotation of the cylinder, φ is its angle of rotation, d is the distance along the probe axis, r is the distance from the cylinder s center to the intersection between the probe axis and the surface, V is the velocity vector of the intersection point of the probe axis and the square cylinder, V y is the component of the velocity along the probe axis (parallel to y-axis), θ is the angle between r and the x-axis and is also the angle between V y and V, h is the offset between the probe axis and the y-axis, b is the distance from the center of the cylinder to an edge, and R is the distance from the center of the cylinder to a corner and is also the radius of the corners. 21

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24 Optical Frequency (THz) Intensity (a.u.) Add/Drop Filter ν Time (ns)

25 Optical Frequency (THz) Freq vs.time Freq vs. Adjusted Time t* = t + a t 2 8 Relative Delay Time (ns) Wavelength (nm)

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