This document summarizes the calibration of the data from the Stardust Dust Flux Monitor Instrument (DFMI) obtained during the Stardust-NExT mission flyby of comet 9P/Tempel 1 (1867 G1). It is intended as a map to the detailed but sparse information available on this topic. It does not cover the full spectrum of instrument operation, instrument calibration and data calibration but is rather a high-level summary of all the information in one place, with pointers to the external documents.
For further details of the DFMI operation and calibration, see the relevant publications: [TUZZOLINOETAL2003]; [GREENETAL2004]; [ECONOMOUETAL2011]; [GREENETAL2011], [TUZZOLINO1994]. Links to some of those documents and/or drafts are in the References section at the end of this document.
The DFMI package comprises four sensors of two types: two PolyVinyliDene Fluoride (PVDF) sensors; two acoustic sensors mounted on the spacecraft Whipple Shield. Both types of sensors, PVDF and acoustic, have a few things in common:
But there the similarities between the PVDF and acoustic sensors end.
N.B., Specifically, it is important to understand that, especially for the acoustic sensors, the events counted in the raw telemetry are not in a direct 1:1 relationship with the number of impacts. See below for more detail.
Instrument calibration is the process of characterizing the performance (i.e. response) of an instrument to input events. It usually involves applying synthetic signals, with a known relationship to events expected during the mission, to an instrument and recording the resultant raw data. The instrument calibration data tie physical phenomena to instrument performance.
There are three aspects to the calibration of the DFMI sensors:
The instrument calibrations of the DFMI sensors were done at ground-based facilities, before launch, using sensors similar to the flight sensors. In this document, the DFMI instrument calibrations will be discussed in detail only as they relate to the data calibration. Refer to the documents mentioned above for details of the ground instrument calibrations.
Data calibration, or calibration of the data, is the process of inverting raw science data telemetry to physical quantities (engineering units) via the instrument characterization obtained from the instrument calibration process. DFMI data calibration converts the raw event counter data to fluences for particles greater than each of several mass thresholds.
The calibrations of PVDF and acoustic sensor data are the two foci of this document.
Fluence is the number of particles per unit effective area (i.e. detected impacts per square meter throughout the flyby). The mass-voltage thresholds' relationships depend on the sensor-particle impact velocities, and, for the acoustic sensor, the mass distribution of the dust particle population (more on this below). All sensor-particle impacts' relative velocities are assumed to be constant and equal to the spacecraft-comet relative velocity (10.9km/s for 9P/Tempel 1; 6.1km/s for 81P/wild 2).
The operation of the PVDF sensor was straightforward. By design the data it returned were nearly direct analogs for fluence and mass distribution.
Impacts on the PVDF sensors generated voltage events that were very short (nanoseconds). This was much shorter than the 2-microsecond time constant of the DFMI electronics (see the figure below). The electronics measured, detected and counted events with voltages above each of four thresholds per sensor. The instrument telemetry returned time-stamped, accumulated counts of these events for each threshold in data packets throughout the flyby encounter; the time between packets ranges from 100ms to 1000ms in increments of 100ms.
Figure 1 from [TUZZOLINO1994] (file dfmi_cal_overview_fig1.png):
Instrument Calibration of the PVDF sensors and electronics was performed on the ground using these methods:
PVDF Mass-Voltage Instrument Calibration
The figures below summarize the results from the hypervelocity impact instrument calibrations. Figure 2a and 2b show the response of the small and large PVDF sensors as a function of mass at 6.1km/s, the 81P/Wild 2 flyby speed; the Wild 2 voltage and mass thresholds are also marked. Figure 2c shows the same data and includes the mass and velocity dependencies.
Figures 2a (Small PVDF sensor) and 2b (Large PVDF sensor) from [TUZZOLINOETAL2003] (files dfmi_cal_overview_fig2ab.png)
Figure 2c from [TUZZOLINO1996] (file dfmi_cal_overview_fig2c.png)
There was a lower gain (higher threshold) setting available via ground command for the small sensor but it was not used.
PVDF Event-Impact Count Instrument Calibration
The figure below from [TUZZOLINO1995] summarizes the instrument calibration of the counting electronics with increasing pulse rates.
Figure 3 (file dfmi_cal_overview_fig3.png):
Using the 9P/Tempel 1 flyby speed compared to that for 81P/Wild 2, and solving for mass using the exponents from Figure 2c above, the tables below summarize the design voltage thresholds in electrons, the corresponding mass thresholds, and the raw counts from the telemetry for the entire 9P/Tempel 1 flyby encounter at each threshold for the Large and Small PVDF sensor.
Based on those plots, these are the 9P/81P mass threshold ratios: 06um and 28um, Fe (Small PVDF sensor, thresholds m1 and m2) (3/1.3) 0.264 = (6.12km/s at Wild 2 / 10.9km/s @ Tempel 1) 06um, Glass (Small PVDF sensor, thresholds m3, m4): (3/0.7) 0.084 = (6.12km/s at Wild 2 / 10.9km/s @ Tempel 1) 28um, Glass (Small PVDF sensor, thresholds M1, M2, M3, M4): (3/0.9) 0.146 = (6.12km/s at Wild 2 / 10.9km/s @ Tempel 1) Translate mass thresholds from Stardust 81P/Wild 2 to NExT 9P/Tempel 1: ch 81P mass x ratio = 9P mass Source -- -------- ------- --------- ------ m1 9.8E-12g x .264 = 2.59E-12g 6um, Fe, Heidelberg m2 1.2E-10g x .264 = 3.2E-11g 6um, Fe, Heidelberg m3 4.3E-9g x .084 = 3.6E-10g 6um, Glass, Munich m4 6.3E-7g x .084 = 5.3E-8g 6um, Glass, Munich M1 8.5E-8 x .146 = 1.24E-8g 28um, Glass, Munich M2 1.7E-6 x .146 = 2.5E-7g 28um, Glass, Munich M3 1.4E-5 x .146 = 2.0E-6g 28um, Glass, Munich M4 1.5E-4 x .146 = 2.2E-5g 28um, Glass, Munich And these are the results 2 2 Large Sensor, 0.02m Small Sensor, 0.002m Threshold -------------------------- -------------------------- Name e- kg counts e- kg counts ===== ======= ======= ====== ======= ======== ====== M1/m1 1.76E09 1.24E-11 13 3.77E06 2.59E-15 4173 M2/m2 2.67E10 2.50E-10 1 7.13E07 3.20E-14 451 M3/m3 2.67E11 2.00E-09 0 1.80E08 3.60E-10 266 M4/m4 2.00E12 2.20E-08 0 6.00E09 5.30E-11 2
The raw count of events at each voltage threshold for a PVDF sensor was essentially 1:1 with the number of impacts on that sensor, as the incremental raw event count rate at any time period was rarely high enough to justify applying the Event-Impact Count Calibration described above in Figure 3. Also, none of the PVDF raw counters went past their maximum 16-bit value of 65535 and rolled over to zero, so no adjustment was required there. Finally, the last raw counts from impacts during encounter occurred three and a half minutes (2010-02-15T04:43:41) after closest approach; after that time all raw counter increases appear to be due to the power supply anomaly.
So treating the raw counts from the table above as impacts and dividing them by their respective PVDF sensor areas, e.g.,
-2 Small PVDF m1 (2.59E-15 kg) fluence = 4173/0.002 = 2.09E06 impacts m
will yield the PVDF fluences in the calibrated data table in this data set (see /DATA/TEMPEL1/DFMI_CAL.LBL).
The relationship between the acoustic sensors' raw data and the fluence and mass distribution of the comet particles was as complex as the PVDF sensor was simple.
Event-Impact Count Relationship
The primary difference in the acoustic sensor is that the voltage signal from a single impact, after rising to a peak voltage (Vp), oscillated ("rang") at about 20kHz and decayed slowly with a time constant of a few milliseconds; see Figures 4b and 4c below. Unlike the PVDF characteristic of one voltage spike and one threshold crossing per impact, such a signal would cross any threshold selected many times per impact event.
So by design the acoustic system electronics used a different strategy: sampling the signal from each of the piezoelectric transducers continuously over two "threshold sampling periods" of 510us (T1) and 210us (T2) at thresholds of V1 = 0.005V and V2 = 0.05V, respectively. See Figure 4e below. The raw event counter N1 was incremented by one for each threshold sampling period T1 in which the V1 threshold voltage was exceeded, no matter how many times the threshold was crossed in that period; likewise for N2, T2 and V2.
Figure 4, from [TUZZOLINOETAL2003] and [GREENETAL2004] (file dfmi_cal_overview_fig4.png):
Mass-Voltage Relationship and Effective Area
Another issue is the varying sensitivity across the sensor element (shield); see Figure 5 below and 4a above. Specifically, any given signal could have been the result of a small particle impacting near the piezoelectric detector or a larger particle impacting farther away. For the same reason, small particles impacting far enough away from the detector will not register raw event count increments; the implication is that the effective area of the sensor is dependent on the particle momentum (mass).
Figure 5, from [GREENETAL2004] (file dfmi_cal_overview_fig5.png):
Miscellaneous: First Layer Penetration and Second Layer Impacts
Only particles that penetrate the first (Bumper) layer of the Whipple Shield make it to the second (Nextel) layer and may then generate raw counts on the second acoustic sensor (N3 and N4). Some of the momentum and energy of penetrating particles is lost during that penetration and must be taken into account in calibrating data from the second sensor system.
Miscellaneous: Event Count Sampling Intervals
As noted above, the accumulated raw event counts for all sensors were time-stamped and returned at intervals of between 100ms and 1000ms throughout the comet flyby encounter. The raw data returned for the acoustic sensor give no indication of where in each interval any incremental raw counts occurred; neither is there any guarantee that incremental raw counts from an impact event will all occur between the boundaries of those intervals. For any two or more consecutive intervals with non-zero raw counter increments it must be considered whether the increments should be combined or kept separate; see data calibration below.
The instrument calibrations of the DFMI acoustic sensors, described in detail in [GREENETAL2004] and [TUZZOLINOETAL2003], are summarized here:
The original hypervelocity instrument calibrations were carried out near 6.12km/s to match the Wild 2 flyby encounter. The translation of those instrument calibration data to the Tempel 1 flyby at 10.9km/s will be covered in the Data Calibration description below.
As noted above, the data calibration of the 9P/Tempel 1 flyby encounter raw data to fluence comprises the following steps:
Data Calibration: Impact Event Counts
The impact event counts result from an interpretation of changes in the raw counters. A section of the raw data has been extracted below as Table 1; the table shows 12s of data from near the time of closest approach (TCA), between two one-second intervals where the raw counters do not change, with 6s of data in the middle excluded as they are redundant for this document. The times have had the date (2011-02-15) truncated, and only the four columns of acoustic sensor data are shown here.
Table 1: 12s of raw data ========================= Shield: ---Front-- ---Back--- Sensitivity: Low High Low High Threshold, V: .05 .005 .05 .005 Time A1a A1b A2a A2b ------------ --- --- --- --- 04:38:30.418 74 16 0 0 04:38:31.406 74 16 0 0 _ 04:38:32.406 74 20 0 0 \ 04:38:32.703 216 139 41 80 )- These two steps will be combined 04:38:33.418 216 140 41 98 _/ ... 04:38:39.418 226 230 41 103 04:38:40.418 226 230 41 103 _ 04:38:41.019 235 244 41 103 \_Note raw counter rollover in A1b 04:38:41.121 242 33 41 103 _/ 04:38:41.418 243 59 41 103 04:38:42.418 243 59 41 103
An important aspect of the data that must be understood is that, when the DFMI is in encounter mode, data are returned at a 100ms interval if and only if there has been a change in one of the PVDF counters, but not less frequently than every 1000ms. The result of that operational policy is that a contiguous (i.e. generated by a single impact event) sequence of acoustic sensor raw counts may be broken up across multiple sets of time-stamped raw data.
The first data calibration step is to calculate the changes in each raw counter channel in each step from one time sample to the next, as well as the duration of each time step. The time durations are rounded to the nearest tenth of a second because that is the increment by which the DFMI returns data; the UTC time of day is based the spacecraft clock, which for these purposes has a resolution of 1/256th of a second and so cannot hit the exact 100ms boundaries other than every 500ms. Those four event deltas and the time durations have been calculated from Table 1 above and displayed in Table 2 below in columns dA1a, dA1b, dA2a, dA2b and dT, respectively.
The second step is to interpret each change in the raw counters as contributing to some number of impact events between the thresholds. The last four columns in Table 2 below contain numbers of impact events which are the results of such an interpretation (N.B. these columns are in order of increasing threshold, which different than the previous four threshold columns), and a description of the analysis follows each row under those columns. Note that, as mentioned above, the breaks in the data will not "respect" a contiguous sequence of acoustic raw counts from a single impact event. Therefore, any time the raw counts change during both of two consecutive time steps it must be considered whether the raw counts should be combined; this is identified as "overlap" or "overflow" in the description.
Table 2: Raw data differenced and re-interpreted as impacts ============================================================ --Raw counter events-- Shield: ---Front-- ---Back--- Sensitivity: Low High Low High Threshold, V: .05 .005 .05 .005 Alternate Ch: CH2 CH1 CH4 CH3 Alternate ID: AC2 AC1 AC4 AC3 Delta count: N2 N1 N4 N3 ----Impact events--- Time of day dA1a dA1b dA2a dA2b dT N1 N2 N3 N4 ------------ ---- ---- ---- ---- --- -- -- -- -- 04:38:31.406 0 0 0 0 1.0 - - - - Start: no change from previous 04:38:32.406 0 4 0 0 1.0 1 0 0 0 Possible overlap but very unlikely 04:38:32.703 142 119 41 80 0.3 2 2 1 1 Very large impact with signal in all 4 channels. However, channel 3 must overflow into next time step and this makes things more complicated. CH3 raw count of 80 @ 510us/count = 40.8ms. CH2 raw count of 142 @ 210us/count = 29.8ms so this is consistent with zero overflow. CH1 raw counts must be maximum of 80. This gives 39 counts in CH1 for another impact. N1 looks low compared with N2 but any other solution is worse. 04:38:33.418 0 1 0 18 0.7 - - - - CH3 raw counts without CH2 means CH3 counts must be an overflow from the previous timestep. All counts and impacts from this step were assigned to previous step. ... 04:38:41.019 9 14 0 0 0.6 2 1 0 0 Could be overlap with next time step but would then need another CH1 only impact to satisfy N1 raw counts. Retain 2 impacts by redistributing raw counts. 04:38:41.121 7 45 0 0 0.1 0 0 0 0 Could be overlap from previous time step and duration is short so probability of overlap is not negligible. Retain 2 impacts but assign all raw counts to previous step. Raw delta calculated across raw counter overflow, 45 = (33-244) + 256, but no evidence for multiple raw counter overflow. 04:38:41.418 1 26 0 0 0.3 1 1 0 0 Assign single impact. 04:38:42.418 0 0 0 0 1.0 - - - - Stop: no change from previous
Data calibration: Mass Thresholds and Effective Areas, Overview
The derivation of the mass of an individual impacting particle on the acoustic sensors requires knowledge of the impact position and the detector sensitivity. For the inflight data, the position is unknown, and the derived momentum (and hence mass) of an impactor is therefore represented by a probability function rather than a specific value.
The same is true for the mass thresholds corresponding to events that barely trigger the sensor (i.e. N1=1). Therefore, estimating mass thresholds and effective areas are interrelated because of this position-dependent sensitivity of the acoustic sensor.
Also, the probability function is dependent on the particle mass distribution, but the mass distribution is one of the parameters that is unknown and being measured. Therefore the data calibration is iterative: it starts with an estimated mass distribution and uses it to calculate the probability function and the relationship between mass threshold and effective area; those mass thresholds and effective areas are used to calculate a new mass distribution. This process continues until the mass distribution does not change significantly from one iteration to the next.
Data Calibration: Mass Thresholds
This data calibration uses the following models from the instrument calibrations described above to correlate a measured voltage from an impact on the acoustic sensor:
Vp = m * v * eS * Rnorm * MER [Equation 1] mt = Vt / (v * eS * Rnorm * MER) [Equation 2a] g (1/(1-g)) mt = [Vt / (v * eS * Rnorm * MER * mpen )] [Equation 2b]
where
Figure 6 below shows the first section of the mass threshold and effective area calculation.
The important concept in this section is that for each row, that row and all rows below it represent shield elements that will detect particles down to at least the mass threshold of that row. Similarly, the cumulative area in Column D is the sum of the area for all such shield elements.
Figure 6 from workbook AC_DFMI.XLS, worksheet "eff area calcs" (file dfmi_cal_overview_fig6.png).
The first nineteen and the last six out of a total of 3,257 rows from the spreadsheet are shown. The yellow cells and columns are model or system inputs; the blue columns apply to the lower voltage threshold channels (N1, N3); the light orange columns apply to the higher voltage threshold channels (N2, N4).
In that figure, each row in column D and beyond corresponds to one shield element calibrated during the fixed-height bead drop tests, and the mass thresholds are determined for each incremental areas (Ai) of the acoustic sensor shield.
Data Calibration: Effective Areas
As mentioned above, the variability of sensitivity across the acoustic sensor means any single detected impact event can be caused by a range of masses of impactor particle. So instead of each detector threshold correlating with a single mass threshold, the acoustic threshold correlates with a probability function representing a range of particle masses. If the mass distribution of the particles is known, then the probability function, as well as an effective area, may be calculated for any mass threshold. This section implements such a calculation.
For the data calibration presented in this data set, the mass distribution model used is
-alpha N(m) = k * m [Equation 3]
N(m) = k * m-α &nsp;&nsp;&nsp;&nsp;[Equation 3]
This is a cumulative mass power-law relation, where N(m) is the fluence (number of particles per square meter) larger than or equal to mass m, and k and alpha are constants. The value for alpha will be an estimate at first, the effective area result will be applied to the actual data, after which the value of alpha will be recalculated and this procedure repeated in an iterative approach. This section gives an example of using a value for alpha to calculate effective areas.
Figure 7 displays more of the effective area calcs worksheet from Figure 6 to include the probability function and effective area calculations.
Figure 7 from workbook AC_DFMI.XLS, worksheet "eff area calcs" (file dfmi_cal_overview_fig7.png).
There are similar columns in the worksheet for the high thresholds. Also, for the acoustic sensor on the second, NEXTEL layer of the Whipple Shield, the mass thresholds are those for particles which penetrate the Bumper shield layer. From [GREENETAL2004], modified for the 9P/Tempel 1 encounter:
The mass threshold corresponding to a detected N3 signal (which is only marginally larger than the threshold for penetration reported by Tuzzolino et al. [2003]), is [6E-8kg]. [...] The mass threshold for N4 is fixed at precisely 10 times that of N3. The effective area of the rear shield sensor is currently not known since it has not been possible to conduct hypervelocity impact tests due to the large size of the shield. However, we can place constraints on the effective area, from the maximum size of the shield (0.7m2) and the size of expected ejecta cones, which gives a minimum area ~0.1 m2. We thus adopt an effective area of (0.3 -0.2/+0.4) m2 for the encounter data.
Data Calibration Denouement: Fluence
From the three steps above, the impact event counts along with the mass thresholds and their effective areas have been calculated. Choosing a mass threshold and dividing its effective area into the impact event counts yields a fluence for that mass threshold.
Data Calibration: Iterating on Mass Distribution Index
Plotting the acoustic sensor fluences with those from the PVDF sensors yields a result such as is shown Figure 8 below. The slope of a linear fit to the fluences in that plot is the exponent alpha of the mass distribution index. If the alpha value from the linear fit differs from the one used to derive the acoustic sensor effective areas, the fit value is used to update the calculation and the process repeated until convergence is achieved. The N1 mass threshold and effective area are chosen so roughly 90% of the impacts are at masses above the threshold.
Figure 8 from workbook AC_T1_CT2IMP.XLS, worksheet "T1 Fluence" (file dfmi_cal_overview_fig8.png).
See the catalog file /CATALOG/REFERENCE.CAT for formal references.
An early draft of the calibration material in Tuzzolino et al., 2003 was provided with the Stardust prime mission cruise phase archive data set; see file jgr_dfmi.pdf under this URL:
http://pdssbn.astro.umd.edu/holdings/stardust-c_e_l-dfmi-2-edr-v1.0/extras/
It was also found here:
http://213.174.143.38/download/jgr-dfmi-pdf-14869049.html
A summary of the PVDF data calibration is provided with this data set; see
/DOCUMENT/DFMICAL.LBL (PDS label)
/DOCUMENT/DFMICAL.PDF (PDF document)
A pre-print of Green et al., 2004 is available
A version of Tuzzolino et al., 1994 is available