Overview of Stardust-NExT DFMI data calibration


Introduction

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.


Overview I: Operation

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:

  1. Both generate a voltage signal when struck by a particle.
  2. Both have multiple voltage threshold detectors to infer information useful in discriminating between magnitudes of particle impacts. In general, the higher-voltage, lower-sensitivity threshold channels for each sensor type are triggered by particles with greater mass.
  3. Both return raw instrument telemetry with time-stamped, accumulated event counts, that have a correlation, which may be direct or indirect, to the number of impacts.
  4. The time-stamped, accumulated raw event counts for all sensors are returned at intervals between 100ms and 1000ms, dependent on the activity of the lowest PVDF thresholds.

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.


Overview II: Instrument calibration

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.


Overview III: Data calibration

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).


PVDF Sensor Operation

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):


PVDF Sensor Instrument Calibration

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):


PVDF Sensor Data calibration

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).


Acoustic Sensor Operation

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.


Acoustic Sensor Instrument Calibration

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.


Acoustic Sensor Data Calibration

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.

  1. Columns A through C supply the constants Vp, v, eS, MER, mpen, and g, used in the models above (Equations 1, 2a and 2b), along with some other constants.
  2. Column F contains R, the peak voltages (Vp) from the fixed-height bead drop instrument calibrations (worksheet "shield map" also Figure 5 above) for each shield element, sorted by increasing voltage i.e. by increasing sensitivity. Zero values, i.e. shield elements with no response, are excluded.
  3. Column G contains Rnorm for Equation 1. These values comprise the voltages from Column F normalized via division by the Tie point voltage of 0.724V (Cell B5). The Tie Point voltage represents a fixed-height bead drop voltage for a hypothetical shield element at the same nominal location of 4cm from the detector as the absolute instrument calibration, and ties the hypervelocity absolute instrument calibration data to the fixed-height bead drop data.
  4. Column E contains the incremental area for each shield element corresponding the the sensitivity.
  5. Column D contains, on each row, the cumulative area for all shield elements with a sensitivity (Rnorm) equal to or greater than the shield element on that row.
  6. Column H contains the mass threshold, mt, for the lower threshold channels (N1, N3) for each shield element, calculated from Equation 2a using the lower voltage threshold (Vt = 0.005V = Vlow = Cell B8) and Rnorm for the row.
  7. Column I contains an alternate mass threshold, mt, using Equation 2b above, the lower voltage threshold, and the Rnorm for the row, for the case where the mass threshold in Column H exceeds mpen (6E-8kg; Cell B11), the mass at which a particle just penetrates the front Bumper shield.
  8. Column J contains the mass threshold for the row, which is the one of the nominal and alternate mass thresholds (Columns H and I) that is appropriate for the Vlow voltage threshold.
  9. Column K contains a red "P" if Column J used the penetration case, and contains a blank if Column J used the non-penetration case.
  10. Columns L through O are analogous to columns H through K, but for the Vhi voltage threshold (0.05V; Cell B9).

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 &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).

  1. Columns A through E contain the same quantities as before; the important ones here are: Column D, the cumulative area of all sensor elements at least as sensitive as the mass threshold of the row; Column E, the incremental area of the shield element of the row.
  2. Column S evaluates the mass distribution function in Equation 3 at the low mass threshold (not shown) for each row. The constants k and alpha are manually entered in Cells B18 and B19, respectively. The value chosen for k is unity because it will cancel out in the effective area calculation.
  3. Column T multiplies the mass distribution function by the total geometric area of the shield (Cell D7) to get the actual number of particles, of mass greater than each mass threshold, which would actually impact the shield. N.B. this is not the number of detected impacts expected. Rather it is the total number of impacts, detected and undetected, expected on the entire shield from particles with masses above the mass threshold for the mass distribution using the specified constant alpha (Cell B19).
  4. Column U contains the detected impact count for the incremental fluence of the mass threshold of each row. The incremental fluence is the difference between two cumulative fluence values (Column S), that in the row and the one above it. The cumulative area of all shield elements sensitive enough to detect this incremental fluence is in Column D. The product of those cumulative area and incremental fluence values will be the number of detected impacts expected for particles with masses between the mass thresholds of the row and of the row above it.
  5. Column V contains the cumulative detected impact counts over all mass thresholds. This is simply the cumulative sum of the detected incremental impacts in Column U. The goal of this column is the value in the last row, Cell V3257, which contains the total number of detected impacts expected for the input mass distribution function.
  6. Column W contains an effective area for the mass threshold in each row. Since the total number of expected impact detections is known (Cell V3257; see previous items), and the actual fluence (Column S) at each mass threshold is also known for the assumed mass distribution, the ratio of those two numbers acts as an "effective area" for the mass threshold in each row. These effective areas, one for each mass threshold, do not represent physical quantities per se, but they do yield a fluence for each mass threshold when divided into to the actual total number of impact detections, which fluence is consistent with the mass distribution modeled via the k and alpha parameters and Equation 3.

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).


References

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

here

A version of Tuzzolino et al., 1994 is available

here


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