============================================================================= 
DIDSY DATA ARCHIVE                                           27th August 1993 
============================================================================= 
                                                                              
                                                                              
This archive is in 3 sections:                                                
                                                                              
    1) Description and DIDSY results from the GEM encounter.                  
                                                                              
    2) How the analysis was performed.                                        
                                                                              
    3) Sensitivity maps of the bumper shield for DID 2, 3 and 4 sensors.      
                                                                              
[NOTE: The sensitivity maps have been pulled out into separate files during   
       PDS ingest.  See the "did*map.tab" files.]                             
                                                                              
                                                                              
Archive compiled by  Dr Neil McBride                                          
                     Unit for Space Sciences                                  
                     Physics Laboratory                                       
                     University of Kent at Canterbury                         
                     Canterbury CT2 7NR, UK                                   
                                                                              
                     Tel:   0227 764000 ext 3242                              
                     Fax:   0227 762616                                       
                     Email: nm1@ukc.ac.uk                                     
                                                                              
                                                                              
                                                                              
============================================================================= 
SECTION 1                                                                     
============================================================================= 
                                                                              
The follow text gives a description of the experiment and the results         
obtained at the GEM encounter. The text essentially makes up the paper        
published in Nature (Vol 362 No 6422 22 April 1993).                          
                                                                              
                                                                              
                                                                              
Dust particle impacts during the Giotto encounter with comet Grigg-Skjellerup 
----------------------------------------------------------------------------- 
                                                                              
By:                                                                           
                                                                              
J.A.M. McDonnell (1)                                                          
N. McBride (1)                                                                
R. Beard (1)                                                                  
E. Bussoletti (2)                                                             
L. Colangeli (3)                                                              
P. Eberhardt (4)                                                              
J.G. Firth (5)                                                                
R. Grard (6)                                                                  
S.F. Green (1)                                                                
J.M. Greenberg (7)                                                            
E. Grun (8)                                                                   
D.W. Hughes (9)                                                               
H.U. Keller (10)                                                              
J. Kissel (8)                                                                 
B.A. Lindblad (11)                                                            
J.-C. Mandeville (12)                                                         
C.H. Perry (5)                                                                
K. Rembor (15)                                                                
H. Rickman (13)                                                               
G.H. Schwehm (6)                                                              
R.F. Turner (5)                                                               
M.K. Wallis (14)                                                              
J.C. Zarnecki (1)                                                             
                                                                              
                                                                              
(1)  Unit for Space Sciences, Physics Laboratory, University of Kent,         
     Canterbury, Kent CT2 7NR, UK.                                            
(2)  Instituto di Fisica Sperimentale, Istituo Universitario Navale, Via A.   
     De Gasperi 5, 80133 Napoli, Italy.                                       
(3)  University of Cassino, Via Zamosch 43, 03043 Cassino (Fr), Italy.        
(4)  Physikalisches Institut, Universitat Bern, CH-3012 Bern,                 
     Sidlerstrasse 5, Switzerland.                                            
(5)  Space Science Dept., Rutherford Appleton Laboratory, Chilton, Didcot,    
     Oxon OX11 OQX, UK.                                                       
(6)  PSS, ESTEC, Postbus 299, 2200 AG Noordwijk, Netherlands.                 
(7)  Rijksuniversiteit te Leiden, Huygens Laboratorium, Postbus 9504, 2300 RA 
     Leiden, Netherlands.                                                     
(8)  Max Planck Institut fur Kernphysik, D-6900 Heidelberg, Germany.          
(9)  Department of Physics, University of Sheffield, Sheffield, S3 7RH, UK.   
(10) Max Planck Institut fur Aeronomie, D-3411 Katlenburg-Lindau,             
     Germany.                                                                 
(11) Lund Observatory, Box 43, S-221 00 Lund, Sweden.                         
(12) ONERA-CERT-DERTS, BP No. 4025, 31055 Toulouse Cedex, France.             
(13) Astronomical Observatory, Box 515, S-751 20 Uppsala, Sweden.             
(14) School of Mathematics, University of Wales, Senghennydd Road, Cardiff    
     CF2 4AG, UK.                                                             
(15) Fakultat fur Physik, Universitat Karlsruhe, D-7500                       
     Karlsruhe, Germany.                                                      
                                                                              
                                                                              
                                                                              
         Summary                                                              
         -------                                                              
         In the European Space Agency's 1992 Giotto Extended Mission (GEM)    
         to comet Grigg-Skjellerup, the Dust Impact Detection System (DIDSY)  
         was successfully operated during a fly-by approaching within some    
         200~km from the nucleus, and gives in situ detections of pristine    
         cometary meteoroids. Three meteoroid impacts on the spacecraft's     
         front shield were detected and the particle masses have been         
         established as 100 (+105/-50) ug, 2 (+4/-1) ug and 20 (+25/-10) ug.  
         The cumulative mass index over this mass range is found to be        
         alpha=-[0.27 (+.13/-.20)] (1 sigma errors), with the upper limit     
         being -0.74 (3 sigma). The slope is consistent with the 1986 Halley  
         data over this mass range, and is supported by data from the GRE     
         experiment which indicates the impact of a very large meteoroid of   
         mass 14 (+40/-4) mg. The low value of alpha signifies a higher rate  
         of mass loss than previously thought and hence a higher (by mass)    
         dust to gas ratio. The value alpha=-0.27 gives the total mass that   
         impacted the spacecraft as approximately 22 mg, this being           
         dominated by the largest particle.                                   
                                                                              
                                                                              
The Dust Impact Detection System (DIDSY) was designed to measure the flux of  
dust particles in the coma of Comet Halley in the mass range 10^-19 kg to     
>10^-6 kg (see refs 1 and 2). Giotto is protected from hypervelocity dust     
impacts by two annular meteoroid bumper shields. The front shield consists    
of 1 mm thick aluminium and is situated 250 mm above a rear Kevlar shield.    
Impacts are detected by three separate subsystems. The first subsystem        
comprises 4 piezoelectric sensors. Three of these sensors (DID2, DID3 and     
DID4) are mounted on the  rear of the front shield and are sensitive to the   
momentum imparted to the shield. DID2 and DID3 can operate independently, or  
measure in coincidence. DID4 operates independently and is located on a 30    
degree section of the shield isolated by acoustically insulating joints.      
Another piezoelectric sensor (DID5) is situated on the rear shield behind     
the DID4 section. The impact plasma and momentum subsystem (IPM, DID1)        
comprises two subunits, located behind an aperture in the front shield. The   
plasma subunit (IPM-P) determines particle mass by measuring the plasma       
produced when a particle impacts on a metal target plate. The momentum        
subunit (IPM-M) uses a piezoelectric detector situated on the rear of the     
metal target plate. IPM-P and IPM-M can measure in coincidence. The           
capacitor impact sensor subsystem (CIS, DID7) comprises a thin-film,          
dielectric-filled capacitor fixed to the front shield. Impacts are indicated  
by brief discharging (a simple schematic of the sensor positions is given     
in section 3).                                                                
                                                                              
The DID1 IPM-P sensor suffered impact damage at the Halley encounter and at   
Grigg-Skjellerup, the instrument was noisy and gave no interpretable          
results. The DID1 IPM-M sensor however, was fully operational. The DID7 CIS   
sensor also suffered impact degradation at Halley, and was largely non-       
operational. The piezoelectric momentum sensors (DID2 to 5) were fully        
operational.                                                                  
                                                                              
The 1986 Halley encounter geometry was such that particles impacted the       
front shield at normal incidence with relative velocity 68.4 km/s. A          
hypervelocity particle having momentum mv will transfer momentum epsilon*mv   
to the shield (due to target ejecta) where epsilon is the momentum            
enhancement factor. The value taken at Halley (ref 3) was epsilon=11. At      
Grigg-Skjellerup the impacting particle trajectories made a 21.2 degrees      
angle with the shield at a relative velocity of 13.99 km/s. These factors     
reduced epsilon significantly. Experiments using the 2 MV dust accelerator    
at the Unit for Space Sciences, Kent, yield a value of epsilon=3.1 +/- 1.0.   
This reduced value of epsilon raises the piezoelectric mass detection         
threshold. Also, the reduced resolved area of the front shield and the fact   
that the activity of Grigg-Skjellerup was estimated to be approximately 1%    
that of Halley, meant that few detections were expected. Pre-encounter        
modelling indicated total fluences between 0 and 40 particles for miss        
distances ranging between 300 and 50 km respectively. The data gathered were  
wholly consistent with these predictions. DIDSY was operated for              
approximately 35 hours from 18:42UT 9th July, with an impact time resolution  
of 2.83s. All times given here are ground receive times (GRT) UT (where GRT   
= spacecraft time + 11m53s).                                                  
                                                                              
Three particle impacts were detected, by sensors DID2, DID3 and DID4,         
compared with 2400 at the Halley encounter. The DIDSY telemetry is            
transferred in data frames of 64 bytes, and a full `DIDSY data block' (DDB)   
is constructed from 8 data frames.  Each DDB contains information on          
particle impacts in the last data gathering interval (2.83s at the Grigg-     
Skjellerup encounter).  At 15:30:43 GRT (coinciding with nutation particle,   
see below) 4 data frames were lost or corrupted, then a good data frame was   
received, then 4 more were lost. These were the only frames lost or           
corrupted during the whole time the experiment was active.  The data drop-    
outs meant that some information was lost from 2 consecutive DDBs (DDB        
numbers 56963 and 56964). However, some reconstruction of the DDBs could be   
performed and it was found that no particle impacts could have occurred       
during the data drop-outs. The first particles detected by DIDSY were         
recorded in DDB number 56966.                                                 
                                                                              
Due to the impact degradation of CIS, the bias voltage was 0.22 V as opposed  
to 2.3 V at Halley. This voltage was stable for 21 hours up to closest        
approach, and then at 15:31:31/32, changed to 0.20 V and remained stable for  
the rest of the operating period. Significantly, this change coincided with   
the impact interval of the third particle, and indicates an impact directly   
on CIS. The CIS voltage was monitored approximately once a second giving a    
better time resolution on event 3. The times and the masses of the 3          
meteoroids are given in Table 1 The first 2 events were near closest          
approach when the spacecraft-comet distance (ref 6) was likely to have been   
<200 km and the third event was in excess of 40 sec after closest approach    
at >500 km from the nucleus.                                                  
                                                                              
                                                                              
    Event                 Names      Time (GRT)          Mass                 
    -----                 -----      ----------          ----                 
    Expected closest      -          15:30:36 (+/-14s)   -                    
    approach (ref 4)                                                          
    Nutation particle     Whopper    15:30:43            14 (+40/-4) mg       
    GRE (ref 5)                                                               
    Maximum optical       -          15:30:43 (+/-3s)    -                    
    brightness OPE (ref 6)                                                    
    DIDSY Event 1         BigMac     15:30:48-51         100 (+105/-60) ug    
    (DID 2 and DID 4)                                                         
    DIDSY Event 2         Barley     15:30:51-54         2 (+4/-1) ug         
    (DID 3)                                                                   
    DIDSY Event 3         Bretzel    15:31:31-32         20 (+25/-10) ug      
    (DID 3 and CIS)                                                           
                                                                              
       Table 1  GEM encounter events. The errors quoted (to 1 sigma)          
       -------  on the 3 DIDSY particle masses incorporate both the           
                statistical and systematic errors and represent the           
                absolute uncertainty in the particle masses.                  
                                                                              
                                                                              
The fluence, being the time integrated particle flux, is shown in Table 2.    
The wide distribution of masses yielded a most significant and unexpected     
mass distribution.                                                            
                                                                              
                                                                              
    log10 Cumulative Fluence (per m^2)    log10 Particle Mass (kg)            
    ----------------------------------    -------------------------           
    0.640                                  -8.80                              
    0.427                                  -7.68                              
    0.125                                  -7.00                              
                                                                              
       Table 2  The cumulative fluence for the three particles                
       -------  detected by DIDSY. The slope gives the cumulative             
                mass distribution index alpha=-0.27.                          
                                                                              
                                                                              
A most probable upper mass cut-off at 10^-4.23 kg (59 mg) was calculated for  
1 detected particle hitting the entire resolved spacecraft area               
(approximately 3.6 m^2). The cumulative mass distribution index alpha, was    
found to have a value of alpha=-0.27. The error in this gradient is           
dominated by the  statistical number uncertainty as opposed to the particle   
mass uncertainty. An analysis based on the null detection of a 4th DIDSY      
particle indicates that alpha=-[0.27 (+.13/-.20)] (1 sigma errors) and could  
be as high as -0.74 (3 sigma limit).                                          
                                                                              
Additional support for a low slope mass distribution was given by results     
from the Giotto Radio Science Experiment (ref 5) (GRE) which indicated that   
a particularly large meteoroid impacted at the rear of the spacecraft (hence  
no DIDSY detection). The effective mass (where m_eff=epsilon x m_real) was    
calculated to be between 30 and 54 mg. Taking epsilon=3.1 as before, gave     
the most likely value of the real mass of the particle as approximately 14    
mg with the lower limit being 10 mg. It is possible for a penetrating impact  
to have little or no momentum enhancement, and so a reasonable upper limit    
is 54 mg. This particle was not used to determine alpha, but signifies that   
the slope of -0.27 is entirely consistent with the detection of this          
particle, and indicates the slope may hold over four decades of mass. An      
integration between mass limits 10^-9.35 and 10^-4.23 kg gives the total      
mass that impacted Giotto as approximately 22 mg. With such a low slope,      
this mass is dominated by the largest impacting particle and is consistent    
with the GRE meteoroid. Assuming rho=1 g/cm^3, the cumulative cross-          
sectional area of the particles between these mass limits is 12 mm^2.         
                                                                              
The low slope found from the 3 DIDSY particles also agrees well with Halley   
data over the same mass range of 10^-9 to 10^-7 kg, where the Halley time     
averaged mass distribution index was found to be -0.2. From 10^-9 to 10^-15   
kg, the Halley index increased to -0.9. Although the Grigg-Skjellerup data    
presented here says nothing about masses <10^-9 kg as such, it is likely      
that the index also increases at smaller mass to account for the              
significance presence of optical scattering particles (ref 6).                
                                                                              
DIDSY can give no information as to the composition of impacting particles    
(ie, solid versus aggregate) and the number of detections were not high       
enough to give information about the variation of the mass distribution       
index with time. However the very low mass distribution slope agrees with     
the Halley data and IRAS dust trail data. The domination of the large         
particles is important for both the modelling of nucleus structure and        
composition, and in modelling the contribution and evolution of cometary      
particles to the interplanetary dust flux. It also signifies a higher rate    
of mass loss than previously thought and hence a higher (by mass) dust to     
gas ratio.                                                                    
                                                                              
Acknowledgements                                                              
----------------                                                              
                                                                              
We acknowledge the UK Science and Engineering Research Council for financial  
support and thank Norbert Schmidt for his help during the encounter project.  
We especially acknowledge the efforts of project scientist Gerhard Schwehm    
and project manager Manfred Grensemann for achieving the `mission             
impossible'.                                                                  
                                                                              
References                                                                    
----------                                                                    
                                                                              
(1) McDonnell, J.A.M., W.M. Alexander, W.M. Burton, E. Bussoletti, D.H.       
Clark, G.C. Evans, S.T. Evans, J.G. Firth, R.J.L. Grard, E. Grun, M.S.        
Hanner, D.W. Hughes, E. Igenbergs, H. Kuczera, B.A. Lindblad, J.-C.           
Mandeville, A. Minafra, D. Reading, A. Ridgeley, G.H. Schwehm, T.J.           
Stevenson, Z. Sekanina, R.F. Turner, M.K. Wallis & J.C. Zarnecki.  ESA SP     
1077, 85-108 (1986).                                                          
                                                                              
(2) McDonnell, J.A.M.. J. Phys. E:Sci. Instrum., 20, 741-758 (1987).          
                                                                              
(3) McDonnell, J.A.M., M. Alexander, D. Lyons, W. Tanner, P. Anz, T. Hyde,    
A.-L. Chen, T.J. Stevenson & S.T. Evans. Adv. Space Res.,  4, 297-301         
(1984).                                                                       
                                                                              
(4). Morley, T., ESOC, private communication, 9th July (1992).                
                                                                              
(5). Patzold, M., P. Edenhofer, M.K. Bird & H. Volland. Astron. Astrophys.,   
in press (1993), and private communication.                                   
                                                                              
(6). Levasseur-Regourd, A.C., B. Goidet, T. Le Duin, C. Malique, J.B.         
Renard & J.L. Bertaux. Planet.Space Sci., 41, No 2, 167-169 (1993).           
                                                                              
                                                                              
                                                                              
============================================================================= 
SECTION 2                                                                     
============================================================================= 
                                                                              
The follow text gives a description of how the data analysis was performed    
for the three particle detections.                                            
                                                                              
                                                                              
When a particle impact is detected by a DIDSY piezoelectric detector, the     
detector produces a voltage V volts which is stored by the onboard            
electronics as a digital value 0 to 255. The conversion between V and         
digital value D(V) for the DIDSY experiment is given by                       
                                                                              
      D(V) = (A*log10(V)+B)*(1-(C/V)^D)                                  (1)  
                                                                              
where A, B, C and D are constants and have been determined for sensors DID2,  
DID3 and DID4 as                                                              
                                                                              
      Sensor  |    A      |    B     |   C    |   D                           
      ------------------------------------------------                        
      DID2:   |   28.004  |  176.66  |  0.03  |  1.760                        
      DID3:   |   47.145  |  155.41  |  0.04  |  7.322                        
      DID4:   |   30.718  |  174.51  |  0.03  |  2.112                        
                                                                              
The three DIDSY events gave digital values given below. V is obtained by      
solving the equation above.                                                   
                                                                              
      Event   |   Sensor  |  D(V)    |   V                                    
      ---------------------------------------                                 
      Event 1 |   DID2    |  197     |  5.335                                 
              |   DID4    |  109     |  0.063                                 
      Event 2 |   DID3    |  102     |  0.077                                 
      Event 3 |   DID3    |  127     |  0.250                                 
                                                                              
Note that event 1 triggered two sensors, DID2 and DID4. This gives the        
useful result that the ratio of voltages produced by DID2 and DID4 is 84.7,   
and any mass-position solution for this impact must satisfy this voltage      
ratio.                                                                        
                                                                              
For a non-penetrating impact (and it is very unlikely that any of the         
detected particles penetrated the shield) by a particle which gives rise to   
a sensor voltage V volts, the particle mass m_p kg is given by                
                                                                              
                 V                                                            
      m_p = ------------ * (Pi/Ps)^-1                                    (2)  
            e*v*cos(t)*S                                                      
                                                                              
where v is the relative impact velocity (m/s), t is the angle the impact      
makes with the shield normal (0 for Halley and 68.8 degrees for Grigg-        
Skjellerup), e is the momentum enhancement factor (epsilon in section 1) and  
was experimentally determined to be 3.1 for the Grigg-Skjellerup encounter,   
and S is the absolute sensitivity of the piezoelectric detectors and is       
approximately 50 kV/N/s. The uncertainty in this value is of order 2. The     
value Pi/Ps is the relative signal attenuation for a particular impact site   
compared to a `direct hit' on the sensor (ie, Pi is signal from impact at     
site i, and Ps is the signal obtained if the impact was on the sensor site,   
all other things being equal.  The signal attenuation for an impact on a      
particular  area element of the front shield is known, due to laser shot      
mapping carried out at the Rutherford Appleton Laboratory (see ref 2 in       
section 1). The values of Pi relative to Ps are given in section 3 for the    
three sensors DID2, DID3 and DID4.                                            
                                                                              
A particle mass probability distribution is obtained by identifying the mass  
required to produce the observed sensor signal from each area element. In     
examining all possible impact sites, a cumulative mass distribution           
N(m)=k*m^alpha is assumed, where N(m) is the cumulative fluence, k is a       
constant and alpha is the cumulative mass distribution index. A probability   
of the particle being between mass m and m+dm can be calculated thus          
                                                                              
P(m) = [ sum(i=1,shield) dN(m)*a(i)*f(m) ] *                             (3)  
       [ sum(m=0,infinity) sum(i=1,shield) dN(m)*a(i)*f(m) ]^-1               
                                                                              
where dN(m) is the differential mass distribution function (the number of     
particles of mass m to m+dm) and a(i) is the area of the ith shield element   
(these areas are given in section3). The function f(m)=1 if the mass m gives  
the observed signal for this area element, and f(m)=0 if it does not. (The    
nomenclature here is such that sum(i=1,shield) means the sum from i=1 to      
i=whole shield) This is an iterative process where particle mass is           
determined using an initial chosen value of alpha. Additionally, possible     
impact sites of events 1 and 3 can be constrained due to event 1 registering  
on DID2 and DID4 giving the voltage ratio 84.7 (see above), and event 3       
being in the region of the CIS sensor.  The mass distribution is then         
calculated using the effective shield areas (see below) so yielding a new     
value of alpha. The process is repeated until alpha converges. The            
determined particle mass however is not strongly dependent on alpha.          
                                                                              
There are 2 sorts of error in the particle mass determination. Firstly, that  
described by the standard deviation of the pseudo-Gaussian mass probability   
function due to uncertainties in impact position, and secondly the            
systematic errors due to uncertainty in the absolute sensor sensitivity and   
momentum enhancement factor. The probability errors affect the determination  
of alpha. The systematic errors do not affect the `relative' positions of     
the mass probability functions but has the effect of moving the mass scale    
either way by a factor of approximately 2. Hence this error does not affect   
the determined mass distribution index.                                       
                                                                              
The fluence is determined from the observed number of impacting particles of  
mass >= m, and the `effective' shield area which is sensitive to these        
particles, which, as we are calculating a cumulative fluence, is also a       
function of N(m). The effective sensitive area does not necessarily equal     
actual geometric sensitive area as small particles impacting a long way from  
a sensor may not be detected, whereas a very large particle will be detected  
at all places on the shield. Thus the actual sensitive shield area has to be  
corrected for small particle masses to obtain a realistice estimate of the    
particle fluence (number per m^2).  The geometric area of the front shield    
is 2.09 m^2 whereas the effective shield sensing areas are 2.09, 1.92 and     
2.09 m^2 for events 1, 2 and 3 respectively. The effective sensitive shield   
area for a particle of mass m_p is given by                                   
                                                                              
      a(eff) = (sum(i=1,shield) a(i)*N(m_pt))/N(m_p)                     (5)  
                                                                              
where m_pt is either the m_p or m_t whichever is greater, and m_t is is the   
detection threshold mass for the shield area element a(i). The value of m_t   
is calculated by using equation (2), the minimum sensor voltage that would    
trigger a detection (D(V)=1) being 0.03 V.                                    
                                                                              
So now the cumulative fluence N(m) (number per m^2) can be calculated by      
                                                                              
      N(m) = n(m)/(a(eff)*cos(t))                                        (6)  
                                                                              
where n(m) is the number of particles detected with mass greater than or      
equal to m kg. The relevant figures are                                       
                                                                              
      Event   |  n(m) | log10(m kg) |  a(eff) m^2 | log10(N(m))               
      ---------------------------------------------------------               
      Event 1 |   1   |   -7.00     |    2.09     |   0.125                   
      Event 2 |   3   |   -8.80     |    1.92     |   0.640                   
      Event 3 |   2   |   -7.68     |    2.09     |   0.427                   
                                                                              
The cumulative mass distribution index alpha, is found by plotting            
log10(N(m)) against log10(m) and taking the gradient. A weighted linear       
regression (each point weighted with root n(m)) gives alpha=-0.27. An         
uncertainty in alpha can be determined by considering the effect of tilting   
the straight line fit about the error weighted mean in this graph, and        
considering when the 3 detections would not be consistent with the gradient,  
within statistical errors. It is found that values of alpha between -0.07     
and -0.40 are consistent with the detection of 3 particles within one sigma   
statistical errors. A 3 sigma limit corresponds to alpha=-0.74. This          
statistical uncertainty is dominant over the mass probability error. The      
systematic errors do not affect this error analysis.                          
                                                                              
                                                                              
                                                                              
============================================================================= 
SECTION 3                                                                     
============================================================================= 
                                                                              
The following tables give the values of Pi, the relative signal strength for  
an impact on the ith area element of the shield compared to the signal        
strength the same impact would give if it were directly on the sensor site    
(signal Ps). In calculating the ratio Pi/Ps, use the value Ps=1E+05 (all 3    
sensor values of Ps have been normalised to this value). The table also       
gives a(i), the area of the ith element of the shield.                        
                                                                              
In conducting the laser shot mapping, the shield was divided into 1032        
elements (not necessarily of equally area or shape). The position of each     
element is given by the values theta and d in the tables. The distance d is   
in m, and is measured radially from the centre of the shield. The angle       
theta is in degrees and is defined thus: set up axes x and y, where the       
origin is at shield-centre and the x axis passes through DID4 sensor (which   
is situated centrally in the 30 degree acoustically isolated section of the   
shield). The y axis is 90 degrees clockwise from the x axis (viewing from     
above the shield). The angle theta is measured clockwise from the y axis,     
about the origin. See the schematic below.                                    
                                                                              
                                                                              
                           o       o                                          
                     o                    o      + = piezoelectric sensor     
                  o                          o                                
                o                              o                              
              o               o o                o                            
             o          o             o           o                           
            o  o     o                   o    + o  o   DID2                   
           o      o o                     o  o      o                         
           o       o                  x    o        o                         
           o       o           o-------    o    +   o  DID4                   
           o       o           |           o        o                         
           o        o          |          o  o      o                         
            o        o       y |         o    + o  o   DID3                   
             o          o             o           o                           
              o               o o       ---      o                            
                o          ---------   |IPM|   o                              
                  o       |   CIS   |   ---  o                                
                     o     ---------      o                                   
                           o       o                                          
                                                                              
          Simple schematic of the front meteor bumper shield                  
          --------------------------------------------------                  
                                                                              
                                                                              
                                                                              
                                                                              
--------------------------------------------------------------------------    
--------------------------------------------------------------------------    
                                                                              
[NOTE: The sheld map tables have been pulled out into separate files with     
       their own labels during PDS ingest.  These files are:                  
                                                                              
         did2map.tab     DID2 shield map                                      
         did3map.tab     DID3 shield map                                      
         did4map.tab     DID4 shield map                                      
]