Algorithms

Before presenting an event to the DPU, the analog electronics decides if it is valid. Many things can produce pulses from the front, back, and coincidence detectors other than an actual particle. The valid event logic can be commanded to require different combinations of pulses before allowing an event to go through to the DPU for processing. The various pulses are counted and downlinked even if no valid event results.

Each valid event presented to the DPU is identified as coming from the HENA-M or HENA-S sensor. HENA-M events consist of an ID, time of flight (MTOF), Wft, Wfb, Wb, Sb, and Ib. HENA-S events consist of time of flight (STOF), Wft, Wfb, pixel ID (PID), and energy (E).

HENA-M

Since the length along the slit where a HENA-M particle passed and the position on the back MCP detector where the particle hit are known, the particle's trajectory can be computed. The trajectory can be expressed as azimuth and elevation with respect to the sensor and can be computed with simple trigonometry. Removing spacecraft spin from the azimuth produces azimuth relative to the sun.

The sensor also measures the particle's time of flight (MTOF) by timing the arrival interval of the front and back detectors' pulses. Since the path length of the particle can be found from the trajectory, the particle's velocity can be found. Instead of velocity, the equivalent corrected TOF (CTOF) is calculated by scaling MTOF by the path length.

The event data is massaged slightly before being used in the event processing algorithm. All the raw values have an offset removed; the offsets for Wft, Wfb, Wb, Sb, and Ib are done by the hardware and MTOF is offset by the software. Then all negative values are clipped to zero. The Ib value is multiplied by 2 to restore it to the range of the other values. All the resulting values range from {0 .. 8191}, except for MTOF which has the range {0 .. 511}.

Pulse Analysis

The following figure shows the computation of the particle's path through the sensor, the computation of the particle's energy (i.e. pulse heights), and the correction of the time-of-flight for path length. The front position, Xf, is computed from Wfb/(Wft + Wfb). The parameters Gf and Of scale the position to the range {-0.5 .. 0.5} and multiplying by Df, the length of the slit, maps the position into centimeters. The two rear positions, Xb and Yb, are computed from Sb/(Wb + Sb + Ib) and from Wb/(Wb + Sb + Ib). These idealized equations are modified via tables to correct sign errors, remove crosstalk coupled from the interstitial to the wedge and strip, etc. The parameters Gxb and Oxb scale the X position to the range {-0.5 .. 0.5} and multiplying by Db, the width of the back detector, maps the position into centimeters. Similarly, the parameters Gyb and Oyb and the width Db are used to scale the Y position into centimeters. The difference dX = Xf - Xb is more important in computing the trajectory than is the actual positions, Xf and Xb.

The energy of the particle is measured at the front and back detectors. The individual energies are computed by summing the values from their respective detectors. Since the gain of a detector varies across its surface, a lookup table (LUT) is used to supply a correction factor. The particle's position on the detector is computed as above, and used as an index into the LUT; the raw energy value is multiplied by the correction factor.

MTOF is corrected for the distance that the particle actually traveled. From the trajectory, dX and Yb, and the space d between the slit and the back detector, the distance can be computed as sqrt(d(Yb)² + dX² + Yb²). For HENA-M, d(Yb) is a constant, dmin. MTOF is scaled by dmin/distance; the corrected TOF (CTOF) will be as if the particle traveled the shortest distance from the slit to the detector, dmin. The CTOF for a particle normal to the stop detector will be unchanged.

The figure and equations above represent an idealized mathematical view. The DPU must deal with the limitations of computer arithmetic and uses the equations in the figure below. The trajectory results are small unsigned integers. The equations at the lower right show how to find the DPU's trajectory parameters; these can be uploaded to calibrate the detector calculations. The TOF correction factor is computed via table lookup. The inputs to the LUTs show small numbers; these are the number of most-significant bits from the inputs to the table used to construct indices into the table.

Event Classification

Events are classified into hydrogen (H) or oxygen (O). If
CTOF < A - B*ln(PHb)
the event is an H; otherwise, it is an O. Both A and B are uploadable parameters. For H events, CTOF is classified into one of ten ranges. CTOF is compared against a sequence of increasing thresholds:
T₀ < T₁ < T₂ < T₃ < T₄ < T₅ < T₆ < T₇ < T₈ < T₉
CTOF will be encoded as:
0 where CTOF < T₁; i where T_i <= CTOF < T_i+1; 9 where T₉ <= CTOF
Note that T₀ is not used; it is implicitly zero. The thresholds are uploadable parameters. For O events, CTOF is classified as above, but into only one of eight ranges. A separate set of uploadable thresholds are used.

Azimuth and Elevation Calculation

Azimuth and elevation is computed relative to the HENA boresight vector using trigonometry as follows:
Azimuth = tan^-1(Yb/d)
Elevation = tan^-1(dX/sqrt(Yb² + d²))
From the current position within the spin, the azimuth is offset to be with respect to the sun.

HENA-S

Since the length along the slit where a HENA-S particle passed and the position on the SSD detector where the particle hit are known, the particle's trajectory can be computed. The trajectory can be expressed as azimuth and elevation with respect to the sensor and can be computed with simple trigonometry. Removing spacecraft spin from the azimuth produces azimuth relative to the sun.

The sensor also measures the particle's time of flight (TOF) by timing the arrival interval of the front and coincidence detectors' pulses. Since the path length of the particle can be found from the trajectory, the particle's velocity can be found. Instead of velocity, the equivalent corrected TOF (CTOF) is calculated by scaling STOF by the path length.

The event data is massaged slightly before being used in the event processing algorithm. All the raw values have an offset removed; the offsets for Wft and Wfb are done by the hardware and STOF is offset by the software. Then all negative values are clipped to zero. All the resulting values range from {0 .. 8191}, except for STOF which has the range {0 .. 511}.

Pulse Analysis

The following figure shows the computation of the particle's path through the sensor, the computation of the particle's energy, and the correction of the time-of-flight for path length. The front position, Xf, is computed from Wfb/(Wft + Wfb). The parameters Gf and Of scale the position to the range {-0.5 .. 0.5} and multiplying by Df, the length of the slit, maps the position into centimeters. The two rear positions, Xb and Yb, are computed from the SSD pixel Id via a lookup table. The lookup tables return the X and Y positions in centimeters. The difference dX = Xf - Xb is more important in computing the trajectory than is the actual positions, Xf and Xb.

The time-of-flight (TOF) used in this process is derived from the start detector timing pulse and the coincidence detector pulse. Whereas the coincidence detector is used simply as a validity check for HENA-M events, its pulse is used to generate a stop pulse for a timing circuit in the case of HENA-S events. The electron optics are optimized to provide accurate timing for events which strike the SSD. There is a systematic delay in the stop timing pulse for the SSD, which depends on the SSD pixel location in the azimuth direction. This dependence is negligible for the angled SSD pixels (see schematic), but not negligible for the horizontal SSD pixels (located adjacent to the backplane MCP). This dependency will be corrected in the DPU, by combining the SSD TOF and pixel (Yb) location data. The TOF is also corrected for the distance that the particle actually traveled. From the trajectory, dX and Yb, and the space d between the slit and the rear detector, the distance can be computed as sqrt(d(Yb)2 + dX2 + Yb2). STOF is scaled by dmin/distance. The corrected TOF (CTOF) for a particle normal to the stop detector will be unchanged.

The SSD produces a pulse that is directly proportional to energy (E). This is sent straight through the pulse analysis subsystem.

Similarly to HENA-M, the HENA-S computations must deal with the limitations of computer arithmetic and use the equations below.

Event Classification

Events are classified into eight ranges of CTOF. CTOF is compared against a sequence of increasing thresholds:
T₀ < T₁ < T₂ < T₃ < T₄ < T₅ < T₆ < T₇
CTOF will be encoded as:
0 where CTOF < T₁; i where T_i <= CTOF < T_i+1; 7 where T₇ <= CTOF
Note that T₀ is not used; it is implicitly zero. The thresholds are uploadable parameters.

The corrected TOF is also combined with the energy to compute the particle mass and species. First, the mass is computed:
mass = B1 + B2*ln(E) + B3*ln(T) + B4*ln(T)*ln(E) + B5*ln(E)² + B6*ln(T)³
where B1 - B6 are uploadable parameters. Then the mass is classified into one of four ranges via four threshold values:
T₀ < T₁ < T₂ < T₃
H, He, CNO, or "bad" species will be encoded as 0 - 3 as follows:
3 where mass < T₀; i where T_i <= mass < T_i+1; 3 where T₃ <= mass
The thresholds are uploadable parameters.

Azimuth and Elevation Calculation

Azimuth and elevation are computed as for HENA-M.

Data Products

HENA produces accumulator (singles) data, pulse-height analysis (PHA) results for each sensor, and images for each sensor. Each data product is collected or integrated over a specified period, then downlinked. The integration times are shown in the following table.

The following figure summarizes event processing for HENA-M and HENA-S. Any input or result that is used in the downlinked data is listed with its range and destination data products.

Units

If image motion compensation is disabled, the azimuth and elevation of events recorded in individual PHA results or accumulated into images use the sensor-based coordinate system shown below. The coordinate system covers the field of view of the entire HENA sensor, 90° in azimuth and 120° in elevation. Azimuth ranges from -45° to +45° and is represented as 0 to 30 giving a 3° resolution. Elevation ranges from -60° to +60° and is represented as 0 to 40 also giving a 3° resolution. Any event outside this field of view is reported as having an elevation of 60.

Ordinarily, image motion compensation is enabled and the spacecraft spin is removed from the azimuth of PHA results and images. The resulting spin-based coordinate system covers the entire spin of 360°. Azimuth ranges from 0° to 360° and is represented as 0 to 120. Elevation range is as for the sensor-based coordinate system. The origin of this coordinate system for HENA-M PHA results and images (0°) is defined when the sun is in the center of the HENA-M field of view. Similarly, the origin of this coordinate system for HENA-S is defined when the sun is in the center of the HENA-S field of view.

Accumulators

In addition to the hardware that presents valid events to the DPU, there is hardware that counts the various pulses that are generated in the detectors. Because of false triggers and noise, these accumulators count many more pulses than are genuine events. There are sixteen accumulators, each 24 bits long.

Every two sectors the accumulators are read and downlinked. Reading the accumulators clears them so that they can count pulses in the new interval. Since the counters are not double buffered, an insignificant dead time occurs during the read.

HENA-M PHA Results

Individual particles from the HENA-M sensor are summarized in the HENA-M pulse height analysis (PHA) data. The computed azimuth and elevation of the particle's trajectory is included. The PHA results also have the most-significant bits of the corrected time-of-flight. The most significant bits of the pulse height computed from the front and back MCP are also included.

• Azimuth 7 bits
• Elevation 6 bits
• CTOF 9 bits
• PH front 5 bits
• PH back 5 bits

Each HENA-M event can be placed in one of five TOF categories:

• very fast ([ctof]=0-1)
• fast ([ctof]=2-3)
• medium ([ctof]=4-5)
• slow ([ctof]=6-7)
• very slow ([ctof]=8-9)

HENA-M PHA data is collected in either FIFO, normal, or priority mode. In FIFO mode, all events are collected first come, first served. In normal mode, the DPU collects events evenly distributed between the TOF categories. In priority mode, a single TOF category, selected by ground command, is collected exclusively. HENA-M PHA results are accumulated over two sectors. How many are actually accumulated depends on available downlink bandwidth.

If raw data collection is enabled, each HENA-M PHA result also includes the relevant raw data for the event:

• Event ID 14 bits
• MTOF 14 bits
• Wft 14 bits
• Wfb 14 bits
• Wb 14 bits
• Sb 14 bits
• Ib 14 bits

HENA-S PHA Results

Individual particles from the HENA-S sensor are summarized in the HENA-S pulse height analysis (PHA) data. The computed azimuth and elevation of the particle's trajectory is included. The PHA results also have the most-significant bits of the corrected time-of- flight. The most significant bits of the energy found from the SSD are also included.

• Azimuth 7 bits
• Elevation 6 bits
• CTOF 10 bits
• Energy 9 bits

Each HENA-S event can be placed in one of four mass categories and one of four TOF categories (i.e. one of sixteen total categories):

• H ([m]=0)
• He ([m]=1)
• CNO ([m]=2)
• "bad" ([m]=3)

• very fast ([ctof]=0-1)
• fast ([ctof]=2-3)
• medium ([ctof]=4-5)
• slow ([ctof]=6-7)

HENA-S PHA data is collected in either FIFO, normal, or priority mode. In FIFO mode, all events are collected first come, first served. In normal mode, the DPU collects events evenly distributed between the mass and TOF categories. In priority mode, a single mass/TOF category, selected by ground command, is collected exclusively. HENA-S PHA results are accumulated over two sectors. How many are actually accumulated depends on available downlink bandwidth.

If raw data collection is enabled, each HENA-S PHA result also includes the mass category and the relevant raw data for the event:

• [m] 2 bits
• Event ID 14 bits
• STOF 14 bits
• Wft 14 bits
• Wfb 14 bits
• E 14 bits
• PID 14 bits

HENA-M TOF Images

The mass classification and TOF classification of a HENA-M event are used to select an image to accumulate the event. For hydrogen events with a low time-of-flight, a high spatial resolution hydrogen image is used. For hydrogen events with a high time-of-flight, a low spatial resolution hydrogen image is used. Otherwise, a low spatial resolution oxygen image is used. Image integration always begins when the sun is in the center of the HENA-M field of view and lasts for one spin.

HENA-S M-TOF Images

The TOF and mass classifications of a HENA-S event are used to select an image to accumulate the event. For each of 8 time-of-flights, there are 3 mass categories for a total of 24 images. Image integration always begins when the sun is in the center of the HENA- S field of view and lasts for one spin. Note: starting HENA-M and HENA-S image integrations 45° apart removes the 45° phase difference between the sensors. In other words, each HENA-M and HENA-S image started in the same spin cover the same part of the sky.

HENA-S Energy Images

Raw SSD energy images are accumulated directly in the detector. In backup mode, these are read out every sector and integrated into full spin images. Integration begins when the sun is in the center of the HENA-S field of view and lasts for one spin.

Return to HENA Software User's Guide. Report problems to John Hayes.