16.4. Tutorials
16.4.1. Using the whisk scan mount
The purpose of this tutorial is to not only demonstrate how to use the whisk scan instrument mount, but to demonstrate how the instrument mount and the platform interact with each other. One of the most common areas of confusion regarding the interaction between the instrument mount and the platform can usually be clarified with a few examples.
Since this tutorial will use the "generic" platform model to help visualize how a the dynamic scanning of the whisk mount traces the primary optical axis of the instrument over the ground, it is suggested that the user understand the role and usage of the platform model (see Configuring the generic platform).
16.4.1.1. Straight and level flight
This first example will use an airborne platform that is configured to flight due North with a perfectly level orientation (all the platform rotation angles are zero). This simple flight can be described by the XML "Platform Position Data" file (see Generic Platform XML File) shown below:
<platform type="generic>
<method type="raw"></method>
<data rotationorder="zyx" angletype="absolute" spatialunits="meters" angularunits="radians">
<entry>
<datetime type="relative">0.000</datetime>
<xlocation>0.00000</xlocation>
<ylocation>-5000.00000</ylocation>
<zlocation>1000.00000</zlocation>
<xrotation>+0.00000</xrotation>
<yrotation>+0.00000</yrotation>
<zrotation>+0.00000</zrotation>
</entry>
<entry>
<datetime type="relative">10.000</datetime>
<xlocation>0.00000</xlocation>
<ylocation>5000.00000</ylocation>
<zlocation>1000.00000</zlocation>
<xrotation>+0.00000</xrotation>
<yrotation>+0.00000</yrotation>
<zrotation>+0.00000</zrotation>
</entry>
</data>
</platform>
You can see that the platform is traveling at an altitude of 1000 m above the origin and has an average speed of 100 m/s (it travels 10,000 meters in 10 seconds). The axis rotation angles are all 0 and, therefore, any interpolated locations or orientations for times between 0 and 10 seconds will also have 0 axis rotation angles.
The instrument mount that will be modeled will have a 15 degree field of view centered about the vertical and have a scan rate of 10 Hz. The following XML description captures these parameters:
<mount type="whisk">
<data temporalunits="hertz" angularunits="degrees">
<scanrate>10.0</scanrate>
<scanrange>
<start>-7.5</start>
<stop>+7.5</stop>
</scanrange>
</data>
</mount>
To visualize how the platform and instrument mount work in conjunction to scan over a scene, a simple tool was created that outputs the location on the ground (assumed to be at an elevation of 0 in this example) viewed at the center of the instrument's optical axis as a function of time. The red data points plotted in Figure 16-1 show the ground track of the instrument's optical axis as a function of time. The green data points show the location of the platform projected onto the same ground plane.
The sinusoidal pattern of the instrument mount scan be observed in this plotted data. The scan pattern is orthogonal to the flight line since this specific mount models an across-track scan of the instrument. The along-track coverage is provided souly by the forward motion of the platform.
The plot in Figure 16-2 shows a simple variant of this example, where the platform is flying in a northeast bound direction. The platform orientation is still ideal with respect to this flight line, so the scan pattern is still orthogonal to the flight line. The apparent compression of the scans in the plot is an artifact of the plot bounds. This example is meant to demonstrate that the instrument mount always scans relative to the platform orientation.
16.4.1.2. Straight flight with platform roll
To further demonstrate the relationship between instrument mount scanning we return to the straight and level, northbound flight line. In this example, the original level flight line will be modified to include a constant roll. Since the default forward axis for the platform is the +Y axis, roll is a rotation about the Y axis. In this example, we have added -0.2 radians of roll, which will roll the plane such that the right wing is up. The modified XML "Platform Position Data" file (see Generic Platform XML File) for this example shown below:
<platform type="generic>
<method type="raw"></method>
<data rotationorder="zyx" angletype="absolute" spatialunits="meters" angularunits="radians">
<entry>
<datetime type="relative">0.000</datetime>
<xlocation>0.00000</xlocation>
<ylocation>-5000.00000</ylocation>
<zlocation>1000.00000</zlocation>
<xrotation>+0.00000</xrotation>
<yrotation>-0.20000</yrotation>
<zrotation>+0.00000</zrotation>
</entry>
<entry>
<datetime type="relative">10.000</datetime>
<xlocation>0.00000</xlocation>
<ylocation>5000.00000</ylocation>
<zlocation>1000.00000</zlocation>
<xrotation>+0.00000</xrotation>
<yrotation>-0.20000</yrotation>
<zrotation>+0.00000</zrotation>
</entry>
</data>
</platform>
The projected instrument optical axis and platform location for this constant roll scenario are plotted in Figure 16-3. If you compare this plot to that in Figure 16-1 you will see that the projected platform location is still at 0 Easting (since we modified the platform orientation and not the location), but the projected optical axis has slid to the right due to the roll of the platform.
16.4.1.3. Straight flight with platform yaw
This example is similar to the last except that the platform will be given a constant yaw or "crab" angle with respect to the flight line. The yaw or crab axis for the platform is the Z axis and a positive 0.2 radian angle will result in the nose of the plane pointing left of the flight line. The modified XML "Platform Position Data" file (see Generic Platform XML File) for this example shown below:
<platform type="generic>
<method type="raw"></method>
<data rotationorder="zyx" angletype="absolute" spatialunits="meters" angularunits="radians">
<entry>
<datetime type="relative">0.000</datetime>
<xlocation>0.00000</xlocation>
<ylocation>-5000.00000</ylocation>
<zlocation>1000.00000</zlocation>
<xrotation>+0.00000</xrotation>
<yrotation>+0.00000</yrotation>
<zrotation>+0.20000</zrotation>
</entry>
<entry>
<datetime type="relative">10.000</datetime>
<xlocation>0.00000</xlocation>
<ylocation>5000.00000</ylocation>
<zlocation>1000.00000</zlocation>
<xrotation>+0.00000</xrotation>
<yrotation>+0.00000</yrotation>
<zrotation>+0.20000</zrotation>
</entry>
</data>
</platform>
The projected instrument optical axis and platform location for this constant yaw scenario are plotted in Figure 16-4. If you compare this plot to that in Figure 16-1 you will see that the projected platform location is still at 0 Easting (since we modified the platform orientation and not the location), but the projected instrument optical axis is no longer orthogonal to the flight line.
16.4.1.4. Straight flight with platform orientation jitter
This final example is to demonstrate the pointing deviations that results from jitter in the platform orientation. In this example, the ideal north bound flight line was modified to have 0.001 degrees of normally distributed noise added to the platform orientation data. The projected instrument optical axis and platform location for this constant yaw scenario are plotted in Figure 16-5. If you compare this plot to that in Figure 16-1 you will see that the projected platform location is still at 0 Easting (since we modified the platform orientation and not the location), but the projected instrument optical axis no longer a well traced path on the ground.
16.4.2. Sawtooth scanning using the tabulated scan mount
This tutorial is mean to demonstrate the "tabulated" instrument mount and how it can be used to produce a "sawtooth" scan. The "sawtooth" scan is a scan pattern that consists of a linear angular scan in one across-track direction which then instantaneously reverses direction and scans back to the starting position. This scan pattern is commonly referred to as a "sawtooth" scan because of the pattern that is scanned on the ground from a moving platform.
This example will use an airborne platform that is configured to flight due North with a perfectly level orientation (all the platform rotation angles are zero). This simple flight can be described by the XML "Platform Position Data" file (see Generic Platform XML File) that was used in the first tutorial in this section.
This example will scan in the across-track direction which is about the Y axis since the DIRSIG4 platform models have a nominal heading in the +Y direction. This mount will linearly scan back and forth between -7.5 and +7.5 degrees at a rate of 10 Hz. Since we want a linear scan rate between the extreme angles and this mount object performs linear interpolation between the supplied angle entries, the user only needs to supply the entries for the extreme angles. Since the tabulated mount requires that you specify a complete scan, the user needs to supply three (3) entries total: the extreme right angle (+7.5 degrees), the extreme left angle (-7.5 degrees) and then the extreme right angle again. Since the scan rate we desire to model is 10 Hz, the time for the full scan should be 0.1 seconds. Therefore, the time for the second entry (midway through the scan) should be 0.05 seconds and the time for the last entry should be 0.1 seconds.
The resulting XML description for this mount scan pattern is shown below:
<mount type="tabulated">
<data rotationorder="zyx" temporalunits="seconds" angularunits="degrees">
<entry>
<time>0.000</time>
<xrotation>0.0</xrotation>
<yrotation>+7.5</yrotation>
<zrotation>0.0</zrotation>
</entry>
<entry>
<time>0.100</time>
<xrotation>0.0</xrotation>
<yrotation>-7.5</yrotation>
<zrotation>0.0</zrotation>
</entry>
<entry>
<time>0.200</time>
<xrotation>0.0</xrotation>
<yrotation>+7.5</yrotation>
<zrotation>0.0</zrotation>
</entry>
</data>
</mount>
The projected instrument optical axis and platform location for this scenario are plotted in Figure 16-6.
16.4.3. Conical scanning using the tabulated scan mount
This tutorial is mean to demonstrate how the "tabulated" instrument mount and how it can be used to produce a "conical" or "rotary" scan. This type of scan pattern is commonly used with laser radar systems.
This example will use an airborne platform that is configured to flight due North with a perfectly level orientation (all the platform rotation angles are zero). This simple flight can be described by the XML "Platform Position Data" file (see Generic Platform XML File) that was used in the first tutorial in this section.
To create this scan pattern, the user will need to configure the "tabulated" instrument mount to use two rotation angles. However, with careful planning and the use of the "rotationorder" attribute, the problem can be simplified to one constant rotation and one dynamic rotation. The constant rotation will be about the Y axis of +7.5 degrees which will rotate the line-of-sight to the "left" of the platform. Then we will add a dynamic rotation about the Z axis which will sweep the line-of-sight in a circle below the platform. They key here is that we want the axis rotations to be performed in a specific order: Y and then Z (assuming X rotation is 0 in this case).
Upon some analysis, we see that this scan pattern can be described with only two time/rotation entries. The Z rotation needs to linearly increase from 0 to 360 degrees during the scan period, and the Y rotation needs to be constant. Note, that the "rotationorder" is "xyz" since we want the Z rotation to be performed after the Y rotation The X axis rotation is first but always zero and therefore could have been placed anywhere in the rotation order. The resulting XML description is shown below:
<mount type="tabulated">
<data rotationorder="xyz" temporalunits="seconds" angularunits="degrees">
<entry>
<time>0.0000</time>
<xrotation>0.0</xrotation>
<yrotation>+7.5</yrotation>
<zrotation>0.0</zrotation>
</entry>
<entry>
<time>0.100</time>
<xrotation>0.0</xrotation>
<yrotation>+7.5</yrotation>
<zrotation>360.0</zrotation>
</entry>
</data>
</mount>
The projected instrument optical axis and platform location for this conical scanning scenario are plotted in Figure 16-6.
