Synthetic Aperture RADAR

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Description

The Synthetic Aperture RADAR (SAR) is a RADAR designed for imaging applications. It extends the base RADAR functionality with parameters for controlling sample timing, resolution, and visualization. When used with a visualization engine, the SAR produces depth maps and textures based on radar returns. In analytical mode, it uses the inherited detection pipeline; when driven by the visualization engine, it processes GPU-traced geometry through the radar equation to produce per-target returns.

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Example Use Cases

• Terrain Mapping: Generate surface elevation maps of planetary bodies from orbit.
• Earth Observation: Simulate SAR imaging missions for land cover or environmental monitoring.
• Target Imaging: Produce radar images of ground targets regardless of lighting or weather conditions.

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Module Implementation

The SAR sensor inherits all detection capabilities from the RADAR base class and adds imaging-specific parameters and a trace-based capture pipeline.

Sampling

The sensor captures data at a configurable sample rate $T_s$. At each simulation step, the scheduler checks whether the current time has exceeded the next scheduled sample time $t_{\text{next}}$:

$$t+\Delta t\ge t_{\text{next}}$$

When this condition is met, a capture is triggered and the next sample time is updated:

$$t_{\text{next}}\leftarrow t+T_s$$

The On Ping method provides an alternative trigger for capture when driven externally by the visualization engine.

Radar Equation

For each detected target, the received power $P_r$ is computed using a simplified form of the radar equation:

$$P_r=\frac{P_{\text{scale}}\cdot G_t^2\cdot \sigma }{R^4}$$

where $P_{\text{scale}}$ is a pre-computed power factor derived from the transmit power, antenna gain, and wavelength (inherited from the base RADAR class), $G_t$ is the one-way beam taper gain, $\sigma$ is the radar cross-section of the target in m², and $R$ is the range to the target in meters.

The received power is clamped to the transmit power $P_t$ to prevent non-physical returns:

$$P_r=\min (P_r,P_t)$$

Beam Tapering

The antenna gain is modeled as a Gaussian beam pattern. For a target at off-boresight angle $\theta$, the one-way taper $G_t$ is:

$$G_t=\exp \left(-k{\left(\frac{\theta }{{\theta }_{bw}}\right)}^2\right)$$

where ${\theta }_{bw}$ is the half-power beamwidth in radians and $k$ is a constant governing the Gaussian roll-off. The taper is applied twice (transmit and receive paths), giving the two-way factor $G_t^2$ in the radar equation above.

Receiver Limits

After computing received power, the sensor applies configurable receiver thresholds. If the signal falls outside the receiver sensitivity window $[P_{\min },P_{\max }]$, the return can be discarded when threshold filtering is enabled. Otherwise, the received power is clamped:

$$P_r=\max (P_{\min },\min (P_r,P_{\max }))$$

Trace Pipeline

When the visualization engine drives the SAR, geometry is resolved via GPU ray casts and the results are processed through two phases:

1. Per-pixel reduction: Raw hit distances are converted to depth in meters, clamped to the sensor range, and range-rate is estimated from the change in depth between pings:

$$\dot{R}=\frac{d_{\text{prev}}-d_{\text{current}}}{\Delta t_{\text{ping}}}$$

2. Per-target aggregation: Hit samples are grouped by target. The cross-section is estimated from the number of illuminated samples and the angular footprint:

$$\sigma =N_{\text{hits}}\cdot {\left(R\cdot \frac{{\theta }_{\text{fov}}}{N_{\text{res}}}\right)}^2$$

where $N_{\text{hits}}$ is the number of samples that struck the target, $R$ is the nearest surface range, ${\theta }_{\text{fov}}$ is the sensor field of view in radians, and $N_{\text{res}}$ is the output resolution. The radar equation and receiver limits are then applied to each aggregated return.

Visualization

When Compress Visualisation is enabled, the depth color gradient is mapped to the actual hit range (nearest to farthest hit) rather than the full sensor range. This provides higher contrast when targets occupy a narrow band of the total detection range.

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Assumptions/Limitations

• Requires a visualization engine for image generation; the analytical mode provides detection data only.
• Inherits all assumptions and limitations from the base RADAR class, including thermal noise and distance noise models.
• The beam pattern assumes a symmetric Gaussian; sidelobe structure is not modeled.
• Cross-section estimation in the trace pipeline depends on the output resolution and does not account for target orientation or material properties.
• Range-rate estimation assumes a fixed ping interval and uses a first-order finite difference.
• The analytical and trace capture paths are mutually exclusive; they cannot operate simultaneously.