The LOS jitter budget: why 50 µrad is harder than it looks
An electro-optical system's range is often limited not by its optics but by its stabilisation. Breaking jitter down by source shows exactly where a design is won or lost.
Why we talk in microradians
A sensor’s practical range is bounded by two things: optical resolution and line-of-sight (LOS) stability. Run a 640×512 MWIR detector at a 2° horizontal field of view and a single pixel subtends roughly 55 µrad. If your line of sight is oscillating at 100 µrad, the target walks two pixels every frame, the image smears over the integration time, and the detector’s nominal resolution — still perfectly valid on paper — is lost in the field.
The working rule is simple: RMS jitter should stay below roughly one third of the narrow-FOV IFOV. For a 55 µrad IFOV that means about 18 µrad RMS, or a peak target in the region of 50 µrad.
Where the disturbance comes from
Jitter never has a single source. In a typical vehicle-mounted system the budget is shared by:
| Source | Band | Character |
|---|---|---|
| Vehicle suspension / hull motion | 1–20 Hz | High amplitude, broadband |
| Motor and drivetrain (cogging, torque ripple) | 50–500 Hz | Speed-dependent, narrowband |
| Wind load and vortex shedding | 0.5–10 Hz | Slow, direction-changing |
| Cable and slip-ring friction torque | DC–5 Hz | Position-dependent, hysteretic |
| Structural resonance | 100–400 Hz | Gain peaking, phase loss |
The point of the table is that because the bands differ, the remedies differ too. Suspension motion is suppressed by closed-loop rejection; torque ripple is solved on the drive side through current control and harmonic compensation; friction torque has to be designed out mechanically — cable routing, bearing preload — because no controller suppresses DC friction for free.
Loop architecture: the rate loop is built on the gyro
The core of stabilisation is a rate loop closed around an angular rate gyroscope mounted on the gimbal body. The position loop sits on top of it at a far lower bandwidth. That separation matters: the position loop tracks the target, the rate loop holds the world still.
Gyro selection sets the noise floor directly. For MEMS devices the two governing parameters are angular random walk (ARW) and bias instability. ARW defines the rate noise density, and the noise the loop actually sees grows with the square root of bandwidth — quadruple the bandwidth and you double the noise floor. Bias instability shows up instead as long-term pointing drift. To avoid spending a large share of the budget on the first line item, specify the gyro against the bandwidth you actually need — not more.
The structure sets the bandwidth
Disturbance rejection scales roughly with loop gain: 40 dB of rejection at 10 Hz requires 100× open-loop gain at that frequency. Only one wall stands in the way of raising it — the first structural mode.
If the gimbal body and bearing assembly resonate near 180 Hz, gain crossover realistically cannot exceed about a fifth or sixth of that, i.e. 30–36 Hz. Three levers remain:
- Stiffen the structure. Frequency scales with the square root of stiffness; reducing inertia is often cheaper than adding stiffness. Bringing the optical payload’s centre of gravity onto the rotation axis cuts both inertia and cross-coupling.
- Notch filtering. Effective, but fragile against a mode that drifts with temperature and ageing — keep the notch narrow and verify the mode frequency.
- Sensor-actuator collocation. Mount the gyro as close to the optical path as physically possible. Every compliant element in between inserts phase between the motion the controller sees and the motion the optics actually make.
Where feedback runs out: feedforward
A closed loop by definition corrects error after observing it. If base motion is already measurable — an IMU on the vehicle — feeding it straight into the rate command partly bypasses that delay. In practice a well-tuned feedforward path buys another 6–10 dB of rejection at low frequency without stressing loop stability at all.
Verification: the budget doesn’t close until jitter is measured
Jitter is verified on a shaker, not in simulation. The typical setup mounts the system on a three-axis vibration table, images a distant target at infinity through a collimator, and tracks the target centroid frame by frame. The output is not a single number but a power spectral density (PSD) curve; RMS jitter falls out of its integral. Only that curve shows where the budget was spent.
Design checklist
- Has narrow-FOV IFOV been calculated, and the jitter target set at a third of it?
- Are disturbance sources separated by frequency band?
- Has the first structural mode been measured — modal test, not analysis?
- How much of the budget does gyro ARW consume at the target bandwidth?
- Has cable and slip-ring friction torque been measured?
- Are results reported as a PSD?
At Inventra we run electro-optical system design from this budget: the specification is first turned into a table, then distributed across the mechanical and control domains.