The LOS jitter budget: why 50 µrad is harder than it looks

Why we talk in microradians

A sensor’s practical range is bounded by two things: optical resolution and line-of-sight (LOS) stability. Take a 640×512 detector as a worked example: run it 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.

The same RMS figure can mean two different images

One number hides a distinction that decides what the operator actually sees. Motion that happens within the detector’s integration time smears the scene across pixels: the frame comes out blurred, the modulation transfer function is degraded, and no amount of downstream processing puts the detail back. Motion that happens between frames leaves each frame sharp and simply moves it: the picture shakes, which is unpleasant to watch but recoverable by a tracker and tolerable to an operator who is not measuring anything.

Both are jitter and both go into the same RMS number. Which one you have depends on where the disturbance energy sits relative to the frame rate and the integration time. Two systems can report identical RMS jitter and hand you one sharp shaking image and one steady blurred one. When the budget is written, note the band as well as the magnitude.

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 gyro parameter that is not on the front page

ARW and bias instability are measured on a bench that is not moving. On a vehicle the term that frequently dominates both is g-sensitivity: the gyro’s bias shifts under acceleration. Under vibration that shift is not symmetric about zero, so an input whose mean is zero produces an output error whose mean is not — the loop is handed a rate that the world is not actually turning at, and the line of sight walks off in a direction no static test predicts. This is why a unit that meets its drift specification on a table can fail it on a shaker while every other parameter stays inside its limit.

Two consequences follow. Read g-sensitivity and vibration rectification alongside ARW, in the units the manufacturer actually publishes them in. And isolate the gyro from the vibration input where the mounting allows it, remembering that any isolator you add is a compliant element between the sensor and the optics — which is the one thing the next section says not to do.

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:

1. 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.
2. Notch filtering. Effective, but fragile against a mode that drifts with temperature and ageing — keep the notch narrow and verify the mode frequency.
3. 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.

The budget the operator lives in

Stabilisation and latency are separate budgets and they get confused constantly. A line of sight can be held to specification and the system still be unusable for manual tracking, because the picture the operator is steering by describes where the target was, not where it is. The operator closes a loop of their own around that delay: they overshoot, see the overshoot late, correct, and overshoot the other way. The symptom looks exactly like poor stabilisation and it is cured somewhere else entirely — in the compression, the link and the display, not in the servo. If a system is being specified for manual tracking, put end-to-end glass-to-glass latency in the requirement next to the jitter figure.

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?
• Is the jitter within the integration time separated from the jitter between frames?
• Has the first structural mode been measured — modal test, not analysis?
• How much of the budget does gyro ARW consume at the target bandwidth, and how much does g-sensitivity consume under the actual vibration input?
• Has cable and slip-ring friction torque been measured?
• Is end-to-end latency specified alongside jitter?
• 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.