Focuser

Role

The Focuser module provides automatic telescope focusing. It moves the motorized focuser across a range of positions, measures star size (HFR — Half Flux Radius) at each point, then computes the optimal position using a degree-2 polynomial fit. With zoning enabled, it also produces a sensor tilt map.

Interface

The interface displays the HFR curve being built in real time, the sequence progress, and the final results (HFR and position). Parameters are accessible via the Parameters button in the top-right corner.

The HFR chart is drawn with error bars representing the standard deviation of measurements at each position, and the polynomial fit appears as a dashed orange line as acquisitions proceed.

Required devices

Parameters

These parameters are accessible from the module Parameters menu. A set of parameters can be saved as a profile.

Exposure

Focus

Algorithm

Focusing proceeds in two phases.

Phase 1 — Exploration

1. The focuser moves to start_position − backlash (mechanical play compensation)
2. It advances to start_position
3. For each iteration:
   • Camera frame reset
   • Frame acquisition, computation of HFR and its standard deviation
   • Recording of the triplet (position, HFR, std dev)
   • Real-time update of the polynomial fit
   • Advance by one step

The degree-2 polynomial fit continuously provides the minimum of the HFR curve:

optimal_position = −k1 / (2 × k2)    [for k0 + k1·x + k2·x²]

Phase 2 — Final positioning

1. The focuser moves back to best_position − backlash
2. It advances to the optimal position computed by the polynomial
3. A final frame is acquired to measure the resulting HFR

HFR chart

The HFR chart is drawn in real time during the exploration phase and updated at each measurement point. It contains two overlaid elements:

• Measured points (green) with error bars representing ±1 standard deviation of measurements at each position
• Polynomial curve (dashed orange) — degree-2 fit updated at each new point

The X axis represents the absolute focuser position, the Y axis the HFR in pixels.

Zoning

Zoning divides the image into an N×N grid and computes an independent polynomial fit for each zone. It enables both a fine analysis of HFR variations across the field and a sensor tilt map.

For each zone, the module computes via Welford’s algorithm (single-pass incremental update):

• The mean HFR of the zone
• The HFR standard deviation of the zone — indicator of local optical quality

Sensor tilt mapping

When zoning is enabled (≥ 2×2), the module automatically generates four mapping images at the end of the sequence. Each represents the optimal focus position for each zone, colour-coded (blue = low position / near focal plane, red = high position / far focal plane).

The width-to-height ratio of each image matches the actual sensor geometry.

rawTilt — Raw per-zone tilt

Each zone is represented by a uniform colour block proportional to its best focus position. No interpolation — spatial resolution equals that of the zoning grid.

localTiltLinear — Local bilinear interpolation

Bilinear interpolation between adjacent zone centres. Produces a smooth map without any assumption about the global shape of the focal plane.

globalTiltLinear — Global plane fit (GSL linear regression)

Least-squares plane fit over all zone positions (GSL library). Ideal for quantifying pure tilt: inclination of the sensor relative to the optical axis. The residual shown in each cell (in yellow) is the deviation between the measurement and the fitted plane.

globalTiltQuadratic — Quadratic surface fit (GSL degree-2)

Degree-2 surface fit. Captures non-planar defects: field curvature, sensor flexion. The colour scale covers the true minimum and maximum of the surface (including the vertex if it lies within the sensor bounds).

Live values

Final result

At the end of the focusing sequence, the module publishes:

These values are also published to other modules (sequencer) via the inter-module event system.

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