FOV)

Quick Estimation is a live finite-conjugate imaging aid in the Open 3D viewer, built for machine-vision setups where the camera (sensor) is fixed and you trade object distance, image distance, magnification, and field of view (FOV) against one another.

It is driven by the conjugate relationship of the fixed lens:

\[\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}, \qquad |m| = \frac{s_i}{s_o}, \qquad \mathrm{FOV} = \frac{\text{sensor semi-height}}{|m|}\]

where \(s_o\) and \(s_i\) are the object and image distances measured from the lens principal planes and \(f\) is the focal length.

The design flow

Pin the sensor in the left panel. Set Field Type to Real Image Semi-Height with the sensor half-height as the Field value. This is the fixed camera; Quick Estimation never changes it.
Turn on Quick Estimation in the Live Controls panel, and enable physical distances so the thickness arrows are visible and hoverable.
Drive a conjugate gap. Drag a thickness arrow, click it to type a value, or right-click it for a role. Whichever gap you touch becomes the independent variable; its conjugate partner re-solves for focus, so the image stays sharp, and the FOV readout follows the new magnification.

Two readings of the same move

Dragging always keeps the image in focus (the other distance auto-solves). What you read off depends on what you are holding fixed:

Fixed object size → fill factor. Set a target Object Height (the real object you want to image). As you drag, the image grows or shrinks on the fixed sensor; the readout shows the fill percentage. Above 100 % the object overfills and is cropped; below 100 % it underfills.
Fixed sensor fill → FOV. With no target set, the FOV that exactly fills the sensor is reported and changes as you drag.

There is exactly one focused conjugate pair per FOV: for a fixed lens and sensor, the target FOV fixes the magnification \(|m| = \text{sensor}/\text{FOV}\), and a given magnification has a unique pair \(s_o = f(1 + 1/|m|)\), \(s_i = f(1 + |m|)\). Snap to FOV jumps both gaps straight to that pair. The Configuration table sweeps the object distance and lists the focused conjugate combinations (object/image distance, magnification, FOV, working distance, real-image validity).

Right-click actions

Object plane / object-distance arrow — set the target Object Height (FOV), snap both gaps to that FOV, open the configuration table, or set the gap role (Independent / Dependent / Constant).
Image plane / image-distance arrow — set the sensor semi-height (the same left-panel Field value) or set the role.

Sensor coverage and recommended sensor

When Quick Estimation is on, the 3D scene draws coverage overlays:

Object plane — a solid circle at the current object FOV and a dashed ghost circle at the previous FOV, so a change reads as bigger or smaller.
Image plane — a solid circle at the image footprint, the recommended rectangular sensor inscribed in it (so you see the image circle covering the sensor), and a dashed ghost of the previous image circle.

The panel reports a recommended sensor: the rectangle whose diagonal matches the image footprint of the object being imaged, with width × height (4:3), the image-circle diameter, and the nearest standard format (1/4" … Full-frame) — so you can size or source a camera the image circle perfectly covers. Overfilling the current sensor recommends a larger format; underfilling recommends a smaller one.

Forbidden values

If you drag the object inside the front focal point — the working distance falls below the focal length — no real image can form. The thickness arrow flashes red with a warning and the live commit is suppressed until you back off.

Validation

The behaviour is guarded across all five machine-vision layouts (150 mm 1×/0.5×, 120 mm, 85 mm, 150 mm measured) by KrakenOS/UI/validate_open3d_quick_estimation_conjugate.py (comprehensive harness Phase 34): focus is held, FOV = sensor / |m|, FOV is monotonic with object distance, both solve directions work, snap_to_fov reproduces the unique conjugate pair, the forbidden region is detected, and the live drag preview does not mutate committed thicknesses.