System Design

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Figure 1

Cross-sectional diagram of the FoveaCam Duo telephoto camera module, showing the optical path and MEMS mirror steering mechanism.

The FoveaCam Duo system consists of three cameras arranged on a horizontal baseline: a central wide-angle camera and two telephoto cameras positioned symmetrically on left and right side of the wide angle camera, each equipped with a MEMS mirror that steers the telephoto optical axis. The telephoto component provides high angular resolution within a narrow field of view ${\theta }_T$ that can be dynamically directed to any region within the extended field of view ${\theta }_W$.

Optical Performance

Specification		Measurements
Optical Field of View	Wide	25.6° × 19.4°
	Fovea	2.86° × 2.15°
Angular Resolution	Wide	~55 px/°
	Fovea	~502 px/°
Steering	Actuation Range	20° × 20°
	Extended FoV	22.9° × 22.2°
MEMS Actuation	Response Time	<1 ms
	Step Precision	~0.08 px/step

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Table 1

Optical performance and electrical actuation specifications of the FoveaCam Duo system.

The telephoto cameras achieve approximately $502$ px/°, roughly $9\times$ the angular resolution of the wide-angle camera and significantly higher than any known stereo setup built for depth sensing. These values are measured through a standard OpenCV checkerboard camera calibration pipeline.

Active Steering Performance

We report actuation performance specifications in Table 1 based on our measurements on optical performance and product specifications reported by the vendor of the MEMS mirrors.

Depth Resolution

The theoretical depth error $\delta Z$ for a parallel stereo pair at distance $Z$ with focal length $f$, baseline $B$, and disparity uncertainty $\delta d$ is:

$$\delta Z=\frac{\delta d\cdot Z^2}{f\cdot B}$$

We list the theoratical depth resolution using measured charactistics from Table 1:

Distance	10 m	50 m	100 m	500 m	1 km
Absolute	1.7 mm	43.4 mm	174 mm	4.34 m	17.4 m
Relative	0.017%	0.087%	0.17%	0.87%	1.74%

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Table 2

Theoretical depth error $\delta Z=\frac{\delta d\cdot Z^2}{f\cdot B}$ for the FoveaCam Duo stereo telephoto pair at representative distances. Using: $f=\mathrm{28,788}$ px, $B=200$ mm, $\delta d=0.1$ px (subpixel).

The resolutions listed above assume perfect sub-pixel matching. Actual performance depends on the accuracy of stereo algorithm used for disparity generation.