Characterization of Visual Sampling.

To characterize the visual sampling of the environment by the fabricated CurvACE prototype, we measured the angular sensitivity function (ASF) of each of the 630 artificial ommatidia (Fig. S5). Fig. 3 A and D shows representative examples of ASFs measured along a single row and a single column, respectively. Most ASFs display the expected Gaussian distribution with respect to the light incidence angle, which validates both the microoptical design and the precise alignment with each individual photodetector. We derived the experimental acceptance angles and interommatidial angles from the measured ASFs. The acceptance angle Δρ of an ommatidium is defined as the full width at half maximum (FWHM) of its Gaussian-like ASF. The horizontal and vertical interommatidial angles Δφ_h and Δφ_v were assessed from the angular position of the peak of the ASFs of two adjacent ommatidia (Fig. 3C). The measured acceptance angles yielded an average of Δρ of 4.2° ± 0.3° (SD) for both horizontal (Fig. 3A) and vertical (Fig. 3D) directions. The vertical interommatidial angles resulted in an average of Δφ_v of 4.26° ± 0.16° (SD) (Fig. 3D), and the horizontal ones ranged from Δφ_h = 4.2° ± 0.8° (SD) in the middle row (Fig. 3A) to 3.7° ± 0.7° (SD) in the top and bottom rows (Fig. 3B). The close match between the experimentally measured acceptance angles and interommatidial angles validates both the ray-tracing design and fabrication process while indicating that the CurvACE prototype, like the fruit fly compound eye (24), performs an adequate sampling of its entire FOV (Fig. 1B). The observed spread in the values of the horizontal interommatidial angles Δφ_h (Fig. 3 A and B) is probably due to the manual process used to mechanically fix the flexible PCB supporting the artificial ommatidia array onto the rigid curved substrate.

Characterization of Ommatidium Light Adaptation.

In the natural world, visual sensors must cope with a wide dynamic range of irradiance, which can span on the order of 8 decades over the course of a day. Light variations within a scene are particularly challenging because they can make part of the visual field nonresponsive due to photoreceptor saturation. Animal retinae partly solve this crucial problem by means of a local light adaptation mechanism integrated within each photoreceptor (3, 4, 25, 26). Similarly, we have equipped each prototype ommatidium with a neuromorphic adaptation circuit (Fig. S2D) that operates independent of its 629 neighbors. The neuromorphic circuit originally proposed by Delbrück and Mead (27) was modified here by cascading a first-order, low-pass filter (Fig. S2D). This modification prevents temporal aliasing and keeps the photodetector bandwidth of 300 Hz practically constant across the entire studied range of ambient lighting conditions. The circuit design was further optimized (SI Text, Photodetector Layer) to minimize the transient gain dispersion of each autoadaptive circuit. Fig. 4 shows the mean steady state and transient responses of 11 artificial ommatidia (photodetectors with optics) in one column to light step increments and decrements presented at four different steady light levels (Fig. S6). At each of these four levels (red circles in Fig. 4), the output response of the individual ommatidia to light steps yields an S-shaped operating curve in a semilog plot. Adaptation to a novel steady irradiance level essentially produces a horizontal shift of the curve without markedly changing its slope, which represents a dynamic sensitivity of about 1,300 mV per decade in the linear part. The steady operating curve (shown in red in Fig. 4) is also a logarithmic function of the adapting light, but with a slope (steady sensitivity) about 12-fold smaller. Thanks to the optimized design of the adaptive photodetector layout, the averaged dispersion of the sensitivity over the four operating curves is as small as 11 mV, that is, only about 2% of the total 600-mV dynamic range.

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Fig. 4.

CurvACE autoadaptation to ambient light at the single ommatidium level. Steady-state (red dots) and transient (green dots) responses of the adaptive analog VLSI photodetectors [design based on a circuit proposed by Delbrück and Mead (27)]. Each of the four dynamic operating curves (in green) shows the V(log I) response, averaged over 11 ommatidia (photodetectors with optics) of one column, to step increments and decrements of irradiance (Fig. S6) about four steady levels (red circles).

The four operating curves demonstrate not only the high sensitivity of the prototype ommatidia but their relative invariance in sensitivity to the ambient light. These V(log I) curves shifting with the operating points are reminiscent of those obtained in analogous experiments carried out on single vertebrate (25) and invertebrate (26) photoreceptors. This local adaptation is essential for efficient sampling of natural environments because it prevents saturation of the photoreceptors by bright spots in the visual scene while allowing them to adapt quickly to untoward illumination changes, such as transitions from a shaded area to a sunny place.

Characterization of Motion Extraction.

In addition to an extensive FOV (Fig. 3) and local adaptation to illuminance (Fig. 4), the CurvACE prototype ommatidia yield a signal acquisition bandwidth of 300 Hz, which is threefold higher than that measured in the ommatidia of fast-flying insects (28). A high bandwidth contributes to the reduction of motion aliasing during fast locomotion. Furthermore, the implemented read-out protocol (Fig. S7) allows a maximum frame rate of 1.5 kfps, which permits frame averaging to improve the signal-to-noise ratio. We experimentally tested CurvACE motion detection capabilities by computing optic flow vectors from visual signals resulting from different types of motion in the presence of random black and white patterns on a wall (Fig. S8). In this first experiment, we used a modified version of the Lucas–Kanade method (29, 30) (SI Text, Optic Flow Characterization and Eqs. S1–S9), which is a particularly efficient image-based processing algorithm used to calculate optic flow vectors in two dimensions. The optic flow vectors measured during roll rotation (Fig. 5A) and linear translation toward a textured wall 0.3 s before collision (Fig. 5B) show coherent patterns of visual rotation and expansion, respectively. The center of rotation and focus of expansion can be clearly identified (red dots in Fig. 5), allowing for estimation of the axis of rotation and of the direction of translation, respectively. The sensor egomotion can be estimated from these flow fields, for instance, by implementing matched filters (31) analogous to the directionally selective, motion-sensitive neurons found in some insect visual systems (5). Furthermore, the embedded inertial sensors can be used for cancelling the rotational component of the measured optic flow, assessing only the translational component. Because this component is related to distance from objects, the optic flow data provided by a CurvACE prototype could assist mobile platforms to perform collision-free navigation (9).

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Fig. 5.

Optic flow fields from the CurvACE prototype. Cylindrical equidistant projections of the optic flow field calculated with a modified version of the Lucas–Kanade method (29, 30) from the visual signals obtained by the CurvACE prototype subjected to roll motion (Fig. S8B) at 32° per second and at a distance of about 1 m to a wall displaying random black and white patterns (A) or to linear translation (Fig. S8C) at 3 cm/s toward the patterned wall at a distance of 1 cm (B). The red spot displays the center of rotation (A) or the focus of expansion (B).

We also characterized motion detection quantitatively at different ambient light levels with a bioinspired local visual processing algorithm based on the “time-of-travel” scheme (32) (Fig. S9). Fig. 6 shows the angular speed ω_median obtained by measuring the rotational optic flow as a function of the yaw rotational speed of CurvACE surrounded by a natural pattern. The experimental data show a good match between the rotational speed perceived by CurvACE and the true rotational speed. The error in the regression coefficient (linearity error) ranges from 5 to 10% (Fig. 6) at the three illumination levels, indicating that the CurvACE sensor takes full advantage of its autoadaptive analog VLSI photodetectors to make motion detection largely invariant to different illumination conditions. With the time-of-travel scheme, any pair of neighboring ommatidia driving a “local motion sensor” is able to measure angular velocities ranging from 50° to 358° per second for the interommatidial angle of 4.2° with sufficient accuracy. Measurement limitation at lower speeds is due to the signal attenuation brought about by the spatiotemporal processing present in each artificial ommatidium (Fig. S9A).

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Fig. 6.

Characterization of CurvACE motion detection capabilities. (A–C) Angular speed characteristics of CurvACE calculated with a method based on the time-of-travel scheme (32) (Fig. S9) assessed by applying steps of yaw rotational speed Ω_yaw to the sensor at 10° per second, lasting 10 s each, with the prototype placed at the center of a 105-cm diameter arena lined with prints of a natural image. The dashed line displays the theoretical trend.