In most animal species, vision is mediated by compound eyes, which offer lower resolution than vertebrate single-lens eyes, but significantly larger fields of view with negligible distortion and spherical aberration, and high temporal resolution in a tiny package. Compound eyes are ideally suited for fast panoramic motion perception. Engineering a miniature artificial compound eye is challenging, because it requires accurate alignment of the photoreceptive and optical components on a curved surface. Here we describe a novel design method for biomimetic compound eyes featuring a panoramic, undistorted field of view in a very thin package. The design consists of three planar layers of separately produced arrays, namely, a microlens array, a neuromorphic photodetector array and a flexible printed circuit board, that are stacked, cut and curved to produce a mechanically flexible imager. Following this method, we have prototyped and characterized an artificial compound eye bearing a hemispherical field of view with embedded and programmable low-power signal processing, high temporal resolution, and local adaptation to illumination. The prototyped artificial compound eye possesses several characteristics similar to the eye of the fruit fly Drosophila and other arthropod species. This design method opens up new vistas for a broad range of applications where wide field motion detection is at a premium, such as collision-free navigation of terrestrial and aerospace vehicles, and for the experimental testing of insect vision theories.