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Do insects with compound eyes have depth perception? They fly as if they do, but their eyes are so close together it seems like the image would be 2 dimensional.

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"1001 questions answered about insects" by Alexander Barrett and Elsie Broughton Klots includes the following passage:

Do insects have depth perception? Depth perception of some sort is important to an animal who has to catch its prey; fortunately most insects have it to a degree. Although they do not have binocular vision that can be compared with man's, it is true that when one eye is covered their depth perception is markedly affected. The criterion of depth seems to depend on the angle of simultaneous stimulation of two corresponding points of the retina of the two eyes.

However it does not mention compound eyes specifically.

There may be other methods of obtaining a perception of distance rather than the binocular vision seen in humans. This paper suggests that there is 'clear evidence' that some insects perceive depth by moving their head to artificially create parallax, which they can then recognise and interpret as depth and distance. They cite the Praying Mantis as an example, which does have compound eyes.

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The sense of depth is required to us to orient ourselves in a 3D world. Insects do orient themselves in the exterior 3D world, thanks to the ability to detect the plane of sunlight polarization, that is used as a navigation compass in foraging expeditions and when coming back home.

You can find a good review on Current Biology (Krapp 2007) and a lecture about insect vision from Cornell University.

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