Wednesday, December 05, 2012

Dragonfly Eyes - the Wonders of Low Resolution


Continuing with the recent theme of analyzing both natural and man made cameras, I thought I'd analyze an insect eye in this post.  In previous posts I've analyzed a gigapixel airborne security video camera and the eye of a raptor.  I'm working on analyses of the F-35's Distributed Aperture System as well as a really gigantic film camera for future posts.

The picture above is of a blue-spotted Hawker dragonfly.  This creature apparently catches its prey in midflight, so it's supposed to have big, high resolution eyes.  According to John Patterson in this Discover magazine article, it has 28,000 lenses in each eye.  Judging from the picture, those eyes are probably covering half of the possible 4*pi solid angle, so each tiny lens is covering a solid angle of 112 microsteradians.  That would be Low Resolution to my mind.  Critters like spiders and grasshoppers, with even smaller eyes, must be commensurately worse.

To give some context, a human in bright light has a pixel field of view of 25 nanosteradians.  You can see across your yard (70 feet) what the dragonfly can see from 1 foot.  If it is going after an 8mm long house fly, it needs to close within 80 cm in order to get a full pixel on the target.  At that range the house fly can probably hear the dragonfly, although I haven't analyzed that and insect hearing might also be much worse than human hearing.  This dragonfly is not a long-range hunter like a bird, but rather an opportunist.  I very much doubt it can pull off a high-relative-speed attack like a Peregrine falcon, which requires good angular resolution and gimbal stabilization.

Interestingly, the creature collects about the same amount of light per pixel that the human eye does.  The entire creature is about 70mm long.  Judging from the picture below, the eyes are probably 10 mm across.  That means those little lenses are 53 microns across.  On a bright day outside, your human pupils constrict to 3 mm, 55 times larger.  But since the dragonfly's pixel field of view is 70 times bigger, it actually receives about 50% more light per pixel than you do.
I used to be concerned that the tiny dragonfly lenses would cause diffraction blurring.  Supposing for a moment that they look at green light, their Rayleigh criterion is about 12 milliradians, nicely matched to their pixel angular field of view of 10.5 milliradians.  If the effective pupil of each lens is substantially smaller than the allotted space (low fill factor), then the dragonfly would have to use a shorter wavelength to avoid diffraction problems.  It doesn't look like a big problem.

I don't think the dragonfly has to stabilize the scenery with it's neck.  A dragonfly flying at 1 meter/second sees scenery 50 cm away to the side going by at 2 radians/second.  To get less than 3 pixels of motion smear, it would have to integrate the exposure for less than 15 milliseconds.  That's just a bit quick, so the creature probably sees some motion blur to the side, but not so much in front of it, since there is considerably less angular motion in the direction of flight.