Optics of the eye


>I'm interested in knowing if the retinal image, that the brain interprets, is inverted and, if so, is the retina exactly at the focal point of the eyeball. When I look at a star, is the eye in part determining the resolution, i.e. were there no scintillation would a point focus exist at the retina ?

The image on the retina is inverted. This fact, and the puzzles it presents, were noted by Descartes some centuries ago.
There is a lot of variation in the focal point of the eye, depending on whether one is farsighted (hypermetropic), nearsighted (myopic), or "normal" (emmetropic). The textbook statement, and the practice of optometrists, is that the normal eye, when relaxed, does not quite focus at infinity but at about 20 feet (six meters) which is why this distance is used for eye charts. This would mean that a star at infinity focusses a little in front of the retina, so there would, in fact, be an out-of-focus blur circle.
In the dark, with a fully expanded pupil, doesn't focus as well, and doesn't necessarily focus in the same place, as with a "normal" pupil size, i.e. I think there's quite a bit of spherical aberration.
Moreover, the media of the eye (aqueous and vitreous humor) are not perfectly transparent; they scatter light (more with increasing age, dammit, which is why older folks have more problems with the glare of oncoming headlights).
Because the lens of the eye is not evenly transparent, the blur "circle" is not the nice, even disk you get with an out-of-focus camera lens, but is actually a sort of pinhole image of the lens of the eye, with crud, structures, imperfections, unevennesses in the tear film, etc. The multirayed "star" appearance is, in fact the blur circle. The detailed appearance is different from person to person. For many people there is a kind of multiple breakup of the image ("monocular diplopia.") My wife, for example, always sees "two" crescent moons (very close together and overlapping.).
Oh, also: the light-sensitive parts of the eye are at the back of the retina, with the cell bodies, blood vessels etc. in front of them where they can block and diffuse the light some more. (Octopi have the sensible arrangement, with the sensitive part being the FRONT of the retina).

Sources of information for optics of the eye

"Perception of Displayed Information", L. M. Biberman, editor, Plenum Press, p18 section 2.2.1.1 "Visual Acuity of the Observer."

Optical Society of America publishes the "Handbook of Optics", a two volume set which makes an excellent reference for most of the field of optics and devotes two chapters to the eye and vision.