The Eye and its Resolution

This is a simulation of the optics of the eye. It includes interactive access to the Pupil Opening, the Eye Lens Focal Length, the Eye Diameter and the Object Distance. It reports the Image Distance from the Lens and the Focal Spot Diameter for an assumed point source of light (Object). It also reports the Angular Resolution (expressed in radians) for that point Source of light. It is important to understand that the Angular Resolution is the ONLY important measure of visual accuity. It is the factor by which images of all objects get "smeared out". A good benchmark value for the Angular Resolution is 0.001 radians (1 milliradian) which means that, in good lighting and with good contrast, an object 10 millimeters (mm) in diameter at a distance of 10 meters (10,000 mm) can be distinguished from amother object of the same diameter placed directly beside it.

The values of the inputs to this simulation are in the approximate ranges for the human eye which has a diameter of about 25 mm and therefore a distant object Eye's Focal Length is a bit less than 25 mm . To relate the Lens Focal Length to the number of diopters of eyeglasses, one should realize that one diopter corresponds to a focal length of 1 meter as measured in air. Then the number of diopters of a 25 mm Focal Length eye is (1000 mm/25 mm)=40 diopters. Because the index of refraction of the vitreous humor of the eye is about 1.34, the actual optical power of the eye is about 60 diopters as measured in air. A conclusion that one could draw from this information is that a one diopter eyeglass lens can change the focal distance of the eye by the factor (1+/-60/1000)=1.033 or 0.967 where the former factor is that for a negative diopter lens and the latter is the factor for a positive diopter lens. These are approximations that are more than adequate for plus or minus a few diopters. As you can clearly see by adjusting the Iris Opening, when it is reduced, both the Spot Diameter and the Angular Resolution are reduced. Similarly, when the Object Distance is increased, the image distance is reduced which also reduces the Spot Diameter and the Angular Resolution. By choosing parameters which cause the Peripheral Rays to intersect at the retina, one obtains the sharpest image, which is equivalent to the smallest Resolved Angle. Obviously, when the Peripheral Rays intersect before the retina or after the retina, the Spot Circle diameter increases as does the Resolved Angle which means details of the image of the object are blurred out. I provide two examples of Resolution tests. The first is two circles that are separated by an angle of 50 milliradians. As the spot diameter increases, the two circles blend (blur) together so that they appear as one elongated spot. This blending fully occurs when the Resolved Angle is 50 milliradians. The other is an Eye Chart Resolution Test. When the Resolved Angle is very large the letters of the eye chart become smeared out which corresponds to what we see in a eye test when we can't accommodate (focus) our eyes to the chart. Although the input options in this simulation correspond to the size in mm of the human eye, for the purposes of the only important parameter of visual accuity, Angular Resolution, they could be all be multiplied (scaled) by the same number and the important result would be the same.