On the resolution of the human eye

When dealing with such matters as depth of field or the impact of diffraction, we often refer to the resolution of the human eye as a benchmark. We may say, for example, that if [the resulting blurring] does not approach the resolution of the human eye (in some viewing context), then the blurring is "negligible".

Just as we tend to do with regard to the resolution of a camera system, we tend to consider "the resolution of the human eye" to be expressible by a single number. We may say that "the resolution of the human eye, for 'normal' vision, is about 30 cycles per degree."

But of course we know that for the camera is is not that simple, and that what is really of importance is the system MTF, a matter than cannot be encapsulated in a single number.

Not surprisingly, so it is for our favorite camera system, the human eye. But other aspects of the perceptual process combine with the MTF itself to lead to an overall representation of visual response called the contrast sensitivity function (CSF) (sort of an "effective MTF").

The CSF is a plot of how "sensitive" the human eye is to changes in color ("contrast") (the way in which any detail is carried) as a function of the spatial frequency of the change in color (simplistically, the "fineness" of the detail).

Of course, the specific function depends on many environmental factors, such as overall luminance, angle of observation, age of the observer, pupil diameter, and the like.

However, typically, this response curve is highest at a spatial frequency (and of course this must be expressed in angular terms, since we have no idea at what distance the "target" may lie) of about 6 cycles per degree.

The response typically falls to a fairly low value below 3 cy/deg and above 12 cy/deg. So what is the significance of 30 cy/deg? Well, that is where the sensitivity function drops to a level such that the eye can just barely resolve detail at that frequency.

Recognizing this should inform our thinking about such matters as image resolution. It can help to explain why it often seems that an image with a resolution that we think is "inferior" to that of the human eye may nevertheless look about as "sharp" as one of higher resolution.

Best regards,

Doug

In the determination of the SQF metric for "image quality" (it actually only deals with the "sharpness" aspect of image quality), we essentially determine the average of the system MTF over "all" spatial frequencies, weighted at each frequency by the eye's "contrast sensitivity" at that frequency.

There are numerous "implementations" of this definition in different software packages. One simplified one that has been widely used (it was in fact originally suggested by the authors of the technique) treats the eye's contrast response as being 1.0 over the range of spatial frequencies from 2 through 12 cycles/degree and zero outside that range.

This of course means that only the portion of the system MTF extending from 2 through 12 cycles/degree is in any way taken into account.

Thus, for example, for a system MTF that dropped rapidly above 12 cycles per degree (again, as transformed into the context of some assumed image viewing context) the SQF could still be quite large.

Yet, if we use the notion that the "resolution" of a system can be described in a single number by the spatial frequency at which the MTF drops to 50% of its value at low spatial frequencies, then we might for this hypothetical system say that its resolution was 18 cycles/degree (again transformed to our assumed viewing context). That is only 60% of what we simplistically call "the resolution" of the human eye (30 cy/deg). Yet the SQF doctrine suggests that, from a "perceived sharpness" standpoint (again in the context of that same assumed viewing context) this image is "as good as it gets".

Best regards,

Doug