MobileRead Forums - View Single Post - What does resolution mean for your tablet/phone/ereader?

jswinden · 11-04-2012, 07:15 PM

There is always a big squabble over resolution of various device screens. "Mine has more ppi therefore it is better" type of arguments. Those are normally useless arguments as they seldom compare meaningful measurements. So lets take a short scientific and mathematical look at what our eyes perceive.

There is a principle of 300 ppi equals the limit of the average human retina at 10 inches. In other words, the average human retina with 20/20 vision can distinguish no more than 300 ppi at a distance of 10 inches. To put it another way, the average human retina with 20/20 vision cannot distinguish individual pixels at a distance of 10 inches when the resolution is 300 dpi or higher. We are talking about the average human retina with 20/20 vision, so a person with better or worse vision could experience different results.

If this principle is true, and I'll let you decide that for yourselves, then we can determine the angle at which the average human retina can no longer distinguish between two pixels at 10 inches by this formula:

alpha = 2 * arctan ( h / 2d)

where h = 1/300 inch (which is what 300 ppi equals), d = 10 inches.

Therefore the angle alpha = 0.000333333 radians. Having determined the angle alpha at which the average human retina can no longer distinguish between two pixels, we can use that with various heights (resolutions) to determine at which distance the average human retina can no longer distinguish two pixels at various resolutions.
The formula is:

d = h / tan(alpha)

where d = distance, h = various heights shown below, angle alpha = 0.000333333 radians.

For h = 1/132" (132 ppi), distance required = 22.7" (iPad1 and 2)
For h = 1/162" (162 ppi), distance required = 18.5" (iPad Mini)
For h = 1/170" (170 ppi), distance required = 17.6" (original Fire)
For h = 1/216" (216 ppi), distance required = 13.9" (Fire HD, Nexus 7)
For h = 1/268" (268 ppi), distance required = 11.2" (iPad3)
For h = 1/326" (326 ppi), distance required = 9.2" (iPhone5)

So in theory the above listed devices would have to be held at least as far from the eye as the listed distance before the average human retina would no longer see any individual pixels. Your eyes, of course, will vary.

11-04-2012, 07:15 PM	#1
jswinden Nameless Being	What does resolution mean for your tablet/phone/ereader? There is always a big squabble over resolution of various device screens. "Mine has more ppi therefore it is better" type of arguments. Those are normally useless arguments as they seldom compare meaningful measurements. So lets take a short scientific and mathematical look at what our eyes perceive. There is a principle of 300 ppi equals the limit of the average human retina at 10 inches. In other words, the average human retina with 20/20 vision can distinguish no more than 300 ppi at a distance of 10 inches. To put it another way, the average human retina with 20/20 vision cannot distinguish individual pixels at a distance of 10 inches when the resolution is 300 dpi or higher. We are talking about the average human retina with 20/20 vision, so a person with better or worse vision could experience different results. If this principle is true, and I'll let you decide that for yourselves, then we can determine the angle at which the average human retina can no longer distinguish between two pixels at 10 inches by this formula: alpha = 2 * arctan ( h / 2d) where h = 1/300 inch (which is what 300 ppi equals), d = 10 inches. Therefore the angle alpha = 0.000333333 radians. Having determined the angle alpha at which the average human retina can no longer distinguish between two pixels, we can use that with various heights (resolutions) to determine at which distance the average human retina can no longer distinguish two pixels at various resolutions. The formula is: d = h / tan(alpha) where d = distance, h = various heights shown below, angle alpha = 0.000333333 radians. For h = 1/132" (132 ppi), distance required = 22.7" (iPad1 and 2) For h = 1/162" (162 ppi), distance required = 18.5" (iPad Mini) For h = 1/170" (170 ppi), distance required = 17.6" (original Fire) For h = 1/216" (216 ppi), distance required = 13.9" (Fire HD, Nexus 7) For h = 1/268" (268 ppi), distance required = 11.2" (iPad3) For h = 1/326" (326 ppi), distance required = 9.2" (iPhone5) So in theory the above listed devices would have to be held at least as far from the eye as the listed distance before the average human retina would no longer see any individual pixels. Your eyes, of course, will vary.