This discussion got me thinking about what the minimum dpi should be for a document based on human perception.
According to wikipedia the human eye perceives about 50 cycles/degree. So the smallest sliver we perceive is about 1/50 of a degree.
If I place a piece of music on a stand 3 feet in front of me this translates to about 1/(36*tan(1/50) -> 80 dpi. For 2 feet it's about 1/(24*tan(1/50) -> 120 dpi. For 1 foot it's about 1/(12*tan(1/50) -> 240 dpi. For 1/2 a foot it's about 1/(6*tan(1/50) -> 480 dpi. These are the minimum dpi's that human's perceive at these distances.
Useful to know.
DPI
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horndude77
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Leonard Vertighel
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I agree with the basic reasoning, but I think that colour depth should also be taken into account. Quoting your example, at 3 feet distance I would expect a monochrome 80 dpi image to look worse than a higher resolution one.
I suppose that it is difficult to determine exact values on a theoretical basis, also due to the fact that the human eye works very differently from a digital scanner. Probably an experiment made with a group of people with good eyesight, showing them printouts at various resolutions from a fixed distance and asking them up to which resolution they perceive a quality difference, would get us a bit closer to the truth. There might still be other factors like scan and print quality involved however.
In the end, I wouldn't be surprised if we came up with the same 300-600 dpi that are usually recommended here on the forums. (When there is very fine detail, you may indeed end up sticking your nose into the sheet to be sure to decipher it correctly.) After all, this is empirical data...
I suppose that it is difficult to determine exact values on a theoretical basis, also due to the fact that the human eye works very differently from a digital scanner. Probably an experiment made with a group of people with good eyesight, showing them printouts at various resolutions from a fixed distance and asking them up to which resolution they perceive a quality difference, would get us a bit closer to the truth. There might still be other factors like scan and print quality involved however.
In the end, I wouldn't be surprised if we came up with the same 300-600 dpi that are usually recommended here on the forums. (When there is very fine detail, you may indeed end up sticking your nose into the sheet to be sure to decipher it correctly.) After all, this is empirical data...
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horndude77
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I agree that an 80 dpi monochrome image will look worse than a higher resolution version at 3 feet. I do wonder what the perceived difference between 80 dpi grayscale and 150+ dpi monochrome would be.
In sampling theory there's a concept of the Nyquist frequency. For band-limited signals you must sample at twice the maximum frequency in the input signal in order to reproduce it exactly. I'm trying to decide if this applies and the minimum frequencies should be doubled.
Even at these doubled frequencies, I agree that in the test you proposed 300-600 dpi would probably win out. If grayscale was also tested instead of monochrome only I think 150 dpi might be competitive. I wonder if a similar test has already been done.
I guess this would be a purely academic exercise since 600dpi monochrome looks great is very practical for storage.
In sampling theory there's a concept of the Nyquist frequency. For band-limited signals you must sample at twice the maximum frequency in the input signal in order to reproduce it exactly. I'm trying to decide if this applies and the minimum frequencies should be doubled.
Even at these doubled frequencies, I agree that in the test you proposed 300-600 dpi would probably win out. If grayscale was also tested instead of monochrome only I think 150 dpi might be competitive. I wonder if a similar test has already been done.
I guess this would be a purely academic exercise since 600dpi monochrome looks great is very practical for storage.