Print resolution (was: Where are the BEST Point and Shoot Photos?)

davem@xxxxxxxxx (Dave Martindale) writes:
John Navas <spamfilter1@xxxxxxxxxxxxxx> writes:

An 8x12 print under normal
viewing conditions and at normal viewing distance of 22" needs only 156
PPI for excellent results, which is only 3 MP. See
<http://www.photokaboom.com/photography/learn/printing/resolution/1_which_resolution_print_size_viewing_distance.htm>

Here is another approach entirely: Ignore web pages, ignore
textbooks, and measure your own resolution limit for yourself. Figure
out how many pixels you need before there's no point in having more.
It's not very difficult:

1. Start with a pattern of alternating black and white lines, each one
pixel wide. If you have an LCD monitor, they can be either vertical or
horizontal. For CRTs it's better if the lines are horizontal (because
CRT high frequency response limits the contrast between adjacent pixels
in the same scanline). Display this pattern on your favourite computer
monitor. Make sure that when viewed up close you have nice contrasty
clearly visible white and black alternating lines. (If you're using an
LCD monitor, set the video card resolution to match the monitor native
resolution).

2. Now move back from the monitor until the black/white line structure
vanishes completely, and the pattern now looks like uniform grey.
Measure your distance from the screen at this point. (If you need
glasses to see well at this distance, wear them - we're trying to
measure what your eyes are capable of). Call this distance D.

3. Next, figure out the size of your monitor in a direction
perpendicular to the lines you've been using. We need the size in both
physical units like inches and in pixels. If you used horizontal lines
in the pattern, measure the vertical height of the image area of your
screen. Call that H. Then determine how many pixels are currently
filling that height, which is the vertical size the video card is set
to - call that quantity P. (If you used vertical lines, measure
horizontal width and horizontal pixel count).

4. Now for the math:
The screen's pixel density is just P/H in pixels/inch or pixels/mm
depending on the units you used. Inverting that (H/P) is the pixel
pitch. At the distance D, each pixel's angular size is arctan(H/P / D).
And the reciprocal of that is the number of pixels per degree you can
see. Divide that by 2 to get cycles/degree, since it takes 2 pixels to
make one cycle in our test pattern.

For example, I just tried this using a CRT monitor. For me, without
glasses, D=50 inches, H=9.25 inches, P=960. So the monitor's pixel
density is 960/9.25 = 104 PPI, and the pixel pitch is 0.0096 inch. The
angular size of one pixel is arctan(0.0096 / 50) = 0.011 degree. The
reciprocal is 91 pixels/degree. So, with this test pattern, I can see
45 cycles/degree. That's below the textbook limit of 60 cycles/degree,
but my eyes are 50+ years old and I have some astigmatism, so I'll
believe that some people have 33% better vision than I. But now I know
my personal limit is 45 cycles/degree, at my current age (it may change
slowly).


To calculate the equivalent PPI value for "eye limited resolution" at
another distance, scale with viewing distance. If eye-limited
resolution happens at 104 PPI for my eye at 50 inches, that's equivalent
to 208 PPI at 25 inches, and 520 PPI at 10 inches. I know my eyes can
see that much detail under the right conditions. (This assumes the
print is in focus, which *would* require reading glasses at 10 inches
for me, but doesn't for the under-40 crowd with normal vision).

However, note that this is an upper bound only for the case where you
can resolve one black/white cycle with only 2 pixels. That is true of
my test pattern, and some computer-rendered images, but cameras cannot
achieve this. Digital images from cameras usually have a measured
resolution limit that is about 70-80% of the theoretical limit, which
means that the actual number of pixels required to resolve N black and
white lines is about 1.25*N to 1.35*N. If you want to make a statement
about "there's no point in printing more than X PPI because your eye
can't see it", you need to allow for this difference between pixel
count and the number of resolved lines.

And that means that, for my eyes and a viewing distance of 10 inches,
there's really no need for more than about 700 PPI.

Now, in fact, half that PPI would yield a pretty good print - this
figure simply says that there would be some visible improvement up to
about 700 PPI, but not beyond that. In practice, I'd be happy to have
400 PPI for everything, calling that "good enough", even though I know
that isn't "as good as what my eyes can see".

There are two principal differences between the calculation above and
the one that John is using to get his 156 PPI figure. First, he assumes
that viewing distance is 1.5 times image diagonal, which is plausible
for general viewing of images but not the photography enthusiast looking
at your large print. Second, the web pages he reference assume a
resolution limit of 60 pixels/degree or 30 cycles/degree, which is below
what the textbooks say, and below what my own eyes tell me. This may be
due to simple confusion between lines and line pair measurements, or
something else, but it's 2/3 of what my eyes do and 1/2 what the
textbooks say.

So, everybody go measure this for yourself!

Dave
.

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