More on DPI, worth reading if you scan and stuff with stills

Question

Even seasoned professionals can't agree on this topic. I'm taking these statements out of context from a listserve and I am posting them without attributing the quotes to real people except to say they are pros. They should know what they're talking about. Yet they don't. Neither do I anymore.
The first salvo:
The 72dpi thing is a myth. The number of pixels is the number of pixels.
72dpi is a print term. The size of the image determines the number of pixels
that will be in each inch of the print.<<<
The counterattack:
<div class="jive-quote">I wouldn't call it a myth, especially since this question specifically
relates to print resolution. DPI is a printer term, but it is also more or
less equivalent to PPI (dots vs. pixels). Pixels are the real resolution
and the "pi" part is merely how many of them you spread over an inch.
This info is metadata reference embedded into the graphic file, so if
you open an image exported from 1080i video as a graphic file, Photoshop
and most other graphics apps will ID this as 72 dpi. At this relationship,
1920x1080 will print an image that is 26.667 inches x 15 inches. If you change the dpi setting under image size, WITHOUT resampling the image, from 72 to 144, then the printable dimensions are cut in half to 13.33 x 7.5 inches. Obviously the smaller you make the image, the more pixels/dots are crammed into an inch.
More dots equals higher APPARENT resolution.
So, although not a true "absolute" value, dpi is still a valuable rule of thumb
for comparison. 1920x1080@72dpi would have less visible "quality" than
a theoretically native 1920x1080@300dpi (if that existed), when both are printedto fill an 8x10inch image area.
If, for instance, you wanted to have a 3D artist create CD cover art (approx 4in.x4in.)they would have to create/render a file that is 1200x1200 (or even biger yet).
Even if this opens in Photoshop as 72dpi, when you change this setting (without resampling) to 300 dpi, the image will correctly print at 4x4in. instead of 16.6x16.6 inches.<
The last rejoinder:
<div class="jive-quote">So, although not a true "absolute" value, dpi is still a valuable
rule of thumb
for comparison. 1920x1080@72dpi would have less visible "quality" than
a theoretically native 1920x1080@300dpi (if that existed), when
both are printed
to fill an 8x10inch image area.
Unfortunately that's not true. As mentioned earlier correctly: a
pixel is a pixel - though dpi is not a 'myth'.
A 1920x1080@72dpi and 1920x1080@300dpi do have a 1920x1080 absolute
count of pixels - so the same resolution/quality. If both of the
mentioned images will be printed out to an 8" wide picture the amount
of pixels available is 1920 (horizontally) in both cases - so no
quality difference, at least when using the same printer.
Changing the dpi will either scale the visual size depending on your
device or the printed size ( also depending on the printer's
capabilities/resolution). Printing the big wallpapers/advertisements
is actually done at around 45 dpi - while it's always a good idea to
have a multiple of the print resolution as source resolution, we
could say we take 90 dpi for a better quality. In the above example
the resulting image size will be around 21" width - in case we map
the available dots directly we'll get 42".
That's what dpi means, dots per inch. If you display/print 1920 at 72
dpi you will get a width of 1920 dots / (72 dots / inch) = 26.67
inch, if you display/print 1920 at 300 dpi you will get a width of
1920 dots / (300 dots / inch) = 6.4 inch. That's quite simple math,
and if you keep the unit types during the calculation, it will show
you whether the calculation is done correctly - dots / (dots / inch)
= dots x inch / dots = inch.
Talking about video and dpi might make sense when it comes to
(control/broadcast/LCD) monitors: so comparing a cheap 14" 320
horizontal lines consumer one to a 14" 800 line studio monitor would
make ~29 dpi versus ~72 dpi. Comparing the same 14" studio monitor to
a 20" 800 line one, will result in ~72 dpi versus 50 dpi. In any case
the source pixels from the image are mapped/interpolated to the
output device's resolution.
It's the same with timecode: if you got 150 pictures, you got 150
pictures and the won't get more or better if you let them run on 1
frame/second, 60 frames/second or 120 frames/second - only the time
it needs to display them does change. But recording with a high-speed
camera at 120 frames/second will give you a much higher motion
resolution than recording with 60 frames/second - and the double
amount of pictures.<
Wait, there is MORE:
<div class="jive-quote">I'm afraid you misread my explanation and qualifiers.
Note the "theoretically" and "if it existed" in:
"theoretically native 1920x1080@300dpi (if that existed)".
In Photoshop you can create both a 1920x1080@72
and a 1920x1080@300. As I explained, the dpi is merely a
metadata reference for the printer. What this value is set at
DOES change the SIZE at which an image is printed at, but
NOT the resolution. Since the same number of pixels squeezed
into less space APPEARS sharper to the eye, 1920 printed
in half the size will look like it has higher resolution than
if it is bigger (viewed at the same distance). In Photoshop,
the dpi value is really just a cross-reference between actual
pixels and the physical dimensions at which these should
be displayed.
The final installment:
We are saying the same thing really, but since the point of
this thread specifically relates to printing a still, the dpi
measurement as a point of reference is still valid. Basically,
what the client really wants to know is, 'at what point does
this printed image start to look unacceptable?' Of course,
that depends on the size at which it is to be printed and
the target medium (such as newspaper versus glossy paper).
bogiesan

Answer 1

The 'DPI Doesn't Matter' comments are generally directed at statements like: " I imported this 300dpi image into FCP and it's wonky. Why does it look like the dog chewed it?"
Yes, scanners measure resolution in DPI. So, to clear things up ... (yea ... right!), Below is the formula which describes the relationship between pixels, physical size (in inches) and DPI. This is an elaboration of Patrick's post.
physical size x DPI = pixel dimension
If you have a 10" wide image and scan it at 300 dpi you will have a 3000 pixel wide digital image. A pretty large image. But what if you want to end up with a 750 pixel wide image?
The equation is transformed into:
pixel dimension/physical size = DPI
so, continuing the previous example, you want a 750 pixel digital image and original media is 10" wide. 750/10 = 75. Set the scanner at 75dpi, verify the resulting file will have a pixel width of 750 and you are good to go.
Just to make things less clear - some more sophisticated scanning software (Silverfast Ai, for example) will also let you put in a multiplier (the Q factor) to the dpi setting which in essence is an oversampling ratio. Set that to 1.0 and your numbers will be as you set them.
Again this is simply to get the file into a pixel dimension that will work in FCP.
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