Printer resolution vs. tonal range (or why bother with 300ppi image files)?

I've seen a number of reviews and posts that recommend, for inkjet

photo printing, that the picture file have a resolution, at final

printed size, of 250-300 ppi (e.g. 2400 x 3000 pixels for an 8x10

image).

 

Yet math tells me that a generic 1440 x 1440 inkjet printer cannot

produce the full range of tones contained in a 24-bit color image at

anything higher than 90 ppi. As follows:

 

A 24-bit image has 256 levels of brightness for each color. To

reproduce those 256 levels accurately the printer must be able to lay

down 256 dots of each color ink per image pixel - i.e. a range of

brightness from zero dots (white) to 256 dots (solid color).

 

To get a range of 256 levels, then, each pixel must be represented on

paper by an array of 16 x16 dots (256 total). Divide 1440 (linear dots)

by 16 (linear dots per pixel) and you get 90 (pixels).

 

If you try to print images at higher resolutions, you must cut down the

number of ink drops available to render each pixel, progressively

'posterizing' the image as fewer and fewer steps are left between pure

white and pure color.

 

At an image resolution of 288 ppi, for example, the printer can only

lay down a 5 x 5 array of dots per pixel (26 tonal levels per color vs.

the original file's 256).

 

The extreme example would be printing a very-high-res scan of 1440 ppi

(at final image size) - in which case the poor printer is left with a

binary choice - each pixel gets 1 dot or 0 dot for each of the 4 (or 6

or 7) printing colors - a very limited palette.

 

It seems to me that what Epson (and other printer makers) must do is

create - in the spooling process - a standard moderate-resolution

version of the image (regardless of the actual file size) that is a

compromise between fine detail and reasonable tonal variation.

 

My own guess is that this 'on-the-fly-resampled' image is actually

about 180 ppi - which works out to a nice digital 8x8 array of printer

dots available for each pixel, or 65 tonal levels for each of the inks.

 

Which guess is born out, somewhat, by the fact that, in making test

prints of the same image at 150, 200, 250 and 300 ppi resolution, I

(personally) can't see any improvement in the prints' rendering of fine

detail in the versions above 200 ppi. So what is the benefit of using

a higher-resolution image file?

 

Anyway I would appreciate any insights or comments.

I don't have an answer but keep in mind that the better ink jet printers aca vary the ink drop size.

the means a modern inkjet printer uses to render tones are

more complex: dots of diffent inks can overlap; the dot size can

be modulated; 6-ink printers use light versions of the cyan and

magenta inks to provide an additional level of control; inks are

not laid down in regular arrays of dots, instead techniques such

as stochastic and fm screening are used

 

combining these measures allows fine gradation at high

enough resolutions, but the gradation will get coarser as details

shrink

 

i was interested by your question so i made a test image of

many overlapping/crossing single pixel lines, geometric patterns

and single pixels

 

the lines/pixels were a mix of neutral, near neutral, and rgbcmy,

all on an off-neutral background

 

on a canon s9000 this pattern is well rendered at 300ppi , using

a loupe to examine the image the single pixels are still square,

each line is sharp, the colours visibly match the target file

 

printed at 600ppi things are fuzzier, but the lines, including

single pixels, are still rendered in a colour that looks

approximately right, but the dot diffusion pattern in visible now so

it is no longer possible to say what the 'real' colour is

 

the printer is laying down dots that would be invisible to the eye

to create an illusion of continuous tone, at normal viewing

distances i'd be happy that it was capable giving me 'many' bits

of colour on the scale of features that my eye can resolve

(whether it is thousands of colours or millions i couldn't say)

 

it cannot do this over the finest features it can render, but my

eyes can't tell anyway, for the fine detail sharpness is more

important than subtleties of tone

Also, keep in mind that one single 300 dpi "dot" reuires about 24 1440 dpi "dots" to fill it. The "area" of these dots is a second-order mathematical relationship, while dpi refers to linear output.

 

Cheers,

Also, dithering algorithms don't actually require you to agregate multiple pixels into one "superpixel". This is the reason why you could (back in the old days) reproduce with arguably reasonable quality a photograph on a 16 color 640x480 display using an error diffusion dither (which pushes the rounding error to nearby pixels before they are rounded so as to preserve the overall tonality). Inkjet printers use a variation of error diffusion dithering.

You're right in your assumption that the driver provides a on-th-fly resampling. But it is an upsampling to 720 dpi! Take a look at following page:

 

http://www.ddisoftware.com/qimage/quality/

 

I very rarely work with 720 dpi images, but with 360 dpi and an appropriately tuned accentuation (USM or whatsoever), you will see the finer details with the naked eye.

<i>But it is an upsampling to 720 dpi!</i>

<p>I remember reading this, but that was when the resolution of the EPSON printers was 720 dpi (e.g., 2880x720). Now that there are 2880x1440 dpi and (soon, presumably) 2880x2880 dpi printers, does that mean the upsampling will be to 1440 dpi and 2880 dpi, respectively?

<p>

Anyway, my experience with the EPSON 820 corroborates yours: changing the printer resolution generally makes no difference.

Andy, which software you use for printing?

Sakari: Direct from PhotoShop via Epson's standard Mac driver (Epson 600 - thus the references to 4 inks).