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All digital images are composed of tiny pieces called pixels. Depending on how closely together these pixels are clustered they give the appearance of a continuous tone. Typically the density that there pixels need to be at to give this appearance is somewhere around 200 ppi. (pixels per inch). This is something that you did not have to worry about when you were using film. You simply made an enlargement to the size you needed and that was it. In the digital world, there is quite a few more factors that come into play when dealing with printing and enlarging images.
The word resolution effectively tells us at what density the image exists. This density or spread of pixels can be altered depending on the need.

For example in a newspaper, the resolution typically hovers around 70 dpi (dots per inch) because quality is not as important as getting the story to the public. If you look very closely at the images in a newspaper you will be able to see the tiny dots that make up the image. This is true in most advertising media as well such as brochures, catalogues etc. It's done to save money on ink and other associated costs. Higher resolution printing requires better quality paper etc and the cost quickly adds up. If a newspaper printed all its images at 200 dpi the costs would be astronomical, not to mention the amount of time it would take to print each paper.

In high quality publications such as photography magazines, the images are printed to look their best. This is because quality is of the utmost importance. This is also why a very good magazine will cost $12 - $25 vs. a newspaper worth $1.
Resizing Images:
There is a strict relationship between the image resolution (dpi) and its size. This relationship is best explained using the Adobe Photoshop Image Size dialog box.

Take the image below as an example.
This image is only 540 x 359 pixels. This dimension at 240 pixels/inch will produce an image that will be 5.72cm wide and 3.8cm tall. This is the effect of resolution on image size. The file size is 567.9K.

Notice that the Resample Image box is not checked, we'll come back to that later.

Now watch what happens when we drop the resolution down to 70 dpi.
At 70 dpi you will notice that the image size changed 19.59 cm x 13.03 cm. The amount of pixels did not change, only the definition of how tightly clustered they are.

Changing the dpi will change the image size, but not the amount of pixels in the image provided the resample box is unchecked. This resolution change also does not affect the file size, the image is still 567.9K. The amount of data that has to be stored remains the same at any resolution.
So, as we can see from the two examples above, if we change the resolution we change the document size and vice versa without affecting the amount of pixels in the image.

Now it gets a little more complicated. Here we'll see what happens when we leave the Resample Image box checked. What this box does is it basically unlocks the relationship between resolution (dpi), and the amount of pixels in the image. This means that you can change the dpi, document size, and pixel dimensions to anything we choose.
 Here for example, I changed the pixel dimensions of the image from 540 pixels wide to 5400. This changes the height from 359 pixels to 3590 (provided you have the constrain proportions box checked).

What you will notice is that the document size changed to 57.15 cm x 29.99 cm without changing the resolution of 240 pixels/inch. Using complicated algorithms Photoshop essentially created the pixels in-between the existing ones to create the pixel dimensions requested.

You will also notice that the file size changed from 567.9K to 55.5M. This is a huge jump in file size, because now there are more pixels to store. This method is called Rezzing-Up. (essentially sizing up the resolution) It will let you print a bigger image than the original would allow.
While the Resample Image box is checked, changing resolution will change the image pixel dimensions to create the document size at that resolution. If you change the pixel dimensions, you will change the document size while keeping the resolution constant. If you change the document size, you change pixel dimensions. It all ties together.
Rezzing-Up Warnings: 
Rezzing-up needs to be done in moderation. It is something that is useful if you need to print a bit bigger than your original would allow. It is very easy to overdo and the results can be very ugly because of the amount of guessing Photoshop has to do to achieve the higher pixel dimensions. Instead of Photoshop you could use a program such as Genuine Fractals which does a much better job of rezzing-up.

Because of the creation of previously non-existent pixels, it is always best to use the highest quality image (lots of pixels) to rezz-up. It will produce much better results than using an image with a lot less pixels. The example below shows what happens when you use a low quality image as your starting point for rezzing-up.
This is a 189 x 189 pixel crop of the original image at 240 pixels / inch.  This is a crop of the left image tripled in resolution in Photoshop.
 This is a 189 x 189 pixel crop of the original image but at 150 pixels / inch. Notice the lower quality of the overall image.  This is a crop of the left image tripled in resolution in Photoshop. See how much worse it looks when you start with a lower quality image? This is because there is less data for Photoshop to use in order to create the extra pixels.
Resolution Needs:
Images posted on the web typically only need around 80 ppi. Most high quality inkjets require a ppi setting of 240  ppi at a minimum, and I have seen some benefit when printing from a 360 ppi image.

Most printers are labelled as having a certain number of dpi, dots per inch. This term is often interchangeable with ppi. The only difference is that in an digital image the image itself is composed of pixels whereas a print is composed of multiple dots of ink. Most inkjets benefit the most from 240 ppi.

High quality printing labs have their own requirements, and it would be a good idea to check with them first before sending your images out for print.
Inkjet Printers: 
Printer manufacturers label their printers as having a certain number of dpi. This often causes a lot of confusion. What this number means is that amount of dots of ink that the printer is able to lay down in a inch. But because each effective pixel reproduced on paper can be a composite of a number of inks you will require more dpi from a printer than the image to be printed.

For example, take the Canon 9900 printer. This printer can print at 4800 x 2400 dpi using 8 ink tanks. This resolution number is a bit misleading because it means that the printer can print 4800 dots horizontally and 2400 dots vertically. Lets use the smaller resolution number to see what the true printer resolution is.

Each pixel in the digital image can be a composite of all 8 colors. What this means is that you might be able to put down 2400 dots in that one inch, but 8 dots will effectively only create one pixel. To get the actual resolution of the printer you have to divide the dpi number (2400) by the number of ink tanks (8). This gives us an effective printing resolution of 300 dpi at the very least. If we were to use the horizontal dimension of 4800 dpi we would have an effective printer resolution of 600 dpi.

So, to achieve the best print quality from this printer, you would output your digital images at 300 pixels per inch to ensure a maximum printing resolution. In reality, not all pixels will be composed of all 8 ink colors, so you can safely use 360 ppi output images.
It All Ties Together: 
Resolution - how tightly packed pixels are, measure in pixels per inch (ppi)
Pixel Dimensions - how many pixels there are in the width and height of an image given as # x # pixels
Dots Per Inch - a measure of how many dots of ink a printer is capable of putting down in an inch
Image Size - how big a document will be if printed as the specified resolution and pixel dimensions

Hopefully this article has cleared up some of the confusion surrounding resolution and how it applies to digital images as well as the different changes that can be brought about by adjusting image sizes in Photoshop.


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