The practical way scaling is used AFTER the scan is this:
Resolution dpi = (pixels of length) / (inches of length)
Suppose our image is 1200 pixels wide. Contemplating printing it, we see that we could print this image at several different sizes, simply by changing the scaled resolution:
You get the idea, the light bulb should be on. This is scaling, the easy way. Given the available image size and the available printer's resolution needs and capability, you pick the best choice for your purpose, balancing resolution against image size. And to do that, if you want 200 dpi on paper, you simply declare to the image "You are 200 dpi now, Shazam!".
But how do we actually make it be 200 dpi? Easy. You can just lie about it. Cross your fingers, and tell the previously scanned image: "Even though your image size is still the same as it was, still the same 1200 pixel dimension, those same 1200 pixels were actually scanned at a different resolution than you first thought, honest, cross my heart." It is still the same 1200 pixel image, it does not change at all on the video screen. But when we print it, the new resolution number is used to calculate the spacing of the pixels on paper, and the image comes out the new size on paper, 6 inches at 200 dpi.
Because, if we really had honestly obtained this 1200 pixel image by scanning at 200 dpi as we now claim, then the original must have been 6 inches in size. That would have been the only answer possible for its real size. 6 inches x 200 pixels per inch = 1200 pixels. The image program has a menu to specify print resolution, and the printer driver will honor it by printing image pixels at that spacing on paper. The printer driver does this resizing on the paper, it believes us. It doesn't know we lied, it works with what it has. But let's not call it lying, let's call it scaling. The only thing difficult about this is the guilty conscience. <grin>
Forgive this paragraph's excessive repetition, but let me try to make this very clear, because this technique is very important if you have a printer. You have this 1200 pixel image (long dimension say, or short side either, just pick the dimension of interest). You want to print that dimension to be 8 inches in size this time. The way to do that is to see that 1200 pixels / 8 inches = 150 dpi. Therefore you scale the image to 150 dpi with the menu for Resolution. This basically claims that you originally scanned the image at 150 dpi. Whether this is true or not doesn't matter, the image is stamped "150 dpi" now, and the printer driver will honor it. Most software will allow you to specify the 8 inches directly, and then it will compute the 150 ppi for you.
It is important to note that NOTHING has changed except this one number that is stored away someplace. This is just a number to be used for printing later. The image pixels did not change, the image size in pixels did not change, and you will not see any change until you print it using this new number for printed resolution. But since you scaled it to 150 dpi, then it will print at 8 inches, simply because there are 1200 pixels, and 8 inches is how far they will go at 150 dpi. Don't let it be hard. Don't make it be hard.
If you have an old 300 dpi laser printer that prefers 100 dpi images, this 150 dpi image is a bit more than is useful and pixels will be discarded, but it will print at 8 inches. If you have a printer that wants 250 dpi, 150 dpi is not enough pixels to be maximally sharp, but it'll be fair quality, and it will be 8 inches. You wanted 8 inches, remember? And so for this 1200 pixel image, 150 dpi is the only choice, because 1200 / 8 = 150.
What do I mean by the printer "prefers" 250 dpi? That's just my cute way of saying that on this specific printer and paper combination, you can see quality losses if you print images with less resolution, but cannot detect quality gains if you print images with greater resolution. It is the practical optimum resolution for this printer/paper combination. 250 to 300 dpi is the right ballpark for today's better photo-quality inkjet printers in the best mode on the best glossy paper.
Another way to select a choice is that if your printer prefers 240 dpi, then 1200 pixels / 240 dpi = 5 inches. If you want 240 dpi,then it simply is not optimum to print it larger. So in this case (image is not large enough), you must decide on either quality or size.
But often a little compromise works out very well. 180 dpi will often look pretty fine, if that's all the pixels that you have.
But there are size limits. Digital cameras are getting larger, but most still produce relatively small images. 3 megapixels will print 6x4 inches fine, and 6 megapixels will print 8x10 inches. Printing larger prints requires a few million more pixels in the CCD cells. Printing requires a lot of pixels, and the same scaling rules are applicable to any image, including those from digital cameras. Therefore, if the digital camera makes an image that is 1024 pixels in length, and if you want to print it at 10 inches in length on paper, then that is obviously only about 100 dpi. Some users may judge these 100 dpi prints as "great", but a larger image scaled to print at 300 dpi will be noticeably better in quality. Pixels count.
Image programs have been quite confusing in the methods offered used for resizing, perhaps because they try to make it easy for us. They seem to try to hide the details to make the program be "easy to use", but the subject is confusing enough already. Still, it is much simpler than we let it be. And programs are getting much better about this, the major ones show this more clearly now.
Adobe Photoshop and Elements use the menu Image - Image Size to do both scaling and resampling with the same one dialog box. It has a checkbox option Resample Image to choose between Resample and Scaling modes. Corel programs are very similar (checkbox may be called Maintain File Size). The newer versions of both Paint Shop Pro and PhotoImpact are very similar now also. All of these now have an excellent tool, showing numeric values for both resolution and printed image size in inches, and you can change either value and the other will track it. This method works really well, all information is shown, inches, pixels, byte size, and we can see exactly what is happening. Not all programs have been so clear about a simple task.
There is a chart a few pages later to help find the menus for scaling or resampling in popular image programs.
In general, if we want increased printed size, then we either use less printed resolution or we need a larger image. If we want increased resolution, we need either a larger image or a smaller printed size. Notice that the term "larger image size" keeps coming up? That means more pixels, and having lots of pixels is important for printing large images (and typically is not so useful for the video screen). The image to be printed large will appear GIGANTIC on your video screen, 2 or 3 times useful size.
It is mathematically impossible to print any 1200 pixel image to be 10 inches at 200 dpi. We would need a 200 x 10 = 2000 pixel image for 200 dpi at 10 inches. Yes, we could resample it larger and make the numbers work, but that's no solution at all, because it does not add detail from the original image. It's the same effect as simply scaling to print at a lower resolution, except with more manipulation and complication and quality risks. Instead, we need a larger scan.
Notice that it does not matter now what original scan resolution produced this 1200 pixel image. Perhaps the original scan was an 8 inch original scanned at 150 dpi. Or maybe 1 inch of film scanned at 1200 dpi. Or ½ inch of film at 2400 dpi. It simply doesn't matter now, this image is 1200 pixels in length. Probably more scan dpi would have been better for a large printed image, to have more pixels now. Maybe we chose the original resolution specifically and wisely for this printing purpose, or maybe we didn't, but now this image size is what we have to work with. All that matters now is that we have some pixels that we want to transfer to paper. The only question is how far apart we want to space those pixels on paper, that is, how large do we want the image to be?
Notice that scaling an image to print at 200 dpi specifies the resolution of the image. You still set your inkjet printer to print at its maximum resolution, 600 dpi, 720 dpi, 1440 dpi (more in the next Printer Basics section). But you tell the image that you want 200 image pixels printed on paper.
I hope scaling is clear, it's fundamentally important for printing.