When an image file is increased in size, software creates new pixels, based on the original pixels. The process is known as interpolation. It's done by complicated mathematical algorithms, and there are dozens of ways of accomplishing it. Some methods are more successful than others.
But the most important thing to appreciate is that interpolation does not add any new detail to an image. It merely creates new pixels - fakes, copies, phonies - all very cleverly based on the originals, but fakes nonetheless.
So, let's look at an example of interpolation. We'll take a 20MB image (right) and double its resolution. First, we make sure the 'Resample Image' box is checked on.
Note that doubling the resolution doesn't double the file size - it quadruples it. Simply the square law, which should be familiar to all photographers, at work. So, a 20MB file becomes 80MB when its resolution is increased by 200%.
Remember that no new data have been added to the image. All the new pixels are fakes. If you stop to think about that for a moment, you'll realise that in the upsized image, only one in four pixels is original. Only one in four pixels is real. Three-quarters are fakes. It's amazing that image quality holds up at all, but with high quality originals and good interpolation, it does.
This takes us on to one of the most enduring myths in digital imaging...
Step or Incremental Interpolation
Many "experts" still suggest that step, or incremental, interpolation is somehow superior to interpolating in a single step. The idea is to upsize in small steps of say, 10% (some even suggest 1%) till the desired file size is reached.
But these experts are wrong.
In our example above, we’ve seen that doubling the resolution leads to a four-fold increase in file size. 75% of the pixels are fakes – but at least they’re first generation fakes. They’re all directly based on the original pixels.
If we increase in 10% steps, after the first step about 17% of the pixels in the new image will be first generation fakes. In the second step, this 17% will give rise to new fakes – second generation fakes – fakes based on fakes. In the third step…well I’m sure you get the idea. After 7 steps, we end up with a file of nearly 80MB. This file will also contain about 75% of fake pixels, but some of these pixels will be seventh generation fakes – not first generation fakes as we would get in a single step process.
It's a relatively simple matter to set up a spreadsheet to prove this, but even common sense tells us this method of interpolation is deeply flawed. If you’re not convinced, it should take no more than half an hour experimentation in Photoshop to prove it with your own eyes.