What’s the DPI?
If a POD printer asks you to submit 300dpi grayscale images from which they can make halftones, it does not mean that output is going to be 300dpi, or that the 256 shades of gray you see in each pixel of your computer screen are going to show up in the output. In fact, there are no shades of gray in the interior of a book; gray is simulated with black dots of different sizes.
To save space and time. A good halftone can result from a 300dpi image because the “grid” finds the average color within each diamond when determining how big a dot to draw. In a 600dpi image with a 106-lpi line screen, the computer finds the average color among 16 different dots in the diamond shape (4×4 pixels). If you send a 300dpi image, the computer finds the average color among 4 different dots (2×2 pixels) in the diamond shape but it’s almost always the exact same “average” color that it would find averaging 16 dots. Remember that although you have 256 shades of gray per dot in your computer grayscale image, the “grid” is only going to guess with a sensitivity of 16 (for 106-lpi or 25 for 85-lpi) shades of gray. Or think of it this way: if you were to send a 600dpi halftone, you’d be sending 16×256=4096 pieces of information in each grid diamond to a process that needs to make a choice with a precision of 1×16=16. That’s overkill (256 times more information than they need), and 4×256=1024 pieces of information (still 64 times more information than they need) is usually more than adequate to produce the halftone. More than double the effective resolution in your original is not going to result in a better halftone.