It's just simple: Dot Per Inch (DPI) is a measurement for printer while Pixels Per Inch (PPI) is measurement for Video Output (Monitor). They are used for different purpose.
As for printing a 416x416 pixels picture in 500 DPI, it is not affecting the image physical size itself. It will still print image with the size of 416x416 physically
>Is it correct to say that if i want an image with 500dots
>per inch quality. And at the same time, i also want an
>image size to be 416 x 416 pixels.
Yes, there is no fault in it. You just reques the image to be printed in a certain size and certain resolution, they aren't related to each other.
>Does it mean that one pixel is equivalent to one dot?
>Is it mandatory?
No, it is not. One pixel does not equal to one dot that way. If you request an image with (One inch in pixel) DPI, you'll get one dot per one pixels.
a 500 DPI image just means that in each one physical inch size of them, there is 500 dots that make the pictures up.
Pixel is not equal to dot. Pixel is value of the height and/or width of one tiny thing in the monitor screen, while dot is one tiny thing in Printed image.
>What is dithering
Dithering is the combining of the limited pallete color to visually produce colors that is not in the pallete. For example, most Printer only have four colors that is black, Cyan, Magenta, and Yellow. If the printer is told to print color that is not in that base color, they will need to combine several different color in a pattern so that human eyes distinguish it as the wanted color. For more info, see: http://en.wikipedia.org/wiki/Dither (tips: you may want to jump directly to the bottom, to the image dithering section and skip the voice dither)
>can i apply that in my solution?
Yes, in fact, all printers use dithering even if we don't tell them to. If they are forced to not use dithering, their image quality would be horrible since they can then only use four color. Imagine seeing a picture that consist of BCMY colors only, they're horrible.