For years now, we have tirelessly preached the old 1.4 rule in dealing with bitmap resolution. Some of you may be willing to take our word for it, others may want to know why. For the former" Because we said so. For the latter, here's the reason:
Bitmaps have to be made into halftones. Each dot in a halftone represents an average of the pixels that lie in the same place in the original image. Halftone dots are laid out in a square grid. Each "dot" in a halftone screen is called a "cell." It is made up of the real pixels for that device. In the case of most PostScript printer, this cell is 16 pixels on a side, yielding 16x16=256 possible levels of gray.
The longest possible distance between the centers of equal-size squares in a grid is the length of the diagonal of any of the squares. The length of the diagonal of a square can be determined by multiplying the length of one of the sides by the square root of two, which is 1.4 and change. If a bitmap has exactly as many pixels per inch as the halftone screen has lines per inch, each pixel will be translated into a halftone dot.
However, the halftone grid will not precisely align with the bitmap array. So you may want to "oversample" the bitmap -- have more pixels than halftone dots, in order to make sure no more detail is lost than is necessary.
This oversampling starts to have a noticeable effect at around 1.14 times the screen frequency, or a 1.14:1 (one-point-one-four to one) oversampling ratio. The greatest practical oversampling ratio, however, is the one that allows for the possibility that a halftone cell may need to be large enough to average the data of a pixel turned at 45 degrees, and thus having a diagonal that is the length of the SIDE of a halftone cell. Which would make it, class? .... right! 1.4 times the size of the pixel.
If you turn that around, that would mean that there were 1.4 times as many pixels as halftone cells in any direction. That means that there would be 1.4 times as many pixels per inch as there would be halftone cells. So, if a 100 line halftone screen is used, then the maximum resolution of a bitmap that will work with that is 140 pixels per inch.
And that's why the number used is 1.4.
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