Scanners are often spec'ed at 600x1200 dpi or 1200x2400 dpi, but offer resolution up to 9600 dpi or more.
So what does that mean?
In the 1200x2400 dpi specification, the lower number is the very important optical resolution of the CCD cell. The larger number is the mechanical stepping of the motor drive. The motor steps are an important scanner specification, but it does not contribute to optical resolution. Resolutions greater than the optical rating are interpolated resolution, done in software after the 1200 dpi optical scan. Interpolated resolution is the least important scanner specification, useful only for line art mode to reduce jaggies, and then only when we have similarly high resolution output device, like a 1200x1200 dpi printer.
The scanner's CCD optical cells (Charge-Coupled Device) are one single row of pixels across the width of the bed area, 3 RGB cells per pixel. A 600x1200 dpi scanner takes samples that are spaced 1/600 inch apart horizontally, so it offers 600 dpi optical resolution. A 600 dpi scanner really cannot do anything else, even if you set it to 2400 dpi. This 600 dpi rating does not mean that it can resolve 600 lpi in a test target, but instead, that the CCD simply takes samples at 600 dpi. Nyquist sampling theory says it can never resolve more than 1/2 of that, or perhaps nearly 300 lpi if the optics are good.
If the scanner bed is 8.5 inches wide, then the sensor is an array of (8.5 inches x 600 dpi) = 5100 pixels in one horizontal line. The flatbed CCD is perhaps a couple of inches wide, with mirrors and a wide angle optical lens that focuses the 8.5 inch image width on the smaller cell. If the lens reduces the bed image to say 1/4 size, then the image projected onto the CCD cell would be 8.5/4 = 2.1 inches wide. Technically, that 2.1 inch sensor is about 5100/2.1 = 2400 dpi. The carriage moves the CCD and lens vertically down the length of the bed with a stepping motor, taking a 5100x1 pixel scan line sampled periodically from the 1/4 size optical image of the scanned photo. We call that 600 dpi, and for all purposes, it is, at the glass bed.
The motor in the 600x1200 dpi scanner can step in 1/1200 inch steps vertically. If we select 300 dpi, it will move four steps at a time vertically, and resample to 50% horizontally, to give a 300x300 dpi image. If we select 1200 dpi, it can step at 1200 dpi vertically. However, the vertical samples will overlap each other by 50% because the 600 dpi CCD cells are twice larger than 1/1200 inch in size. Horizontally it must still sample at 600 dpi too, but images must be a square resolution, so the software interpolates horizontally to create a 1200x1200 dpi image. This won't be the same as a "true" 1200 dpi CCD can do, either horizontally or vertically.
The word interpolate means to calculate or estimate intermediate values occurring between two known values. Old-timers may recall interpolating intermediate values from log and trig tables. In the case of the scanner, interpolated resolution similarly creates pixels of averaged color and intensity between every real pixel of 600 dpi horizontal data in order to match the extra 1200 dpi vertical motor steps to create a 1200x1200 dpi image. For example, to create another pixel between adjacent pixels with Red values 100 and 110, the new pixel will have Red value 105, so the transition is 100, 105, 110. The same for the Blue and Green values. The 1200x1200 dpi image will look larger, but the interpolation will make it slightly blurred.
Does this interpolation give more resolution? No, of course not. There is no added detail present from the original photograph. It's just a larger image, which simply repeats existing data, and at best it's a mix of real and faked data. You can blow it up in your photo editor later, same thing. Interpolated images have a vague unsharp look. The added intermediate 105 value blurred the "edge" between the 100 and 110 values in adjacent pixels.
What about the high interpolated resolutions?
9600 dpi maybe? Is this useful?
For Line art mode, yes, interpolation might be useful, provided we have some use for the large image. A 2400 dpi line art scan might be appropriate for a real 2400 dpi printer (more likely an imagesetter for newspaper/magazine reproduction). The pixels are smaller, and the jaggies on the line edges are much reduced. Line art is a special case. If you have a 1200 dpi printer, you could scan Line art at 1200 dpi (could, not necessarily should, 300 dpi often looks fine). Correspondingly the same for 600 dpi, 300 dpi, and 180 dpi printers, scan line art at those numbers.
For Color or Grayscale modes, no, these interpolated resolutions are NOT generally useful at all, the results are too poor. Some sample scans are provided (112K) to show why high values of interpolated resolution are NOT useful for color photos.
So why is the scanner manufactured with the 300x600 specification? What good are 600 steps per inch at the motor if the CCD cells can't match it?
That's the wrong way to look at it, it's not the general purpose.
Stepping motors are used because of their unique characteristics. A stepping motor doesn't start and rotate continuously like regular motors, but instead moves one precise step, a very few degrees with each input pulse, and then stops, and is locked in position magnetically. If the software wants it to keep moving, more input pulses are required. The controlling signal basically has no choice but to count steps, and so can know very accurately how far the motor has moved at all times. There is no slippage like in rotating motors.
The 1/600 inch steps are indeed very useful when we scan at say 140 dpi. At some point in time, the scanner must take a row of samples at say row 129 of the 140 rows in the third inch of the photo. Whatever the dimension is, in this case we obviously need samples every 1/140 inch (0.00714 inch), and having finer motor steps certainly helps positioning to the right location on every row. The motor can always get within half of a 1/600 inch motor step, or within 0.000833 inch of the correct calculated location (in the worst case). That's within approximately 1/8 pixel in this 140 dpi case, and roughly ½ pixel up near 300 dpi (which has much smaller pixels; it's the same linear accuracy). In most cases, it will be much closer than half a step. The 600 dpi scanner models using 1200 dpi steps can be even more accurate for this purpose, even when scanning at 140 dpi.
Higher values of interpolated resolution ARE suitable for Line art mode (1-bit 2-color, either Black or White, no Gray, like ClipArt or fax) when you desire a really huge image, and have a high resolution printer. We have come to think of interpolation as causing very poor quality in color images, but it shines for Line art, for which it is intended. Values like 1200 and 2400 dpi are for commercial printing of Line art. The Line art interpolation can create more pixels to smooth the Jaggies on the lines, like in penciled cartoon drawings. We like faked data then, it's pretty clear how to smooth the lines, there are only two color choices, either another black dot is added, or it is not. It is assumed of course that our output device can handle this larger image. And there are practical limits, there is little benefit of exceeding 800 to 1200 dpi even for interpolated Line art. Smooth is smooth.
If you have a 600 dpi printer, then scanning and printing Line art at 600 dpi can be advantageous. Depending on what you are scanning of course. Scanning newspapers or fax at 600 dpi would be nonsense for example. Sometimes if scanning text pages to make a simple copy, often 300 dpi is plenty regardless of your printer. But when scanning Line art, ideally you want to match your printers dpi resolution. If you have a 600 dpi printer, scan Line art at 600 dpi. If you have a 720 dpi scanner, try 720 dpi. Interpolated resolution is not a problem for Line art, it smoothes the jaggies. If your printer has two numbers, like 300x600 or 720x1440, scan at the lower of the two numbers. Do experiment a little.
However, interpolated resolution is simply not generally appropriate for Gray or Color modes because there are more than 2 colors, and it is a much bigger problem than just smoothing the jaggies. Such attempts will simply average adjacent dots to create new pixels for enlarged blank areas of the same color. If a 300 dpi scan is increased in size to 2400 dpi, only 1/8 of the data in each direction is real, therefore, only 1/64 of the total data is real. This kinda loses the effect... Interpolation adds no additional detail, and you can do the same resize later (by resampling) in your graphics application anyway. Scanning Color or Gray modes at higher than optical resolution is not a good plan.