Multi-sampling and "2400x4800 dpi" scanners

Many flatbed scanners claim to offer a vertical resolution that is
twice the horizontal resolution, such as 2400x4800 dpi. I understand
this to mean that, while there are only 2400 cells in the CCD, the
stepping motor can move by steps of 1/4800th of an inch.

Additionally, these scanners' CCDs usually do not have a single row of
2400 cells, but two rows of 1200 each, which are positioned at an
half-pixel offset.

Now, if this is true (please confirm), don't we effectively have 4x
multi-sampling when scanning at 1200 dpi?

There are several issues that I don't find clear.

First: when scanning at 1200 dpi, do scanners actually use both CCD
arrays and "mix" the results (I'm not simply saying "average" the
results, since it might be too simplicistic given the half-pixel
offset), or do they only "turn on" one array?

Second: when scanning at 2400 dpi, do scanners give out pixels in the
order "1st pixel of 1st array | 1st pixel of 2nd array | 2nd pixel of
1st array | 2nd pixel of 2nd array", or do they somehow consider the
fact that nearby pixel overlay one another by half their width?
Of course, this also applies vertically, since while the motor moves by
1/2400th of an inch steps, pixels are 1/1200th of an inch "wide".

Third: when scanning at "4800" dpi, what do scanners do about the
horizontal resolution? Interpolation, I suppose. What kind of
interpolation? Does it vary from scanner to scanner?
And, do scanners that claim 2400x4800 resolution *really move the motor
by 1/4800th steps when instructed to scan at 4800 dpi*, or do they just
interpolate (since I know there are also other reasons for having
1/4800th stepping motors)? Does this vary from scanner to scanner?


Now, let's see how all this relates to multi-sampling.

Let's suppose I want to scan at 4800 dpi, with 2x multi-sampling -- for
the moment, let's ignore the fact that it might really be 4x
multi-sampling because of the double CCD array.

The scanner gives me an image. I can turn it into *two* images, one
made of the even lines of the original image, and the other made of the
odd lines (clearly, I must first downsample the original image
horizontally, since it was interpolated to 2x by the scanner).
I can then average the two images. Have I just obtained 2x
multi-sampling?

Apparently not, since I forgot that even and odd lines were sampled at
1/4800th of an inch apart from each other.

But I do know they're separated by a consistent 1/4800th of an inch. So
I could first sub-pixel-align the two images (a no brainer, since I
know they're misaligned by exactly one pixel), and only then do the
merge.

Have I now obtained 2x multi-sampling? Apparently, I have. But now I
wonder: what would have happened if I had just scaled down the original
image to half its size vertically?
Wouldn't that be equivalent to the procedure I described of splitting
it in two, aligning and merging?

Programs usually offer more than one algorithm for scaling down images:
bilinear, bicubic, etc.
Which of these is equivalent to splitting/aligning/merging, if any?


Now you probably also see why I asked all those questions about scanner
behavior above, since to answer my doubts about multi-sampling one must
be aware of how the scanner really behaves, and whatever it does to the
data *before* giving them out to the user.

Perhaps this whole article can be "scaled down" to the question: is
scanning at 4800 dpi and then scaling down to 1200 dpi (with what?
bilinear, bicubic...) equivalent to 4x multi-sampling at 1200 dpi?
(Make substitutions between 4800, 2400 and 1200 above, and you'll get
the other possible scenarios)


by LjL
ljlbox@xxxxxxxxxx

.

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