Don said:
That's very interesting! I always assumed any interpolation above
optical resolution was done in software. In other words (in the above
case) I thought the same result would be achieved by scanning at 3200
and then using PS, for example, to upsample to 6400.
Not always. Some, indeed most flatbeds these days, exploit what is
known as "half stepping" of the stepper motor drive. These half steps
are less precise than the full step and less robust because only half
the holding force is produced by the motor coils, however it effectively
doubles the precision of the stepper motor at no cost - albeit with
reductions in other parameters. Even so, in a normal stepper motor,
only a single doubling of precision is possible.
When used in a scanner, this permits the scan head to be moved at twice
the precision that it was originally designed. Usually, the minimum
step the scanner is designed for moves the scan head by the same
distance as the CCD elements are separated. This means that the sample
pitch in the x and y axes are the same, which fits directly with the
square aspect ratio pixels in most displays and image formats. However,
if the scanner motor is half stepped then the y sample pitch is halved
relative to the x sample pitch (which is fixed by the CCD design). This
doesn't match well with standard display and image formats, so the
pixels in the x axis are interpolated to simulate the intermediate data.
The interpolation can be simple pixel doubling or linear or even cubic
interpolation, depending on the complexity of the software, but it is
only applied along the axis of the CCD - the new data in the orthogonal
axis is real, coming from true image samples, albeit with the same MTF
as the original native optical resolution, since neither optic nor CCD
element dimensions have changed.
This is very different from the full interpolation that you get in
Photoshop or other image processing packages where the data in both axes
is interpolated - hence the terms *bi*-linear and *bi*-cubic
interpolation. In that case, no new real data is available and the only
change in the noise characteristics of the image is a direct function of
the noise shaping of the interpolation algorithm.
In principle, there is nothing to prevent a scanner manufacturer
designing their stepper motor to move the scan head by small fractions
of the CCD element pitch, thus enabling even more than a doubling of the
sampling density on one axis relative to the other. However this would
have little benefit in true resolution terms because of the finite size
of the CCD element and the lens resolution limits. Assuming an
unachievable in practice 100% fill factor, the MTF of the CCD itself is
63% at the Nyquist limit of its native sampling density, and falls to
zero at twice that limit - although it then increases again with a phase
inversion. Taking account of the lens resolution, this subsequent
increase in MTF is very marginal. In the case of a modern flatbed CCD,
most of which now use the HyperCCD approach first implemented on flatbed
scanners by Epson, the CCD is already oversampled in its own axis - so
even in that axis the MTF at the Nyquist limit is already very low
indeed. Thus the half stepping technology, which did provide a
significant resolution increase in one axis with linear CCD based
scanners, produces only a very marginal resolution increase with
HyperCCD based scanners and may, depending on the interpolation
algorithm used, actually produce a net reduction in overall resolution!
Since it offers so little in terms of the parameter they are selling it
on, which must be balanced against the cost of higher precision
mechanics and longer scan times, it is not a marketable option and I am
not aware of any scanner manufacturers which do this. Consequently, the
limit for the sample density is a doubling of the native CCD sample
density in the orthogonal axis due to half-stepping the motor drive,
since that can be offered at no cost to the manufacturer.
Any scan at more than twice the native optical resolution uses
interpolation in both axes, albeit with twice as much real data in one
axis as the other.
But, if I understand your explanation correctly, (in the above case)
each line is sampled twice and both samples are then saved to produce
the 6400 dpi.
Yes, but only up to double the CCDs sampling density because of the
half-stepping motor option.
Due to stepper motor jitter (and other inaccuracies)
this may result in the second sample not being perfectly aligned with
the first, which then accounts for the marginal increase in the axis
of the scan, right?
Yes, but even though the alignment will be worse than a full step, it is
still a small fraction of the instantaneous field of view (IFOV) of each
CCD element, and is consequently irrelevant to all intents and purposes.
Although, wouldn't the same stepper motor jitter (and other
inaccuracies) produce some lateral movement too, marginally increasing
resolution in the axis of the CCD as well?
Yes, but with the same caveat - it is irrelevant.
Does this apply to all flatbed scanners (or only to the Epson)?
Most modern flatbeds use half stepping to double the resolution in one
axis. Normally these are obvious from the asymmetric resolution
'specification' (eg. "Incredible 600x1200dpi!" or "Exceptional
1200x2400dpi!" or "Amazing 3200x6400dpi").
In addition though, most modern high resolution flatbeds use the
HyperCCD design, where each colour is actually produced from two rows of
CCD elements at half the sampling density but staggered by half a sample
pitch. This results in a sampling density which is virtually equal to
the optical resolution limit of the system - so aliasing is virtually
eliminated. However it also means that the resolution advantage of half
stepping in the orthogonal axis is also dramatically reduced too - if
not reversed as explained above.
If it does, that implies that scanning at maximum interpolated
resolution is actually useful and, for example, scanning at 19200 -
even though my own flatbed is rated at 4800 optical - is equivalent to
4x multiscanning?
No - it is only true up to twice the CCD sampling density. Some older
scanners were marketed with claims of resolution which were actually the
result of interpolation, but that has since been made illegal. However
since half stepping resolution is real, it is still legal to claim it
(even if it is marginal at best with a HyperCCD). If your scanner is
indeed a true 4800ppi (which significantly limits the options as to
which it is - somewhat contradicting your reasons for persevering with a
Nikon LS-30 ;-) ) then this double data gathering would only be
applicable to a 9600ppi resolution - again yielding a noise benefit
equivalent to 2x multiscanning. If, as is more likely, the 4800ppi
limit is the upper figure of the resolution specification of your
scanner then it is already taking the half stepping into account and the
real optical resolution is only 1200ppi with 2x multiscan performance
achieved at 4800ppi.
Downsampling to 600 or 1200 from there would then
increase the multiscanning effect/equivalent even more. Correct?
Usually, but it depends on how the scanner captures the lower
resolutions. Some scanners, eg. more recent Nikon film scanners,
produce low resolutions by downsampling the full optical resolution
themselves, so no further advantage is possible. Most, however, scan
low resolutions by multistepping the motor and dropping pixels. In
those cases the downsampling approach in the final application will
yield a noise improvement equivalent to the scale. So a 1200ppi
original rescaled to 600ppi will give the equivalent of 4x multiscan, or
2x noise improvement, assuming that the bit depth of the image is
sufficient to realise it.
And while am at it, I recently read (don't remember where) that
maximum CCD density is (currently) fixed at 2400 dpi due to the size
of each CCD using the current manufacturing process. According to this
article scanners, like mine, rated at 4800 actually have two CCD
arrays offset by half a dot to produce the optical equivalent of 4800.
Is this correct?
Partially. This is actually a very old technique which has been
deployed on military surveillance systems for years. The size is not
limited to 2400ppi, that is just a design criteria for that particular
CCD. Practically speaking, the size of the CCD element is only limited
by the storage capacity required to achieve a useful signal to noise
ratio and the resolution limits of the optical system it is designed to
operate with. Typically that is around the 2-3um region but it can be
higher or lower depending on the design criteria.
The only flatbed scanner I am aware of with 4800ppi optical resolution
though is the recently introduced Epson 4870. If this is not the
scanner in question then it might be worth checking your specification
again to be sure that this is not the half stepping resolution and you
really have a 2400x4800ppi scanner.
If yes, what about overlap? If individual CCD elements are too big to
fit on a single array wouldn't then there be lateral overlap between
neighboring CCDs on the two arrays, in effect, limiting the claimed
optical resolution?
Again, partially true. The resolution is obtained by staggered pixels
to produce double the sampling density but with a Point Spread Function
(PSF) and (Modulation Transfer Function) MTF of the single, larger, CCD
element. As mentioned above, this prevents aliasing by conforming to
the Nyquist criteria, but a consequence of doing this is that the
contrast at the limiting resolution is reduced to near zero. Unlike in
electronics, where a flat passband and brick wall cut-off are practical,
this is not the case in optics - so eliminating response above the
Nyquist limit comes at the expense of reduced MTF below it. However,
since the pixels have 4x the area of an equivalent full resolution
single line solution, they have much less noise - less than half the
noise - so their output can be sharpened considerably more before noise
becomes objectionable. Unlike a conventional linear CCD, unsharp
masking is an integral part of the HyperCCD operating principle. You
will see a lot of comparisons on the net of various scanners where any
USM is turned off - ostensibly to provide an equivalent comparison on a
flat playing field. Unfortunately this does exactly the opposite of
what the reviewers actually intended. :-(
