jim wrote:
>
> Jeff Miller wrote:
>
>
>>Hmmm, would it be fair to say there's a difference of opinion
>>between Jerry and Fred in these latest responses? The sigma-delta
>>converter I'm looking at has a nominal sample rate of 5Ms/S, but a
>>nominal bandwidth of 2.45Mhz. You don't think that spatial data above
>>2.45Mhz will simply get tossed, Jerry? Perhaps it's much the same thing
>>as blurring the image.
>>
>>I'm a _little_ disturbed that I might be "wasting" half or 3/4 of my
>>pixels. EM photos are breathtaking because they are so sharp and
>>detailed. I wish I could turn the digital filter on and of. Don't think
>>I can. But for final images, I don't think there's any real limitation
>>on resolution. For display, I could sample at 2Kx2K and dither(?) down
>>to 1Kx1K... though I may need IMAQ Vison (~$700) to do it in real time.
>>For rendering to posters I should be able to capture 32kx32k.
>>
>>Now that Fred mentions it I am aware of "screening" issues when
>>scanning. And sure enough as I understand it the solution is to scan at
>>2X or more of the screening frequency.
>>
>>I'm leaning toward the sigma-delta converters with built-in filtering so
>>I think I'll be fine in the vertical.
>>
>>But now Fred's got me thinking about the horizontal. How do I "filter"
>>in that dimension? Or oversample for that matter? Perhaps if I can
>>figure out the ultimate resolution (which has mostly to do with "probe
>>size", which as I understand it is approximately equal to the area of
>>the cathode that deos the actual emitting: about 25nm for Tungsten
>>filaments, maybe 10nm for LaB6 cathodes, and 1-2nm for feild emission
>>sources, motly I use Tungsten and LaB6) and then scale my scan for
>>10nm/pass for Tungsten and 5nm/pass for LaB6...
>>
>>Hmm, well this will be interesting anyway.
>
>
> Hi Jeff,
> I haven't been following this before today, but from what I can tell
> you have not really revealed the necessary information to address the
> issue of aliasing. If I understand you have a signal that is both
> digital and analog. In the vertical direction in order to correctly deal
> with aliasing you need to know how many scan lines are being mapped to
> how many rows in the array that will store the data.
> In the horizontal direction that is where the sampling rate comes into
> play. If you scan 500 lines at 10 times a second you have 5000 lines per
> second. If your sampler is taking 5 million samples a second then you
> will have 1000 samples per line. So that is the natural size of the
> array that your data will fit into 500x1000. If you want to put it into
> a 512X512 or 1024X1024 or whatever sized array you need to resample
> using an appropriate resampling scheme. Spline based interpolation works
> well for image processing resampling - especially if you use tension
> splines with adjustable tension. That allows you to deal with some of
> the tradeoffs between aliasing and image clarity on the fly.
>
> -jim
>
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OK, first off let me say I realized later I was confused (and likely
confusing you guys a bit) by getting my horizontal confused with the
vertical- not that I confused the two per se, but I confused them in the
common contextual meaning.
So now I see that Jerry and Fred do agree. Where Jerry says horizontal
filtering is "easier than vertical. Just low-pass the data stream.", I
think the sigma-delta converter/filter will do that for me whether I
like it or not.
I'm still not quite clear on how to over sample/filter the vertical, then.
Jim, the SEM's I'll be working with were born strictly analog. Their
operating principle is remarkably simple. They use a pair of scanning
coils, one for x and one for y. They can be driven at virtually any
speed, limited only by the frequency response of the coils and by
secondary considerations such as response of the detector (generally
5-10Mhz nominal) and some sensitivity tradeoffs. Typically they are
raster-scanned. In all cases the CRT deflection yoke is driven at the
exact same speeds, in sync, by the same circuit that drives the SEM
deflection coils. The signals are voltage divided down to drive the SEM
coils depending on magnification selected: at low mags the scanning
coils are driven hard, at high mags they're barely "tickled" so the beam
is driven over a very small area of the sample. In most cases several
nominal scanning speeds and formats are available to the operator,
generally at least a "high speed" low-res scan with 500-2000 lines/image
at 2-5 refreshes/sec and a low speed, hi res scan of 5-10K lines or so
for photography: a single exposure can take 10 seconds or more. The
phosphors used in the CRTs are of a special long decay type so the
images persist for viewing by the operator in high speed mode, but of
course that only works so well and is a major source of annoyance at
higher resolutions. It's not uncommon to drive at NTSC rates as well,
interlacing and all, so images can be recorded to tape, sent remotely,
etc.: but at higher magnifications this is seldom done, for some reason
S/N starts falling apart, if only because at higher mags the (DC driven)
"condenser" lens is driven harder which narrows the beam and (I think)
limits the number of electrons available to hit the target.
I'll be retrofitting with a delta-sigma converter with a nominal sample
rate of 5 Ms/sec and a built in digital filter with a nominal bandwidth
of 2.45 Mhz. I say nominal because I'll be lowering the clock speed
considerably for saving images to disk at high mags and high
resolutions. The digital filter is driven by the same clock source as
the sampling portion, therefore the bandwidth is always limited to half
the sampling rate. It is important to understand that I'll be using
down counters and DACS to drive the scanning coils in sync with the
pixel clock: the whole awkward console is divorced.
The PCI card doing the high level stuff has an on-board buffer of 32
Mbytes, and I'll be using 16 bit resolution. Therefore my maximum
"native" sampled array will be 4Kx4K. I'll also have "fast scan" modes
of 512x512, 1024x1024, and 2Kx2K. But ultimately there is no hard limit
to the size of the arrays other than the resolution of my DACS, I don't
think: the board can save to disk as fast as the disk subsystem and PCI
bus allows. Driven at low speeds I suppose 65K*65K should be possible,
even desirable for posters.
Ultimate magnification and resolving power (i.e.: resolution) is
dependent mostly upon the type of cathode. I believe the figures are
approximately 25nM for Tungsten, 10 nM for Lanthanum Hexaboride, and
1-2nM for field emission sources. I'm using W and LaB6 now, but I'll be
trying to upgrade to FE (aka FESEM) in the future. In fact I will need 1
nM resolution if I'm going to explore single electron transistor
technology.
So given that the horizontal is filtered by the A/D as a matter of
course, I'm wondering first if keeping the scan line width at 1/2 or
less of the spot sizes mentioned above qualifies as a type of
oversampling and will eliminate vertical aliasing without post
processing. If not, it might beg the question as to why I'm going with a
delta-sigma with built in filter, given the fact that I'll need post
processing anyway to clean up the vertical.
I don't _think_ aliasing/Moire' is an issue in the traditional strictly
analog arrangement, but I could be wrong. Although it's obvious why
there would not be aliasing in the horizontal, I'd be stumped as to why
it would not be an issue in the vertical, given that in a sense the line
vs. line scanning is still discreet.
Hmmm. There's nothing stopping me from grabbing a frame using a
traditional top down scan pattern and then exchanging x for y drive and
taking one side-to-side. By rotating, correlating, and differentiating
the two images with the knowledge that one is anti-aliased horizontally
and the other is anti-aliased vertically perhaps I can isolate aliasing
effects. Complicated by the fact that the gain of the x and y drive
channels would have to be closely matched.
But I digress. Assuming my half spot size scan scheme doesn't work or is
not generally applicable, what are the types of algorithms to be on the
lookout for (or have you already answered that question, Jim) and are
there any free utilities I should look for to do it? Will Photoshop do
it, do you know?
I'm sure NI's IMAQ Vision product would do it, and probably in RT too.
Can't afford it.
Looking forward to trying it but it may be a couple months before it's
finished. The NI IMAQ PCI-1422 image capture board (designed to drive
hi-res parallel digital output cameras, but very flexible and comes with
friendly utilities for defining new camera types) set me back a pretty
penny and it will be a while before I can afford the A/D, D/A, and LVDS
conversion EVM's to go with it. Lots of wiring to do as well.
Thanks for all the insight so far! I have to studd Fred's most recent
post more carefully.
-Jeff