Board index » lasik-eyes » LASIK, islands (central or otherwise), and technology needed to detect cornea aberrations reliably

2004-06-07 12:18:33 AM
The replacement retina mentioned here only having 1000 points gave me
an idea.
Search for ophthalmologist nyquist frequency for more information.
e.g.,
www.emedicine.com/oph/topic759.htm
journalofvision.org/3/10/6/article.aspx
Any engineer with the basic college courses would understand the
nyquist frequency- I would hope especially any working on things that
damage people's vision for life. Basically the ability to detect
something is limited by the sampling rate. If you want to reliably
detect say pennies that are lined up every inch, then you sample for
the pennies every 1/2 inch (twice the rate of the phenomenum). If you
sample every 3/4 inch for instance, then you'll miss at least 1 penny
(on average) every 4-8 inches.
Relating this to wavefront on a messed up LASIK (or PRK, etc) cornea,
sampling at the highest possible rate would detect the most problems.
Even if the lasers are not capable of correcting at those rates, then
the best technique would obviously be (in my opinion) to sample at the
highest possible rate and average across a localized area to smooth
things out as much as possible. Hence the ray tracey's accuracy for
detecting problems is better because it has a higher sampling rate
(hearsay). Other techniques might have more treatment advantages for
other reasons, but on retreatments, accurate diagnosis would be
critical (as some of the posters on this board have learned the hard
way).
The sampling must occur at twice the rate of that which is trying to
be detected so if you're doing an 8mm diameter treatment zone then
here's the size of an aberrations or island that you could reliably
detect with various resolutions (sampling sizes). So sampling 100
times would mean that you would reliably detect something that would
occur 50 times (100 is twice the reliable sampling frequency) in the
test area. For an 6mm cornea zone ~3*3*3.14 (the radius squared times
pie). Rounding down to say ~28mm (28,000 um), then sampling 100 times
would reliably detect a problem that is 28,000/50 or 560um. A problem
1/2 that size would be detected 1/2 the time. Would everyone here
agree that 560um is a HUGE aberration in a cornea? At 8mm it would be
even more sampling needed because the size of the treatment area would
be almost twice as big (4*4*3.14 or ~50mm). Now suppose we wanted to
reliably detect 10 um or larger aberrations. We would need to sample
5,600 times over a 6mm area to detect it reliably.
How many devices do that? What's the sampling rate on the Alcon?
Alegretto? VISX, etc?
For homework, determine the size of an island detectable at each of
these different sampling rates and please verify my math for accuracy.
see #11 here
woodhams.com/wood2b5.html
and
www.inviewvision.com/interwave.html
# of samples size of aberration detected reliably
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ccastaccount@comcast.net (wavefront information) wrote:
than 0.3 mm on a side. Keep in mind that Fourier optics
dictate that it is the size of the entire lens, not the
minute aberrations that determine the focusing quality.
In other words, you get the most bang for the buck by
fixing the largest, lowest order aberrations that span
the entire lens. At the lowest order this means identifying
the ellipsoidal nature of the lens and applying correction
to make it more spherical. (From a mathematical point of
view, this entails identifying the first derivative of
radius of curvature and applying the best correction that
brings the derivative to zero across the entire lens.)
I only need to measure 4 independent samples across a lens
to estimate its ellipsoidal nature. Higher orders will
simply require more samples. 100 samples across a lens
can provide a fit to a nearly 100 term polynomial describing
the lens -- possibly a huge amount of overkill!
In order for a tiny, localized aberration to have a
significant effect on the lens optics, it would need to
extend very far in its third dimension (essentially be an
extremely high peak or deep trough). I believe that the
elasticity of cornea tissue preclude such features. For
instance, can a 0.3x0.3 mm aberration be 1 mm high **AND**
exist only within that 0.3x0.3 mm sector and nowhere else?
There is a huge body of literature on this subject under
key words such as "reflector synthesis" which discuss the
tradeoffs and nature of the Fourier relation in lens
design.
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How can 100 samples satisfy a 100 factor polynomial? Not sure what
you mean.
1 mm is 1000 um. 1000 um would be (guessing) ~80 diopters so that's
not a good example. Could a 20 um abberation exist across a 100um
area? You're hypothesis is it would flatten out naturally just from
the elasticity of the cornea? So if you had a 50um abberation over a
100um area it might flatten to say 25um? That would be ~2 diopters
worth. Wouldn't that be big enough to effect the optics?
Ar Fai Ve <80211b@80211b.wifi.net>wrote in message news:<80211b-90773F.17222510062004@newssvr23-ext.news.prodigy.com>...

lasik-eyes

ccastaccount@comcast.net (wavefront information) wrote in message news:<703973fa.0406111708.4d5da7c1@posting.google.com>...
before one's surgery, instead of after?
SErebel
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ccastaccount@comcast.net (wavefront information) wrote in message news:<703973fa.0406111708.4d5da7c1@posting.google.com>...
then solve a matrix equation involving 100 observations
over which the 100 term polynomial is sampled. Approaches
such as Wavefront are going to oversample (e.g. make many
more observations than required for solving) and then perform
a least squares fit to arrive at the correction values that
have the best results across the entire lens.
(= 3.14e-8 sq-meter) area does not suggest one should apply a 1.6
diopter correction to the entire eye! Imagine that the entire
focusing area of the eye (6mm radius =>1.13e-4 sq-meter) is ideally
shaped except for the one aberration you suggest. This one
aberration is 0.03% of the area of the eye and cannot significantly
affect the focusing of the entire eye.
The term diopter is related to the focal length of the lens
*** taken as a whole ***. If you want to define a local
diopter concept, then you need to work with the local radius
of curvature. Again, your example of the 100 micron aberration
that is 20 microns high has a ***local*** radius of curvature
of maybe 80 microns. Compare this radius of curvature to that
of the entire 6 mm radius lens.
And I go back to my point that it is aberrations that comprise
a large fractional area of the lens that first require corrections.
These are what the Wavefront analysis will solve for. In a perfect
world, one could design an approach that detects even sub-micron
aberrations and corrects for them. However, the smaller the
area of the aberration, the less that its correction will improve
the overall focusing power of the eye.
To conclude: for you to claim that Wavefront is getting it wrong
or using the wrong Nyquist sampling rate, then you need to (a)
identify realistic aberration that is missed and (b) prove that
this aberration significantly affects the focusing power of the
lens.
Wavefront employs a mathematical approach that differs very little
from proven and validated approaches commonly employed in optics
and antenna theory.
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2. What is your opinion- "(a)identify realistic aberration that is
missed"?
3. What is the sampling rate used for "Wavefront" as you term it?
4. Why are so many people suffering from aberrated vision from
aberrations in their cornea that would likely be missed on a 100 point
wavefront device?
There is much more to vision than acuity in bright light with high
contrast right?
In my opinion, 100 points isn't nearly enough to catch corneal
aberrations that significantly effect vision quality. By comparing
the Diopters of the entire lens, you are only discussing vision acuity
predicted for the lens based on the 100 points.
Ar Fai Ve <80211b@80211b.wifi.net>wrote in message news:<80211b-14BD49.20291013062004@newssvr23-ext.news.prodigy.com>...

ccastaccount@comcast.net (wavefront information) wrote:
of the measurements.
is being (a) missed by Wavefront and (b) detectable by human
subjects? Bausch & Lomb claim that their aberrometer measures
through 5th order (18 spatial modes I believe). Conventional
optical corrections (defocus and astigmatism) only involve
through 2nd order. These 3 additional orders of modes provide
a tremendous improvement in the deviation between the actual
shape of the cornea surface and the predicted shape that is
constructed from the 5 orders of measured modes. Furthermore,
it only takes 18 (well chosen) samples to estimate strengths
of these 18 modes. Therefore, 100+ samples combined with a
least squares estimation or singular value decomposition (SVD)
approach will provide reliable estimates of modal strengths,
resulting in the an accurate functional fit of the eye being
measured.
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Perhaps we're talking about 2 different things. I'm talking about
retreatments for detecting irregularities from other surgery. Maybe
you're referring to nice healthy corneas that haven't been injured for
life by LASIK? You are mentioning a bunch of stuff while overlooking
the obvious issue I am raising. Quoting from my original post
(below), it doesn't matter what mathematics you apply to your 100
points if ALL 100 points completely miss an area of the cornea that is
up to 560um wide and as high as the ablation depth. So say you have a
500 um wide "island" that is 48um (~4 diopters?) tall.
You would sample 100 points and do your fancy mathematical fitting
without adjusting for or correcting the obvious island? This is an
extreme example to make a point.
here's the size of an aberrations or island that you could reliably
detect with various resolutions (sampling sizes). So sampling 100
times would mean that you would reliably detect something that would
occur 50 times (100 is twice the reliable sampling frequency) in the
test area. For an 6mm cornea zone ~3*3*3.14 (the radius squared times
pie). Rounding down to say ~28mm (28,000 um), then sampling 100 times
would reliably detect a problem that is 28,000/50 or 560um. A problem
1/2 that size would be detected 1/2 the time. Would everyone here
agree that 560um is a HUGE aberration in a cornea?
Ar Fai Ve <80211b@80211b.wifi.net>wrote in message news:<80211b-73D06B.00541417062004@newssvr22-ext.news.prodigy.com>...

ccastaccount@comcast.net (wavefront information) wrote:
points are not infinitely small. They are actually tiny micro
detectors that are fully adjacent to one another. Each detector
collects the light energy striking its surface area, not just
the light striking a single infinitesimal point. If your 560 um
aberration causes any scattering, it will be received by one
(and likely more) of these detectors. To say that these detectors
will miss an aberration is wrong. Think about the meaning of "wave" in
wavefront. The light beam used has a finite width, and any
scattering from aberrations will be represented in the change
of the light beam's intensity and surface of constant phase (wave
front).
occurring? Have you confirmed this? I bet if you run this
extreme example through the wavefront sensor, and if the
scattering from the island is significant, then it will be
present in the measurement and factor into the modal extractions
that I discussed previously. If it is not shown in the measurement,
then how can you possibly claim that it is detectable by
the human eye? Do you have experimental evidence to support
this?
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ccastaccount@comcast.net (wavefront information) wrote in message news:<703973fa.0406181850.3f05f309@posting.google.com>...
title it sure does look like you're talking about islands and the
content doesn't appear to contradict that. I think it is critical to
distinguish between what wavefront measures and what of that data can
be used to retreat a cornea.
My personal experience (of one eye with undetected central islands
which underwent a wavefront retreatment) is that the island doesn't
show up until you get up to the 11th or 12 order or so - then it
starts to be visible, and by the 24th it is there in all its glory.
Problem is, lasers don't treat 24 orders, they treat 4 to 6. It's my
understanding that's at least part of why central irregularities are
not fixable with Wavefront.
Rebecca
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Again, what is your explanation for why wavefront retreatments aren't
more reliable and more successful? What data (clinical or otherwise)
do you have?
In some cases I've heard about islands being there before and after
wavefront.
What is the size of this surface area? To cover a 6mm diameter zone
fully with 100 samples (best case- assuming no overlap), the area of
each sample would have to be ~28,000 um/100 or 280um. Does each
sample detect any aberrations within a 280um area? What if the light
is scattered away from the sensor? Does it measure the magnitude of
the amount of light expected vs. the light received to know if the
amount of light is less than what would be expected in an unaberrated
cornea?
the light striking a single infinitesimal point.

ccastaccount@comcast.net (wavefront information) wrote:
Wavefront is only through 5th order. In the case of an island,
any 0th-5th order corrections which span the entire eye and
most certainly underly the island will be accounted for while
the higher order components related to the island will be
left untouched. In other words, laser correction does occur
at the site of an island, no matter what its size. But if
the island contains higher order components, then the
island will still be there after laser correction.
However, it is far better that Wavefront be robust to and not
change the high order modes associated with islands than to
allow the islands to corrupt the overall fit and induce, say,
an overcorrection across the entire eye thanks to a single
higher order bump.
measures the position of a laser beam spot that is reflected
off the eye during the Wavefront scan. I do not know the
width of the laser beam or effective capture area and pixel
spacing of the CCD employed to determine the precision to
which the Wavefront hardware can detect an aberration.
Whether the laser beam hits or misses a sub-280um aberration
during the Wavefront scan does not really matter since
Wavefront only intends to model through the lowest 5 orders
of aberrations.
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Ar Fai Ve <80211b@80211b.wifi.net>wrote in news:80211b-
EE3279.02242523062004@newssvr23-ext.news.prodigy.com:
span the entire 6.0mm zone of analysis. This is where topography has an
edge.
DrG
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1. So we agree that taking 100 points is Not precise enough to detect
many aberrations.
the bad results from wavefront PRK or LASIK.
that? It matters to the person who has the aberrations.
aberrations? Seems like pretty simple math.
there after Wavefront that could have been treated before Wavefront,
then wouldn't it be more "robust" to fix it?
6. Do you want to discuss some ideas about how to treat these
aberrations instead of discussing whether ignoring them is a bad idea?
Ar Fai Ve <80211b@80211b.wifi.net>wrote in message news:<80211b-EE3279.02242523062004@newssvr23-ext.news.prodigy.com>...

ccastaccount@comcast.net (wavefront information) wrote:
have negligible contribution to the overall focusing
power of the eye/lens.
to aberrations. The direct cause and effect must be
quantified. Anyone hypothesizing claims of poor vision due
to aberrations post-lasik should get measured using an
aberrometer with far denser sampling than what Wavefront
internally uses. Ray tracing and other basic principles
of optics can be applied to determine if the higher order
aberrations detected actually have a non-neglible impact
on the focusing of the lens.
Keep in mind that a regular pair of glasses will not correct for
higher order aberrations pre-lasik either.
vision and something singular like a 24th order islan.
Why ruin the focusing properties of the largest portion
of the eye just to compensate for a discontinuity that is
a minute fraction of the lens area?
a first order correction (as opposed to 5th order). If the
sample point is directly on an island, a catastrophically
incorrect estimate of the correction for the entire eye
would result. By robust I imply oversampling followed by
a numerical fit which accurately estimates the orders of
interest. Allowing higher order aberrations to corrupt
low order modes would result in a horrible outcome.
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I would like for you to evaluate the aberrations in my eyes. Please
email me and I will come wherever you are at my expense if you have
this equipment available you refer to. You seem far more
knowledgeable to me than anyone I've talked to so far about these
issues. Why don't more Doctors understand this better BEFORE they do
permanent surgery on someone?
1. IF the "disontinuity" (ies) are causing bad vision quality, then
why can't they be corrected without "ruin" (ing) the focusing
properties of the eye (the "lens")? This is the crux of our
discussion. This seems like a trivial engineering problem on
non-living tissue that doesn't move (saccadic eye movements, etc).
The issue we're discussing is how to do this after refractive surgery.
You seem to have given up all hope of being able to do this and I
disagree. The answer(s) might be simpler than you think, but I need a
lot more information to know more.
agree that oversampling is required for accurate diagnosis.
3.A. If the aberration is an island, then why can't the island be
targeted directly without effecting the rest of the eye? Why does the
entire eye need to be treated?
3.B. If the aberration(s) are spherical in nature (the most common
type of aberrations after lasik- do they occur 100% of the time with
standard lasik?), then again why not target the aberrations with more
specificity? Some doctors do a snail like pattern to increase the
size of the ablation zone don't they? Other Doctors do wavefront to
increase the ablation zone don't they (but this doens't completely fix
it does it?)?
3.C. In any case, why couldn't a protective gel or other protective
technique be used to keep the laser energy from ablating the low point
(the valleys)?