Diopter 20/X Equivalence?
Bob Penoyer
20/40, or generally, 20/X?
Mike Tyner
"best-fit" equations don't have much predictive value.
Plus, dioptric value isn't a single variable since astigmatism
is usually present, and the relationship is greatly affected by
age, myopia vs hyperopia, lighting conditions, and psychology.
Roughly, a -2.00 myope should be able to manage 20/100
in low light, 20/40 with squint, 20/25 with a pinhole.
-MT
"Bob Penoyer" <rpen...@NOSPAMieee.org> wrote in message
news:8e3vgss4rbcqb0rbh...@4ax.com...
Michael Pace
Bob Penoyer <rpen...@NOSPAMieee.org> wrote in message
news:8e3vgss4rbcqb0rbh...@4ax.com...
> Is there a mathematical relationship between diopters and 20/20,
> 20/40, or generally, 20/X?
Not really. Snellen notation is acuity test shorthand for distance/size,
where distance is the distance from the eye to the test target in feet (20)
or metres (6) and size is the number specifying a particular standard test
object. For size, the number isn't an actual measure of anything, it simply
denotes the "20" , the "40" or whatever standard target. In metric, the
objects are the same, but have different names: 6, 12, 18. The mathematics
involved is that the critical detail of the test object will subtend 1" of
arc at 20ft for "20", at 40ft for "40", at 60ft for "60 and so on. Dr
Snellen could just have easily used "A", "B", "C" etc as the names of the
standard test objects so we would use 20/A, 20/B etc and patients wouldn't
think it was an actual fraction. As the numbers go up, so do the sizes of
the targets.
It isn't necessary to use 20 or 6 as the first number; testing at any
distance is okay as long as the standard test objects are used. Thus one
can see acuity recorded at 10/20 or 5/160 or 3/12. Snellen acuity is useful
as it allows a patient's best corrected vision to be compared over time and
in different locations with different examiners with confidence that the
measures are the same.
So, knowing that Snellen notation specifies test distance/test object how
does that relate to refractive error measured in diopters? A person's
visual acuity depends on a number of factors only one of which is refractive
error. For people with astigmatism and for younger people with hyperopia,
the amount of refractive error will not be a very good predictor of distance
acuity. For myopes the amount of refractive error will be a better
predictor of distance acuity, providing the actual test distance is
significantly further away than the far point of the eye-- a low myope,
tested at 3 ft, is likely to have normal acuity.
For people with reduced vision due to disease, the refractive error will
have little value in predicting acuity.
Refractive error in diopters and Snellen acuity bear about the same
relationship to each other as size of gas tank in a vehicle does to the gas
mileage of that vehicle. If you know one, you can make guesses about the
other but you will often be wrong.
Bob Penoyer
>
>Bob Penoyer <rpen...@NOSPAMieee.org> wrote in message
>news:8e3vgss4rbcqb0rbh...@4ax.com...
>> Is there a mathematical relationship between diopters and 20/20,
>> 20/40, or generally, 20/X?
>
>Not really.
<snip>
>Refractive error in diopters and Snellen acuity bear about the same
>relationship to each other as size of gas tank in a vehicle does to the gas
>mileage of that vehicle. If you know one, you can make guesses about the
>other but you will often be wrong.
Well, okay. I know little to nothing about optics. But I am an
engineer with a reasonable mathematical background.
It _seems_ like there ought to be a relationship. For example, if a
person with 20/40 vision must be 20 feet from an object to see it when
a person with 20/20 vision can see it at 40 feet, then the labels
certainly mean more than A, B, or C-type labels. And, if a -1.00
diopter myope can focus on an object at 1 meter while a -10.00 diopter
myope can focus on an object at 1/10 meter, then diopters, too, use a
distance relationship. Thus, it seems to me that there should be a
relationship between the two measures.
So, if a 20/400 myope requires 8 diopters of correction and a 20/600
requires 10 diopters of correction, etc., a relationship begins to
appear. (These are obviously just arbitrary number choices on my
part.) Whether a simple mathematical relationship exists, there _must_
be empirical data between visual acuity and the number of diopters
needed to achieve correction. (I'm assuming no astigmatism or other
anomalies.)
Am I way off base with this reasoning?
GEM
the Snellen fraction.
The 20/40 (in UK 6/12) means that at 20 feet (the top number is the distance
of the test letter) the subject can see a letter which the "normal" person
would be able to see at 40 feet (the bottom number of the fraction). It is
the angle of subtense of the letter which is atually being measured, so the
20/40 letter has twice the angle of subtense at the eye as the 20/20 letter.
So 20/20 in feet is almost exactly the same as 6/6 in metres.
There is no simple correlation with dioptric power, as has been covered here
on numerous occasions. If we were all simple myopes, with the same pupil
size, and eyes which had the same resolving power, then there would be, but
we aren't so there isn't.
Many very capable mathematicians, visual scientists and optometrists have
produced formulae which produce some useable correlation, but with so many
provisos that they can produce no accurate results at all.
GEM
Bob Penoyer <rpen...@NOSPAMieee.org> wrote in message
news:aes1hss667h7s1845...@4ax.com...
William Stacy
Bob Penoyer wrote:
It _seems_ like there ought to be a relationship.
> Am I way off base with this reasoning?
This question has been addressed so often here that we once had a collaborative
effort and derived the infamous "dead horse equation" a couple of years ago.
Not really useful for anything, but it exists somewhere in cyberspace (try a
dejanews search on that quote).
NFN NMI L. a.k.a. S.T.L.
diopter myope can focus on an object at 1 meter while a -10.00 diopter
myope can focus on an object at 1/10 meter>>
Um, don't the diopters refer to the strengths of the lenses that are needed to
correct the myopia?
-*---*-------
S.T. "andard Mode" L. ***137***
STL's Wickedly Nifty Quotation Collection: http://quote.cjb.net
Mike Tyner
"Bob Penoyer" wrote in message
> So, if a 20/400 myope requires 8 diopters of correction and a 20/600
> requires 10 diopters of correction, etc., a relationship begins to
> appear. (These are obviously just arbitrary number choices on my
> part.) Whether a simple mathematical relationship exists, there _must_
> be empirical data between visual acuity and the number of diopters
> needed to achieve correction. (I'm assuming no astigmatism or other
> anomalies.)
>
> Am I way off base with this reasoning?
Not at all, just oversimplified. There are several contributing variables
and you have only accounted for one of them - myopia. Your equation
would only hold for myopes in a certain range, without astigmatism,
of a certain age, under defined lighting conditions, and other stuff
that makes it useless as a predictor other than as a vague rule of thumb.
-MT
-MT
Michael Pace
GEM <gor...@gemcc.u-net.com> wrote in message
news:OXeQ4.137$U3.7...@newsr2.u-net.net...
> I do not understand the response about using labels instead of numbers in
> the Snellen fraction.
>
> The 20/40 (in UK 6/12) means that at 20 feet (the top number is the
distance
> of the test letter) the subject can see a letter which the "normal" person
> would be able to see at 40 feet (the bottom number of the fraction). It
is
> the angle of subtense of the letter which is atually being measured, so
the
> 20/40 letter has twice the angle of subtense at the eye as the 20/20
letter.
> So 20/20 in feet is almost exactly the same as 6/6 in metres.
>
I'm Canadian and also use metric Snellen.
What I meant was that the "40" or the "12" is not a measure of the eye or
target, ie the target is not 40 inches or 12 mm in size. The "40" or the
"12" refers to the distance from the eye at which the target will subtend
1"--yes, if the target 40/12 target is placed at 20 ft or 6 metres it will
subtend double the angle it subtends at 40ft/6M. I sometimes wish that they
were labelled A, B, C so that I wouldn't get involved in explaining why
someone with 6/3 (20/10) does not have "twice the vision" as someone with
6/6 (20/20).
When patients ask me to explain 6/6 to them or ask how to convert it to
diopters I find that they more quickly grasp that Snellen is just an
arbitrary measure and not a biological constant if I put up the /6 line and
say "It means the smallest line of Snellen letters you can successfully read
at 6M is this one. This is the smallest line that, in theory, the human eye
is capable of seeing at 6M. Of course, in practice, we find that many
people can see one or two more smaller lines."
Michael Pace
Bob Penoyer <rpen...@NOSPAMieee.org> wrote in message
news:aes1hss667h7s1845...@4ax.com...
> "Michael Pace" <mpa...@home.com> wrote:
>
> >
> >Bob Penoyer <rpen...@NOSPAMieee.org> wrote in message
> >news:8e3vgss4rbcqb0rbh...@4ax.com...
> >> Is there a mathematical relationship between diopters and 20/20,
> >> 20/40, or generally, 20/X?
> >
> >Not really.
> snip<
>
> It _seems_ like there ought to be a relationship.
It is human nature to want to quantify things and goddammit it seems to me
that there ought to be a relationship (at least for myopes) too. But in
practice, there just isn't. Some 1D myopes get uncorrected 20/25 and some
get 20/100. I have 0.50D myopic patients who wear their glasses full time
and can't bear the world without them, and 5.00D patients who only use their
glasses for driving and the movies. Who knows why.
One of the problems with deriving a relationship is that the standard eye
charts have rather large jumps--the sequence goes 10, 15,
20,25,30,40,50,60,70,80,100,200,300,400. If your uncorrected vision is
actually 20/32 you will measure 20/ 40. It gets worse at the high
end--seven choices between 20/20 and 20/100 but none between 20/100 and
20/200. Researchers in vision science and clinicians who work with the
partially sighted often will use other scales with finer gradations to
measure acuity, but those scales are too time consuming to be of use in
general practice.
Snellen is fine in general practice because uncorrected acuity is not an
important measure. The important thing is best corrected acuity and one
wants to be able to tell if there have been subtle changes signifying
potential pathology. A fine scale between 20/15 and 20/100 suits this
purpose. Once best corrected acuity drops below 20/100, Snellen isn't a
great measure of function and other tests become more important.
Anyway, if someone with money to burn wants to fund a study of the
relationship between uncorrected acuity and refractive error, I'm sure there
is a Msc student somewhere who would do it
mp
MWhite4981
Like you, I would prefer a formula. But, there are other variables. Just to
name a few:
Lighting. It should be a constant, but it does vary.
Printed charts and projected charts are influenced by age of chart or projector
bulb, quality of reflective screen, cleanliness, etc.
Pupil size. Aside from influence by lighting level, normal pupils can vary
from 1.5 to 8+mm. This has a major effect on depth of focus, same as a 35mm
camera.
Squinting of the lids creates a slit aperture, increasing depth of focus. The
effect of squinting will be greater with horizontally vs. vertically oriented
astigmatism (with minus cylinder). Therefore, the effects of astigmatism vary
with axis as well as magnitude.
Psychology. It is just good old physics as the image contacts the eye, is
converted to an electrical signal and sent to the occipital cortex. From
there, it is perceptual psychology. Now, we are dealing with the human thing
and you know how that varies. One guy tears an ACL and finishes the season (
it happened at Marshall this past football season ), while another has muscle
spasms and wants to retire on workers comp. Attitude and effort can have a
huge effect.
I could go on and on, but I'm burning bandwidth.
Regards, Ed White
Bob Penoyer
>Hey, Bob.
>Like you, I would prefer a formula. But, there are other variables. Just to
>name a few:
<snip>
>I could go on and on, but I'm burning bandwidth.
>Regards, Ed White
I'm beginning to get the idea. Thanks to all who responded.
William Stacy
it for publication? Maybe not.
Bill
John Connolly wrote:
> On Thu, 04 May 2000 07:53:34 -0700, William Stacy <wst...@obase.net> wrote:
> Bob Penoyer wrote:
> >
> >It _seems_ like there ought to be a relationship.
> >
> >> Am I way off base with this reasoning?
> >
> >This question has been addressed so often here that we once had a collaborative
> >effort and derived the infamous "dead horse equation" a couple of years ago.
> >Not really useful for anything, but it exists somewhere in cyberspace (try a
> >dejanews search on that quote).
>
> -----------------------------
>
> On 20 Sep 1997 17:17:21 GMT, w...@ix.netcom.com(William Stacy) wrote:
>
> >OK here's the data for hyperopes with less than .5 cyl, along with
> >ages..............
>
> Using this latest hyperope data, along with Bill's earlier data on myopes,
> the "final???" William Stacy Dead-Horse Equation, fitted to 236 points [135
> myopes (<.5 cylinder) and 101 hyperopes (<.5 cylinder)] is:
>
> Diopters = +-[Log(20/xxx)]/.43 = +-2.3Log(20/xxx) = +-Ln(20/xxx)
>
> Standard Deviation = +-0.75
>
> The Natural log result is, of course, complete happenstance. :-)
>
> Complete 236 point data listing available on request.
>
> -----------------------------------------------------------------
>
> The equation for the 101 point hyperope data, only, is:
>
> Hyperope Diopters = -[Log(20/xxx)]/.49 = -2.05Log(20/xxx)
>
> Standard Deviation = +-0.73 diopters
>
> and the hyperope data listing is:
>
> Initial Corr. Age Obsd. Calc. diff.
>
> 20/25- 20/25 14 0.5 0.2 0.3
> 20/20-- 20/20 19 0.25 0.0 0.3
> 20/50 20/20 63 1 0.8 0.2
> 20/100 20/20 55 1.25 1.4 -0.2
> 20/50+- 20/20 26 0.25 0.8 -0.6
> 20/20 20/20 42 1 0.0 1.0
(Most of the data snipped).