20-1000 in diopters?
Ryo Imamura
How does one convert the often used ratios "20-?" into diopters, which I
am more used to hearing. Thanks.
Mike Tyner, OD
Ryo Imamura wrote:
>
> How does one convert the often used ratios "20-?" into diopters, which I
> am more used to hearing. Thanks.
If there's a formula, it has several variables and more than one solution.
The bad vision (eg 20/400) could be from myopia, or farsightedness, or
astigmatism, or an organic cause. These "diopter" prescriptions might all
cause about 20/400 vision:
-4.00
-2.25 - 3.75 * 135
+4.00 (at age 50)
+0.50 with esotropia or "crossed eyes"
--
Mike Tyner, OD
drm...@bham.com
William Stacy
In <33F37D...@bham.com> "Mike Tyner, OD" <drm...@bham.com> writes:
These "diopter" prescriptions might all
>cause about 20/400 vision:
>
> -4.00
> -2.25 - 3.75 * 135
> +4.00 (at age 50)
> +0.50 with esotropia or "crossed eyes"
>
I agree with your post except for the last example, where the .5 is not
the "cause" of the 20/400, but certainly can be the refractive error
(so could 0.00) as in any case of poor vision due to pathology.
Bill
Bob S.
Mats Söderman wrote:
>
> Raymond A. Chamberlin <ra...@sirius.com> wrote in article
> <34052459...@news.sirius.com>...
> > Ryo Imamura <Ry...@worldnet.att.net> wrote:
> >
> > >How does one convert the often used ratios "20-?" into diopters, which I
> > >am more used to hearing. Thanks.
> >
> >
> >
>
> You don´t. 20/20 etc is the size of a letter, and diopters is the power of
> a lens.
>
> Yours
> Mats
>
According to the approx. formula posted here earlier,
20-1000 would correspond to approx -6.3 diopters.
Mats Söderman
Bob S.
John Connolly wrote:
>
> On Wed, 03 Sep 1997 07:47:22 -0400, "Bob S."
> <bo...@ix.nospam.netcom.com> wrote:
>
> >John Connolly wrote:
> >>
> >> On 2 Sep 1997 17:41:17 GMT, "Mats Söderman" <mv3...@venus.swipnet.se>
> >> wrote:
> >>
> >> >> Ryo Imamura <Ry...@worldnet.att.net> wrote:
> >> >>
> >> >> >How does one convert the often used ratios "20-?" into diopters, which I
> >> >> >am more used to hearing. Thanks.
>
> >> >You don´t. 20/20 etc is the size of a letter, and diopters is the power of
> >> >a lens.
> >>
> >> At first, it seems that, assuming zero astigmatism, there should be,
> >> at least, an empirical correlation. However, in addition to
> >> myopia/hyperopia, the 20-? measurement is affected by condition of the
> >> macula/fovea, clarity of the vitreous, etc. So Mats is right.
>
> >I still don't get it.... it seems to me that even in spite of the above
> >mentioned mitigating factors.... a particular (approximately) lens,
> >measured in diopters, when applied to all people with 20/X vision,
> >should allow them to discern letters on the 20/20 line.
>
> Perhaps you don't get it because my reply, above, was seriously
> incomplete and confusing. It refers to eyes which have problems which
> make them _not_ correctable to 20/20. Eyes which are low in
> astigmatism and are correctable to 20/20 (which we might refer to as
> pure "opes" :-), or "healthy") should behave as you say; i.e., they
> should obey a universal correlation between a "diopter" measurement
> and a 20/? measurement. I would guess that such a correlation has
> been worked out, but I don't have a reference.
OK, gotcha now. By the way, I saw such a mathematical correlation
posted here a short while ago, and it seems like it works to me. It is:
Correction in Diopters = log(VA) / .27
where VA is a fraction similar to 20/50 or 20/200 etc.
Bob
Jimmy Thompson
Jimmy R. Thompson
Computing Devices International
jrt0...@dnaco.net
bh...@globalnet.co.uk
>John Connolly wrote:
>>
>> On 2 Sep 1997 17:41:17 GMT, "Mats Söderman" <mv3...@venus.swipnet.se>
>> wrote:
>>
>> >Raymond A. Chamberlin <ra...@sirius.com> wrote in article
>> ><34052459...@news.sirius.com>...
bh...@globalnet.co.uk
Unfortunately not. How well the eye sees depends on several factors;
Pupil size (which controls how "easily" the wrong lens will blur ),
Age (controls accomodative power of the eye), the clarity of the
"media" (i.e how clear the cornea and internal liquid is), whether the
eye is long or short sighted , or astigmatic (this affects how
blurred, "blurred" really is) and it is also affected by the way in
which the brain perceives the information the eyes give it.
Between the age of zero to about ten years, the visual cortex area of
the brain undergoes a process known as "plasticity". This is a time
during which the brain "locks onto" its environment and establishes it
as "normal". Therefore of the eye does not have corrected vision when
it needs it (during this period), the brain will accept this vision as
normal. In later life then, when glasses are worn, the very best
vision that can be established will be the best the brain can
recognise (and in this case - may be less than 20/20).
So basically there cannot be any reliable relationship between the
Dioptre and visual acuity.
Good luck - Brad Rogers
bh...@globalnet.co.uk
>John Connolly wrote:
>>
>> On 2 Sep 1997 17:41:17 GMT, "Mats Söderman" <mv3...@venus.swipnet.se>
>> wrote:
>>
>> >Raymond A. Chamberlin <ra...@sirius.com> wrote in article
>> ><34052459...@news.sirius.com>...
>> >> Ryo Imamura <Ry...@worldnet.att.net> wrote:
>> >>
>> >> >How does one convert the often used ratios "20-?" into diopters, which I
>> >> >am more used to hearing. Thanks.
>>
>> >You don´t. 20/20 etc is the size of a letter, and diopters is the power of
>> >a lens.
>>
>> At first, it seems that, assuming zero astigmatism, there should be,
>> at least, an empirical correlation. However, in addition to
>> myopia/hyperopia, the 20-? measurement is affected by condition of the
>> macula/fovea, clarity of the vitreous, etc. So Mats is right.
>>
>
>I still don't get it.... it seems to me that even in spite of the above
>mentioned mitigating factors.... a particular (approximately) lens,
>measured in diopters, when applied to all people with 20/X vision,
>should allow them to discern letters on the 20/20 line.
There cannot be any linear relationship between dioptre and visual
acuity that is DEFINEABLE because how well the eye sees is
inheritantly dependant upon several factors. e.g Age (affects
accomodation), pupil size (affects depth of field and so how "pin
sharp" things are), retinal condition (see above) and neurological
perception (which basically means how the brain interprets the
information recieved by the eye) which is totally subjective anyway!
Not only this, but from the age zero to about ten, the visual cortex
of the brain is undergoes a process called plasticity. This process is
about the brain "locking onto" its environment and recognising it as
the standard. Therefore if you need glasses when you are young - and
don't wear them, your brain forms with the perception that that is
"normal". When, in later life glasses are worn, the very best vision
that can be achieved - is that which has been experienced during
plasticity - which might be less than 20/20!
Good Luck! - Brad Rogers
bh...@globalnet.co.uk
On Wed, 03 Sep 1997 07:47:22 -0400, "Bob S."
<bo...@ix.nospam.netcom.com> wrote:
>John Connolly wrote:
>>
>> On 2 Sep 1997 17:41:17 GMT, "Mats Söderman" <mv3...@venus.swipnet.se>
>> wrote:
>>
>> >Raymond A. Chamberlin <ra...@sirius.com> wrote in article
>> ><34052459...@news.sirius.com>...
>> >> Ryo Imamura <Ry...@worldnet.att.net> wrote:
>> >>
>> >> >How does one convert the often used ratios "20-?" into diopters, which I
>> >> >am more used to hearing. Thanks.
>>
>> >You don´t. 20/20 etc is the size of a letter, and diopters is the power of
>> >a lens.
>>
>> At first, it seems that, assuming zero astigmatism, there should be,
>> at least, an empirical correlation. However, in addition to
>> myopia/hyperopia, the 20-? measurement is affected by condition of the
>> macula/fovea, clarity of the vitreous, etc. So Mats is right.
>>
>
>I still don't get it.... it seems to me that even in spite of the above
>mentioned mitigating factors.... a particular (approximately) lens,
>measured in diopters, when applied to all people with 20/X vision,
>should allow them to discern letters on the 20/20 line.
The problem is that sight is subjective. It can be affected by so many
different factors; Pupil size affects how "easily" the wrong power
lens will make vision blurred, Age can affect the ability of the eye
to accomodate, Ocular health may have ramifications for the
"clearness" of the inside of the eye - as well as the condition of the
retina. Different people see differently!
Apart from this, between the age of zero to about ten, the brain
undergoes a process known as plasticity. During this time it "locks
onto" its environment (smell, toutch sight e.t.c) and establishes this
as "normal". Therefore if a young child who needs glasses, doesn't
wear them, they may find that in later life when they eventually wear
a pair, the best vision they get is the SAME as the vision they had as
a child (which may be less than 20/20).
So i'm afraid there cannot be any reliable correlation between visual
acuity and the Dioptre.
Good luck! - Brad Rogers
Visionxcl
interesting question, and only an approximate answer possible. typically
-1.00 is about 20/40, by -1.50 vision is 20/80 to 20/100, and at -2.00
about 20/200. -3.00 about 20/400. Above -4.00 20/600 or worse.
the real answer depends on the optics of corneal curvature vs axial length
- an eye with steep cornea and average length can be equally nearsighted
with an eye with a flat cornea that is very long - but they may not have
the same uncorrected acuity. Some eyes are -8.00 and 20/400, just like
some eyes that are -3.00.
Vision decreases seemingly exponentially with increasing prescription, and
quickly reaches 20/200 or legal blindness. Beyond that blurry is blurry
and hard to distinguish as far as distance vision goes.
William Stacy
In <19970911033...@ladder01.news.aol.com> visi...@aol.com
(Visionxcl) writes:
>
>Vision decreases seemingly exponentially with increasing prescription,
and
>quickly reaches 20/200 or legal blindness.
Sorry, visionxcl, but 20/200 due to ametropic error is NOT "legal
blindness", and has NOTHING to do with that term. And I seriosly
question your exponential statement. If it were exponential, it
*would* lend itself to a formula...
Bill
Bob S.
John Connolly wrote:
>
> On 11 Sep 1997 04:21:42 GMT, w...@ix.netcom.com(William Stacy) wrote:
>
> >In <19970911033...@ladder01.news.aol.com> visi...@aol.com
> >(Visionxcl) writes:
> >
> >>
> >>Vision decreases seemingly exponentially with increasing prescription,
>
> >question your exponential statement. If it were exponential, it
> >*would* lend itself to a formula...
>
> here. See below:
>
> -------------------------------------------------
>
> On Wed, 03 Sep 1997 12:30:24 -0400, "Bob S."
> <bo...@ix.nospam.netcom.com> wrote:
> >>I saw such a mathematical correlation
> >>posted here a short while ago, and it seems like it works to me. It is:
> >>
> >>Correction in Diopters = log(VA) / .27
> >>
> >>where VA is a fraction similar to 20/50 or 20/200 etc.
>
> >Back when I was a "healthy myope" my right eye was 20/200 and needed a
> >spherical correction of -3.5 diopters to get to 20/20.
>
> >[log(20/200)]/.27 = -3.7
>
> >Not bad!
John, thanks for relieving me of the obligation to repeat myself!!
Bob
William Stacy
In <3418cdc1.115370600@News> spamf...@home.com (John Connolly)
writes:
>
>On 11 Sep 1997 04:21:42 GMT, w...@ix.netcom.com(William Stacy) wrote:
>
>>I seriosly
>>question your exponential statement. If it were exponential, it
>>*would* lend itself to a formula...
>>Back when I was a "healthy myope" my right eye was 20/200 and needed
a
>>spherical correction of -3.5 diopters to get to 20/20.
>
>>[log(20/200)]/.27 = -3.7
>
>>Not bad!
OK so maybe I should have acknowledged the existence of a formula.
Problem is, the formula is a very crude approximation that doesn't hold
up in real life, and is therefore completely useless. There are 20/200
eyes that are -1.75 and there are 20/200 eyes that are + 6.00.
Bill
bh...@globalnet.co.uk
On Wed, 03 Sep 1997 15:40:18 GMT, spamf...@home.com (John Connolly)
wrote:
>On Wed, 03 Sep 1997 07:47:22 -0400, "Bob S."
><bo...@ix.nospam.netcom.com> wrote:
>
>Perhaps you don't get it because my reply, above, was seriously
>incomplete and confusing. It refers to eyes which have problems which
>make them _not_ correctable to 20/20. Eyes which are low in
>astigmatism and are correctable to 20/20 (which we might refer to as
>pure "opes" :-), or "healthy") should behave as you say; i.e., they
>should obey a universal correlation between a "diopter" measurement
>and a 20/? measurement. I would guess that such a correlation has
>been worked out, but I don't have a reference.
>
Sorry, but there is no such relationship - because vision is
subjective and because the eye is a living organ, (the optical
principles that apply to optical instruments therefore cannot apply).
William Stacy
In <341f2660.203607016@News> spamf...@home.com (John Connolly) writes:
>On 11 Sep 1997 15:06:50 GMT, w...@ix.netcom.com(William Stacy) wrote:
>
>>Problem is, the formula is a very crude approximation that doesn't hold
>>up in real life, and is therefore completely useless. There are 20/200
>>eyes that are -1.75 and there are 20/200 eyes that are + 6.00.
>
>
>assumptions used to derive it. The assumptions implicit in this expression
>are, minimally:
>
>1. The eye should be correctable to 20/20.
>
>2. It, obviously, cannot apply to hyperopia (However, with a minus sign in
>front of it, who knows?:-)).
>
>3. Astigmatism must be minimal.
>
>All three assumptions (and more) could be included in the single assumption
>that we are dealing with a young healthy eyeball whose only defect is that
>it's too long.
>
I'll go along with assumption 1, but 2 should lend itself to the same
calculation if age is factored in.
I see no reason for 3 since astigmatism can *easily* be factored in.
>The first example, above (-1.75), probably does not meet condition
#3,
You are ignoring the most important variable of all: pupil diameter.
It is likely that a -1.75 with a 6 mm pupil will have close to the same
acuity as a -5.00 with a 2 mm pupil.
the
>expression has limited application, but it is far from being
"completely
>useless."
>
I can't think of an application for it.
Bill
William Stacy
In <341c4030.107081628@News> spamf...@home.com (John Connolly)
writes:
>You have "limited" imagination. :-) At the least you can use it to
choose
>a pair of drugstore "granny" glasses to try on :-)
Now that *would* take some imagination, given that drugstore glasses
only correct hyperopia/presbyopia...
Bill
William Stacy
In <341f773e.121177732@News> spamf...@home.com (John Connolly)
writes:
>
>Not so. In my experience drug stores also sell glasses for myopia,
but not
>astigmatism.
Not in California and most states.
>
>I assume that your concentration on this trivial point is tacit
concession
>on the three more substantial points in the post.
Not. Why did you ignore the pupil size problem? That problem can cause
error by several diopters. If you *could* buy myopic glasses in the
store, you'd be better off trying them on one by one than relying on
that clever formula.
I'll patiently wait to hear a REAL use for it.
Bill
William Stacy
I've been known to beat a dead horse, so why not finish this one off,
too?
I just queried my patient database for the last 150 or so simple myopic
eyes (which I defined as having less than .50 cyl.) for which I have
unaided visual acuity, manifest refractive error and corrected visual
acuity. The results along with the "computed" value using that famous
formula:
d=log(20/xxx)/.27
are presented below, along with the dioptric error induced by that
formula.
I guess the proof is in the pudding. (let me know if my "calculations"
are in error)
Unaided acuity Refraction Corrected "Computed" Error
(manifest) acuity Rx
20/40- -0.75 20/20- -2.57 1.82
20/80 -3.00 20/20 -5.13 2.13
20/400 -3.50 20/20 -11.10 7.60
20/40 -0.75 20/20- -2.57 1.82
20/60-- -0.75 20/20- -4.07 3.32
20/20 -0.25 20/20 0.00 -0.25
20/40 -0.50 20/20 -2.57 2.07
20/25 -0.50 20/20 -0.83 0.33
20/100- -0.75 20/20 -5.96 5.21
20/200 -1.25 20/25 -8.53 7.28
20/200 -3.00 20/20- -8.53 5.53
20/70 -1.00 20/20 -4.64 3.64
20/100 -1.75 20/20 -5.96 4.21
20/70 -0.50 20/20 -4.64 4.14
20/50- -1.00 20/20 -3.39 2.39
20/200 -2.75 20/20 -8.53 5.78
20/400 -4.25 20/40+ -11.10 6.85
20/40 -1.00 20/20 -2.57 1.57
20/60 -1.00 20/20 -4.07 3.07
20/50 -0.25 20/20 -3.39 3.14
20/20-- -1.50 20/20 0.00 -1.50
20/30- -0.75 20/20 -1.50 0.75
20/400 -2.50 20/20- -11.10 8.60
20/200 -2.50 20/20- -8.53 6.03
20/50- -0.50 20/20-- -3.39 2.89
20/50- -0.25 20/20 -3.39 3.14
20/30- -0.50 20/20- -1.50 1.00
20/30- -0.50 20/20 -1.50 1.00
20/30- -0.75 20/20 -1.50 0.75
20/200 -1.75 20/20 -8.53 6.78
20/200 -1.75 20/20 -8.53 6.78
20/400 -3.75 20/20 -11.10 7.35
20/20- -0.25 20/20 0.00 -0.25
20/40- -0.50 20/20 -2.57 2.07
20/50- -1.00 20/25 -3.39 2.39
20/50- -0.75 20/20-- -3.39 2.64
20/60 -1.00 20/20 -4.07 3.07
20/200 -1.50 20/20 -8.53 7.03
20/20- -0.25 20/20 0.00 -0.25
20/400 -3.50 20/20--- -11.10 7.60
20/25- -0.25 20/20 -0.83 0.58
20/40 -0.50 20/20 -2.57 2.07
20/40 -0.75 20/20- -2.57 1.82
20/60 -0.50 20/20 -4.07 3.57
20/200 -2.00 20/20- -8.53 6.53
20/60- -0.75 20/20-- -4.07 3.32
20/60- -0.50 20/20 -4.07 3.57
20/100- -1.25 20/20 -5.96 4.71
20/100- -1.00 20/20 -5.96 4.96
20/80 -0.75 20/20 -5.13 4.38
20/40- -0.75 20/25-- -2.57 1.82
20/40- -0.25 20/25-- -2.57 2.32
20/40 -0.50 20/25- -2.57 2.07
20/400 -3.50 20/25+ -11.10 7.60
20/400 -3.75 20/20 -11.10 7.35
20/70 -0.50 20/20- -4.64 4.14
20/400 -6.75 20/25-- -11.10 4.35
20/40+ -0.75 20/20 -2.57 1.82
20/80 -2.50 20/20- -5.13 2.63
20/80 -2.50 20/20- -5.13 2.63
20/400 -3.25 20/20 -11.10 7.85
20/400 -2.75 20/20 -11.10 8.35
20/200 -3.75 20/30 -8.53 4.78
20/200 -3.75 20/20 -8.53 4.78
20/200 -1.00 20/25- -8.53 7.53
20/200 -1.25 20/25 -8.53 7.28
20/60 -0.75 20/20- -4.07 3.32
20/60 -1.00 20/20 -4.07 3.07
20/80 -1.50 20.20 -5.13 3.63
20/80 -1.25 20/20 -5.13 3.88
20/30 -0.50 20/20 -1.50 1.00
20/400- -2.50 20/20-- -11.10 8.60
20/400- -2.25 20/20 -11.10 8.85
20/200 -2.00 20/20 -8.53 6.53
20/400 -4.50 20/20/-- -11.10 6.60
20/100 -0.25 20/20- -5.96 5.71
20/400 -4.00 20/20-- -11.10 7.10
20/400 -4.25 20/20- -11.10 6.85
20/60- -0.75 20/30-- -4.07 3.32
20/40- -0.75 20/20 -2.57 1.82
20/200 -0.50 20/40 -8.53 8.03
20/60 -0.25 20/20- -4.07 3.82
20/50-- -1.75 20/20 -3.39 1.64
20/200 -1.50 20/20 -8.53 7.03
20/70 -1.25 20/20 -4.64 3.39
20/200 -1.50 20/20 -8.53 7.03
20/200 -1.25 20/20 -8.53 7.28
20/200 -1.75 20/20 -8.53 6.78
20/200 -1.50 20/20 -8.53 7.03
20/200 -2.00 20/20 -8.53 6.53
20/200 -1.75 20/30+ -8.53 6.78
20/200 -2.00 20/20 -8.53 6.53
20/40 -0.75 20/20- -2.57 1.82
20/80 -2.75 20/20 -5.13 2.38
20/50- -1.25 20/20 -3.39 2.14
20/400 -3.00 20/20 -11.10 8.10
20/30 -0.25 20/20 -1.50 1.25
20/40- -0.75 20/25 -2.57 1.82
20/50 -0.75 20/20 -3.39 2.64
20/100 -1.25 20/25 -5.96 4.71
20/80 -3.00 20/20- -5.13 2.13
20/40 -0.75 20/20 -2.57 1.82
20/60 -1.25 20/20 -4.07 2.82
20/60 -1.00 20/20 -4.07 3.07
20/60+- -1.00 20/40- -4.07 3.07
20/200 -2.75 20/20 -8.53 5.78
20/200 -3.50 20/40+ -8.53 5.03
20/100 -1.25 20/20 -5.96 4.71
20/20- -0.25 20/20 0.00 -0.25
20/100- -1.25 20/30+- -5.96 4.71
20/70 -0.25 20/25 -4.64 4.39
20/25- -0.25 20/20- -0.83 0.58
20/200 -2.25 20/20- -8.53 6.28
20/200 -2.25 20/20- -8.53 6.28
20/25- -0.50 20/25 -0.83 0.33
20/25- -0.25 20/20 -0.83 0.58
20/200 -2.00 20/20- -8.53 6.53
20/30 -0.25 20/20- -1.50 1.25
20/30 -0.25 20/20 -1.50 1.25
20/300 -2.25 20/20- -10.03 7.78
20/300 -2.50 20/20-- -10.03 7.53
20/100- -2.00 20/30-- -5.96 3.96
20/100- -2.00 20/20 -5.96 3.96
20/40- -0.50 20/25 -2.57 2.07
20/70 -1.00 20/20 -4.64 3.64
20/200 -1.50 20/20 -8.53 7.03
20/400 -2.00 20/20 -11.10 9.10
20/50 -0.50 20/20 -3.39 2.89
20/50 -1.00 20/20 -3.39 2.39
20/100 -2.00 20/20 -5.96 3.96
20/200 -1.75 20/20 -8.53 6.78
20/60- -1.50 20/20 -4.07 2.57
20/30- -0.25 20/20 -1.50 1.25
20/40- -1.00 20/30-- -2.57 1.57
20/400 -3.50 20/20- -11.10 7.60
20/400 -3.50 20/20 -11.10 7.60
20/50- -0.25 20/20 -3.39 3.14
20/400 -6.00 20/30-- -11.10 5.10
20/400 -5.75 20/20 -11.10 5.35
20/400 -4.25 20/20 -11.10 6.85
20/50- -0.25 20/20 -3.39 3.14
20/20 -0.25 20/20 0.00 -0.25
20/200 -4.25 20/20 -8.53 4.28
20/400- -3.25 20/20 -11.10 7.85
20/400- -3.25 20/20 -11.10 7.85
20/300 -4.25 20/20- -10.03 5.78
20/300 -4.00 20/20 -10.03 6.03
20/100+ -0.25 20/25-- -5.96 5.71
20/100+ -0.25 20/20- -5.96 5.71
20/200+ -0.75 20/25+- -8.53 7.78
20/200+ -1.25 20/20 -8.53 7.28
20/60 -1.50 20/20 -4.07 2.57
20/60 -0.25 20/20 -4.07 3.82
20/400- -2.75 20/20- -11.10 8.35
20/400- -2.50 20/20 -11.10 8.60
20/25- -0.25 20/20 -0.83 0.58
20/400 -2.25 20/20 -11.10 8.85
20/400 -4.00 20/20-- -11.10 7.10
20/400 -4.00 20/20- -11.10 7.10
20/60- -0.75 20/30-- -4.07 3.32
20/50 -0.75 20/20 -3.39 2.64
20/40-- -1.50 20/20 -2.57 1.07
20/40-- -0.75 20/25 -2.57 1.82
20/200 -1.75 20/20 -8.53 6.78
20/70 -0.75 20/20 -4.64 3.89
20/200 -1.50 20/20 -8.53 7.03
20/200 -1.25 20/20 -8.53 7.28
20/100- -1.50 20/20 -5.96 4.46
20/200 -1.75 20/25- -8.53 6.78
20/200 -2.25 20/20 -8.53 6.28
It looks to me like the only people this works well for have 20/20
uncorrected acuity
Bill
BobNewsGrp
Well, the horse looks dead to me. But as already pointed out, your
calculations
ARE in error. Here is the corrected table:
Unaided acuity Refraction Corrected "Computed" Error
(manifest) acuity Rx
20/40- -0.75 20/20- -1.11 -0.36
20/80 -3.00 20/20 -2.23 0.77
20/400 -3.50 20/20 -4.82 -1.32
20/40 -0.75 20/20- -1.11 -0.36
20/60-- -0.75 20/20- -1.77 -1.02
20/20 -0.25 20/20 0.00 0.25
20/40 -0.50 20/20 -1.11 -0.61
20/25 -0.50 20/20 -0.36 0.14
20/100- -0.75 20/20 -2.59 -1.84
20/200 -1.25 20/25 -3.70 -2.45
20/200 -3.00 20/20- -3.70 -0.70
20/70 -1.00 20/20 -2.02 -1.02
20/100 -1.75 20/20 -2.59 -0.84
20/70 -0.50 20/20 -2.02 -1.52
20/50- -1.00 20/20 -1.47 -0.47
20/200 -2.75 20/20 -3.70 -0.95
20/400 -4.25 20/40+ -4.82 -0.57
20/40 -1.00 20/20 -1.11 -0.11
20/60 -1.00 20/20 -1.77 -0.77
20/50 -0.25 20/20 -1.47 -1.22
20/20-- -1.50 20/20 0.00 1.50
20/30- -0.75 20/20 -0.65 0.10
20/400 -2.50 20/20- -4.82 -2.32
20/200 -2.50 20/20- -3.70 -1.20
20/50- -0.50 20/20-- -1.47 -0.97
20/50- -0.25 20/20 -1.47 -1.22
20/30- -0.50 20/20- -0.65 -0.15
20/30- -0.50 20/20 -0.65 -0.15
20/30- -0.75 20/20 -0.65 0.10
20/200 -1.75 20/20 -3.70 -1.95
20/200 -1.75 20/20 -3.70 -1.95
20/400 -3.75 20/20 -4.82 -1.07
20/20- -0.25 20/20 0.00 0.25
20/40- -0.50 20/20 -1.11 -0.61
20/50- -1.00 20/25 -1.47 -0.47
20/50- -0.75 20/20-- -1.47 -0.72
20/60 -1.00 20/20 -1.77 -0.77
20/200 -1.50 20/20 -3.70 -2.20
20/20- -0.25 20/20 0.00 0.25
20/400 -3.50 20/20--- -4.82 -1.32
20/25- -0.25 20/20 -0.36 -0.11
20/40 -0.50 20/20 -1.11 -0.61
20/40 -0.75 20/20- -1.11 -0.36
20/60 -0.50 20/20 -1.77 -1.27
20/200 -2.00 20/20- -3.70 -1.70
20/60- -0.75 20/20-- -1.77 -1.02
20/60- -0.50 20/20 -1.77 -1.27
20/100- -1.25 20/20 -2.59 -1.34
20/100- -1.00 20/20 -2.59 -1.59
20/80 -0.75 20/20 -2.23 -1.48
20/40- -0.75 20/25-- -1.11 -0.36
20/40- -0.25 20/25-- -1.11 -0.86
20/40 -0.50 20/25- -1.11 -0.61
20/400 -3.50 20/25+ -4.82 -1.32
20/400 -3.75 20/20 -4.82 -1.07
20/70 -0.50 20/20- -2.02 -1.52
20/400 -6.75 20/25-- -4.82 1.93
20/40+ -0.75 20/20 -1.11 -0.36
20/80 -2.50 20/20- -2.23 0.27
20/80 -2.50 20/20- -2.23 0.27
20/400 -3.25 20/20 -4.82 -1.57
20/400 -2.75 20/20 -4.82 -2.07
20/200 -3.75 20/30 -3.70 0.05
20/200 -3.75 20/20 -3.70 0.05
20/200 -1.00 20/25- -3.70 -2.70
20/200 -1.25 20/25 -3.70 -2.45
20/60 -0.75 20/20- -1.77 -1.02
20/60 -1.00 20/20 -1.77 -0.77
20/80 -1.50 20.20 -2.23 -0.73
20/80 -1.25 20/20 -2.23 -0.98
20/30 -0.50 20/20 -0.65 -0.15
20/400- -2.50 20/20-- -4.82 -2.32
20/400- -2.25 20/20 -4.82 -2.57
20/200 -2.00 20/20 -3.70 -1.70
20/400 -4.50 20/20/-- -4.82 -0.32
20/100 -0.25 20/20- -2.59 -2.34
20/400 -4.00 20/20-- -4.82 -0.82
20/400 -4.25 20/20- -4.82 -0.57
20/60- -0.75 20/30-- -1.77 -1.02
20/40- -0.75 20/20 -1.11 -0.36
20/200 -0.50 20/40 -3.70 -3.20
20/60 -0.25 20/20- -1.77 -1.52
20/50-- -1.75 20/20 -1.47 0.28
20/200 -1.50 20/20 -3.70 -2.20
20/70 -1.25 20/20 -2.02 -0.77
20/200 -1.50 20/20 -3.70 -2.20
20/200 -1.25 20/20 -3.70 -2.45
20/200 -1.75 20/20 -3.70 -1.95
20/200 -1.50 20/20 -3.70 -2.20
20/200 -2.00 20/20 -3.70 -1.70
20/200 -1.75 20/30+ -3.70 -1.95
20/200 -2.00 20/20 -3.70 -1.70
20/40 -0.75 20/20- -1.11 -0.36
20/80 -2.75 20/20 -2.23 0.52
20/50- -1.25 20/20 -1.47 -0.22
20/400 -3.00 20/20 -4.82 -1.82
20/30 -0.25 20/20 -0.65 -0.40
20/40- -0.75 20/25 -1.11 -0.36
20/50 -0.75 20/20 -1.47 -0.72
20/100 -1.25 20/25 -2.59 -1.34
20/80 -3.00 20/20- -2.23 0.77
20/40 -0.75 20/20 -1.11 -0.36
20/60 -1.25 20/20 -1.77 -0.52
20/60 -1.00 20/20 -1.77 -0.77
20/60+- -1.00 20/40- -1.77 -0.77
20/200 -2.75 20/20 -3.70 -0.95
20/200 -3.50 20/40+ -3.70 -0.20
20/100 -1.25 20/20 -2.59 -1.34
20/20- -0.25 20/20 0.00 0.25
20/100- -1.25 20/30+- -2.59 -1.34
20/70 -0.25 20/25 -2.02 -1.77
20/25- -0.25 20/20- -0.36 -0.11
20/200 -2.25 20/20- -3.70 -1.45
20/200 -2.25 20/20- -3.70 -1.45
20/25- -0.50 20/25 -0.36 0.14
20/25- -0.25 20/20 -0.36 -0.11
20/200 -2.00 20/20- -3.70 -1.70
20/30 -0.25 20/20- -0.65 -0.40
20/30 -0.25 20/20 -0.65 -0.40
20/300 -2.25 20/20- -4.36 -2.11
20/300 -2.50 20/20-- -4.36 -1.86
20/100- -2.00 20/30-- -2.59 -0.59
20/100- -2.00 20/20 -2.59 -0.59
20/40- -0.50 20/25 -1.11 -0.61
20/70 -1.00 20/20 -2.02 -1.02
20/200 -1.50 20/20 -3.70 -2.20
20/400 -2.00 20/20 -4.82 -2.82
20/50 -0.50 20/20 -1.47 -0.97
20/50 -1.00 20/20 -1.47 -0.47
20/100 -2.00 20/20 -2.59 -0.59
20/200 -1.75 20/20 -3.70 -1.95
20/60- -1.50 20/20 -1.77 -0.27
20/30- -0.25 20/20 -0.65 -0.40
20/40- -1.00 20/30-- -1.11 -0.11
20/400 -3.50 20/20- -4.82 -1.32
20/400 -3.50 20/20 -4.82 -1.32
20/50- -0.25 20/20 -1.47 -1.22
20/400 -6.00 20/30-- -4.82 1.18
20/400 -5.75 20/20 -4.82 0.93
20/400 -4.25 20/20 -4.82 -0.57
20/50- -0.25 20/20 -1.47 -1.22
20/20 -0.25 20/20 0.00 0.25
20/200 -4.25 20/20 -3.70 0.55
20/400- -3.25 20/20 -4.82 -1.57
20/400- -3.25 20/20 -4.82 -1.57
20/300 -4.25 20/20- -4.36 -0.11
20/300 -4.00 20/20 -4.36 -0.36
20/100+ -0.25 20/25-- -2.59 -2.34
20/100+ -0.25 20/20- -2.59 -2.34
20/200+ -0.75 20/25+- -3.70 -2.95
20/200+ -1.25 20/20 -3.70 -2.45
20/60 -1.50 20/20 -1.77 -0.27
20/60 -0.25 20/20 -1.77 -1.52
20/400- -2.75 20/20- -4.82 -2.07
20/400- -2.50 20/20 -4.82 -2.32
20/25- -0.25 20/20 -0.36 -0.11
20/400 -2.25 20/20 -4.82 -2.57
20/400 -4.00 20/20-- -4.82 -0.82
20/400 -4.00 20/20- -4.82 -0.82
20/60- -0.75 20/30-- -1.77 -1.02
20/50 -0.75 20/20 -1.47 -0.72
20/40-- -1.50 20/20 -1.11 0.39
20/40-- -0.75 20/25 -1.11 -0.36
20/200 -1.75 20/20 -3.70 -1.95
20/70 -0.75 20/20 -2.02 -1.27
20/200 -1.50 20/20 -3.70 -2.20
20/200 -1.25 20/20 -3.70 -2.45
20/100- -1.50 20/20 -2.59 -1.09
20/200 -1.75 20/25- -3.70 -1.95
20/200 -2.25 20/20 -3.70 -1.45
These look like reasonable errors to me!!
Bob S.
Mike Tyner, OD
William Stacy wrote:
>
> ... AVERAGE overcorrection of 1.25 diopters (among those overcorrected), an
> amount that would not be tolerated by most patients, and probably
> damaging to the eyes of young myopes.
How does overcorrection "damage" the eye?
William Stacy
In <341d77b0.41517792@News> spamf...@home.com (John Connolly) writes:
>Even calculated correctly the equation is, as might be expected, a
_very_
>crude approximation.
I'd say. If we even accept + or - .5 diopter error (for the purpose of
avoiding a trip to the optometrist), 115 out of 171 would still be
unacceptably overcorrected, 42 out of 171 would be acceptable, and 14
of the 171 would still be unacceptably undercorrected.
The formula is fatally skewed toward overcorrection and is a caballo
muerte, IMO.
Bill
William Stacy
In <341D2F...@aol.com> BobNewsGrp <bobne...@aol.com> writes:
>
>Well, the horse looks dead to me. But as already pointed out, your
>calculations
>ARE in error. Here is the corrected table:
Well I appreciate the correction. So it looks like using the base 10
logarithm did make the formula work better, but the new numbers show an
AVERAGE overcorrection of 1.25 diopters (among those overcorrected), an
amount that would not be tolerated by most patients, and probably
damaging to the eyes of young myopes.
In this sample, 6 times as many eyes would be overcorrected as would be
undercorrected, and as most people know, undercorrection is by far
preferred to overcorrection in myopia.
Bill
Bob S.
> >calculations
> >ARE in error. Here is the corrected table:
>
> logarithm did make the formula work better, but the new numbers show an
> AVERAGE overcorrection of 1.25 diopters (among those overcorrected), an
> amount that would not be tolerated by most patients, and probably
> damaging to the eyes of young myopes.
>
> In this sample, 6 times as many eyes would be overcorrected as would be
> undercorrected, and as most people know, undercorrection is by far
> preferred to overcorrection in myopia.
>
> Bill
You want dead??? I'LL show you a dead horse...
Actually, my spreadsheet showed an average error of less than 1 diopter.
Now, my preferred method has always been to start with the correct
answer,
and work backwards until you get the data. Since that is not possible
here,
the next best method is to tweak your model to fit the data!! (I know,
this
is driving you nuts). Using your empirical database, the average
diopter
error can be reduced to near 0 by changing the denominator from .27 to
..43
Thus:
Correction in Diopters = log(20/xxx) / .43
OK, discuss among yourselves....
OLD OLD NEW NEW
Unaided acuity Refraction Corrected "Computed" Error "Computed"
Error
(manifest) acuity Rx Rx
20/40- -0.75 20/20- -1.11 -0.36 -0.7 0.05
20/80 -3.00 20/20 -2.23 0.77 -1.4 1.6
20/400 -3.50 20/20 -4.82 -1.32 -3.03 0.47
20/40 -0.75 20/20- -1.11 -0.36 -0.7 0.05
20/60-- -0.75 20/20- -1.77 -1.02 -1.11 -0.36
20/20 -0.25 20/20 0.00 0.25 0 0.25
20/40 -0.50 20/20 -1.11 -0.61 -0.7 -0.2
20/25 -0.50 20/20 -0.36 0.14 -0.23 0.27
20/100- -0.75 20/20 -2.59 -1.84 -1.63 -0.88
20/200 -1.25 20/25 -3.70 -2.45 -2.33 -1.08
20/200 -3.00 20/20- -3.70 -0.70 -2.33 0.67
20/70 -1.00 20/20 -2.02 -1.02 -1.27 -0.27
20/100 -1.75 20/20 -2.59 -0.84 -1.63 0.12
20/70 -0.50 20/20 -2.02 -1.52 -1.27 -0.77
20/50- -1.00 20/20 -1.47 -0.47 -0.93 0.07
20/200 -2.75 20/20 -3.70 -0.95 -2.33 0.42
20/400 -4.25 20/40+ -4.82 -0.57 -3.03 1.22
20/40 -1.00 20/20 -1.11 -0.11 -0.7 0.3
20/60 -1.00 20/20 -1.77 -0.77 -1.11 -0.11
20/50 -0.25 20/20 -1.47 -1.22 -0.93 -0.68
20/20-- -1.50 20/20 0.00 1.50 0 1.5
20/30- -0.75 20/20 -0.65 0.10 -0.41 0.34
20/400 -2.50 20/20- -4.82 -2.32 -3.03 -0.53
20/200 -2.50 20/20- -3.70 -1.20 -2.33 0.17
20/50- -0.50 20/20-- -1.47 -0.97 -0.93 -0.43
20/50- -0.25 20/20 -1.47 -1.22 -0.93 -0.68
20/30- -0.50 20/20- -0.65 -0.15 -0.41 0.09
20/30- -0.50 20/20 -0.65 -0.15 -0.41 0.09
20/30- -0.75 20/20 -0.65 0.10 -0.41 0.34
20/200 -1.75 20/20 -3.70 -1.95 -2.33 -0.58
20/200 -1.75 20/20 -3.70 -1.95 -2.33 -0.58
20/400 -3.75 20/20 -4.82 -1.07 -3.03 0.72
20/20- -0.25 20/20 0.00 0.25 0 0.25
20/40- -0.50 20/20 -1.11 -0.61 -0.7 -0.2
20/50- -1.00 20/25 -1.47 -0.47 -0.93 0.07
20/50- -0.75 20/20-- -1.47 -0.72 0 0.75
20/60 -1.00 20/20 -1.77 -0.77 -1.11 -0.11
20/200 -1.50 20/20 -3.70 -2.20 -2.33 -0.83
20/20- -0.25 20/20 0.00 0.25 0 0.25
20/400 -3.50 20/20--- -4.82 -1.32 -3.03 0.47
20/25- -0.25 20/20 -0.36 -0.11 -0.23 0.02
20/40 -0.50 20/20 -1.11 -0.61 -0.7 -0.2
20/40 -0.75 20/20- -1.11 -0.36 -0.7 0.05
20/60 -0.50 20/20 -1.77 -1.27 -1.11 -0.61
20/200 -2.00 20/20- -3.70 -1.70 -2.33 -0.33
20/60- -0.75 20/20-- -1.77 -1.02 -1.11 -0.36
20/60- -0.50 20/20 -1.77 -1.27 -1.11 -0.61
20/100- -1.25 20/20 -2.59 -1.34 -1.63 -0.38
20/100- -1.00 20/20 -2.59 -1.59 -1.63 -0.63
20/80 -0.75 20/20 -2.23 -1.48 -1.4 -0.65
20/40- -0.75 20/25-- -1.11 -0.36 -0.7 0.05
20/40- -0.25 20/25-- -1.11 -0.86 -0.7 -0.45
20/40 -0.50 20/25- -1.11 -0.61 -0.7 -0.2
20/400 -3.50 20/25+ -4.82 -1.32 -3.03 0.47
20/400 -3.75 20/20 -4.82 -1.07 -3.03 0.72
20/70 -0.50 20/20- -2.02 -1.52 -1.27 -0.77
20/400 -6.75 20/25-- -4.82 1.93 -3.03 3.72
20/40+ -0.75 20/20 -1.11 -0.36 -0.7 0.05
20/80 -2.50 20/20- -2.23 0.27 -1.4 1.1
20/80 -2.50 20/20- -2.23 0.27 -1.4 1.1
20/400 -3.25 20/20 -4.82 -1.57 -3.03 0.22
20/400 -2.75 20/20 -4.82 -2.07 -3.03 -0.28
20/200 -3.75 20/30 -3.70 0.05 -2.33 1.42
20/200 -3.75 20/20 -3.70 0.05 -2.33 1.42
20/200 -1.00 20/25- -3.70 -2.70 -2.33 -1.33
20/200 -1.25 20/25 -3.70 -2.45 -2.33 -1.08
20/60 -0.75 20/20- -1.77 -1.02 -1.11 -0.36
20/60 -1.00 20/20 -1.77 -0.77 -1.11 -0.11
20/80 -1.50 20.20 -2.23 -0.73 -1.4 0.1
20/80 -1.25 20/20 -2.23 -0.98 -1.4 -0.15
20/30 -0.50 20/20 -0.65 -0.15 -0.41 0.09
20/400- -2.50 20/20-- -4.82 -2.32 -3.03 -0.53
20/400- -2.25 20/20 -4.82 -2.57 -0.7 1.55
20/200 -2.00 20/20 -3.70 -1.70 -2.33 -0.33
20/400 -4.50 20/20/-- -4.82 -0.32 -3.03 1.47
20/100 -0.25 20/20- -2.59 -2.34 -1.63 -1.38
20/400 -4.00 20/20-- -4.82 -0.82 -3.03 0.97
20/400 -4.25 20/20- -4.82 -0.57 -3.03 1.22
20/60- -0.75 20/30-- -1.77 -1.02 -1.11 -0.36
20/40- -0.75 20/20 -1.11 -0.36 -0.7 0.05
20/200 -0.50 20/40 -3.70 -3.20 -2.33 -1.83
20/60 -0.25 20/20- -1.77 -1.52 -1.11 -0.86
20/50-- -1.75 20/20 -1.47 0.28 -0.93 0.82
20/200 -1.50 20/20 -3.70 -2.20 -2.33 -0.83
20/70 -1.25 20/20 -2.02 -0.77 -1.27 -0.02
20/200 -1.50 20/20 -3.70 -2.20 -2.33 -0.83
20/200 -1.25 20/20 -3.70 -2.45 -2.33 -1.08
20/200 -1.75 20/20 -3.70 -1.95 -2.33 -0.58
20/200 -1.50 20/20 -3.70 -2.20 -2.33 -0.83
20/200 -2.00 20/20 -3.70 -1.70 -2.33 -0.33
20/200 -1.75 20/30+ -3.70 -1.95 -2.33 -0.58
20/200 -2.00 20/20 -3.70 -1.70 -2.33 -0.33
20/40 -0.75 20/20- -1.11 -0.36 -0.7 0.05
20/80 -2.75 20/20 -2.23 0.52 -1.4 1.35
20/50- -1.25 20/20 -1.47 -0.22 -0.93 0.32
20/400 -3.00 20/20 -4.82 -1.82 -3.03 -0.03
20/30 -0.25 20/20 -0.65 -0.40 -0.41 -0.16
20/40- -0.75 20/25 -1.11 -0.36 -0.7 0.05
20/50 -0.75 20/20 -1.47 -0.72 -0.93 -0.18
20/100 -1.25 20/25 -2.59 -1.34 -1.63 -0.38
20/80 -3.00 20/20- -2.23 0.77 -1.4 1.6
20/40 -0.75 20/20 -1.11 -0.36 -0.7 0.05
20/60 -1.25 20/20 -1.77 -0.52 -1.11 0.14
20/60 -1.00 20/20 -1.77 -0.77 -1.11 -0.11
20/60+- -1.00 20/40- -1.77 -0.77 -1.11 -0.11
20/200 -2.75 20/20 -3.70 -0.95 -2.33 0.42
20/200 -3.50 20/40+ -3.70 -0.20 -2.33 1.17
20/100 -1.25 20/20 -2.59 -1.34 -1.63 -0.38
20/20- -0.25 20/20 0.00 0.25 0 0.25
20/100- -1.25 20/30+- -2.59 -1.34 -1.63 -0.38
20/70 -0.25 20/25 -2.02 -1.77 -1.27 -1.02
20/25- -0.25 20/20- -0.36 -0.11 -0.23 0.02
20/200 -2.25 20/20- -3.70 -1.45 -2.33 -0.08
20/200 -2.25 20/20- -3.70 -1.45 -2.33 -0.08
20/25- -0.50 20/25 -0.36 0.14 -0.23 0.27
20/25- -0.25 20/20 -0.36 -0.11 -0.23 0.02
20/200 -2.00 20/20- -3.70 -1.70 -2.33 -0.33
20/30 -0.25 20/20- -0.65 -0.40 -0.41 -0.16
20/30 -0.25 20/20 -0.65 -0.40 -0.41 -0.16
20/300 -2.25 20/20- -4.36 -2.11 -2.74 -0.49
20/300 -2.50 20/20-- -4.36 -1.86 -2.74 -0.24
20/100- -2.00 20/30-- -2.59 -0.59 -1.63 0.37
20/100- -2.00 20/20 -2.59 -0.59 -1.63 0.37
20/40- -0.50 20/25 -1.11 -0.61 -0.7 -0.2
20/70 -1.00 20/20 -2.02 -1.02 -1.27 -0.27
20/200 -1.50 20/20 -3.70 -2.20 -2.33 -0.83
20/400 -2.00 20/20 -4.82 -2.82 -3.03 -1.03
20/50 -0.50 20/20 -1.47 -0.97 -0.93 -0.43
20/50 -1.00 20/20 -1.47 -0.47 -0.93 0.07
20/100 -2.00 20/20 -2.59 -0.59 -1.63 0.37
20/200 -1.75 20/20 -3.70 -1.95 -2.33 -0.58
20/60- -1.50 20/20 -1.77 -0.27 -1.11 0.39
20/30- -0.25 20/20 -0.65 -0.40 -0.41 -0.16
20/40- -1.00 20/30-- -1.11 -0.11 -0.7 0.3
20/400 -3.50 20/20- -4.82 -1.32 -3.03 0.47
20/400 -3.50 20/20 -4.82 -1.32 -3.03 0.47
20/50- -0.25 20/20 -1.47 -1.22 -0.93 -0.68
20/400 -6.00 20/30-- -4.82 1.18 -3.03 2.97
20/400 -5.75 20/20 -4.82 0.93 -3.03 2.72
20/400 -4.25 20/20 -4.82 -0.57 -3.03 1.22
20/50- -0.25 20/20 -1.47 -1.22 -0.93 -0.68
20/20 -0.25 20/20 0.00 0.25 0 0.25
20/200 -4.25 20/20 -3.70 0.55 -2.33 1.92
20/400- -3.25 20/20 -4.82 -1.57 -3.03 0.22
20/400- -3.25 20/20 -4.82 -1.57 -3.03 0.22
20/300 -4.25 20/20- -4.36 -0.11 -2.74 1.51
20/300 -4.00 20/20 -4.36 -0.36 -2.74 1.26
20/100+ -0.25 20/25-- -2.59 -2.34 -1.63 -1.38
20/100+ -0.25 20/20- -2.59 -2.34 -1.63 -1.38
20/200+ -0.75 20/25+- -3.70 -2.95 -2.33 -1.58
20/200+ -1.25 20/20 -3.70 -2.45 -2.33 -1.08
20/60 -1.50 20/20 -1.77 -0.27 -1.11 0.39
20/60 -0.25 20/20 -1.77 -1.52 -1.11 -0.86
20/400- -2.75 20/20- -4.82 -2.07 -3.03 -0.28
20/400- -2.50 20/20 -4.82 -2.32 -3.03 -0.53
20/25- -0.25 20/20 -0.36 -0.11 -0.23 0.02
20/400 -2.25 20/20 -4.82 -2.57 -3.03 -0.78
20/400 -4.00 20/20-- -4.82 -0.82 -3.03 0.97
20/400 -4.00 20/20- -4.82 -0.82 -3.03 0.97
20/60- -0.75 20/30-- -1.77 -1.02 -1.11 -0.36
20/50 -0.75 20/20 -1.47 -0.72 -0.93 -0.18
20/40-- -1.50 20/20 -1.11 0.39 -0.7 0.8
20/40-- -0.75 20/25 -1.11 -0.36 -0.7 0.05
20/200 -1.75 20/20 -3.70 -1.95 -2.33 -0.58
20/70 -0.75 20/20 -2.02 -1.27 -1.27 -0.52
20/200 -1.50 20/20 -3.70 -2.20 -2.33 -0.83
20/200 -1.25 20/20 -3.70 -2.45 -2.33 -1.08
20/100- -1.50 20/20 -2.59 -1.09 -1.63 -0.13
20/200 -1.75 20/25- -3.70 -1.95 -2.33 -0.58
20/200 -2.25 20/20 -3.70 -1.45 -2.33 -0.08
Bob
William Stacy
In <341D32...@bham.com> "Mike Tyner, OD" <drm...@bham.com> writes:
>
>William Stacy wrote:
>>
>> ... AVERAGE overcorrection of 1.25 diopters (among those
overcorrected), an
>> amount that would not be tolerated by most patients, and probably
>> damaging to the eyes of young myopes.
>
>
By inducing additional myopia beyond what would otherwise develop, of
course. I mean even the staunchest of classic genetic determinists
would shy away from overcorrecting myopia in the formative years,
wouldn't they?
The behaviorists would simply faint dead away at the thought.
Bill
William Stacy
In <341D73...@ix.nospam.netcom.com> "Bob S."
<bo...@ix.nospam.netcom.com> writes:
Using your empirical database, the average
>diopter
>error can be reduced to near 0 by changing the denominator from .27 to
>..43
How wonderful. You even reduced the number of overcorrected myopes.
Those on the other side, who are now more significantly undercorrected
might not like it, but at least you'll do less harm (sorry Mike).
Your reduction of the average error reminds me of a 6 foot tall horse
who couldn't swim but ventured out to cross a stream that was an
average of 5 feet deep.
Bill
William Stacy
>You want dead??? I'LL show you a dead horse...
>Actually, my spreadsheet showed an average error of less than 1
diopter.
(My 1.25 was the average of those OVERCORRECTED. But I'll recheck
my numbers.)
>Now, my preferred method has always been to start with the correct
>answer,
>and work backwards until you get the data. Since that is not
possible
>here,
>the next best method is to tweak your model to fit the data!! (I
know,
>this
>is driving you nuts).
Not at all. I love the exercise.
Using your empirical database, the average
>diopter
>error can be reduced to near 0 by changing the denominator from
27 to
>..43
>
>Thus:
>
>Correction in Diopters = log(20/xxx) / .43
>
>OK, discuss among yourselves....
(big table snipped)
OK I'll plug the .43 into my database and see what happens. Looks
promising, but I'm still waiting for a REAL application of all of this.
BTW, the .43 may only work in MY exam room, with MY particular
intolerance for the guessing of Snellen letters by simple myopes...
Bill
p.s. the 'simple' only means little or no astigmatism. It has nothing
to do with intellect.
William Stacy
In <341E76...@ix.nospam.netcom.com> "Bob S."
<bo...@ix.nospam.netcom.com> writes:
to get a feel for how good or bad a
>person's vision is when he tells me his uncorrected vision is 20/200,
or
>that his lenses are -2.5 diopters.
I'll agree to that use of it.
Bill
*
* *
* HORSE *
* *
* R.I.P.*
* *
*********
Bob S.
William Stacy wrote:
>
> In <341D73...@ix.nospam.netcom.com> "Bob S."
> <bo...@ix.nospam.netcom.com> writes:
> >diopter
> >error can be reduced to near 0 by changing the denominator from .27 to
> >..43
>
> Those on the other side, who are now more significantly undercorrected
> might not like it, but at least you'll do less harm (sorry Mike).
>
> Your reduction of the average error reminds me of a 6 foot tall horse
> who couldn't swim but ventured out to cross a stream that was an
> average of 5 feet deep.
>
> Bill
You just can't stay away from that "dead horse" metaphor, can you?
There's probably NO real application for this other than to "get you in
the right ball park". For myself, not being part of the vision
profession, my only interest was to get a feel for how good or bad a
person's vision is when he tells me his uncorrected vision is 20/200, or
that his lenses are -2.5 diopters.
I knew you'd enjoy the increase in undercorrections.
Bob S.
Dennis Yelle
In article <5vr60r$k...@dfw-ixnews6.ix.netcom.com> w...@ix.netcom.com(William Stacy) writes:
>Well that dead horse rose up and kicked me you know where.
[...]
>So here is the corrected table ("where cyl is greater than -.5 or cyl
>is null"):
>
>Unaided Manifest Calculated Error
>acuity ref. ref.
> 20/40 -0.75 -1.11 0.36
> 20/30 -0.25 -0.65 0.40
> 20/70-- -0.75 -2.02 1.27
> 20/20 -0.25 0.00 -0.25
> 20/25 -0.75 -0.36 -0.39
Bill, thanks for the data, but you left out corrected acuity.
Corrected acuity was in the other table.
Also, it looks like you are using the original formula which
seems to be wrong. Others have indicated that the denominator
should be about .43 or .42 instead of the wrong one originally
posted, but, I suppose, with this new data, the "best" denominator
might be a little bit different.
Anyway, can you please send the data again including the corrected acuity?
Thanks.
Dennis
--
den...@netcom.com (Dennis Yelle)
"You must do the thing you think you cannot do." -- Eleanor Roosevelt
William Stacy
In <dennisEG...@netcom.com> den...@netcom.com (Dennis Yelle)
writes:
>Bill, thanks for the data, but you left out corrected acuity.
>Corrected acuity was in the other table.
>Also, it looks like you are using the original formula which
>seems to be wrong. Others have indicated that the denominator
>should be about .43 or .42 instead of the wrong one originally
>posted, but, I suppose, with this new data, the "best" denominator
>might be a little bit different.
>
>Anyway, can you please send the data again including the corrected
acuity?
Ok if I can get to it, I'll show corrected acuities along with the
"new" formula results (although that new denominator was based on my
erroneous data, so I think someone else might 'fit' a better number to
the data than I could)...
Bill
Raymond A. Chamberlin
visi...@aol.com (Visionxcl) wrote:
>
...........
>
>- an eye with steep cornea and average length can be equally nearsighted
I.e., would require the same number of diopters to correct it
spherically, I assume.
>with an eye with a flat cornea that is very long - but they may not have
>the same uncorrected acuity. Some eyes are -8.00 and 20/400, just like
>some eyes that are -3.00.
>
............
>
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
...........
>
>I can't think of an application for it.
Well, if you have more or less uncomplicated eyes, after trying out
the Snellen charts at a DMV office, you can run right down to your
local drugstore and buy the right pair of Dr. Dean Edell eyeglasses
and laugh properly at all those optometrist cartoons in the funny
papers. (Of course, if you didn't make it to the DMV, you could take
a little more time at that druggist's with a trial-and-error approach.
;-) ) I go down to OSH (isn't that 'H' for 'hardware'?) and try to
buy hardware and mostly what they sell these days are candy bars and
Dr. Dean eyeglasses. Actually, the main reason for getting acquainted
with the analytical expression is not that you really need it to pick
out eyeglasses, but rather, to depreciate the mysticism that ODs like
to pump out about what they do.
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
.............
>
>At the least you can use it to
>choose
>>a pair of drugstore "granny" glasses to try on :-)
>
>
>Now that *would* take some imagination, given that drugstore glasses
>only correct hyperopia/presbyopia...
And then we should get back into the "scientific" reasons why that is.
No not *that* again. ;-) So, you use the formula to convince some
legislators not paid off by the optometric profession to change the
law.
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
.............
>
>And I seriosly
>question your exponential statement. If it were exponential, it
>*would* lend itself to a formula...
Even by now you won't admit that it *does*?
Ray
Raymond A. Chamberlin
bh...@globalnet.co.uk wrote:
>
...............
>
>Unfortunately not. How well the eye sees depends on several factors;
>Pupil size (which controls how "easily" the wrong lens will blur ),
>Age (controls accomodative power of the eye), the clarity of the
>"media" (i.e how clear the cornea and internal liquid is), whether the
>eye is long or short sighted , or astigmatic (this affects how
>blurred, "blurred" really is) and it is also affected by the way in
>which the brain perceives the information the eyes give it.
>
>Between the age of zero to about ten years, the visual cortex area of
>the brain undergoes a process known as "plasticity". This is a time
>during which the brain "locks onto" its environment and establishes it
>as "normal". Therefore of the eye does not have corrected vision when
>it needs it (during this period), the brain will accept this vision as
>normal. In later life then, when glasses are worn, the very best
>vision that can be established will be the best the brain can
>recognise (and in this case - may be less than 20/20).
>
>So basically there cannot be any reliable relationship between the
>Dioptre and visual acuity.
Phooey on all this engendering of optometric mystique that goes on
here forever! Supposing you have a vehicle tire of a given design.
You can take data on a number of them and get repeatable curves of
their average lifetime as functions of speed, inflation, temperture,
etc. Sure, you may have a tire go out early from running over a bear
trap in the road or having some manufacturing defect, but that doesn't
invalidate the data you've gotten for more normal situations. I think
it's pretty clear that the original posters of this eternal question
are not trying to get a mathematical curve that holds for messed up
retinae, brains and whatever -- just maybe straight spherical-lens
defocusing on the retina, given otherwise good hardware, wetware or
whatever. Sure, the problem involves subjectivity in a sense; it is,
after all, *psycho*physical. But if the chart and the questioning
procedure are done right, the psycho end is converted back to at least
a crude physical measure, through verbal responses from the brain
which don't incur too many distorting signals. Clearly a Snellen
chart is a very bum choice to use as the optical object, but even it,
with reasonable selection of characters, provides a crudely linear
element in the system that (when used in such manner as to eliminate
memorization) doesn't normally freak the brain into too many aberrant
gyrations. The relationship that was posted for such spherical
defocusing was logarithmic, which sounds reasonable (and very
psychophysical). I have not been able to find anything on the simple
decrease in resolution of a defocused image as a function of distance
along the optical axis from the focal plane -- a strictly *objective*
relationship, which should involve a one-dimensional Fourier transform
to spatial frequency, which should linearly follow visual acuity in
the sense of one-dimensional resolution. Someone questioned the data
posted for the logarithmic relationship. I assume the objection was
only on the scaling, not the general shape of the curve. Useful
knowledge of the world is increased by *analyzing* parts of it, not
trying to extend concepts like visual acuity to cover all possible
problems the eye-visual=brain-system can have. At some point, even
for legal/bureaucratic purposes one has to chop such things as
comprehensive 20/20 (6/6) sort of alchemy into functional pieces.
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
............
>
>OK so maybe I should have acknowledged the existence of a formula.
>
>Problem is, the formula is a very crude approximation that doesn't hold
>up in real life, and is therefore completely useless. There are 20/200
>eyes that are -1.75 and there are 20/200 eyes that are + 6.00.
Maybe it is *optometrists* that are crude, rather useless and don't
hold up in real life. If they'd factor out different eye problems,
analyze them according to physical knowledge and synthesize better
solutions -- at the going price the same tasks are done *outside* of
optometry, maybe we'd erect more monuments to them, such as the
Freemason symbols on $1 bills. ;-)
Ray
Raymond A. Chamberlin
spamf...@home.com (John Connolly) wrote:
>
............
>
>2. It, obviously, cannot apply to hyperopia (However, with a minus sign in
>front of it, who knows?:-)).
Yes, what "obviously" indicates it "cannot", with proper mathematical
account of signs? Why should linear optics get excited about zero?
>
>3. Astigmatism must be minimal.
Certainly, for *this* simple formula, but one can't "obviously" rule
out a more complex formula that would account for a reasonable range
of regular (cylindrical) astigmatism.
>All three assumptions (and more) could be included in the single assumption
>that we are dealing with a young healthy eyeball whose only defect is that
>it's too long.
Well, kick out #2 and say 'long' *or* 'short'.
>The first example, above (-1.75), probably does not meet condition #3, and
>the second example (+6.00) does not meet condition #2. In summary, the
>expression has limited application, but it is far from being "completely
>useless."
Right.
Ray
Raymond A. Chamberlin
spamf...@home.com (John Connolly) wrote:
>
............
>
>The log of a fraction is a negative number. Thus, obviously, the original
>equation cannot represent hyperopia, even if the phase of the moon is
>"factored in."
As a first-order approximation, at least, for images at a distance
large compared to the lens system, defocusing a given distance either
in front of or behind a focal plane is obviously the same. The
association of 'plus' and 'minus' to convex and concave lenses or
equivalent lens systems is obviously an arbitrary convention.
Therefore, one should be allowed to put absolute-value signs around
both sides of the equation proposed.
>>I see no reason for 3 since astigmatism can *easily* be factored in.
>
>Whether anything can be "factored in" is irrelevant to the discussion of
>requirements for the validity of the given equation. As written, the
>equation predicts spherical corrections for 20/20 correctable myopic
>non-astigmatic eyes, period.
Correct. I don't think the factoring-in of this would be "eas[]y".
>
>>>The first example, above (-1.75), probably does not meet condition
>>>#3,
>
>>You are ignoring the most important variable of all: pupil diameter.
>>It is likely that a -1.75 with a 6 mm pupil will have close to the same
>>acuity as a -5.00 with a 2 mm pupil.
>
>Yes, and I'm also ignoring the length of the eyeball, the curvature of the
>cornea, and the power of the natural lens. It is the essence of an
>approximate empirical correlation that it substitutes one independent
>variable for several. Of course, this depends on cancellation effects.
>
>>>The expression has limited application, but it is far from being
>>>"completely useless."
>
>>I can't think of an application for it.
>
>You have "limited" imagination. :-)
Hey, hey! I'll have you know that the word hereabout is that Dr.
Stacy once arranged to have his assistant sunbathe with a bunch of
photochromic lenses distributed about her body -- in order to advance
some applied science (if not optometry) in respect to UV measurement.
Now, don't you think that was imaginative -- and might've even sold a
few more copies of Popular Optometry or whatever? Trouble is: we all
knew it wouldn't come to pass. She copped out. Dr. Stacy used also
to venture dollar-valued wagers, but we haven't seen any of these
posted for some time. (Oops, maybe the word wasn't supposed to be
promulgated, and that those days are gone forever.)
>At the least you can use it to choose
>a pair of drugstore "granny" glasses to try on :-)
Is Dr. Dean Edell a granny now?
Ray
William Stacy
In <342380be.171024054@News> spamf...@home.com (John Connolly)
writes:
>
>
>On Fri, 19 Sep 1997 08:02:23 GMT, ra...@sirius.com (Raymond A.
Chamberlin)
>wrote:
>
>>As a first-order approximation, at least, for images at a distance
>>large compared to the lens system, defocusing a given distance either
>>in front of or behind a focal plane is obviously the same. The
>>association of 'plus' and 'minus' to convex and concave lenses or
>>equivalent lens systems is obviously an arbitrary convention.
>>Therefore, one should be allowed to put absolute-value signs around
>>both sides of the equation proposed.
>
>
meant it
>that way, and the meaning was lost by my excessive literal mindedness.
>
>Therefore:
>
>|D| = |[Log(20/xxx)]/0.42| = |2.4Log(20/xxx)| or, for non
nitpickers:
>
>D = +-2.4Log(20/xxx) and S.D. = 0.8 for myopia.
>
>If hyperopic data :-) becomes available the constant will change,
perhaps
>back toward the original 3.7 (1/.27), and the standard deviation will
>increase. Perhaps separate constants for myopia and hyperopia are
>empirically desirable.
>
I'll post some hyperopic data for you if you want, but I'm sure that
unlike myopia, where unaided VA is relatively stable with age,
hyperopic unaided VA drops with age due to decreasing accommodative
amplitude. I've forgotten the precise numbers, but it declines more or
less linearly beginning in the 20s, when + 5.00 can be overcome,
levelling off at more or less zero at age 55.
So I'm sure you math types will come up with an expression that
incorporates the age factor; otherwise, the formula will only work for
prebyopic hyperopes, not young ones.
IMO, a far more accurate way to self prescribe would involve taking
careful acuity measurements AT DIFFERENT TEST DISTANCES, and fitting
the data to a suitable curve. E.g., a 3 diopter myope might see 20/400
at 20 feet, the equivalent of 20/100 at 6 feet, the equivalent of 20/40
at 3 feet, and 20/20 at 33 cm.
Another example, a 20 year old 3 diopter hyperope might see 20/20 at
all test distances except at 8 inches, while at age 45 his acuities
might be 20/100 at 20 ft, 20/200 at 6 feet, 20/400 at 3 feet, etc.
Bill
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
............
>
>I'll patiently wait to hear a REAL use for it.
How did *my* other use for it fit on you?
Ray
Raymond A. Chamberlin
spamf...@home.com (John Connolly) wrote:
>
...............
>
>Not so. In my experience drug stores also sell glasses for myopia, but not
>astigmatism.
Not in CA, US.
>However, I did err in throwing in the word "granny."
>
>I assume that your concentration on this trivial point is tacit concession
>on the three more substantial points in the post. Therefore, we can return
>
>the approximation: Myope Diopters = [log(20/XXX)] /.27 back to Bob S.,
>unscathed :-)
Well, it should be scathed to:
|sph. power| = |[log10 (VA)] / 0.27|,
where sph. power is in diopters and VA is expressed as a fraction
equal to the conventional 20/... or 6/... . However, there's still a
slight problem here, in that the curve should be referenced
differently to avoid the problem of improper fractions of VA like
20/15 and 20/10 (which should certainly not equate to 20/27 and 20/40,
respectively). Actually, I doubt that the whole curve should
approximate a logarithmic relationship. It's now 1:30 pm; I'd rather
think about that defect some other time.
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
............
>
The below calculations are off by a constant factor due to the formula
given's using the *common* logarithm (log), not the *natural*
logarithm (ln) that you have used. The calculated power for the first
example would then come out -1.1, giving an error of 0.36. But beyond
that, where do you show the amount of correction you actually used to
achieve the "Refraction acuity" you show? Did you *always* prescribe
the "manifest" power? The "Corrected Rx" you give is apparently the
correction required to achieve 20/20 VA according to the formula.
>Unaided acuity Refraction Corrected "Computed" Error
> (manifest) acuity Rx
> 20/40- -0.75 20/20- -2.57 1.82
> 20/80 -3.00 20/20 -5.13 2.13
> 20/400 -3.50 20/20 -11.10 7.60
> 20/40 -0.75 20/20- -2.57 1.82
> 20/60-- -0.75 20/20- -4.07 3.32
> 20/20 -0.25 20/20 0.00 -0.25
> 20/40 -0.50 20/20 -2.57 2.07
> 20/25 -0.50 20/20 -0.83 0.33
> 20/100- -0.75 20/20 -5.96 5.21
> 20/200 -1.25 20/25 -8.53 7.28
> 20/200 -3.00 20/20- -8.53 5.53
> 20/70 -1.00 20/20 -4.64 3.64
> 20/100 -1.75 20/20 -5.96 4.21
> 20/70 -0.50 20/20 -4.64 4.14
> 20/50- -1.00 20/20 -3.39 2.39
> 20/200 -2.75 20/20 -8.53 5.78
> 20/400 -4.25 20/40+ -11.10 6.85
> 20/40 -1.00 20/20 -2.57 1.57
> 20/60 -1.00 20/20 -4.07 3.07
> 20/50 -0.25 20/20 -3.39 3.14
> 20/20-- -1.50 20/20 0.00 -1.50
Does this mean 20/20-- or (20/20)-- ? If the former, then you
apparently made someone who could see much better than normal see only
normal. Why?
Likewise, is this 20/40+ or (20/40)+ ? This is of lesser concern.
Do you have data on hyperopes?
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
..............
>
>The behaviorists would simply faint dead away at the thought.
Better dead behaviorists than dead horses.
Ray
>Bill
Raymond A. Chamberlin
"Bob S." <bo...@ix.nospam.netcom.com> wrote:
>
.............
>
>You want dead??? I'LL show you a dead horse...
>Actually, my spreadsheet showed an average error of less than 1 diopter.
>Now, my preferred method has always been to start with the correct
>answer,
>and work backwards until you get the data. Since that is not possible
>here,
>the next best method is to tweak your model to fit the data!! (I know,
>this
>is driving you nuts). Using your empirical database, the average
>diopter
>error can be reduced to near 0 by changing the denominator from .27 to
>..43
>
>Thus:
>
>Correction in Diopters = log(20/xxx) / .43
>
>OK, discuss among yourselves....
>
.................
>
ĄBravísimo! ĄĄĄEl caballo vive!!!
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>In <341d77b0.41517792@News> spamf...@home.com (John Connolly) writes:
>
>
>>Even calculated correctly the equation is, as might be expected, a
>_very_
>>crude approximation.
>
>I'd say. If we even accept + or - .5 diopter error (for the purpose of
>avoiding a trip to the optometrist), 115 out of 171 would still be
>unacceptably overcorrected, 42 out of 171 would be acceptable, and 14
>of the 171 would still be unacceptably undercorrected.
Where do these numbers come from and are they applied after correcting
your calculations to those using common logarithms? Would there be an
"acceptable" empirical alignment, with such factor in front of the
expression as would best fit a log curve to your data (assuming your
data are totally valid)?
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
..............
>
>In this sample, 6 times as many eyes would be overcorrected as would be
>undercorrected, and as most people know, undercorrection is by far
>preferred to overcorrection in myopia.
You can always put a fudge factor in to best fit the curve to whatever
data is considered the most reliable empirical data. The idea here
was pragmatism, not a Nobel prize in math or physics. Then you can
advertise another fudge factor (or a whole set of them, as might befit
the range of opinions) to satisfy undercorrection of myopes. After
all, what do *you* do? You measure as accurately as you can and then
decide, with the client, on some amount of myopic fudge-factor or
none, right?
Ray
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
..............
>
>(I
>know,
>>this
>>is driving you nuts).
>
>Not at all. I love the exercise.
Anything, as long as you don't have to go to the library, right?
(Inhouse joke.)
>
...........
>
>Looks
>promising, but I'm still waiting for a REAL application of all of this.
It sells calculators. Maybe Dr. Dean can get his name on some of them
also.
>BTW, the .43 may only work in MY exam room, with MY particular
>intolerance for the guessing of Snellen letters by simple myopes...
OK, you have a different fuge-factor for each optometrist. This is
determined by assigning ordinal numbers to the letters of the last
names of each, adding them up, taking the square root and dividing the
result into 50. Hey, what are we doing anyhow? Actually, what we're
doing is measuring optometrists with their clients and one lousy
little formula. I PROPOSE THAT OPTOMETRISTS START PAYING FEE FOR THIS
EVALUATION PROCEDURE TO THEIR CLIENTS. (Either that or clients should
patent their eye parameters and charge royalties.)
Ray
William Stacy
In <34232851...@news.sirius.com> ra...@sirius.com (Raymond A.
Chamberlin) writes:
You measure as accurately as you can and then
>decide, with the client, on some amount of myopic fudge-factor or
>none, right?
True. Rarely more than .25 D from the measured value, but it IS a fudge
factor.
Bill
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
>In <341E76...@ix.nospam.netcom.com> "Bob S."
><bo...@ix.nospam.netcom.com> writes:
>
> to get a feel for how good or bad a
>>person's vision is when he tells me his uncorrected vision is 20/200,
>or
>>that his lenses are -2.5 diopters.
>
>I'll agree to that use of it.
>
>Bill
>
> *
> * *
> * HORSE *
> * *
> * R.I.P. *
> * *
> *********
Now what are you doing horsing around in the cemetery?
*
* *
* OPTOM *
* ETRY *
* R.I.P. *
* *
*********
And in the year of our Lord 2000, it came to pass that everyone had an
autorefractor in his/her road machine, and new ocular-corrective
lenses were dispensed from the dashboard of each each time same turned
on the ignition key. The horse may be dead, but horsepower is now
measured in diopters. Let's throw more logs onto the fire; it «lens»
more credibility and less mystique to what ODs are supposed to be
doing.
Ray (Old optoms never diopter; they just undercorrect.)
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
...............
>
>Your reduction of the average error reminds me of a 6 foot tall horse
>who couldn't swim but ventured out to cross a stream that was an
>average of 5 feet deep.
That was only a problem before quantum mechanics. The tunneling
effect is a horse of another color, charge, spin, whatever. Horse
sense wins over what done by the flippers of mirrors and lenses.
Ray
Raymond A. Chamberlin
spamf...@home.com (John Connolly) wrote:
>
>On Mon, 15 Sep 1997 13:41:19 -0400, "Bob S." <bo...@ix.nospam.netcom.com>
>wrote:
>
>>Correction in Diopters = log(20/xxx) / .43
>
>
>I have a copy of Excel97 on my computer which I had never used. My last
>exposure to a spreadsheet was 10 years ago with Lotus 123 version 1.0 (It
>required that the 5 1/4 floppy installation disk be kept in the A drive!).
>
>Anyway, because I wanted to check out Excel and because I had no other
>data, I repeated Bob S.'s work on the "dead horse" equation. The
>regression coefficient from a least squares fit was 0.42 (close enough!),
>and the standard deviation for Bill Stacy's 170 points was 0.8 diopters.
No animal, not even an optometrist, can say neigh to that.
Ray
William Stacy
In <34222d00...@news.sirius.com> ra...@sirius.com (Raymond A.
Chamberlin) writes:
>
>spamf...@home.com (John Connolly) wrote:
As written, the
>>equation predicts spherical corrections for 20/20 correctable myopic
>>non-astigmatic eyes, period.
>
>Correct. I don't think the factoring-in of this would be "eas[]y".
>
Oh come now boys. All you do is use a starburst target, move it to the
far point of clarity for the primary axis, then move it inward to the
point where the complementary lines are just clear and to arrive at a
sphero-cylindrical Rx by simple arithmetic.
>>You have "limited" imagination. :-)
>
>Hey, hey! I'll have you know that the word hereabout is that Dr.
>Stacy once arranged to have his assistant sunbathe with a bunch of
>photochromic lenses distributed about her body -- in order to advance
>some applied science (if not optometry) in respect to UV measurement.
>Now, don't you think that was imaginative -- and might've even sold a
>few more copies of Popular Optometry or whatever? Trouble is: we all
>knew it wouldn't come to pass. She copped out.
Fact is, her husband didn't like the idea of being polka-dotted. She's
on maternity leave now so I guess the uniform tan idea worked for her.
I'd still like to have some sunburn data through the various lens
types. Any takers? I'll supply the lenses...
Dr. Stacy used also
>to venture dollar-valued wagers, but we haven't seen any of these
>posted for some time. (Oops, maybe the word wasn't supposed to be
>promulgated, and that those days are gone forever.)
>
I had ONE taker on the bet (that she couldn't reduce her myopia by
homeopathic means). The year's gone by and she lost, but hasn't paid up
yet.
Bill
William Stacy
In <3422397b...@news.sirius.com> ra...@sirius.com (Raymond A.
Chamberlin) writes:
>> 20/20-- -1.50 20/20 0.00 -1.50
>
>Does this mean 20/20-- or (20/20)-- ? If the former, then you
>apparently made someone who could see much better than normal see only
>normal. Why?
>
No, that is common convention for "he read the 20/20 row except he
missed 2 letters on that row"
However, as you'll see in later posts, that was one of the errant data
group.
>>
>> 20/40+ -0.75 20/20 -2.57 1.82
>
>Likewise, is this 20/40+ or (20/40)+ ? This is of lesser concern.
And, likewise, this means "he read all of the 20/40 row and was able to
make out just one letter on the next more difficult (20/30) row.
>Do you have data on hyperopes?
Funny you should ask. I offered to do some. Anyone want to see it?
Bill
Raymond A. Chamberlin
bh...@globalnet.co.uk wrote:
>
............
>
>Sorry, but there is no such relationship - because vision is
>subjective and because the eye is a living organ, (the optical
>principles that apply to optical instruments therefore cannot apply).
When was the last time you applied to an institution (of higher
learning, of course)? What is the name of this religion of yours?
Ray
William Stacy
In <34242c19.214897405@News> spamf...@home.com (John Connolly)
writes:
However, it is still possible that, at
>each age our hyperope will show the same functional relationship
between VA
>and required correction. If so, we will publish and name it the
"William
>Stacy Dead-Horse Equation." :-)
Somehow I'd hoped to leave a slightly more sophisticated legacy...
Bill
William Stacy
OK here's the data for hyperopes with less than .5 cyl, along with
ages, using the .27 denominator:
Unaided Age Manifest Computed Error Best corrected
acuity hyperopia hyperopia acuity
20/25- 14 0.50 0.36 0.14 20/25
20/20-- 19 0.25 0.00 0.25 20/20
20/50 63 1.00 1.47 -0.47 20/20
20/100 55 1.25 2.59 -1.34 20/20
20/50+- 26 0.25 1.47 -1.22 20/20
20/20 42 1.00 0.00 1.00 20/20
20/25 42 0.75 0.36 0.39 20/20
20/60+ 12 1.00 1.77 -0.77 20/30+-
20/25- 20 0.75 0.36 0.39 20/20
20/60 37 0.50 1.77 -1.27 20/20-
20/20 15 0.75 0.00 0.75 20/20
20/200 51 1.00 3.70 -2.70 20/20
20/200 51 1.50 3.70 -2.20 20/20
20/40++ 75 0.50 1.11 -0.61 20/25
20/25- 34 0.50 0.36 0.14 20/20
20/20 46 0.25 0.00 0.25 20/20
20/70 56 0.75 2.02 -1.27 20/25
20/30- 18 0.25 0.65 -0.40 20/25-
20/200 51 1.75 3.70 -1.95 20/20
20/20 56 0.75 0.00 0.75 20/20
20/20- 21 0.50 0.00 0.50 20/20
20/20- 49 0.75 0.00 0.75 20/20
20//80- 64 2.25 2.23 0.02 20/20-
20/20 35 0.75 0.00 0.75 20/20
20/20 47 0.50 0.00 0.50 20/20
20/20- 39 1.75 0.00 1.75 20/20
20/30-- 48 2.25 0.65 1.60 20/20
20/40-- 44 0.50 1.11 -0.61 20/20
20/80+ 54 1.25 2.23 -0.98 20/30+
20/20 14 0.25 0.00 0.25 20/20
20/20- 29 0.75 0.00 0.75 20/20
20/20- 29 0.75 0.00 0.75 20/20
20/25- 54 0.75 0.36 0.39 20/20
20/30 12 0.25 0.65 -0.40 20/25
20/20 13 1.00 0.00 1.00 20/20
20/20 49 0.25 0.00 0.25 20/20
20/100 61 1.00 2.59 -1.59 20/30--
20/100 61 1.50 2.59 -1.09 20/20--
20/30 59 0.50 0.65 -0.15 20/20
20/100 57 0.75 2.59 -1.84 20/60
20/100 57 1.25 2.59 -1.34 20/20--
20/20 50 0.75 0.00 0.75 20/20--
20/70- 62 1.75 2.02 -0.27 20/20
20/20 48 0.25 0.00 0.25 20/20
20/25 21 0.25 0.36 -0.11 20/20
20/20 28 0.50 0.00 0.50 20/20
20/25 52 0.50 0.36 0.14 20/20
20/60+- 76 0.25 1.77 -1.52 20/40+
20/20- 40 0.75 0.00 0.75 20/20
20/20-- 14 0.50 0.00 0.50 20/20
20/20 48 0.50 0.00 0.50 20/20
20/20 52 0.00 0.00 0.00 20/20
20/30 45 0.00 0.65 -0.65 20/20-
20/50 42 1.75 1.47 0.28 30/30
20/20 14 0.00 0.00 0.00 20/20
20/25+- 19 0.25 0.36 -0.11 20/20-
20/20- 52 0.50 0.00 0.50 20/20
20/200 51 1.50 3.70 -2.20 20/20-
20/40++ 75 0.75 1.11 -0.36 20/25
20/25- 34 0.50 0.36 0.14 20/20
20/25+ 43 0.25 0.36 -0.11 20/20
20/20 13 0.00 0.00 0.00 20/20
20/70 56 0.75 2.02 -1.27 20/30
20/70 56 1.00 2.02 -1.02 20/20-
20/200 57 2.75 3.70 -0.95 20/20
20/20 61 0.25 0.00 0.25 20/20
20/25- 64 0.50 0.36 0.14 20/20
20/20- 62 0.50 0.00 0.50 20/20
20/20- 49 0.00 0.00 0.00 20/20
20/25 59 4.50 0.36 4.14 20/20
20/100- 53 1.25 2.59 -1.34 20/20-
20/100- 53 1.75 2.59 -0.84 20/20
20//80- 64 1.50 2.23 -0.73 20/20--
20/20 35 0.50 0.00 0.50 20/20
20/30+- 6 1.00 0.65 0.35 20/20-
20/30-- 48 1.50 0.65 0.85 20/20
20/20 29 0.00 0.00 0.00 20/20
20/80+ 54 1.50 2.23 -0.73 20/30-
2025-- 73 1.00 0.36 0.64 20/25
20/25- 54 0.75 0.36 0.39 20/20
20/25 16 1.00 0.36 0.64 20/20
20/30 8 0.50 0.65 -0.15 20/25
20/20-- 56 0.00 0.00 0.00 20/20
20/20- 49 0.75 0.00 0.75 20/20
20/200 55 3.25 3.70 -0.45 20/20
20/100 61 1.00 2.59 -1.59 20/40+
20/30+ 64 0.50 0.65 -0.15 20/20
20/70+ 53 0.75 2.02 -1.27 20/20-
20/20-- 20 0.25 0.00 0.25 20/20
20/100 57 1.25 2.59 -1.34 20/20--
20/30 56 1.25 0.65 0.60 20/20
20/20 43 0.00 0.00 0.00 20/20
20/25 21 0.25 0.36 -0.11 20/20-
20/20- 40 0.50 0.00 0.50 20/20-
20/40 53 1.25 1.11 0.14 20/20
20/20-- 42 0.75 0.00 0.75 20/20
20/50- 56 0.25 1.47 -1.22 20/30
20/25 54 0.75 0.36 0.39 20/20
20/20 21 0.50 0.00 0.50 20/20
20/20-- 14 0.50 0.00 0.50 20/20
20/25 46 0.50 0.36 0.14 20/20
Raymond A. Chamberlin
w...@ix.netcom.com(William Stacy) wrote:
>
............
>
>I had ONE taker on the bet (that she couldn't reduce her myopia by
>homeopathic means). The year's gone by and she lost, but hasn't paid up
>yet.
Just your luck! They might've hired you for a booth over at the
Indian casino if you'd showed a profit. Guess you'll just have to go
back to rolling eyeballs.
Ray
Raymond A. Chamberlin
Having only an electronics engineering background, but feeling that
there ought to be some readily available theoretical backing for the
below empirical findings of the relation between Snellen acuity and
spherical focusing correction for human eyes in diopters, I looked for
a relationship, in an optics text, of spatial-frequency or resolution
range of a defocused image versus its distance along the optical axis,
in each direction from the focal plane, as might be found by Fourier
transformation; however, I could not find anything I could recognize.
I am cross-posting this to sci.optics. I wonder if anyone there might
wish to add theoretical justification for the below empirically found
logarithmic relationship between the mentioned parameters:
Ray
**************************************************************
spamf...@home.com (John Connolly) wrote:
>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
>20/25 20/20 42 0.75 0.2 0.6
>20/60+ 20/30+- 12 1 1.0 0.0
>20/25- 20/20 20 0.75 0.2 0.6
>20/60 20/20- 37 0.5 1.0 -0.5
>20/20 20/20 15 0.75 0.0 0.8
>20/200 20/20 51 1 2.0 -1.0
>20/200 20/20 51 1.5 2.0 -0.5
>20/40++ 20/25 75 0.5 0.6 -0.1
>20/25- 20/20 34 0.5 0.2 0.3
>20/20 20/20 46 0.25 0.0 0.3
>20/70 20/25 56 0.75 1.1 -0.4
>20/30- 20/25- 18 0.25 0.4 -0.1
>20/200 20/20 51 1.75 2.0 -0.3
>20/20 20/20 56 0.75 0.0 0.8
>20/20- 20/20 21 0.5 0.0 0.5
>20/20- 20/20 49 0.75 0.0 0.8
>20/80- 20/20- 64 2.25 1.2 1.0
>20/20 20/20 35 0.75 0.0 0.8
>20/20 20/20 47 0.5 0.0 0.5
>20/20- 20/20 39 1.75 0.0 1.8
>20/30-- 20/20 48 2.25 0.4 1.9
>20/40-- 20/20 44 0.5 0.6 -0.1
>20/80+ 20/30+ 54 1.25 1.2 0.0
>20/20 20/20 14 0.25 0.0 0.3
>20/20- 20/20 29 0.75 0.0 0.8
>20/20- 20/20 29 0.75 0.0 0.8
>20/25- 20/20 54 0.75 0.2 0.6
>20/30 20/25 12 0.25 0.4 -0.1
>20/20 20/20 13 1 0.0 1.0
>20/20 20/20 49 0.25 0.0 0.3
>20/100 20/30-- 61 1 1.4 -0.4
>20/100 20/20-- 61 1.5 1.4 0.1
>20/30 20/20 59 0.5 0.4 0.1
>20/100 20/60 57 0.75 1.4 -0.7
>20/100 20/20-- 57 1.25 1.4 -0.2
>20/20 20/20-- 50 0.75 0.0 0.8
>20/70- 20/20 62 1.75 1.1 0.6
>20/20 20/20 48 0.25 0.0 0.3
>20/25 20/20 21 0.25 0.2 0.1
>20/20 20/20 28 0.5 0.0 0.5
>20/25 20/20 52 0.5 0.2 0.3
>20/60+- 20/40+ 76 0.25 1.0 -0.7
>20/20- 20/20 40 0.75 0.0 0.8
>20/20-- 20/20 14 0.5 0.0 0.5
>20/20 20/20 48 0.5 0.0 0.5
>20/20 20/20 52 0 0.0 0.0
>20/30 20/20- 45 0 0.4 -0.4
>20/50 30/30 42 1.75 0.8 0.9
>20/20 20/20 14 0 0.0 0.0
>20/25+- 20/20- 19 0.25 0.2 0.1
>20/20- 20/20 52 0.5 0.0 0.5
>20/200 20/20- 51 1.5 2.0 -0.5
>20/40++ 20/25 75 0.75 0.6 0.1
>20/25- 20/20 34 0.5 0.2 0.3
>20/25+ 20/20 43 0.25 0.2 0.1
>20/20 20/20 13 0 0.0 0.0
>20/70 20/30 56 0.75 1.1 -0.4
>20/70 20/20- 56 1 1.1 -0.1
>20/200 20/20 57 2.75 2.0 0.7
>20/20 20/20 61 0.25 0.0 0.3
>20/25- 20/20 64 0.5 0.2 0.3
>20/20- 20/20 62 0.5 0.0 0.5
>20/20- 20/20 49 0 0.0 0.0
>20/25 20/20 59 4.5 0.2 4.3
>20/100- 20/20- 53 1.25 1.4 -0.2
>20/100- 20/20 53 1.75 1.4 0.3
>20//80- 20/20-- 64 1.5 0.0 1.5
>20/20 20/20 35 0.5 0.0 0.5
>20/30+- 20/20- 6 1 0.4 0.6
>20/30-- 20/20 48 1.5 0.4 1.1
>20/20 20/20 29 0 0.0 0.0
>20/80+ 20/30- 54 1.5 1.2 0.3
>2025-- 20/25 73 1 0.2 0.8
>20/25- 20/20 54 0.75 0.2 0.6
>20/25 20/20 16 1 0.2 0.8
>20/30 20/25 8 0.5 0.4 0.1
>20/20-- 20/20 56 0 0.0 0.0
>20/20- 20/20 49 0.75 0.0 0.8
>20/200 20/20 55 3.25 2.0 1.2
>20/100 20/40+ 61 1 1.4 -0.4
>20/30+ 20/20 64 0.5 0.4 0.1
>20/70+ 20/20- 53 0.75 1.1 -0.4
>20/20-- 20/20 20 0.25 0.0 0.3
>20/100 20/20-- 57 1.25 1.4 -0.2
>20/30 20/20 56 1.25 0.4 0.9
>20/20 20/20 43 0 0.0 0.0
>20/25 20/20- 21 0.25 0.2 0.1
>20/20- 20/20- 40 0.5 0.0 0.5
>20/40 20/20 53 1.25 0.6 0.6
>20/20-- 20/20 42 0.75 0.0 0.8
>20/50- 20/30 56 0.25 0.8 -0.6
>20/25 20/20 54 0.75 0.2 0.6
>20/20 20/20 21 0.5 0.0 0.5
>20/20-- 20/20 14 0.5 0.0 0.5
>20/25 20/20 46 0.5 0.2 0.3
>
Raymond A. Chamberlin
REPOST, because I don't see it in sci.optics on this date:
Having only an electronics engineering background, but feeling that
there ought to be some readily available theoretical backing for the
below empirical findings of the relation between Snellen acuity and
spherical focusing correction for human eyes in diopters, I looked for
a relationship, in an optics text, of spatial-frequency or resolution
range of a defocused image versus its distance along the optical axis,
in each direction from the focal plane, as might be found by Fourier
transformation; however, I could not find anything I could recognize.
I am cross-posting this to sci.optics. I wonder if anyone there might
wish to add theoretical justification for the below empirically found
logarithmic relationship between the mentioned parameters:
Ray
**************************************************************
spamf...@home.com (John Connolly) wrote:
>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
Ross Drewe
Raymond A. Chamberlin <ra...@sirius.com> wrote:
> Having only an electronics engineering background, but feeling that
> there ought to be some readily available theoretical backing for the
> below empirical findings of the relation between Snellen acuity and
> spherical focusing correction for human eyes in diopters, I looked
> for a relationship, in an optics text, of spatial-frequency or
> resolution range of a defocused image versus its distance along the
> optical axis, in each direction from the focal plane, as might be
> found by Fourier transformation; however, I could not find anything
> I could recognize.
I did not see the beginning of this thread. I've seen the hyperope data
set but not the myope set, and I don't know what population this data
is taken from. Some comments may be out of line because I don't have
the context of the thread.
1. It's pretty terrible data, at least the 101 point hyperope set is.
For a start, there are some obviously wrong points. Eg, it's impossible
to have an uncorrected VA of 20/25 with 4.5D of spherical error.
Secondly, there are some poor corrected VAs, implying the existence of
other problems - if you're trying to establish the effect of refractive
error on VA, these data points shouldn't be in the data set. There's
also a large age range and this introduces all kinds of problems,
particularly if the group has not been preselected to be free of
cataract, eye disease, previous eye surgery, etc. Even if screened for
ocular health, there is the problem of accommodation in young
hyperopes, invalidating the uncorrected VA unless measured with
accommodation paralysed. It's easier to get good tight data with myopes
because they're not tempted to accommodate to overcome their visual
blurring. I've graphed the hyperope data and it's much more scattered
than it ought to be, unless there are mitigating factors mentioned
earlier in the thread. Published studies in myopia
show that log VA vs log refractive error (in myopia) is linear - in
contrast to the result you quote on William Stacey's data.
2. It's easy to get a (rather loose) theoretical justification for a
linear log-log relationship. Assume a simplified eye with the corneal
and lenticular lens powers replaced by an equivalent single lens - this
is quite good enough for this purpose. Assume a constant axial eyeball
length and constant pupil size. Assume myopic refractive error is D
dioptres. Tracing a single paraxial ray from infinity is sufficient to
define the radius of the blur circle, r, which is the image on the
retina of a point at infinity. The algebra is very simple, and shows
that r is proportional to D. No problem so far. The next bit is
trickier - what is the relationship between r and the VA? There must be
published work in the literature on visual optics, but I can't give you
any refs myself. It's reasonable to guess that, as a first
approximation, the degradation in acuity for parallel lines should be
related to some function of r, and for Snellen letters and other 2D
figures, should be related to r^2 (the area of the blur circle).
Because of the way the Snellen VA is defined, this means that VA should
be proportional to 1/r^2, very approximately. Other effects may mean
that the exponent is not actually 2, but the physics of it suggest that
a power law 1/r^k is likely to be good fit, and any such relationship
gives a linear log VA / log refractive error plot. The analysis is
fairly robust with respect to the actual functional relationship, since
it is known by context to be smooth, monotonic.
Conclusion: log(VA) vs log(refractive error) should be roughly linear.
It sounds like you're the sort of man who'd enjoy trying to tidy this
up with a 2D-Fourier analysis of how defocussing affects edge contrast,
image saturation etc, but this stuff gets complicated very fast, and
worse, it interacts with cortical perceptual processes which are highly
nonlinear.
3. Empiric studies: a lot of good clinical studies were done earlier
this century, before everyone got distracted by antibodies and PCR. An
English textbook I have shows the data of Hirsch (1945) which plots as
a nice straight line on a log-log plot, from which I derive
log10 (VA) = -1.3534 (log10(-D)) - 0.5068,
where VA = decimal form of Snellen VA, D = myopia in dioptres
--
Ross Drewe
Raymond A. Chamberlin
Chris Wyatt <clw...@buffnet.net> wrote:
>
.............
>
>here's a different (incorrect?) perspective:
>
>a slightly modified version of the Newtonian equation would work
>
> -xx' = f^2 or - diopters = f^2/1000 (in mm)
>
>if you'd like to calculate the number of diopters that are
>equivalent to a shift of .3 mm for a lens of 25 mm focal length
>i'd guess the result is about 0.5 D. The sign convention can be
>left for the user.
>
>to add snellen acuity to the mix doesn't seem like much more than trig
>and algebra.
Looks very incorrect to me. I don't know how Newton comes into the
above, but you seem to be redefining the diopter in your equations to
your own whim. Then you speak of a "shift", whatever that is, and
then you say there's nothing to the actual problem presented here,
i.e., how do the manifested diopters vary with the Snellen acuity
reading for the same eye?
1 diopter is defined, in a convergent or divergent lens or lens
system, as simply a measure of the "power" of such alternative entity
as has a focal length of 1 reciprocal meter. This measure is not
calculated as the square of the focal length. As I don't relate to
the "shift", I don't know what you're "guess"ing at, but I thought the
whole idea here was *not* to guess but to use a formula. Lastly, the
whole given problem, that of relating Snellen acuity to what would be
the lens power required to fully correct the point of ocular focus, is
*not* just a matter of trig and algebra.
Ray
Raymond A. Chamberlin
ra...@sirius.com (Raymond A. Chamberlin) wrote:
>jfcon...@homXe.com (John Connolly) wrote:
>
>>
>.............
>>
>>And what happens as VA approaches one, i.e. 20/20, and D approaches
>>zero? :-)
>
>Hope he gets back here to answer that. I'd like to see the answer.
>Maybe I can also dig up Hirsch (1945) at the UCBSO library though.
I found "Hirsch (1945)" = "Relation of Visual Acuity to Myopia",
Monroe J. Hirsch, AB, Standford U. (monograph). The subjects were all
myopic UCB students. (Not enough myopes at Stanford? Probably don't
have to pay UCB students as much.) Plotting the log curve John found
best fit Bill's myope and heterope data on Hirsch's spread of data,
which went only from -0.5 to -13.5 D (20/20 to 20/2500), it fits as
well to that data, from -0.5 to -2.25 D (20/33 to 20/190).
Furthermore, there is a clump of Hirsch's data points that are not a
bad fit to the log curve at -3.9 (20/1000).
Hirsch's exponential curve (power of 0.663) gives -0.5 for 20/20 but
for 0.0 D it requires 20/0 acuity. Hirsch does not claim the curve
holds for values less negative than -0.5 or for different age ranges
or different means of determining VA (he used Clason VA meter to
project Snellen-chart letters, with diopter values taken as the
weakest lens which gave a maximum VA).
Hirsch gave two areas of practical application: 1) prevention of
overcorrection of myopia, and 2) prevention of wrong readings for VA
due to squinting or memorization in the one sense and malingering in
the other. The latter he relates to U. S. Army selective service
requirements and those in certain industries. (No mention that he had
a grant from the Army.)
Ray
Chris Wyatt
Actually, i was trying to learn more, without sounding like I know the
answer. Sorry for not explaining my guessing more clearly.
You are correct, the "shift" of which I wrote as you have pointed out,
was an attempt to correlate 1 diopter of power change to some physical
distance in front of a simple lens. Sorry that's not what you had in
mind.
Maybe my thoughts of correlation of diopters and 1000's of mm of power
are correct only when applied to a simple lens of focal length f using
the formula written above.
The whim I used in defining a diopter as the equivalent shift in
position of an object of 1000 mm in front of a lens works quite well for
dioptric power calculations needed for microscope eyepieces and other
simplistic systems.
As far as the Newton reference, the equation xx' = f^2 is sometimes
referred to as the Newtonian form of the lens equation. First appearing
around the early 1700's in Newton's Opticks. (Hecht 2nd edition, p143)
Raymond A. Chamberlin
Chris Wyatt <clw...@buffnet.net> wrote:
>
................
>
>You are correct, the "shift" of which I wrote as you have pointed out,
>was an attempt to correlate 1 diopter of power change to some physical
>distance in front of a simple lens. Sorry that's not what you had in
>mind.
>
>Maybe my thoughts of correlation of diopters and 1000's of mm of power
>are correct only when applied to a simple lens of focal length f using
>the formula written above.
>
>The whim I used in defining a diopter as the equivalent shift in
>position of an object of 1000 mm in front of a lens works quite well for
>dioptric power calculations needed for microscope eyepieces and other
>simplistic systems.
>
>As far as the Newton reference, the equation xx' = f^2 is sometimes
>referred to as the Newtonian form of the lens equation. First appearing
>around the early 1700's in Newton's Opticks. (Hecht 2nd edition, p143)
But the relationship is *not* square-law, it's a reciprocal linear
relationship: 1 diopter, as applied to a convergent or divergent
lens, is simply *defined* as the reciprocal of the focal length of
same lens in meters. I don't see what that has to do with Newton or
any square law, and it certainly isn't any *problem* but rather a
definition. What was posted *is* an empirical problem for which I was
trying to locate a theory, assuming an approximation to the resolution
of a defocused image through an ideal spherical lens.
Ray