Two different ways of writing prescriptions
JonS2001
astigmatism. In one type the cylinder is written as an addition, and in the
other as a minus.
Therefore:
SPH: -5.25 CYL: -1.25 AXIS: 90
would be the same as:
SPH: -6.50 CYL: +1.25 AXIS: 270
am i correct?
What is the origin of these two different forms, and who uses each type?
JonS2001
What do you mean "left eye"? I only wrote down a prescription for one eye in
my example.
Could you explain how this system works?
Greatest Prime
> From: jons...@aol.com (JonS2001)
> Organization: AOL, http://www.aol.co.uk
> Newsgroups: sci.med.vision
> Date: 25 Feb 2001 17:00:52 GMT
> Subject: Two different ways of writing prescriptions
Actually, there are an infinity of ways of writing such a prescription. Two
crossed cylindrical lenses are the equivalent of a single spherical lens.
Both methods are equivalent. In a sense, it is like describing a lens in
German or French. Either one can do it accurately. But Spanish, Italian, and
Japanese can do so also.
Mathematicians have developed methods that can give unique prescriptions,
but such methods are not used in the vision optics industry. You would have
to get away from using cylinder as a description.
For those interested in technical details, the required correction can be
described by Zernicke functions (polynomials) that are orthonormal.
Bill
William Stacy
Two crossed cylindrical lenses are the equivalent of a single spherical lens.
That is only correct if the two cylinders are of equal power and their major axes
are oriented perpendicularly. Any unequal cylinders that are crossed at any angle,
and any equal cylinders that are crossed at any angle other than 90 are equivalent
to single sphero-cylindrical lenses, not spherical ones.
w.stacy, o.d.
xxxx
angle, at say, 30 degrees, between their axes. Is that equivalent to
some cyl + sph, or is it much more complicated than that?
Jack
"William Stacy" <wst...@obase.net> wrote in message
news:3A9A711C...@obase.net...
William Stacy
resulting sphero-cylindrical equivalent.
Greatest Prime
> Newsgroups: sci.med.vision
> Date: Mon, 26 Feb 2001 12:08:31 -0500
> Subject: Re: Two different ways of writing prescriptions
curvature (focal length) lenses crossed at right angles. spherical lens has
the same focal length as one of the cylindrical lenses.
As "xxxx" <yy...@yyy.com> points out, two crossed cylindrical lens can be
looked at as a spherical lens and a cylindrical lens. The sphere will vary
with crossing angle as will the cylinder and orientation. There will be no
unique description except for right angle crossed equal curvature
cylindrical lenses.
Using Zernike polynomials gets around this limitation. There will be a
unique expression for that arrangement. It will include a spherical
component and two hyperbolic components. This combination can only
approximate a cylinder because, from the point of view of a lens designer, a
cylindrical lens has high order aberrations. The orientation of the
individual hyperbolic components must be specified. That is, the orientation
of the polynomials must be specified.
Bill
Andrey Durasov
Someone may find physics (or just optics) boring, but there's no other
way to explain this, so if you're ready - let's go.
Astigmatism is a property of an optic lens (in the eye it can be cornea
or crystalline lens) to focus light rays so, that they can't come to one
point (A - negative preposition, STIGMA - point). This is explained by
different refractive power of an optic lens measured in different
directions - meridians, each of which has its own focal point. The
steepest (maximal refraction) and the flattest (minimal refraction)
meridians are called main meridians, usually they are perpendicular to
each other. These are basics about astigmatism.
Some more words about refraction (simplified). Emmetropia is a
refraction when light focuses on the retina. Myopia is a strong
refraction (light focuses in front of the retina), hyperopia is a weak
refraction (light focuses behind the retina). Astigmatism can accompany
each of these refractions.
Now we are coming to correcting lenses and correction of astigmatism.
Lenses can be spheric (SPH) that means that they correct all meridians
equally (their power is equal in all meridians) and cylindrical (CYL) -
they are optically effective in one meridian and ineffective (plano) in
perpendicular meridian. Actually, for astigmatism correction toric
lenses are used (they have one power in one meridian and different power
in other meridian), but glasses are still prescribed in SPH-CYL form.
The last portion of prescription is AXIS - the direction of cylinder
axis, i.e. optically INeffective meridian, so the axis of CYL is
perpendicular to meridian it corrects.
Sign of the lens shows how does the lens affect refraction. If the lens
is increasing refraction, it has "+" sign, and vice versa.
Let's reconstruct the astigmatism in your case. As you remember, SPH
acts equally on both meridians, then one of them (at 180 degrees, as
axis is 90 degrees) is further reduced by CYL. So we have -5.25 at 90
degrees and -6.5 at 180 degrees.
To correct the astigmatism we have first to correct one meridian to
emmetropia with SPH (remember, this will also affect the other
meridian), then the rest of the other meridian is corrected with CYL
(I'm talking only about this SPH-CYL form of prescription, other forms
are possible but are not discussed). If we take SPH -5.25, we correct 90
meridian, but leave 180 meridian -1.25 undercorrected, so CYL -1.25 is
used at 90 degrees (axis perpendicular to meridian being corrected). If
we take SPH -6.5, we correct 180 meridian, but 90 meridian is now 1.25
overcorrected (its power decreases 1.25 more than needed), so we have to
increase it with CYL +1.25 at 180 degrees (not 270).
Either form is possible, but there are some considerations. As you may
have noticed, CYL power is the same in plus and minus form (that is
because we have the same astigmatism), but SPH power is different. So
one consideration may be to choose the combination with least possible
SPH, this would make the spectacles thinner. In myopic and hyperopic
astigmatism SPH and CYL with this approach will have the same sign (see
your example). The other case is mixed astigmatism (myopia in one
meridian and hyperopia in another). It can be -1.5x+1.5 or -1.0x+2.0
or -2.0x+1.0 (all these cases with 3.0 D of astigmatism). We can choose
here also the least SPH combination or the combination best tolerated by
the patient. The special case are children with that kind of
astigmatism. Since their refraction with age tends to shift towards
myopia, it is preferable from beginning to use "-" cylinder to avoid the
sign change in the future (-1.0x+2.0 > -2.0x+1.0 > -3.0x+0.0 > -4.0x-1.0
and at this point the "-" cylinder is already evident).
Sorry if it was too much, my apologies for some roughness in terms, I'm
sure native English-speakers will correct me if necessary.
Regards,
A.B.Durasov, MD
Greatest Prime
> From: "Andrey Durasov" <Andrey....@sendmail.ru>
> Organization: IAC Samara-Internet, Ltd.
> Newsgroups: sci.med.vision
> Date: Tue, 27 Feb 2001 00:28:29 +0400
> Subject: Re: Two different ways of writing prescriptions
>
One source of confusion is that astigmatism does not mean the same
optimetricly as it does opticly. That is, to vison people, astimatism
corresponds to a cylindrical component in the structure of the vision
system. This corresponds to different curvatures in meridians of different
orientations.
To the lens designer, astigmatism is a problem found in circularly symmetric
spherical lenses. It cannot be corrected by adding cylindrical lenses. It is
corrected by trying to combine lens elements with equal and opposite
astigmatism. The term anastigmat has been used to describe som ot them. The
process has nothing to do with optometry.
Bil
Mike Tyner
calculated, and it measures as one would expect with real lenses. Doctors
who fit toric contacts often use cross-cyl calculators, and in school we
learned a graphical (geometric) technique for figuring it out on paper.
Before calculators it was pretty tough to get through the math each time you
wanted a result. Nobody wrote a calculator just the way I want, so I wrote
my own.
When I plug in the two lenses you describe, 30 degrees apart, I get
pl - 100 x 090
comb w/ pl - 100 x 060
----------------------------
yields -0.13 -1.73 x 075
-MT
"xxxx" <yy...@yyy.com> wrote in message
news:97gve5$pe4ct$1...@ID-69489.news.dfncis.de...
> Can someone here please try this. Stack two blanks, each, say
>
> sph=0, cyl= -1.00,
>
> with axes set 30 degrees apart, in the instrument (that looks like a
> microscope) that you use to measures the glasses the patient brings in.
> Try to measure the Rx in the usual way. Does the instrument handle as
> it does for a single lens? What Rx does it read? Try different angles.
> I would love to do this but I do not have access to such an instrument.
> It would be comforting to see the results at 0 and 90 deg fall in to the
> expected values, but what do angles between 0 and 45 deg produce? Does
> the instrument even lead to a reliable reading? It must repeat after 45
> deg just by symmetry.
>
> Maybe the general case is always an equivalent Rx lens, maybe not.
> This should settle it more easily than working out the theory.
>
> > As "xxxx" <yy...@yyy.com> points out, two crossed cylindrical lens can
> be
> > looked at as a spherical lens and a cylindrical lens. The sphere will
> vary
> > with crossing angle as will the cylinder and orientation. There will
> be no
> > unique description except for right angle crossed equal curvature
> > cylindrical lenses.
> >
> > Bill
> >
>
>
Michael Pace
resolved to an equivalent sphero/cyl with principal meridians 90 degrees
apart. The eye itself consists of a number of sphero/cyl surfaces at
various axis that are resolved into a single sphero/cyl power with principal
meridians 90 degrees apart that we call refractive error. Its like vectors,
you can start a complex journey with any number of twists and turns in three
dimensional space, but at the end of the day it can all be resolved down to
a single line connecting the start and finish points. So too with the
journey light takes through a lens combination; if you ignore aberrations,
the combination can be expressed as a single lens.
A lensometer (the instrument you are talking about) is designed with
rotatable targets 90 degrees apart to read the power of spectacle lenses
along the two principal meridians. They are not designed to read the power
at all the meridians inbetween, nor does it measure aberrations. You use it
by rotating the targets until one is clear, note the power and then change
the power until the other one is clear. The lensometer will read the
equivalent sphero/cyl at whatever the equivalent axis is.
xxxx <yy...@yyy.com> wrote in message
news:97gve5$pe4ct$1...@ID-69489.news.dfncis.de...
> Can someone here please try this. Stack two blanks, each, say
>
> sph=0, cyl= -1.00,
>
> with axes set 30 degrees apart, in the instrument (that looks like a
> microscope) that you use to measures the glasses the patient brings in.
> Try to measure the Rx in the usual way. Does the instrument handle as
> it does for a single lens? What Rx does it read? Try different angles.
> I would love to do this but I do not have access to such an instrument.
> It would be comforting to see the results at 0 and 90 deg fall in to the
> expected values, but what do angles between 0 and 45 deg produce? Does
> the instrument even lead to a reliable reading? It must repeat after 45
> deg just by symmetry.
>
> Maybe the general case is always an equivalent Rx lens, maybe not.
> This should settle it more easily than working out the theory.
>
> > As "xxxx" <yy...@yyy.com> points out, two crossed cylindrical lens can
> be
> > looked at as a spherical lens and a cylindrical lens. The sphere will
> vary
> > with crossing angle as will the cylinder and orientation. There will
> be no
> > unique description except for right angle crossed equal curvature
> > cylindrical lenses.
> >
> > Bill
> >
>
>
Greatest Prime
> From: "Mike Tyner" <mty...@mindspring.com>
> Organization: MindSpring Enterprises
> Newsgroups: sci.med.vision
> Date: Tue, 27 Feb 2001 15:48:01 -0500
> Subject: Re: Two different ways of writing prescriptions
>
> Yes, crossed cylinders produce a predictable vector sum that can be
> calculated, and it measures as one would expect with real lenses. Doctors
> who fit toric contacts often use cross-cyl calculators, and in school we
> learned a graphical (geometric) technique for figuring it out on paper.
> Before calculators it was pretty tough to get through the math each time you
> wanted a result. Nobody wrote a calculator just the way I want, so I wrote
> my own.
Vector sum? What vectors? It is a vector sum only in the sense of a Hilbert
space such as set up with orthonormal functions such as Zernicke
polynomials. The cylinder "vectors" are not independent. Invoking vectors
adds to any confusion that may already be there.
Bill
Mike Tyner
fits very nicely into the vector concept. It's helpful when you need to
approximate them in your head.
-MT
"Greatest Prime" <Fish...@mediaone.net> wrote in message
news:B6C2B323.23D47%Fish...@mediaone.net...
Greatest Prime
> Organization: MindSpring Enterprises
> Newsgroups: sci.med.vision
> Subject: Re: Two different ways of writing prescriptions
>
> fits very nicely into the vector concept. It's helpful when you need to
> approximate them in your head.
>
> -MT
>
*transform* as a vector. The sum of two vectors must be another vector. The
sum of two vectors as you describe is not a vector. That is, it is not
another cylindrical lens with some axis. It is a combination of a sphere and
a cylindrical lens. This means that it does not transform as a vector and,
therefore is not a vector.
On the other hand, If you do go to the Zernicke representation of a wave
surface, you do have a vector in the sense that it is a sum of componenents.
You get a displacement called piston; two wedge components at right angles
to each other; quadratic components starting with sphere; two astigmatisms
at 45 degrees angles to each other; and an infinite sum of aberrations
including high order aberrations that are more complicated than quadratic.
The vector is given as a sum of these aberrations. Adding two of these
together give another vector of the same kind and components of the sum is
found by adding the individual components of the original vectors. How do
you do addition of your cylindrical vectors?
I did not mean to go into so much detail that only just begins to delve into
the subject.
Bill
Mike Tyner
"Greatest Prime" <Fish...@mediaone.net> wrote
> The sum of two vectors must be another vector. The
> sum of two vectors as you describe is not a vector. That is, it is not
> another cylindrical lens with some axis.
I guess it's a cylindrical lens with no axis?
Cylinders can sum and cancel to yield sphere, no question. But go one mile
north and one mile east and you're still somewhere along a line that points
precisely northeast. The leftover sphere is just a frequent flyer bonus.
-MT
Greatest Prime
> From: "Mike Tyner" <mty...@mindspring.com>
> Organization: MindSpring Enterprises
> Newsgroups: sci.med.vision
> Date: Thu, 1 Mar 2001 17:10:19 -0500
> Subject: Re: Two different ways of writing prescriptions
>
>
Thus,the sum is not a vector.
> -MT
>
>
>
Maybe you need to go to quaternions. When you multiply them together you end
up with a scalar part and a vector part. :-)
Bill
Mike Tyner
"Greatest Prime" <Fish...@mediaone.net> wrote
> Maybe you need to go to quaternions. When you multiply them together you
end
> up with a scalar part and a vector part. :-)
I started out to help someone understand the concept of crossed cylinders,
and it still makes sense to say that they work "like vectors," particularly
since you can calculate them by drawing what my geometry teacher always
called "plane vectors".
I'm pretty sure expanding the comparison into three dimensions won't make it
any clearer. And I'm pretty sure anyone who estimates crossed cylinders in
their head pictures the axis as a resultant of two vectors.
Engineers. Sheesh.
-MT
Greatest Prime
> From: "Mike Tyner" <mty...@mindspring.com>
> Organization: MindSpring Enterprises
> Newsgroups: sci.med.vision
> Date: Fri, 2 Mar 2001 16:01:54 -0500
> Subject: Re: Two different ways of writing prescriptions
>
>
> "Greatest Prime" <Fish...@mediaone.net> wrote
>
>> Maybe you need to go to quaternions. When you multiply them together you
> end
>> up with a scalar part and a vector part. :-)
This was a joke! See the smiley.
>
> I started out to help someone understand the concept of crossed cylinders,
> and it still makes sense to say that they work "like vectors," particularly
> since you can calculate them by drawing what my geometry teacher always
> called "plane vectors".
I think you usually give good explanations but cylindrical lenses as vectors
. . .?
If an analogy is no good, don't use it.
>
> I'm pretty sure expanding the comparison into three dimensions won't make it
> any clearer. And I'm pretty sure anyone who estimates crossed cylinders in
> their head pictures the axis as a resultant of two vectors.
>
> Engineers. Sheesh.
>
> -MT
>
I can sheesh optometrists and ophthalmologists too. I related my experience
trying to get a negative correction to compensate for positive lensing from
ny developing cataract. The ophthalmologist royally screwed up my the
prescription. She had trouble operating the phoropter.
Then I went to an optometrist in the same practice. He would not listen to
me to give me a lens negative enough. He indicated that one line on the
chart was the equivalent of 0.25 D. That did not give me confidence. With
badgering, I got a bit more negative. But as I measure it, I can still use
an extra 0.5 to 0.75 D. Sheesh.
Dick Claiborne
"JonS2001" <jons...@aol.com> wrote in message
news:20010225120052...@ng-ma1.aol.com...
In your example, your plus cylinder lens would be axis 180. We only use
axis 1-180. Converting from plus to minus or minus to plus is very easy.
Step 1 - Algebraically add sph and cyl power
Step 2 - Change the sign of the cyl (if it's + change to - or vice-versa)
Step 3 - Add or subtract 90 degrees to the axis (less than 90 add, more than
90 subtract)
So -6.50 +1.25 X 180 would become -5.25 -1.25 X 090.
-3.00 +2.00 X 045 would become -1.00 -2.00 X 135
-4.00 -1.25 X 160 would become -5.25 +1.25 X 070
Optometrists usually use minus cylinder phoropters and write RX's in that
form. Ophthalmologists usually use plus cylinder phoropters and write RX's
in that form. Why did this get started? I have no clue. I know some
lenses have the cylinder on the front side of the lens, or at least they
used to. Most newer lenses have the cylinder ground upon the back or minus
surface.
I can tell you from using both minus and plus cylinder phoropters that the
plus cylinder one is much easier to learn on (IMO). Since Ophthalmologists
are not formally trained in refraction, perhaps they liked the easier one.
Just a guess. I'm sure one of the more learned O.D.'s in the group will
have the true answer.
Sheesh, I hope my math was correct or I'll never hear the end of it...
JonS2001
Jon
Bloody Viking
William Stacy (wst...@obase.net) wrote:
: That is only correct if the two cylinders are of equal power and their major axes
: are oriented perpendicularly. Any unequal cylinders that are crossed at any angle,
: and any equal cylinders that are crossed at any angle other than 90 are equivalent
: to single sphero-cylindrical lenses, not spherical ones.
How does the eye doc diagnose the cylinder component? The spherical component
is easy enough to understand. The doc simply tries different lenses until you
see clear. The spherical component could be easally diagnosed if you are
farsighted and go to a drugstore with the reading glasses.
--
FOOD FOR THOUGHT: 100 calories are used up in the course of a mile run.
The USDA guidelines for dietary fibre is equal to one ounce of sawdust.
The liver makes the vast majority of the cholesterol in your bloodstream.
Mike Tyner
"Bloody Viking" <nos...@ripco.com>
>
> How does the eye doc diagnose the cylinder component? The spherical
component
> is easy enough to understand. The doc simply tries different lenses until
you
> see clear.
By offering you choices between more cylinder and less, bracketing to some
hopefully-consistent endpoint.
Axis is determined similarly, by offering it more-and-less at 45 degrees on
either side, and bracketing to a consistent axis.
Which you do first (amount or axis) is a matter of personal taste and
technique. Bracketing can find cyl and axis without any prior knowledge, but
it helps greatly to have an estimate before you start flipping lenses. Three
popular starting points are retinoscopy, old glasses, and computerized
refraction done in pre-testing.
So when they ask "which is better, one or two" and you feel stupid because
you can't tell a difference between one and two, SING OUT! "No difference"
means you've arrived.
-MT
amounts more and less