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I have astigmatism but i also am near sighted and farsighted. Can i
still wear contacts that will help treat my eyes or will i have to
keep wearing glasses?— Preceding unsigned comment added by 68.96.170.70 ( talk • contribs) 21:26, 4 August 2005 (UTC)
I have a question.My optician had mentioned that toric contact lenses are good for improving eyesight.I have amblyopia in the left eye and this is hereditary and it's a lost cause.My right eye has seen a consistent decrease in vision because of the strain and is currently at -8.5D.I am nearsighted and I wear glasses.I want to shift to wearing lenses permanently. I'm told,It's only with toric lenses that I'll get a perfect number Is this true?Anyone to advise? —The preceding unsigned comment was added by SpinMojo ( talk • contribs) 08:17, August 31, 2006.
Presenting the following for discussion, given that it was edited out as anecdotal:
"In at least one person, the brain's compensation for the distortion has presented as visual snow."
This was a major personal issue (having previously been diagnosed as simply myopic, and thus assuming a neurological basis for the 'flickering' of striped patterns, film-grain effect on my vision, etc), and I believe mention of it may help others... or I may just be the odd duck out. Any other astigmats care to back this up, or discuss their perceptions of the distortion? In particular, the supposed hallmark of the condition -- lines looking curved -- never occurred to me, rather an increasing fuzziness and 'flickeriness' given symmetrical differences between eyes.
The illustrations do give a good impression of the fuzziness, so let me extend appreciation to whoever submitted those. [Unsigned comment by User:69.37.164.129, August 24, 2005]
You deleted my graphic from Astigmatism on 12 Sept. Your "Wrong image removed" comment is vague. I'm happy to make changes based on logical arguments. See the review history of my POTD image for root canal.
Similar astigmatism images for reference:
I've readded the image and await your substantial justification.
jk 18:32, 28 December 2005 (UTC)
x x x x x
I have nominated the image above for deletion. Discussion at IFD#April_11. -- srleffler 11 April 2006
Contact lens is currently nominated to be improved on Wikipedia:Article Improvement Drive. Please support the article with your vote. -- Fenice 10:51, 16 January 2006 (UTC)
I don't know if others have noticed this, but I know I have astigmatism and the "simple eye test" didn't do anything for me. Is this test correct?
I see that the optics use of "astigmatism" has been added here. While it may not be obvious, the optics and ophthalmology uses of the term do not refer to the same effect. The ophthalmological condition is a result of a misshapen lens (or cornea). The optical aberration happens even for perfectly-formed spherical optics. These two concepts need to be split into two separate articles.-- Srleffler 13:16, 30 March 2006 (UTC)
Actually, if astigmatism is defined as a variation of system focal length with clocking angle around the optical axis, it does mean the same thing to both optical design and opthalmics. Centered optical systems with figure-of-revolution surfaces have no axial astigmatism, but nearly all have astigmatism away from the axis. This includes the human eye, which does exhibit appreciable astigmatism away from the foveal area, as a raytrace of Pomerantzoff's eye model shows in ZEMAX. Centered systems with non-figure of revolution surfaces, such as poorly made lenses or mirrors, as well as misshapen corneas, have on-axis astigmatism as well as away from the axis.
I agree that the whole classical optics section could use a major structural scrub. As it has been written by numerous contributors, it is inherently disjointed and uncorrelated, with numerous undefined and/or un-crossreferenced terms.
But as you say, Wikipedia is one of the best things to ever come from the Internet. —This unsigned comment was added by JonesMI ( talk • contribs) .
I'm here considering classic optics, not ophtalmics. I have met different definitions for these two terms, and the one presented in this article is one of them, but I believe it's not the official one. Here, tangential is presented as the vertical meridionnal plane, and sagital the horizontal one. I know this assumption is often used in optical design programs (at least for the tangential plane, Zemax uses this definition, indeed). But I believe the true definition is that the tangential plane is the one containing the axis of symmetry (usually the optical axis) and the field point. The sagital plane is then defined to be the orthogonal plan to the tangential plane that intersects the axis of symmetry at the entrance pupil . The reason why optical design programs use the asumption that the tangential plane is the vertical one is because most of the designs are rotationnaly symmetric, and one can then always word only with a vertical field, as working with any other field would be equal by rotation. Even with that asumption, Sagital plane IS NOT horizontal as it intersects the axis of symmetry (which is horizontal) at the entrance pupil. I know that Zemax doesn't consider it to be horizontal. When designing a program, if you want to define a field that is diagonal (not only vertical) then the data computed isn't really the tangential data as it is not referring to an actual focus point. -- Palleas 15:01, 04 April 2006 (UTC)
In optics, astigmatism is a monochromatic aberration in which an optical system has different focal planes for ray fans in cut planes through the optical axis (meridional planes) at different rotation angles. The vertical meridional plane is termed the tangential plane, and the horizontal meridional plane is termed the sagittal plane. Lenses and mirrors which are either misaligned, or have one or more slightly cylindrical or toroidal surfaces will produce astigmatic images over most or all of the image format. Third order astigmatism in uncorrected optical systems such as paraboloidal mirrors increases with the square of the angle off axis. Optical systems which are corrected to minimize third-order astigmatism are called anastigmats. In broadband, white-light refractive or diffractive optical systems, astigmatism can be a function of wavelength.
I'm just not totally following Palleas' paragraph above. The sagittal plane IS always orthogonal to the tangential plane, as Zemax does say in their latest April 4, 2006 manual, at the top of page 53, which states, The term "tangential" refers to data computed in the tangential plane, which is the plane defined by a line and one point: the line is the axis of symmetry, and the point is the field point in object space. The sagittal plane is the plane orthogonal to the tangential plane, which also intersects the axis of symmetry at the entrance pupil position. Zemax even holds to this definition for non-rotationally symmetric systems.
I got out the MIL-HDBK-141 and Warren Smith's 3rd edition of "Modern Optical Design", and can't seem to find any definition inconsistencies between these references and the Zemax manual. From the MIL-HDBK-141 in section 5.4.1.1, p. 5-5, "A special ray that lies in a plane containing the optical axis and the object point is called a meridional ray". The tangential meridional plane is defined at the entrance pupil to contain the vertical axis, and the sagittal meridional plane contains the horizontal axis at the entrance pupil. Also, see the drawing on page 70 of Smith's book, which illustrates exactly the same thing and labels it as such.
Different definitions for identical ray/pupil geometries should not exist. I don't feel comfortable with optical design and opthalmics having different definitions. Perhaps Wikipedia is the right place to resolve this and give the world a unified definition.
-- Mike 02:56, 7 April 2006 (UTC)
Nothing like going to work and not thinking about this for a day to get a fresh perspective. After reading Smith's book tonight, I'm beginning to see the conflicting definitions you're referring to. This topic is almost as multiply defined as photometry; it just depends how far back into optics history you read. Quoting from Warren Smith's latest book may help clear this up - let me know if it does or doesn't. I quote from Smith's 3rd Edition of Modern Optical Engineering, McGraw-Hill, 2000, pp. 69-70, complete with Smith's italics:
"If a lens system is represented by a drawing of its axial section, rays which lie in the plane of the drawing are called meridional or tangential rays. ... Similarly, the plane through the axis is referred to as the meridional or tangential plane, as may any plane through the axis."
" Rays which do not lie in a meridional plane are called skew rays. The oblique meridional ray through the center of the aperture of a lens system is called the principal, or chief, ray. If we imagine a plane passing through the chief ray and perpendicular to the meridional plane, then the (skew) rays from the object which lie in this sagittal plane are sagittal rays."
"As shown in Fig. 3.7, the image of a point source formed by an oblique fan of rays in the tangential plane will be a line image; this line, called the tangential image, is perpendicular to the tangential plane; i.e., it lies in the sagittal plane. Conversely the image formed by the rays of the sagittal fan is a line which lies in the tangential plane."
Thus the term "sagittal meridional plane" would seem to be OK to use, but could possibly be confused with a sagittal ray fan. You and Palleas are half right; the sagittal plane is a skew plane which is orthogonal to the tangential plane - but, the sagittal plane does contain the optical axis and is thus also a meridional plane. The confusion may stem from naming the ray fan, not the plane. Sagittal rays are indeed skew, or out-of-plane, rays. The tangential image is formed by a vertical fan of meridional rays emanating from an object point and intersecting the entrance pupil along the vertical or Y-axis. The sagittal image is formed by a horizontal fan of skew rays emanating from the same object point and intersecting the entrance pupil along the horizontal or X-axis.
Hecht defines sagittal as I have stated above [Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. ISBN 0-201-11609-X.]. See, in particular, figures 6.22 and 6.23. I agree with what you have quoted from Smith, above, but not completely with your interpretation of it. Smith is very clear that the sagittal plane is the plane passing through the chief ray (i.e. containing it), and perpendicular to the meridional plane that contains the object point being considered. Assuming we are talking about an off-axis object point, the sagittal plane so defined is absolutely not a meridional plane, and does not contain the optic axis. See the figures in Hecht if this is not clear. This plane is skew, and a plane by definition cannot be both skew and meridional.
Note also that Smith clearly defines the sagittal plane as the plane containing the sagittal rays. You seem to be making a distinction between the plane of the sagittal ray fan and the "sagittal plane".--
Srleffler 03:14, 8 April 2006 (UTC)
Mike here - OK, good on you, you're right - the sagittal plane as named is orthogonal to the tangential plane and inclined to contain the chief ray, not the optical axis. The sagittal meridional plane lies in the Y=0 plane and contains the optical axis, and may or may not contain the chief ray depending on downstream folding and coordinate rotations. The sagittal plane and sagittal meridional plane should intersect at the entrance pupil. Guess I'm used to folding systems up with mirrors, Risley prisms, etc., where multiple coordinate rotations complicate terminology used for straight-through systems. I remember that plot in Hecht (I don't even know where my old first edition copy is), and it would be good to include in the astigmatism section, or your own drawing in Powerpoint to avoid copyright hassles. This is definitely an instance where a word is worth a millipicture.
See if this paragraph is better worded. I still want to get in that non-rotationally symmetric systems (and the human eye with a warped cornea) or misaligned good optics can have axial astigmatism, that third-order astigmatism increases with the square of the field angle, and that astigmatism can often be a function of wavelength, especially in broadband systems. I'd rather not define astigmatism as a monochromatic aberration for that reason. —The preceding unsigned comment was added by JonesMI ( talk • contribs).
In optics, astigmatism is an aberration in which an optical system has different focal lengths for ray fans through the entrance pupil at different clocking orientations. Defined at the system entrance pupil, the vertical meridional plane is termed the tangential plane, and the inclined plane orthogonal to the tangential plane and containing the chief ray is termed the sagittal plane. Lenses and mirrors which are either misaligned, or have one or more slightly cylindrical or toroidal surfaces will produce astigmatic images over most or all of the image format. Third order astigmatism in uncorrected optical systems such as paraboloidal mirrors increases with the square of the angle off axis. Optical systems which are corrected to minimize differences in tangential and sagittal third-order astigmatism are called anastigmats. In broadband, white-light refractive or diffractive optical systems, astigmatism can be a function of wavelength.
I think the content here is good, and I'm fine with the things you mention that you want to include. I think, though, that this paragraph is probably too technical for the introduction to the article. We need to write for a general audience, as well as possibly for a more technical audience, so we need to start with a fairly general description that is more accessible.
I have been thinking for a day or two, that it might be good to write the article from the point of view that we are describing two distinct optical effects with the same term. The first effect would be the third-order Seidel aberration, which creates a different focal point for rays in the tangential and sagittal planes (as defined above). The second effect is that systems with imperfect rotational symmetry produce different foci for rays in two orthogonal meridional planes. The ophthalmic use of the term would then fall into the second category, and the article can unify both the optics and ophthalmic uses (as is proper, since the optics in ophthalmology is still optics). What do you think? When I have time, I'll take a stab at restructuring the article along these lines.-- Srleffler 04:53, 9 April 2006 (UTC)
Your organization seems reasonable - basic Seidel intro first, especially with Hecht's diagram, that really helps visualize things. Then a generalization and ramp-up of technical detail to discuss non-rotationally symmetric systems, beginning with astigmatism in the human eye. The existing diagrams showing different blurring in different meridians are excellent here.
The next section could cover optical systems either having poorly made optics or are misaligned. I can supply a couple of ZEMAX plots showing effects of surface error and misalignment on astigmatism if that would help.
The last section could deal with intentionally non-rotationally symmetric reflective systems that balance astigmatism over the 3D field to give nearly diffraction-limited performance without central obstructions and spider vane diffraction. This section could be brief in the aberration section, and pointed to and more thoroughly dealt with in the telescope section (my specialty area), as it includes off-axis, decentered telescopes such as Yolo's, Schiefspieglers, Stevick/Pauls, Herrig designs, toroidal mirrors via warping harnesses such as Jose Sasian's work at U of Ariz, etc. I have already made placeholders for some of these in the List of telescope types section, and was going to start writing on them as time permits, including figures using real ZEMAX layout and raytrace plots of several of my own personal designs and some published designs with proper credit.
Or, I could just back off and leave it in your hands. I'm brand new to this Wikipedia thing, and the possibility that I have strayed into someone else's project uninvited has occurred to me.-- Mike 11:42, 9 April 2006 (UTC)
OK, I started editing it along these lines. It's sketchy, but hopefully this will form a rough "template" for the structure of the article. I ended up splitting off Astigmatism (eye) into a new article after all. Astigmatism can contain a summary or overview of the subject, leaving the technical detail for the new Astigmatism (eye). The "main" template is used to make a link at the start of the ophthalmic section, to direct readers to the main article on that topic. I deleted a couple of the more technical sections, but didn't attempt to summarize the rest. It's getting late, so I can't do any more on this tonight. Feel free to edit what I have written. It could use more work.-- Srleffler 05:25, 10 April 2006 (UTC)
Just wondering why the ophthalmological use of "astigmatism" was chosen to be moved to Astigmatism (eye) rather than the optics use moved to Astigmatism (optics). No doubt there is overlap, but I would guess that most people searching for "astigmatism" are looking for the medical condition. - AED 05:18, 10 April 2006 (UTC)
Might be good to put a selection right at the start of astigmatism, something like
I'm also working on the tangential/sagittal plane drawings, should have something by the weekend.-- Mike 10:48, 11 April 2006 (UTC)
OK - working on the tan/sag diagrams this evening, and have come to some points of discussion. Hecht's diagram shows the sagittal plane simultaneously going through an object point, the center of the entrance/exit pupil, and through a corresponding image point, seemingly defining that the (paraxial) chief ray lies totally in this plane from object to image. The entrance and exit pupils are coplanar and not separated in this drawing. This may be useful to illustrate the terminology but is in general not what happens. The simplest case would be a telecentric lens, with an inclined object chief ray, and a horizontal image chief ray. In that case, the exit pupil sagittal plane is horizontal and parallel to (but does not contain) the optical axis.
My two discussion points are:
1. When the entrance and exit pupils are not coplanar, which is the majority of the time, there would actually be two sagittal planes, one containing the chief ray segment from the object point to the entrance pupil center, and the other containing the chief ray segment from the exit pupil to the image point. The planes will in general not be parallel, depending on the pupil locations and system magnification.
2. Whether the pupils are coplanar or separated, in the presence of lateral color (which is a paraxial aberration, not even third order), and in the presence of distortion (which varies both with field angle and wavelength), the chief ray segment from the system exit pupil to the image point is not parallel the chief ray segment entering the entrance pupil from the object.
I think it is more accurate and general to modify Hecht's diagram to show separate entrance and exit pupil sagittal planes at different inclinations θ1 and θ2. I created a simple ZEMAX plot of a telecentric paraxial doublet that illustrates this clearly.
Discussion?-- Mike 22:36, 11 April 2006 (UTC)
-- OK - I have actually already drawn up Hecht's drawing with color coding, and a different viewpoint to hopefully make it sufficiently different from Hecht's drawing to avoid any copyright arguments. When I finish it I'll post it up. I'm also about finished with the more detailed drawing showing the object and image sag planes at different angles, with the entrance and exit pupils separated. It actually doesn't look that bad clutter-wise, so I'll submit it to the team here for scrutiny.
Maybe there could be both plots, one in the introductory section, then one in the no-opthalmics section for more detail.-- Mike 19:15, 12 April 2006 (UTC)
what causes astigmatism? is it genetics? can astigmatism be caused by environmental factors? is the cause unknown? can it be cured by laser treatment (not sure if that is discussed)? these questions need to be addressed. PMoney 08:25, 19 June 2006 (UTC)
I recently went to have my eyes checked and was told that I have astigmatism, albeit "just a little." He came to his conclusion based on a series of tests with white superimposed on green and red backgrounds. I observed the letters through a phoropter. I was asked which letters appeared clearer: the ones superimposed on the green or red background? This does not appear to be a reasonable test for astigmatism. If I am not mistaken, shouldn't an astigmatism chart be used if one was to diagnose astigmatism? Anyone have any ideas? mezzaninelounge 05:53, 20 July 2006 (UTC)
The green-red test takes advantage of the wavelength difference between the two colors. If the green letters are sharper than the red, more myopic correction is apprpropriate. Hope this helps. PedEye1 21:46, 31 March 2007 (UTC)
The cross example seems a bit far-fetched. Is it confusing the image with the tracing of rays through a cross-shaped pattern on the lens? The varying focus is not an effect of the image, unless we're talking about off-axis effects.— Preceding unsigned comment added by 192.187.147.51 ( talk • contribs) 23:30, 4 January 2007 (UTC)
I recently went for a consultation for Laser eye corrective surgery, and was told because I have astigmatism. Laser Eye Surgery is not reccommended as it can possible make your sight worse. He said this is the case with all astigmatisms. Should this be mentioned in the main article? Randomjack 09:23, 21 February 2007 (UTC)
I dont believe the consultant was being entirely thruthful. With modern machines, you can treat astigmatism. Although laser surgery is not suitable for everybody. —Preceding unsigned comment added by 78.105.217.216 ( talk) 23:09, 13 March 2009 (UTC)
I came to this article, which is quite good, hoping to find out how the axis of astigmatism is interpreted from my Rx, but there was no mention of this. MaxEnt 03:47, 23 August 2007 (UTC) Note: I found something at Eyeglass prescription instead. MaxEnt 03:49, 23 August 2007 (UTC)
As a student Thomas Young discovered that he had problems with one eye in 1793. [1] In the following years he was able to do research on his seeing problems. [2] He presented his findings in an Bakerian lecture in 1801. [3]
Independent from Young George Biddell Airy discovered the phoneme of astigmatism on his own eye. [4] Airy presented his observations on his own eye in February 1825 at the Cambridge Philosophical Society. [5] [6] Airy was able to produce lenses to correct his seeing problems by 1825, [7] [8] while other sources put this into 1827 [9] when Airy obtained cylindrical lenses froom an optitian from Ipswich. [10] The name for the condition was not given by Airy, but from William Whewell. [11] [12] [13]
By the 1860s astigmatism was a well established concept in ophthalmology. [14] And chapters in books describe the discovery of astigmatism. [15] [16]
{{
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—— Preceding unsigned comment added by Stone ( talk • contribs) 12 February 2011 (UTC)
WHAT'S AN ASTIGAMATIC SYSTEM? "FORM A CROSS"??? THIS IS CONFUSING FROM TEH VERY FIRST SENTENCE — Preceding unsigned comment added by 216.183.185.133 ( talk) 20:05, 16 April 2012 (UTC)
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I have astigmatism but i also am near sighted and farsighted. Can i
still wear contacts that will help treat my eyes or will i have to
keep wearing glasses?— Preceding unsigned comment added by 68.96.170.70 ( talk • contribs) 21:26, 4 August 2005 (UTC)
I have a question.My optician had mentioned that toric contact lenses are good for improving eyesight.I have amblyopia in the left eye and this is hereditary and it's a lost cause.My right eye has seen a consistent decrease in vision because of the strain and is currently at -8.5D.I am nearsighted and I wear glasses.I want to shift to wearing lenses permanently. I'm told,It's only with toric lenses that I'll get a perfect number Is this true?Anyone to advise? —The preceding unsigned comment was added by SpinMojo ( talk • contribs) 08:17, August 31, 2006.
Presenting the following for discussion, given that it was edited out as anecdotal:
"In at least one person, the brain's compensation for the distortion has presented as visual snow."
This was a major personal issue (having previously been diagnosed as simply myopic, and thus assuming a neurological basis for the 'flickering' of striped patterns, film-grain effect on my vision, etc), and I believe mention of it may help others... or I may just be the odd duck out. Any other astigmats care to back this up, or discuss their perceptions of the distortion? In particular, the supposed hallmark of the condition -- lines looking curved -- never occurred to me, rather an increasing fuzziness and 'flickeriness' given symmetrical differences between eyes.
The illustrations do give a good impression of the fuzziness, so let me extend appreciation to whoever submitted those. [Unsigned comment by User:69.37.164.129, August 24, 2005]
You deleted my graphic from Astigmatism on 12 Sept. Your "Wrong image removed" comment is vague. I'm happy to make changes based on logical arguments. See the review history of my POTD image for root canal.
Similar astigmatism images for reference:
I've readded the image and await your substantial justification.
jk 18:32, 28 December 2005 (UTC)
x x x x x
I have nominated the image above for deletion. Discussion at IFD#April_11. -- srleffler 11 April 2006
Contact lens is currently nominated to be improved on Wikipedia:Article Improvement Drive. Please support the article with your vote. -- Fenice 10:51, 16 January 2006 (UTC)
I don't know if others have noticed this, but I know I have astigmatism and the "simple eye test" didn't do anything for me. Is this test correct?
I see that the optics use of "astigmatism" has been added here. While it may not be obvious, the optics and ophthalmology uses of the term do not refer to the same effect. The ophthalmological condition is a result of a misshapen lens (or cornea). The optical aberration happens even for perfectly-formed spherical optics. These two concepts need to be split into two separate articles.-- Srleffler 13:16, 30 March 2006 (UTC)
Actually, if astigmatism is defined as a variation of system focal length with clocking angle around the optical axis, it does mean the same thing to both optical design and opthalmics. Centered optical systems with figure-of-revolution surfaces have no axial astigmatism, but nearly all have astigmatism away from the axis. This includes the human eye, which does exhibit appreciable astigmatism away from the foveal area, as a raytrace of Pomerantzoff's eye model shows in ZEMAX. Centered systems with non-figure of revolution surfaces, such as poorly made lenses or mirrors, as well as misshapen corneas, have on-axis astigmatism as well as away from the axis.
I agree that the whole classical optics section could use a major structural scrub. As it has been written by numerous contributors, it is inherently disjointed and uncorrelated, with numerous undefined and/or un-crossreferenced terms.
But as you say, Wikipedia is one of the best things to ever come from the Internet. —This unsigned comment was added by JonesMI ( talk • contribs) .
I'm here considering classic optics, not ophtalmics. I have met different definitions for these two terms, and the one presented in this article is one of them, but I believe it's not the official one. Here, tangential is presented as the vertical meridionnal plane, and sagital the horizontal one. I know this assumption is often used in optical design programs (at least for the tangential plane, Zemax uses this definition, indeed). But I believe the true definition is that the tangential plane is the one containing the axis of symmetry (usually the optical axis) and the field point. The sagital plane is then defined to be the orthogonal plan to the tangential plane that intersects the axis of symmetry at the entrance pupil . The reason why optical design programs use the asumption that the tangential plane is the vertical one is because most of the designs are rotationnaly symmetric, and one can then always word only with a vertical field, as working with any other field would be equal by rotation. Even with that asumption, Sagital plane IS NOT horizontal as it intersects the axis of symmetry (which is horizontal) at the entrance pupil. I know that Zemax doesn't consider it to be horizontal. When designing a program, if you want to define a field that is diagonal (not only vertical) then the data computed isn't really the tangential data as it is not referring to an actual focus point. -- Palleas 15:01, 04 April 2006 (UTC)
In optics, astigmatism is a monochromatic aberration in which an optical system has different focal planes for ray fans in cut planes through the optical axis (meridional planes) at different rotation angles. The vertical meridional plane is termed the tangential plane, and the horizontal meridional plane is termed the sagittal plane. Lenses and mirrors which are either misaligned, or have one or more slightly cylindrical or toroidal surfaces will produce astigmatic images over most or all of the image format. Third order astigmatism in uncorrected optical systems such as paraboloidal mirrors increases with the square of the angle off axis. Optical systems which are corrected to minimize third-order astigmatism are called anastigmats. In broadband, white-light refractive or diffractive optical systems, astigmatism can be a function of wavelength.
I'm just not totally following Palleas' paragraph above. The sagittal plane IS always orthogonal to the tangential plane, as Zemax does say in their latest April 4, 2006 manual, at the top of page 53, which states, The term "tangential" refers to data computed in the tangential plane, which is the plane defined by a line and one point: the line is the axis of symmetry, and the point is the field point in object space. The sagittal plane is the plane orthogonal to the tangential plane, which also intersects the axis of symmetry at the entrance pupil position. Zemax even holds to this definition for non-rotationally symmetric systems.
I got out the MIL-HDBK-141 and Warren Smith's 3rd edition of "Modern Optical Design", and can't seem to find any definition inconsistencies between these references and the Zemax manual. From the MIL-HDBK-141 in section 5.4.1.1, p. 5-5, "A special ray that lies in a plane containing the optical axis and the object point is called a meridional ray". The tangential meridional plane is defined at the entrance pupil to contain the vertical axis, and the sagittal meridional plane contains the horizontal axis at the entrance pupil. Also, see the drawing on page 70 of Smith's book, which illustrates exactly the same thing and labels it as such.
Different definitions for identical ray/pupil geometries should not exist. I don't feel comfortable with optical design and opthalmics having different definitions. Perhaps Wikipedia is the right place to resolve this and give the world a unified definition.
-- Mike 02:56, 7 April 2006 (UTC)
Nothing like going to work and not thinking about this for a day to get a fresh perspective. After reading Smith's book tonight, I'm beginning to see the conflicting definitions you're referring to. This topic is almost as multiply defined as photometry; it just depends how far back into optics history you read. Quoting from Warren Smith's latest book may help clear this up - let me know if it does or doesn't. I quote from Smith's 3rd Edition of Modern Optical Engineering, McGraw-Hill, 2000, pp. 69-70, complete with Smith's italics:
"If a lens system is represented by a drawing of its axial section, rays which lie in the plane of the drawing are called meridional or tangential rays. ... Similarly, the plane through the axis is referred to as the meridional or tangential plane, as may any plane through the axis."
" Rays which do not lie in a meridional plane are called skew rays. The oblique meridional ray through the center of the aperture of a lens system is called the principal, or chief, ray. If we imagine a plane passing through the chief ray and perpendicular to the meridional plane, then the (skew) rays from the object which lie in this sagittal plane are sagittal rays."
"As shown in Fig. 3.7, the image of a point source formed by an oblique fan of rays in the tangential plane will be a line image; this line, called the tangential image, is perpendicular to the tangential plane; i.e., it lies in the sagittal plane. Conversely the image formed by the rays of the sagittal fan is a line which lies in the tangential plane."
Thus the term "sagittal meridional plane" would seem to be OK to use, but could possibly be confused with a sagittal ray fan. You and Palleas are half right; the sagittal plane is a skew plane which is orthogonal to the tangential plane - but, the sagittal plane does contain the optical axis and is thus also a meridional plane. The confusion may stem from naming the ray fan, not the plane. Sagittal rays are indeed skew, or out-of-plane, rays. The tangential image is formed by a vertical fan of meridional rays emanating from an object point and intersecting the entrance pupil along the vertical or Y-axis. The sagittal image is formed by a horizontal fan of skew rays emanating from the same object point and intersecting the entrance pupil along the horizontal or X-axis.
Hecht defines sagittal as I have stated above [Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. ISBN 0-201-11609-X.]. See, in particular, figures 6.22 and 6.23. I agree with what you have quoted from Smith, above, but not completely with your interpretation of it. Smith is very clear that the sagittal plane is the plane passing through the chief ray (i.e. containing it), and perpendicular to the meridional plane that contains the object point being considered. Assuming we are talking about an off-axis object point, the sagittal plane so defined is absolutely not a meridional plane, and does not contain the optic axis. See the figures in Hecht if this is not clear. This plane is skew, and a plane by definition cannot be both skew and meridional.
Note also that Smith clearly defines the sagittal plane as the plane containing the sagittal rays. You seem to be making a distinction between the plane of the sagittal ray fan and the "sagittal plane".--
Srleffler 03:14, 8 April 2006 (UTC)
Mike here - OK, good on you, you're right - the sagittal plane as named is orthogonal to the tangential plane and inclined to contain the chief ray, not the optical axis. The sagittal meridional plane lies in the Y=0 plane and contains the optical axis, and may or may not contain the chief ray depending on downstream folding and coordinate rotations. The sagittal plane and sagittal meridional plane should intersect at the entrance pupil. Guess I'm used to folding systems up with mirrors, Risley prisms, etc., where multiple coordinate rotations complicate terminology used for straight-through systems. I remember that plot in Hecht (I don't even know where my old first edition copy is), and it would be good to include in the astigmatism section, or your own drawing in Powerpoint to avoid copyright hassles. This is definitely an instance where a word is worth a millipicture.
See if this paragraph is better worded. I still want to get in that non-rotationally symmetric systems (and the human eye with a warped cornea) or misaligned good optics can have axial astigmatism, that third-order astigmatism increases with the square of the field angle, and that astigmatism can often be a function of wavelength, especially in broadband systems. I'd rather not define astigmatism as a monochromatic aberration for that reason. —The preceding unsigned comment was added by JonesMI ( talk • contribs).
In optics, astigmatism is an aberration in which an optical system has different focal lengths for ray fans through the entrance pupil at different clocking orientations. Defined at the system entrance pupil, the vertical meridional plane is termed the tangential plane, and the inclined plane orthogonal to the tangential plane and containing the chief ray is termed the sagittal plane. Lenses and mirrors which are either misaligned, or have one or more slightly cylindrical or toroidal surfaces will produce astigmatic images over most or all of the image format. Third order astigmatism in uncorrected optical systems such as paraboloidal mirrors increases with the square of the angle off axis. Optical systems which are corrected to minimize differences in tangential and sagittal third-order astigmatism are called anastigmats. In broadband, white-light refractive or diffractive optical systems, astigmatism can be a function of wavelength.
I think the content here is good, and I'm fine with the things you mention that you want to include. I think, though, that this paragraph is probably too technical for the introduction to the article. We need to write for a general audience, as well as possibly for a more technical audience, so we need to start with a fairly general description that is more accessible.
I have been thinking for a day or two, that it might be good to write the article from the point of view that we are describing two distinct optical effects with the same term. The first effect would be the third-order Seidel aberration, which creates a different focal point for rays in the tangential and sagittal planes (as defined above). The second effect is that systems with imperfect rotational symmetry produce different foci for rays in two orthogonal meridional planes. The ophthalmic use of the term would then fall into the second category, and the article can unify both the optics and ophthalmic uses (as is proper, since the optics in ophthalmology is still optics). What do you think? When I have time, I'll take a stab at restructuring the article along these lines.-- Srleffler 04:53, 9 April 2006 (UTC)
Your organization seems reasonable - basic Seidel intro first, especially with Hecht's diagram, that really helps visualize things. Then a generalization and ramp-up of technical detail to discuss non-rotationally symmetric systems, beginning with astigmatism in the human eye. The existing diagrams showing different blurring in different meridians are excellent here.
The next section could cover optical systems either having poorly made optics or are misaligned. I can supply a couple of ZEMAX plots showing effects of surface error and misalignment on astigmatism if that would help.
The last section could deal with intentionally non-rotationally symmetric reflective systems that balance astigmatism over the 3D field to give nearly diffraction-limited performance without central obstructions and spider vane diffraction. This section could be brief in the aberration section, and pointed to and more thoroughly dealt with in the telescope section (my specialty area), as it includes off-axis, decentered telescopes such as Yolo's, Schiefspieglers, Stevick/Pauls, Herrig designs, toroidal mirrors via warping harnesses such as Jose Sasian's work at U of Ariz, etc. I have already made placeholders for some of these in the List of telescope types section, and was going to start writing on them as time permits, including figures using real ZEMAX layout and raytrace plots of several of my own personal designs and some published designs with proper credit.
Or, I could just back off and leave it in your hands. I'm brand new to this Wikipedia thing, and the possibility that I have strayed into someone else's project uninvited has occurred to me.-- Mike 11:42, 9 April 2006 (UTC)
OK, I started editing it along these lines. It's sketchy, but hopefully this will form a rough "template" for the structure of the article. I ended up splitting off Astigmatism (eye) into a new article after all. Astigmatism can contain a summary or overview of the subject, leaving the technical detail for the new Astigmatism (eye). The "main" template is used to make a link at the start of the ophthalmic section, to direct readers to the main article on that topic. I deleted a couple of the more technical sections, but didn't attempt to summarize the rest. It's getting late, so I can't do any more on this tonight. Feel free to edit what I have written. It could use more work.-- Srleffler 05:25, 10 April 2006 (UTC)
Just wondering why the ophthalmological use of "astigmatism" was chosen to be moved to Astigmatism (eye) rather than the optics use moved to Astigmatism (optics). No doubt there is overlap, but I would guess that most people searching for "astigmatism" are looking for the medical condition. - AED 05:18, 10 April 2006 (UTC)
Might be good to put a selection right at the start of astigmatism, something like
I'm also working on the tangential/sagittal plane drawings, should have something by the weekend.-- Mike 10:48, 11 April 2006 (UTC)
OK - working on the tan/sag diagrams this evening, and have come to some points of discussion. Hecht's diagram shows the sagittal plane simultaneously going through an object point, the center of the entrance/exit pupil, and through a corresponding image point, seemingly defining that the (paraxial) chief ray lies totally in this plane from object to image. The entrance and exit pupils are coplanar and not separated in this drawing. This may be useful to illustrate the terminology but is in general not what happens. The simplest case would be a telecentric lens, with an inclined object chief ray, and a horizontal image chief ray. In that case, the exit pupil sagittal plane is horizontal and parallel to (but does not contain) the optical axis.
My two discussion points are:
1. When the entrance and exit pupils are not coplanar, which is the majority of the time, there would actually be two sagittal planes, one containing the chief ray segment from the object point to the entrance pupil center, and the other containing the chief ray segment from the exit pupil to the image point. The planes will in general not be parallel, depending on the pupil locations and system magnification.
2. Whether the pupils are coplanar or separated, in the presence of lateral color (which is a paraxial aberration, not even third order), and in the presence of distortion (which varies both with field angle and wavelength), the chief ray segment from the system exit pupil to the image point is not parallel the chief ray segment entering the entrance pupil from the object.
I think it is more accurate and general to modify Hecht's diagram to show separate entrance and exit pupil sagittal planes at different inclinations θ1 and θ2. I created a simple ZEMAX plot of a telecentric paraxial doublet that illustrates this clearly.
Discussion?-- Mike 22:36, 11 April 2006 (UTC)
-- OK - I have actually already drawn up Hecht's drawing with color coding, and a different viewpoint to hopefully make it sufficiently different from Hecht's drawing to avoid any copyright arguments. When I finish it I'll post it up. I'm also about finished with the more detailed drawing showing the object and image sag planes at different angles, with the entrance and exit pupils separated. It actually doesn't look that bad clutter-wise, so I'll submit it to the team here for scrutiny.
Maybe there could be both plots, one in the introductory section, then one in the no-opthalmics section for more detail.-- Mike 19:15, 12 April 2006 (UTC)
what causes astigmatism? is it genetics? can astigmatism be caused by environmental factors? is the cause unknown? can it be cured by laser treatment (not sure if that is discussed)? these questions need to be addressed. PMoney 08:25, 19 June 2006 (UTC)
I recently went to have my eyes checked and was told that I have astigmatism, albeit "just a little." He came to his conclusion based on a series of tests with white superimposed on green and red backgrounds. I observed the letters through a phoropter. I was asked which letters appeared clearer: the ones superimposed on the green or red background? This does not appear to be a reasonable test for astigmatism. If I am not mistaken, shouldn't an astigmatism chart be used if one was to diagnose astigmatism? Anyone have any ideas? mezzaninelounge 05:53, 20 July 2006 (UTC)
The green-red test takes advantage of the wavelength difference between the two colors. If the green letters are sharper than the red, more myopic correction is apprpropriate. Hope this helps. PedEye1 21:46, 31 March 2007 (UTC)
The cross example seems a bit far-fetched. Is it confusing the image with the tracing of rays through a cross-shaped pattern on the lens? The varying focus is not an effect of the image, unless we're talking about off-axis effects.— Preceding unsigned comment added by 192.187.147.51 ( talk • contribs) 23:30, 4 January 2007 (UTC)
I recently went for a consultation for Laser eye corrective surgery, and was told because I have astigmatism. Laser Eye Surgery is not reccommended as it can possible make your sight worse. He said this is the case with all astigmatisms. Should this be mentioned in the main article? Randomjack 09:23, 21 February 2007 (UTC)
I dont believe the consultant was being entirely thruthful. With modern machines, you can treat astigmatism. Although laser surgery is not suitable for everybody. —Preceding unsigned comment added by 78.105.217.216 ( talk) 23:09, 13 March 2009 (UTC)
I came to this article, which is quite good, hoping to find out how the axis of astigmatism is interpreted from my Rx, but there was no mention of this. MaxEnt 03:47, 23 August 2007 (UTC) Note: I found something at Eyeglass prescription instead. MaxEnt 03:49, 23 August 2007 (UTC)
As a student Thomas Young discovered that he had problems with one eye in 1793. [1] In the following years he was able to do research on his seeing problems. [2] He presented his findings in an Bakerian lecture in 1801. [3]
Independent from Young George Biddell Airy discovered the phoneme of astigmatism on his own eye. [4] Airy presented his observations on his own eye in February 1825 at the Cambridge Philosophical Society. [5] [6] Airy was able to produce lenses to correct his seeing problems by 1825, [7] [8] while other sources put this into 1827 [9] when Airy obtained cylindrical lenses froom an optitian from Ipswich. [10] The name for the condition was not given by Airy, but from William Whewell. [11] [12] [13]
By the 1860s astigmatism was a well established concept in ophthalmology. [14] And chapters in books describe the discovery of astigmatism. [15] [16]
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—— Preceding unsigned comment added by Stone ( talk • contribs) 12 February 2011 (UTC)
WHAT'S AN ASTIGAMATIC SYSTEM? "FORM A CROSS"??? THIS IS CONFUSING FROM TEH VERY FIRST SENTENCE — Preceding unsigned comment added by 216.183.185.133 ( talk) 20:05, 16 April 2012 (UTC)
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