Talk:Astigmatism

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[edit] Green and Red

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)

You might get a better answer if you posted your question over at talk:Astigmatism (eye).--Srleffler 11:04, 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)

[edit] Contacts and astigmatism?

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? [Unsigned comment by User:68.96.170.70, August 4, 2005]

Contact lenses can correct both myopia or hyperopia and astigmatism at the same time. You can not be hyperoptic and myoptic at the same time. --Marco 13:34, 23 December 2005 (UTC)
Perhaps by "near sighted and farsighted" he means that he has neither hyperopia nor myopia—that he has only astigmatism. Or perhaps he means that he has presbyopia and one of the other two.--Srleffler 23:31, 23 December 2005 (UTC)
Doesn't really matter, he can still have contact lenses unless he needs extreme correction. Contact lenses can provide better correction than glasses so this should not be the case, unless you glasses and contact lenses... --Marco 21:52, 24 December 2005 (UTC)
I think Srleffler was simply drawing attention to the fact that 68.96.170.70 never claimed to be myopic and hyperopic. In layman terms, it is indeed possible to possess the ability to see things near (i.e. nearsighted) and possess the ability to see far (i.e. farsighted) at the same time. I think it's fair to say that contact lenses are frequently an option for those who are myopic, hyperopic, astigmatic, and presbyopic. Given that there are many other factors that determine whether someone is a suitable candidate for contact lens wear, 68.96.170.70 should talk to his eye doctor. - AED 04:44, 28 December 2005 (UTC)
This person can be myopic and hyperopic. If the person suffers a small spherical refractive error but a slightly larger astigmatic error then the eye will display properties of both myopia and hyperopia making the subject both near sighted and far sighted —The preceding unsigned comment was added by 86.141.99.171 (talk • contribs) 13:54, September 12, 2006.

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.

Toric contact lenses are for correcting astigmatism. If you have astigmatism, you need them. If you don't have astigmatism, a toric lens won't do anything for you.--Srleffler 14:39, 31 August 2006 (UTC)

[edit] Corroboration?

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]

[edit] Image

Image:Astigmatism 2 eyes illus.png
Aspherical cornea (top, exagerated) and normal eye below.

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)


The image displays the Aberration_in_optical_systems#Curvature_of_the_field_of_the_image, not Astigmatism.
The former means, that there is a perfect focus, but the focal surface (Petzval surface) is not a plane.
The latter means (in the most basic sense), that the focus for rays through a slit aperture in one direction is unequal to the focus of of rays through a slit aperture in the orthogonal direction. I.e. the lens is partly cylindrical.
Pjacobi 21:40, 28 December 2005 (UTC)
From your images given, only the first tries to displays astigmatism, but it's not easy to see, as a serious drawing error has happened. The two sets of three rays each are in orthogonal planes (one up-down, one left-right). This is drawn perspecticely correct, except the points marking the lens crossings. They should look like:_
     x

x    x    x

     x
I tried the Google image search and find these examples most correct:
Pjacobi 21:53, 28 December 2005 (UTC)
I agree with removing these. JK's image is just not very good. It does not clearly illustrate the phenomenon. Even knowing what astigmatism is and how it works, I had a hard time seeing how his image represented it. In a scientific article, it's always better to have no image than to have a confusing or misleading one.--Srleffler 14:58, 30 December 2005 (UTC)
I agree with the statement that no image is better than a misleading one, and I think it's gonna be tough to find an image that clearly explains what happens in an astigmatic eye. But in the more 'scientific' part of the article, I think an image is needed, even if it's not gonna be understood by everyone reading this article (particularly if one comes just to have information on ophtalmics astigmatism). I think an image that, for example, clearly shows the difference between tangential and sagital would be a good idea. I also tend to agree that the article should be split in a "classical optics" article and an "ophtalmics" article. -- Palleas 11:35, 05 April 2006 (UTC)

I have nominated the image above for deletion. Discussion at IFD#April_11. --srleffler 11 April 2006

[edit] Article Improvement Drive

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)

[edit] Re: A simple eye test

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?

It is intended to be a crude version of a sunburst or clock-dial test, but isn't going to work for the vast majority of people who follow the instructions. I'm going to remove that section and add some information about those tests. -AED 17:07, 30 March 2006 (UTC)

[edit] Split

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)

[edit] Optics/Opthalmics use of astigmatism

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) .

In the context of clinical ophthalmology, "astigmatism" usually refers to the on-axis aberration. I'm not sure if the best way to address these contextual differences is to expand on them or to split the article. -AED 18:20, 30 March 2006 (UTC)

[edit] Sagittal / Tangential

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)

Yes, you're correct except that (I believe) the sagittal plane is the plane that is orthogonal to the tangential plane, which intersects the axis of symmetry at the entrance pupil and contains the field point. See the definitions of tangential and sagittal rays at ray (optics). The first paragraph of this article was expanded a week or two ago, and appears to have become incorrect. --Srleffler 21:48, 5 April 2006 (UTC)
I have removed the following paragraph from the article, and replaced it with the version from March 23 for now.--Srleffler 21:53, 5 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.

My bad, I forgot to mention that the sagittal plane contained the field point, and I sure believe it does. --Palleas 10:40, 10 April 2006(UTC)

[edit] JonesMI Comments on Tangential/Sagittal Issues

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)

There seems to be some disagreement still here. I think we all agree on the definition of the tangential plane, and on what a meridional ray/plane is. The issue is the sagittal plane. Palleas and I believe the (correct) sagittal plane is not a meridional plane at all, but a skew plane which is orthogonal to the tangential plane, and which does not contain the optic axis, but rather intersects it at the entrance pupil location. Note that the Zemax manual quote you posted agrees with this interpretation, if one assumes that the sagittal plane defined there includes the field point. The plane then is in general not a meridional plane. (If one doesn't assume the plane includes the field point, then the definition is insufficient, since there are an infinite number of planes orthogonal to the tangential plane, which intersect the axis at the entrance pupil location.) For additional support see the definition of sagittal rays at ray (optics), which I took from Greivenkamp's excellent little book (referenced there). The issue here is that there is more than one plane orthogonal to a given plane, so a plane orthogonal to the tangential plane need not be a meridional plane.
The MIL-HDBK-141 definition disagrees with the other definitions, but then it doesn't assert to be defining "sagittal plane" but rather "sagittal meridional plane". Perhaps this is just something different. Or perhaps this reference is itself in error. I don't have access to Smith's book so I can't easily review what he says. Could you post his definition here? Given the MIL-HDBK quote, it appears that there are two definitions of "sagittal" in use. If one is not a simple error, we probably have to figure out in what contexts each is used, and discuss both in the article.--Srleffler 03:50, 7 April 2006 (UTC)
By the way, we probably can't "resolve" the issue and give the world a unified definition. By policy, Wikipedia does not attempt to resolve differences of opinion, but rather to document them. If both definitions are actually in use, we need to explain them and clarify the difference. This is a better service to readers anyway, who may encounter the "unfavored" definition elsewhere.--Srleffler 04:05, 7 April 2006 (UTC)
Basically I was saying two things : first that the tangential plane is not always vertical, in the definitions I know, it is defined as containing the field point and the axis of symmetry. The second thing is, as Srleffler explained, that the sagital plane is not horizontal, as it is orthogonal to the tangential plane, and contains the field point while intersecting the axis of symmetry at the entrance pupil. --Palleas 11:01, 10 April 2006(UTC)

[edit] Good Old Warren Smith To The Rescue

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, fig. 6.22. Note that the sagittal plane does not contain the optic axis.
Hecht, fig. 6.22. Note that the sagittal plane does not contain the optic axis.
Hecht, fig. 6.23.
Hecht, fig. 6.23.

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)

Unfortunately, we can't use Hecht's pictures in the article, due to copyright restrictions. It's "fair use" to use a low-quality reproduction in the context of a discussion of Hecht's book. It's not "fair use" to use it to illustrate an article on the concept of astigmatism. Maybe we can get a suitable drawing made. I think part of what made this discussion difficult is that only a 3D picture is really satisfactory. One can't really understand the sagittal plane from a 2D perspective. Even given an exact geometric definition, one still by default envisions a meridional plane if not directly confronted with an image showing that it is not.
The Zemax plots you suggested sound like a good idea, and the content you have proposed sounds good (and goes beyond what I would have thought of).
You never need to feel "uninvited" on Wikipedia. Nobody "owns" a Wikipedia article, and everyone is welcome to contribute at any time, and in any way they please. In fact, Wikipedia has a guideline that encourages people to be bold in editing pages. Go ahead and edit! Be aware, that of course this applies to others too. Other people may well edit what you wrote, or even delete some of it. Don't take it personally. Work out compromises. This is the Wikipedia way. It works surprisingly well, on the whole.--Srleffler 18:26, 9 April 2006 (UTC)
By the way, before posting your own personal telescope designs, be sure to read Wikipedia:No original research. The gist of it is that the results of "original research" should only be put on Wikipedia if they have already been published elsewhere. Original drawings are fine, as long as the concept has been published before.--Srleffler 03:22, 11 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)

[edit] Split

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)

See above, and the new text. I'm trying to encompass both uses of the term in this article, in summary style, so this article will contain a summary or overview of ophthalmic astigmatism that particularly focuses on how it relates to the more general use of the term in optics. The new article Astigmatism (eye) would contain the technical details relevant only to those with greater interest in the medical condition. Let me know if Astigmatism (eye) is not the best name for this. I plan to fix I have fixed the links to this page as appropriate.--Srleffler 05:32, 10 April 2006 (UTC)

[edit] Diagrams

Might be good to put a selection right at the start of astigmatism, something like

  • Astigmatism (eye)
  • Astigmatism (optics)

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.

Image:1 to 1 telecentric 2L paraxial relay lens.gif

Discussion?--Mike 22:36, 11 April 2006 (UTC)

Another approach would be to focus on the object space sagittal plane. The rays can be shown throughout the system, but one need only show (and define) a single sagittal plane. Rays that propagate in the sagittal plane in object space are sagittal rays, and remain so even in image space. We don't necessarily need to show the image space "sagittal" plane, and it might be clearer not to. The definition presently in the article considers object space only. We do need to mention in the article that the sagittal plane is not a single plane for the whole system, but changes in each optical space.--Srleffler 05:22, 12 April 2006 (UTC)
I agree with Srleffler. Although I get your point, I think it's clearer to just show a single sagittal plane. I think Hecht's diagram is very good, and we should try to make up one that is of the same type. --Palleas 09:35, 12 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)

[edit] Causes/Origins

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)

[edit] Focusing a cross

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.

If your object is a cross, and it is oriented with its legs in the major directions of the astigmatism, then its two different directions of legs will focus as two different depth. The relevant property of the cross is its orthogonal linear features, such than blur along the linear feature will not be noticable in the image. Like if you used a plus sign or a letter T in the little text image example. Perhaps there's a better way to phrase it? Dicklyon 00:37, 5 January 2007 (UTC)
As to whether it is off-axis only or on-axis, that depends on the type of astigmatism. In the human eye, a cylindrical error will result in on-axis astigmatism. In most man-made optical systems, the lenses are spherical (no cylindrical error), so the astigmatism will only be off-axis. Dicklyon 00:40, 5 January 2007 (UTC)
See a not-so-good illustration of cross image here: [1]. Dicklyon 01:12, 5 January 2007 (UTC)

[edit] Laser Surgery & Astigmatism

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)

Not in this article, but possibly in Astigmatism (eye) or in Refractive surgery or one of the articles on specific laser surgery procedures. The change should probably be made by someone who knows more about it, though. There are a variety of "laser eye surgery" techniques, some of which are used to correct astigmatism.--Srleffler 12:45, 21 February 2007 (UTC)

[edit] Axis of opth astig

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)