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A few things:
-- Bob Mellish 17:08, 9 March 2006 (UTC)
-- Srleffler 17:53, 9 March 2006 (UTC)
-- Bob Mellish 01:35, 10 March 2006 (UTC)
Excellent diagrams, Bob! The dashed "virtual" extensions on the rays are good, and they pointed out to me that the definition of P and P' that I had written was unclear if not outright incorrect. -- Srleffler 02:18, 10 March 2006 (UTC)
Thanks Srleffler for integrating the section I wrote about the back focal plane into this article - and improving it. -- Richard Giuly 08:51, 28 July 2006 (UTC)
H for 'Haupt' would fit as German for 'principal' or main, as in main station = Hauptbahnhof -- 195.137.93.171 ( talk) 06:24, 7 March 2008 (UTC)
I've seen HH' called the 'Hiatus' - that could well be used in German, too - a lot of German is Latin-based. (I don't know if 'Hiatus' is really Latin - just sounds like it !) If the planes are ever transposed so that the the space is used twice, (negative gap) then Hauptplan would be a better word. (I don't know if that is possible - diverging lenses ? Concave lens made of air underwater ?) -- 195.137.93.171 ( talk) 02:42, 8 March 2008 (UTC)
I noticed what I think is an error in the diagram of "various lens shapes" -- in 8. the R1 label should I think be + not - I don't know how to go about correcting an image, sorry if this is the wrong place to mention it. akay ( talk) 13:55, 26 January 2021 (UTC)
"a ray that passes through one of them will also pass through the other"
I know what you mean , but the diagram shows that is not what you have written. The beam does not pass through either NP, and only an axial ray will pass through both NPs ! The ray is aimed at the NP, but is refracted to pass (through the midpoint) between the NPs. (I suspect 'midpoint' is only true for the simple symmetrical case, and is not a general rule.) The exit ray appears to have come from the other NP after being refracted by the last surface.
I think listing & linking to 'misconceptions' is misleading and unnecessary. If I understand it correctly, the distinctions are petty and misleading, in themselves. Isn't the 'entrance pupil' where the iris diaphragm appears to be, when viewed from the front of the lens ? And the nodal point is at the centre of that ?
If you are not convinced, consider the trivial case of the pinhole camera. All nodal points and planes co-incide at the hole. If you close the iris to a point, you have a 'virtual pinhole' where the point seems to be, when viewed from in front. I leave the maths to you ...
-- 195.137.93.171 ( talk) 03:01, 7 March 2008 (UTC)
I suggest : replace
The nodal points are widely misunderstood in photography, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the iris diaphragm of the lens is located there, and that this is the correct pivot point for panoramic photography, so as to avoid parallax error. These claims are all false, and generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. The correct pivot point for panoramic photography can be shown to be the centre of the system's entrance pupil.[1][2][3]
with
The correct pivot point for panoramic photography can be shown to be the first nodal point, at centre of the system's entrance pupil, where the diaphragm appears to be.
The rest seems redundant and unsupported, if not actually wrong ! If we are to expand Wikipedia to refute everything that is false, then it will be infinte. Let's put the 'true facts' in first.
-- 195.137.93.171 ( talk) 03:01, 7 March 2008 (UTC)
No-one out there really studied optics? Love Wikipedia !
I challenge anyone to come up with a definitive solution in a text-book or a peer-reviewed scientific journal. Until then I would suggest that the Wikipedia community should not pretend to have the answer to the controversy ! Delete ?
Google Scholar, anyone ?
Personally I think that this article is confusing, and that the front and rear principal planes (=entry & exit pupils) each contain a principal point called the front or rear nodal point. If you rotate a camera to take a panorama you rotate the camera about the front nodal point. If you rotate just the lens, you are better to use the rear nodal point, but some blurring of objects near the camera will inevitably result (unless the two nodes are the same point). You can see where the front plane/pupil is by simply looking at the diaphragm through the front of the lens. Ditto for the back. Due to refraction in the glass elements, the physical diaphragm is (probably) not really where the 'pupil' appears to be visually.
I think my opinion is as good as any I've seen ! It is based on the principle that the light you use to see the diaphragm ought to behave the same as the light you use to make an image with the lens. No ?
Good luck with the research ! If I get really bored I might even dig out my textbooks. -- 195.137.93.171 ( talk) 05:44, 7 March 2008 (UTC)
"The nodal point is not at the center of the entrance pupil." I can disprove that with a fairly simple thought experiment. It's not obvious, but not complicated either ! Look at the image.
1) The object of choosing the point about which to rotate the camera is that the entrance pupil should be stationary.
2) The angle between the ray illustrated and the axis is not special - any ray aimed at the front nodal point N must emerge as if from the rear one, parallel to the input direction. (See definition of nodal point !)
3) If the aperture is positioned to prevent vignetting when stopped down to a small hole, all rays aimed at the front nodal point must pass through the centre of the physical aperture. (Definition of
vignetting)
4) All those lines converging on one point must be radii of a circle, centred on the nodal point (just considering the 2D plane of the image, it is the same for a sphere !)
5) The
principle of reciprocity states that light going along any path A->B and light going from B->A will follow exactly the same path, but in opposite directions (Look for a source if you want, or just think about it! Hint: light takes the quickest path ...)
6) If all the rays aimed at N pass inwards through the hole at the centre of the aperture, any light emitted through the hole or reflected from its rim must pass outwards along the same set of paths. (follows from 5) )
7) Therefore an eye observing light emitted through the hole or reflected from its rim will see the hole as if it were at N, the nodal point
8) The entrance pupil is where the 'mirage' of the aperture appears to be, when viewed from the front.
9) The nodal point N is seen at the center of the entrance pupil.
10) Rotating the camera about the nodal point does not move the centre of the entrance pupil.
I wish I had time to do a 3D visual simulation of it, but if you take it one step at a time, you should understand.
Nothing there says (or feels like) 'paraxial approximation'.
Nothing relies on symmetry of the lens.
There may be second-order effects in extreme wide-angle lenses, which distort the entrance pupil so that the centre appears to be off-centre, but I think that means that the pupil will move when you rotate the camera, no matter which point is the centre of rotation. You would have to move it as well as rotate it in order to keep the aperture still ! Not a good lens for panoramas.
Of course, the diaphragm may be in the 'wrong' place - ie not in the place that gives zero vignetting ( point 3) above ). This is usually the case when the diaphragm is exposed - ie in front of the glass, as in 'convertible lenses' where you unscrew the front element and just use the back half ! In that case, yes, go with the hole, not the node ! —Preceding unsigned comment added by 195.137.93.171 ( talk) 12:50, 7 March 2008 (UTC)
Hope this helps explain, and defuses the controversy.
It's like arguing over whether a glass is half-full or half-empty - just different ways of describing the same thing !
You will probably find authoritative papers supporting each side, since there is no contradiction !
Please, please remove the section about misunderstandings - no-one is wrong. It just looks silly.
-- 195.137.93.171 ( talk) 11:35, 7 March 2008 (UTC)
If I remember correctly, putting the pupil at a point other than the principal plane also tends to invite (cautious weasel wording ...) barrel or pincushion distortion, as well as vignetting. Hence my use of the word 'wrong'. OK, my 'proof' only works for normal lenses, but are people likely to try making panoramas with others ?
A really great, but mind-bending, example is your favourite front- telecentric lens, where you put the aperture at the rear focal plane. Then the entrance pupil appears at infinity. So you rotate the lens about a point at infinity ? You move it in a plane perpendicular to the optical axis. Not your normal panorama. However, the absence of parallax is precisely the sort of reason that telecentric lenses are used in optical projectors for measuring 3D objects. (The barrel/pincushion distortion could be tricky - or does it disappear again at that extreme ?) It does begin to make sense eventually.
I'm not sure if I really want to think about the nodal points of a telecentric lens. I suspect one (or both) of them may not exist (or be simultaneously at +/- infinity, at least)?
Considering the absolute extremes of optical design may not help the novice or lay-reader, but will test the generality of statements for those experts seeking absolute truth and precision. (The exception proves the rule ?) How do we satisfy both categories of reader here ? If extreme examples are to be used, I think we should at least warn users that they are extreme. Maybe experts will read this discussion page, so we could keep it really simple up-front in the article ?
-- 195.137.93.171 ( talk) 21:20, 7 March 2008 (UTC)
I deleted this section.
An aperture at the rear focal plane can be used to filter rays by angle, since:
- It only allows rays to pass that are emitted at an angle (relative to the optical axis) that is sufficiently small. (An infinitely small aperture would only allow rays that are emitted along the optical axis to pass.)
- No matter where on the object the ray comes from, the ray will pass through the aperture as long as the angle at which it is emitted from the object is small enough.
Note that the aperture must be centered on the optical axis for this to work as indicated.
Angle filtering is important for DSLR cameras having CCD sensors. These collect light in "photon wells"—the floor of these wells is the actual light gathering area for each pixel. [2] Light rays with small angles with the optical axis reach the floor of the photon well, while those with large angles strike the sides of the wells and may not reach the sensitive area. This produces pixel vignetting.
1) It seemed out-of-place - not really central to "Cardinal point" - the original theme of this article.
2) The image shows light emitted axially from the object, but the text discusses light hitting a sensor perpendicularly, instead
3) I suspect "photon wells" are not really shaped like
water wells, but are
Quantum wells - a concept in
quantum physics. A bucket you can collect photons in, if you like, but don't picture a real bucket with conical sides and a handle - it's just a metaphor !
4) all materials reflect more if light hits them at a shallow angle than if the light hits at right-angles - that could explain the drive for axial light.
5) maybe that image and explanation belong in an article on
telecentric lenses - it's very specialised ?
-- 195.137.93.171 ( talk) 03:54, 7 March 2008 (UTC)
I deleted this image
1) Too small to see
2) It is a weird
telecentric lens - a very special case that doesn't behave like a normal lens.
3) the only parallel rays come from different points on the object !
4) it's just a co-incidence that the parallel rays depicted cross at the BFP
4a)parallel rays from points that are closer together will cross behind the BFP
4b)parallel rays from points that further apart will cross in front of the BFP
You want an object at infinity, with the image formed in the BFP. This isn't !
Sorry - again, the diagram may be of some use on the telecentric lens page ?
-- 195.137.93.171 ( talk) 04:09, 7 March 2008 (UTC)
Did I pass? Your turn. Why did the f:64 school of photography not use 35mm cameras ? And why can a very small hawk not see better than a human ? And how small should a pinhole be ? -- 195.137.93.171 ( talk) 06:46, 7 March 2008 (UTC)
I note that you seem to be equating 'focal plane' and 'aperture' in your Fourier 'explanation' - another symptom of a 'telecentric lens' !
Maybe if I put the two diagrams side-by-side you may appreciate why I thought the first one was just as telecentric as the second?
The rays are identical !
You have chosen to plot 'telecentric rays'.
I agree that it could be a simple lens.
A simple lens can be a telecentric lens.
It becomes telecentric when you put the aperture in the focal plane !
Any lens can be a telecentric lens.(citation
[3]?)
I think the term 'telecentric lens' is very misleading. Telecentricity is more a function of the aperture than the glass. Perhaps we should rather speak of a 'telecentric aperture'? 'Telecentric optical system' would be best.
Maybe it's not a weird lens, but the focal plane seems a weird place to put the aperture.
Does this clarify ?
I still think the diagrams are misleading and confusing, due to the telecentricity.
By the way, please don't delete the images - the
telecentric page has a 'diagram request' on it, and I've linked these in the talk page.
Oh - just re-read that page - why do you deny that either lens is telecentric ?
I thought the whole point of the second image was demonstrating telecentricity ?
That page uses the definition :
Telecentric: The chief rays, that is the rays through the center of the entrance or exit pupil, are all parallel to the optical axis, on one or both sides of the lens, no matter what part of the image space or object space they go through.
Isn't that true in the diagrams - the middle one of the three rays from each of the two object points ? Am I missing something ? I don't think I'm being dense - this really isn't clear.
Each different point on the object 'sees' the entrance pupil in a different place, immediately below it, but 'located' infinitely far away.
Not meaning to be personal, but would I be wrong in deducing that you are primarily a microscopist ? That would explain the predilection for telecentricity. WP:NPOV ? WP:UNDUE ? Am I doing it right ?
For my side, I declare working in planar gradient-index optics, optical waveguide, fibre-optics, integrated optics modulators, laser diodes. Then I was sidelined into QA/QC - microscopy, photography, optical metrology etc. Then I got into IT - 7 years as a web-developer, now unemployed. I'm now tickling some dormant grey cells and practicing typing English rather than script languages. (Feel free to delete the last 2 paras - some of this should probably be moved to our personal talk pages when resolved !)
It's been a good meeting of minds. Sorry if I overdid the 'Be bold' Wikipedia philosophy. I'm not really a vandal. Still - it has to beat months or years of inactivity.
-- 195.137.93.171 ( talk) 23:38, 7 March 2008 (UTC)
Would it appear petulant to suggest that vacuum would be a better example ? -- 195.137.93.171 ( talk) 06:31, 7 March 2008 (UTC)
I updated the formerly-blue focal-plane images with SVGs. Now that I can see them clearly, I still don't really like them. As was discussed above, they are telecentric lenses, which is an unusual case. It was only in the last few days that I started to realize that an optical microscope is essentially telecentric, which is why microscopists talk of the back focal plane as the location for the apertue, whereas photographers think of the back focal plane as almost equivalent with the image plane. I'm not sure if this page or photographic lens or optical microscope should make this distinction; perhaps they all should. Just to clarify, am I technically correct about the back focal plane? Unless someone objects, I may start making these clarifications. —Ben FrantzDale ( talk) 01:19, 20 May 2008 (UTC)
It is requested that an optical diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
We could do with a diagram for surface vertex, obvious as it may be. —Ben FrantzDale ( talk) 20:55, 26 May 2008 (UTC)
I'll try again. Sorry for the delay - I let life get in the way of wikipeding for a bit !
The more I think about it, the more I am convinced this section is just plain wrong.
The nodal points are widely misunderstood in photography, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the iris diaphragm of the lens is located there, and that this is the correct pivot point for panoramic photography, so as to avoid parallax error. These claims are all false, and generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. The correct pivot point for panoramic photography can be shown to be the centre of the system's entrance pupil.
For practical lenses, designed to minimise vignetting and distortion, it is not necessary to make the distinction - the front nodal point is the centre of the system's entrance pupil. That is why experiments can show either point to be correct. People that show 'entrance pupil' is correct don't show that 'nodal point' is wrong.
A simple thought experiment will help clear up the confusion. We need to separate the nodal point and entrance pupil, and think about what happens.
Consider a lens which is specially constructed so that the aperture stop has two degrees-of-freedom. Not only can you vary its radius, but also its physical position by moving it parallel to the optical axis. This lets you investigate the more general case of unusual lenses, where the front nodal point is not at the centre of the system's entrance pupil.
Before you move the aperture away from its normal position, you rotate the camera about the agreed common point (front nodal point = centre of the entrance pupil). Why ? Because that is the point at which the lens focuses all light from the object point to the same constant stationary image point on the film even when the camera is rotated. There is no 'parallax'. Near objects do not move relative to distant objects. The camera's 'point-of-view' does not move. The image on film is not blurred by motion.
Note that it is not the aperture stop that is focussing the light, it is the refractive (glass) part of the lens. The front nodal point is a property of the glass, not of the aperture. The aperture only determines whether a ray passes through the lens to the film or not - not where it lands on the film, nor where it intersects other rays.
Now move the aperture along the optical axis. The entrance pupil is where the aperture appears to be, so it has to move along the optical axis, too. The glass hasn't moved, so the front nodal point has not moved, so it is no longer at the centre of the entrance pupil.
OK Now what happens when the camera is rotated about the same point as before (the front nodal point, no longer at the centre of the entrance pupil)? Nothing that contributes to the mapping of points in image space to points on film has changed. The glass hasn't been moved so it must focus the light exactly as it did before - to the same point on the film.
Therefore moving the aperture stop axially does not affect the motion, or lack of motion, of the image on the film. The aperture doesn't affect the focussing (bending of rays). It plays no part in the mapping of points in object space to points in image space.
If you follow the Wikipedia article quote above and change the panoramic-pivot-point to follow the motion of the entrance pupil instead, what happens? If you had rotated about that new point before moving the aperture, then the image would have moved across the film. The movement is determined by the focussing properties of the lens - by the refraction - by the glass - not by the aperture. Therefore the image will be blurred now.
QED ?
I do not find responses of the form "That is meaningless" or "You are confused" to be useful. They may lead me to question whether you understand what I say, or what is happening physically. I believe that the above is perfectly clear and meaningful.
-- 195.137.93.171 ( talk) 01:23, 3 July 2008 (UTC)
in simple terms [...] the aperture determines the perspective of an image by selecting the light rays that form it. Therefore the center of perspective and the no-parallax point are located at the apparent position of the aperture, called the “entrance pupil”. Contrary to intuition, this point can be moved by modifying just the aperture, while leaving all refracting lens elements and the sensor in the same place.
In general, when we impose a small aperture, the in-focus image stays the same, except for getting dimmer as we make the aperture smaller. The out-of-focus image also gets dimmer, by the same amount on average, but this is accomplished by leaving intact the portion of the blur that corresponds to having the center of perspective at the aperture, while eliminating all other portions of the blur.
Is there a good reason why the object point, image point, object plane, image plane, object distance and image distance are not defined in this article ? If not here, where do they belong ? Redbobblehat ( talk) 23:51, 8 August 2009 (UTC)
1. By ray-tracing : (I quote Malacara pp.25-26 [9] verbatim because my grasp is not sufficient to paraphrase) "By tracing two paraxial rays, the six cardinal points for a lens may be found... Figure 19 shows the six cardinal points of a lens when the object index of refraction is no and the image side index of refraction is nk. The points F1, F2, P1, P2 are located by tracing a paraxial ray parallel to the optical axis at a height of unity. A second ray is traced parallel to the optical axis but from right to left. The incoming rays focus at F1 and F2 and appear to refract at the planes P1 and P2. This is why they are called principal planes. These planes are also planes of unit magnification. The nodal points are located by tracing a ray back from C parallel to the ray direction F1A. If this later ray is extended back towards the F2 plane, it intersects the optical axis at N1. This construction to locate N1 and N2 shows that a ray which enters the lens headed towards N1 emerges on the image side from N2 making the same angle with the optical axis."
2. Experimentally : "Figure 14-8 illustrates a procedure by which the focal points and principal points for a thick lens may be experimentally determined." (Concepts of Classical Optics, John Strong, 2004, pp.311-312 [10].) Redbobblehat ( talk) 12:12, 10 August 2009 (UTC)
In the subsection Cardinal point (optics)#Nodal points it said that "If the medium on both sides of the optical system is the same (e.g., air), then the front and rear nodal points coincide with the front and rear principal planes, respectively." I changed "planes" into "points" here, as having points coincide with planes sounds a bit like sorcery...
I did not change another statement in the same sentence, as it is not wrong but only incomplete. Fot the nodal points to coincide with the corresponding principal points, it is not necessary that the medium on either side is the same, but the refractive index. If the media are different but happen to have the same refractive index, the nodal points will also coincide with the corresponding principal points.
-- HHahn (Talk) 12:57, 15 January 2010 (UTC)
I restored some material that was deleted by another editor today, trying to merge his new material into the old. His edits added some good explanation, but deleted too much valuable information and left the article with a poor lead section. A good lead always starts by explaining what the subject of the article is. You can't start an encyclopedia article with a qualification like "Strictly speaking the concept of cardinal points applies only to..."
There may be differences in perspective at work here. For nearly all real optical systems, the cardinal points allow useful approximate modelling of the true performance of the system. Modern optical design is done primarily by ray tracing and other computational techniques, using cardinal points and other paraxial properties only as a rough first approximation to the system's performance. I applaud the effort to introduce some information on the important concept of transformations between optical spaces in an ideal system, however. Hopefully this can be expanded further.
I'm not comfortable with including peripheral definitions such as those for "optical space", "optical axis", and "Rotationally symmetric optical system" as subsections, especially not so high in the article. Generally, material like that should be in other articles that we can link to. I removed optical axis since there is already an article on that. For the others I'm not sure yet whether the definitions should be moved into new articles, or whether the material can be dealt with some other way. As it is, it breaks the flow of the article too much and pushes the definitions of the cardinal points themselves down where the reader is less likely to see them.-- Srleffler ( talk) 05:06, 19 August 2010 (UTC)
TedEyeMD ( talk) 21:48, 19 August 2010 (UTC)
I took a look at Greivenkamp's book, which is a reference I have used in the past when writing material for this article. He does refer to "cardinal points and planes", on page 6. He does not refer to vertices as cardinal points, and I am fine with not referring to them as such in the article.
Information on practical application of the cardinal points in the analysis of real optical systems is at least as important as explanation of their theoretical importance to idealized systems. We need both in the article. It may well be best to explain the theoretical/idealized case first.
Your point about the incompleteness of the section on ideal optical systems is well taken. I actually fell asleep before finishing this sorry I will fix it today. TedEyeMD ( talk) 13:19, 20 August 2010 (UTC)
As far as whether or not only IRSFOS systems have cardinal points or all rotationally symmetric focal optical systems (RSFOS) have cardinal points is a question of viewpoint. To me, only ideal systems can have cardinal points. When taken as a whole non ideal systems do not have cardinal points, but certainly the paraxial regions of such systems do have cardinal points. If you want to say the "system" has cardinal points becasue its paraxial region has cardinal points well I suppose you could say that. However, I have found that many people are unclear on the difference between the entire system and the paraxial region. It is perhaps a fine distinction but to me some degree of clarity is added when one distinguishes between the system as a whole and the system's paraxial region. I am basically following the approach taken by Welford in Aberrations of Optical Systems. First, Welford establishs the properties of ideal optical systems even though he states a priori that such systems do not exist in practice (except for a plane mirror). Then he shows that this is useful because real optical systems do behave ideally in the paraxial region which can have a significant size in some cases.
I agree that the application of cardinal points to optical design is an important feature, but first I think we should be clear on what the cardinal points are before going on to applications. TedEyeMD ( talk) 13:19, 20 August 2010 (UTC)
I expanded the introduction and renamed it to what I thought was a more appropriate and informative title for the paragraph. I expanded the discussion on optical spaces. I added a section explaining the difference between afocal systems that even if ideal and rotationally symmetric lack cardinal pionts and focal systems which have cardinal points. This also seemed a good place to introduce the notion of focal points. TedEyeMD ( talk) 19:17, 21 August 2010 (UTC)
Hi I noticed some of your changes today. You added some links to other wikipedia pages which is helpful but I have a few concerns. For instance the link to rotational symmetry goes to a page that describes n-fold rotational symmetry. The problem is that the type of rotational symmetry I am referring to here is not n-fold so I think the link may be more confusing than helpful. Similarly the link to optical system goes to a general page on optics and the reader has to go along way to find optical system. The link to ray defines ray in terms of physical optics and this is counter to a decades long trend to make geometrical optics as free of physical optics as possible. The point about usage of conjugate is well taken.
When you talk about writing for a high school audience you raise a very important point. At what level should the article be directed to? Certainly I have found many Wikipedia pages that are well above high school even undergraduate level. Could you provide some link that would provide guidance on this point?
Also, I would like to add some illustrations could you provide some guidance on how to add drawings and illustrations? TedEyeMD ( talk) 01:19, 24 August 2010 (UTC)
By the way thanks so much for helping with the reference to Welford's book. Also, I don't think the wikipedia page on the paraxial approximation is very good. The paraxial approximations are really three specific approximations and the wiki page simply talks about the small angle approximation. So, again I have removed the link to that page since I am going to go into that subject in some detail on this page. So, I took all references to paraxial out and will discuss paraxial rays later in detail. TedEyeMD ( talk) 01:37, 24 August 2010 (UTC)
Well yes and no. Sure 'ideally we should link to other articles, and certainly such links do keep articles from becoming bloated. On the other hand when the linked to article is not just uninformative, but has a high potential to mislead then I think a link should be removed otherwise the reader may not simply ignore the linked to article, the reader may be confused by the linked to article. While the ideal solution is to edit the linked to article may not be practical because of time constraints. So I think there is something to be said for omitting links in certain cases.
Could you provide some guidance on how to generate and insert diagrams? Thanks TedEyeMD ( talk) 18:55, 24 August 2010 (UTC)
I noticed that a couple of times srleffler has restored something to the effect of exact calculation requires the application of Snell's law and the law of reflection each time the ray reaches an interface between two media. I have several problems with this sentence. First, it implies that both the laws of reflection and refraction are used every interface. In fact at any one interface only one or the other is used not both. Second, the law of reflection is just a special case of Snell's law so you technically don't need to mention it. Third, in addition to Snell's law and the law of relection there is the law of rectilinear propagation that is just as important in exact ray ttracing. Forth, there is no need to be so detailed here. This section deals with the concept of treating an optical system as a physical device for achieveing a mathematical transformation. the details of ray tracing need not be mentioned here. so I deleted it. TedEyeMD ( talk) 01:09, 25 August 2010 (UTC)
The fact that one is a special case of the other does not preclude mentioning both, however the fact that it has no place in an introductory level article on cardinal points does preclude mentioning. If you want to trace multiple rays then for each ray going into the optical system multiple rays come out. None of your illustrations show this and it would really confuse introductory level readers (the high school students you referred to earlier). Moreover it would take things to a higher level of approximation and as you note we are dealing with the lowest level of approximation so multiple reflections do not belong here. I find it very difficult to justify a discussion of fresnel's laws and multiple reflections in this article. I am aware of no textbook that introduces multiple reflections at this stage except perhaps to mention that they should be ignored at this point. 75.33.34.83 ( talk) 00:08, 27 August 2010 (UTC)
Do not read too much into my wording "optical system as a physical device for achieveing a mathematical transformation" I debated over how to word it and considered doing it the other way around, but I chose this wording for pedagogical reasons. By wording it this way my intent was to surprise the reader since we usually think as you do that the physics is primary and the math secondary. Pedagogically by wording it the other way around I wanted to catch the reader off guard and make them really think about this. Our differences are due not to a difference in technical background but rather to a difference in pedagogy. I too am a physicist and an optical engineer that has taught optics at the post graduate and post doctoral level. As an engineer I am well aware of the approximations made in applying paraxial optics to real world optical systems. However, as an educator I am also quite aware that there is a great deal of confusion between first order optics, paraxial optics, and Gaussian optics. The three are clearly related but in fact different. Worse, often the literature confuses the three using them synonymously which is inappropriate. It was my intention to do a complete rewrite of this article. I am doing that rewrite bit by bit for a few reasons. First, when I started editing this article there was some serious misinformation such as including lens vertices as cardinal points. Also, there was a lot of extraneous information about stops and pupils that was very interesting but not about cardinal points. So, I thought some changes were immediately necessary. Second, it will take some time to do a full rewrite so I was trying to do it piecemeal.
I realized immediately from all the discussion of stops and pupils and the inclusion of vertices into the cardinal ponts that you are definitely interested in the practical applications and I think that's great. However, there is no need to sacrifice rigor for practicallity. My plan was to start with theoretical rigor. Which is why I started by using the word ideal. If you begin with only ideal optial systems have cardinal points then no approximation is necessary. I planned later to introduce approximations. I would explain each approximation as it was introduced and why. The reader would finish with a very clear understanding not only that the cardinal points only approximate the behavior of real world optical systems they would also know precisely what the approximations were and what the implications of those approximations are. My approach is first let's explain exactly what the cardinal points are without approximation which means with ideal systems then show how by using approximations we can apply the concept to real optical systems. However, I would put the approximation lower in the article. I certainly realize that you want people to know that the cardinal points approximate the behavior of real systems. I have absolutely no intention of "glossing over" that point. Indeed, I want the reader not only to know that the cardinal points approximate the behavior of real world systems but also to know why the cardinal points approximate the behavior of real world systems. However, you keep redoing the changes I make so I have to re-edit and don't have time to introduce new material. Please be assured I will bring in approximations quite explicitly. Indeed to do so I would really appreciate it if you could help me find out how to introduce my own illustrations that would help a lot thanks. 75.33.34.83 ( talk) 00:08, 27 August 2010 (UTC)
A specific comment: In this edit you moved the list of the three cardinal points back down to where it was (and made some other changes in the wording). This is a problem, because as the intro stands you use the specific cardinal points in discussion before you have introduced them to the reader. You have to say what the cardinal points are before you say something like "only four points are necessary: the focal points and either the principal or nodal points". It just doesn't flow right the way it is.-- Srleffler ( talk) 03:31, 28 August 2010 (UTC)
I moved the more mathematical material discussed above lower in the article, because it is less approachable than some of the other material, and because it was left incomplete by the editor who added it. It didn't actually get around to explaining how the cardinal points are related to the mapping between optical spaces.-- Srleffler ( talk) 23:28, 7 September 2013 (UTC)
The recommended file format for drawings and diagrams on Wikipedia is SVG. Inkscape is a free editor for these files. For more info, see How to draw a diagram with Inkscape. You upload the image at Wikipedia:Upload. Be sure to read and follow the prompts. When uploading images, you have to specify the license under which they are released. The upload page's prompts try to help you with this. For an image you drew yourself common choices would include the CCbySA license, or just releasing the image to the public domain.-- Srleffler ( talk) 06:25, 28 August 2010 (UTC)
There are numerous names for this addition to the gaussian model, IMO "Toepler points" is the most distinctive :
AFAIK (from citation) they originate in Toepler, A. Bemerkungen ueber die Anzahl der Fundamentalpuncte eines beliebigen Systems von centrirten brechenden Kugelflaechen: Pogg. Ann., cxlii. (1871), pp.232-251.
The main use of toepler points (AFAIK) is to actually measure the focal length of a lens, using the conjugate distances at unit magnification. This method is implicit in Newton's conjugate equation, but for a full description of the method (and his contraption "the focometer") see Thompson, S.P. 1912 The Trend of Geometrical Optics : "Proceedings of the Optical Convention 1912" p.297-307. -- Redbobblehat ( talk) 01:11, 11 February 2011 (UTC)
(BTW: Gauss, C.F. Dioptrische Untersuchungem Goettingen, 1841. The "nodal points" were proposed/added by Listing, J.B. Beitrag zur physiologischen Optik Goettinger Studien, 1845 ( in german). Apparently the term "cardinal points" was coined by Felice Casorati (mathematician) and Galileo Ferraris - but I haven't found chapter and verse for that one.) -- Redbobblehat ( talk) 01:11, 11 February 2011 (UTC)
Section: Principal planes and points
This section and the accompanying diagram “Various lens shapes...” do not explain the concept clearly. The diagram shows a random collection of arrows impinging on lenses from all directions, signifying nothing. I respectfully suggest that this section be rewritten with a more meaningful diagram. -- Prof. Bleent ( talk) 14:41, 24 April 2015 (UTC)
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A few things:
-- Bob Mellish 17:08, 9 March 2006 (UTC)
-- Srleffler 17:53, 9 March 2006 (UTC)
-- Bob Mellish 01:35, 10 March 2006 (UTC)
Excellent diagrams, Bob! The dashed "virtual" extensions on the rays are good, and they pointed out to me that the definition of P and P' that I had written was unclear if not outright incorrect. -- Srleffler 02:18, 10 March 2006 (UTC)
Thanks Srleffler for integrating the section I wrote about the back focal plane into this article - and improving it. -- Richard Giuly 08:51, 28 July 2006 (UTC)
H for 'Haupt' would fit as German for 'principal' or main, as in main station = Hauptbahnhof -- 195.137.93.171 ( talk) 06:24, 7 March 2008 (UTC)
I've seen HH' called the 'Hiatus' - that could well be used in German, too - a lot of German is Latin-based. (I don't know if 'Hiatus' is really Latin - just sounds like it !) If the planes are ever transposed so that the the space is used twice, (negative gap) then Hauptplan would be a better word. (I don't know if that is possible - diverging lenses ? Concave lens made of air underwater ?) -- 195.137.93.171 ( talk) 02:42, 8 March 2008 (UTC)
I noticed what I think is an error in the diagram of "various lens shapes" -- in 8. the R1 label should I think be + not - I don't know how to go about correcting an image, sorry if this is the wrong place to mention it. akay ( talk) 13:55, 26 January 2021 (UTC)
"a ray that passes through one of them will also pass through the other"
I know what you mean , but the diagram shows that is not what you have written. The beam does not pass through either NP, and only an axial ray will pass through both NPs ! The ray is aimed at the NP, but is refracted to pass (through the midpoint) between the NPs. (I suspect 'midpoint' is only true for the simple symmetrical case, and is not a general rule.) The exit ray appears to have come from the other NP after being refracted by the last surface.
I think listing & linking to 'misconceptions' is misleading and unnecessary. If I understand it correctly, the distinctions are petty and misleading, in themselves. Isn't the 'entrance pupil' where the iris diaphragm appears to be, when viewed from the front of the lens ? And the nodal point is at the centre of that ?
If you are not convinced, consider the trivial case of the pinhole camera. All nodal points and planes co-incide at the hole. If you close the iris to a point, you have a 'virtual pinhole' where the point seems to be, when viewed from in front. I leave the maths to you ...
-- 195.137.93.171 ( talk) 03:01, 7 March 2008 (UTC)
I suggest : replace
The nodal points are widely misunderstood in photography, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the iris diaphragm of the lens is located there, and that this is the correct pivot point for panoramic photography, so as to avoid parallax error. These claims are all false, and generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. The correct pivot point for panoramic photography can be shown to be the centre of the system's entrance pupil.[1][2][3]
with
The correct pivot point for panoramic photography can be shown to be the first nodal point, at centre of the system's entrance pupil, where the diaphragm appears to be.
The rest seems redundant and unsupported, if not actually wrong ! If we are to expand Wikipedia to refute everything that is false, then it will be infinte. Let's put the 'true facts' in first.
-- 195.137.93.171 ( talk) 03:01, 7 March 2008 (UTC)
No-one out there really studied optics? Love Wikipedia !
I challenge anyone to come up with a definitive solution in a text-book or a peer-reviewed scientific journal. Until then I would suggest that the Wikipedia community should not pretend to have the answer to the controversy ! Delete ?
Google Scholar, anyone ?
Personally I think that this article is confusing, and that the front and rear principal planes (=entry & exit pupils) each contain a principal point called the front or rear nodal point. If you rotate a camera to take a panorama you rotate the camera about the front nodal point. If you rotate just the lens, you are better to use the rear nodal point, but some blurring of objects near the camera will inevitably result (unless the two nodes are the same point). You can see where the front plane/pupil is by simply looking at the diaphragm through the front of the lens. Ditto for the back. Due to refraction in the glass elements, the physical diaphragm is (probably) not really where the 'pupil' appears to be visually.
I think my opinion is as good as any I've seen ! It is based on the principle that the light you use to see the diaphragm ought to behave the same as the light you use to make an image with the lens. No ?
Good luck with the research ! If I get really bored I might even dig out my textbooks. -- 195.137.93.171 ( talk) 05:44, 7 March 2008 (UTC)
"The nodal point is not at the center of the entrance pupil." I can disprove that with a fairly simple thought experiment. It's not obvious, but not complicated either ! Look at the image.
1) The object of choosing the point about which to rotate the camera is that the entrance pupil should be stationary.
2) The angle between the ray illustrated and the axis is not special - any ray aimed at the front nodal point N must emerge as if from the rear one, parallel to the input direction. (See definition of nodal point !)
3) If the aperture is positioned to prevent vignetting when stopped down to a small hole, all rays aimed at the front nodal point must pass through the centre of the physical aperture. (Definition of
vignetting)
4) All those lines converging on one point must be radii of a circle, centred on the nodal point (just considering the 2D plane of the image, it is the same for a sphere !)
5) The
principle of reciprocity states that light going along any path A->B and light going from B->A will follow exactly the same path, but in opposite directions (Look for a source if you want, or just think about it! Hint: light takes the quickest path ...)
6) If all the rays aimed at N pass inwards through the hole at the centre of the aperture, any light emitted through the hole or reflected from its rim must pass outwards along the same set of paths. (follows from 5) )
7) Therefore an eye observing light emitted through the hole or reflected from its rim will see the hole as if it were at N, the nodal point
8) The entrance pupil is where the 'mirage' of the aperture appears to be, when viewed from the front.
9) The nodal point N is seen at the center of the entrance pupil.
10) Rotating the camera about the nodal point does not move the centre of the entrance pupil.
I wish I had time to do a 3D visual simulation of it, but if you take it one step at a time, you should understand.
Nothing there says (or feels like) 'paraxial approximation'.
Nothing relies on symmetry of the lens.
There may be second-order effects in extreme wide-angle lenses, which distort the entrance pupil so that the centre appears to be off-centre, but I think that means that the pupil will move when you rotate the camera, no matter which point is the centre of rotation. You would have to move it as well as rotate it in order to keep the aperture still ! Not a good lens for panoramas.
Of course, the diaphragm may be in the 'wrong' place - ie not in the place that gives zero vignetting ( point 3) above ). This is usually the case when the diaphragm is exposed - ie in front of the glass, as in 'convertible lenses' where you unscrew the front element and just use the back half ! In that case, yes, go with the hole, not the node ! —Preceding unsigned comment added by 195.137.93.171 ( talk) 12:50, 7 March 2008 (UTC)
Hope this helps explain, and defuses the controversy.
It's like arguing over whether a glass is half-full or half-empty - just different ways of describing the same thing !
You will probably find authoritative papers supporting each side, since there is no contradiction !
Please, please remove the section about misunderstandings - no-one is wrong. It just looks silly.
-- 195.137.93.171 ( talk) 11:35, 7 March 2008 (UTC)
If I remember correctly, putting the pupil at a point other than the principal plane also tends to invite (cautious weasel wording ...) barrel or pincushion distortion, as well as vignetting. Hence my use of the word 'wrong'. OK, my 'proof' only works for normal lenses, but are people likely to try making panoramas with others ?
A really great, but mind-bending, example is your favourite front- telecentric lens, where you put the aperture at the rear focal plane. Then the entrance pupil appears at infinity. So you rotate the lens about a point at infinity ? You move it in a plane perpendicular to the optical axis. Not your normal panorama. However, the absence of parallax is precisely the sort of reason that telecentric lenses are used in optical projectors for measuring 3D objects. (The barrel/pincushion distortion could be tricky - or does it disappear again at that extreme ?) It does begin to make sense eventually.
I'm not sure if I really want to think about the nodal points of a telecentric lens. I suspect one (or both) of them may not exist (or be simultaneously at +/- infinity, at least)?
Considering the absolute extremes of optical design may not help the novice or lay-reader, but will test the generality of statements for those experts seeking absolute truth and precision. (The exception proves the rule ?) How do we satisfy both categories of reader here ? If extreme examples are to be used, I think we should at least warn users that they are extreme. Maybe experts will read this discussion page, so we could keep it really simple up-front in the article ?
-- 195.137.93.171 ( talk) 21:20, 7 March 2008 (UTC)
I deleted this section.
An aperture at the rear focal plane can be used to filter rays by angle, since:
- It only allows rays to pass that are emitted at an angle (relative to the optical axis) that is sufficiently small. (An infinitely small aperture would only allow rays that are emitted along the optical axis to pass.)
- No matter where on the object the ray comes from, the ray will pass through the aperture as long as the angle at which it is emitted from the object is small enough.
Note that the aperture must be centered on the optical axis for this to work as indicated.
Angle filtering is important for DSLR cameras having CCD sensors. These collect light in "photon wells"—the floor of these wells is the actual light gathering area for each pixel. [2] Light rays with small angles with the optical axis reach the floor of the photon well, while those with large angles strike the sides of the wells and may not reach the sensitive area. This produces pixel vignetting.
1) It seemed out-of-place - not really central to "Cardinal point" - the original theme of this article.
2) The image shows light emitted axially from the object, but the text discusses light hitting a sensor perpendicularly, instead
3) I suspect "photon wells" are not really shaped like
water wells, but are
Quantum wells - a concept in
quantum physics. A bucket you can collect photons in, if you like, but don't picture a real bucket with conical sides and a handle - it's just a metaphor !
4) all materials reflect more if light hits them at a shallow angle than if the light hits at right-angles - that could explain the drive for axial light.
5) maybe that image and explanation belong in an article on
telecentric lenses - it's very specialised ?
-- 195.137.93.171 ( talk) 03:54, 7 March 2008 (UTC)
I deleted this image
1) Too small to see
2) It is a weird
telecentric lens - a very special case that doesn't behave like a normal lens.
3) the only parallel rays come from different points on the object !
4) it's just a co-incidence that the parallel rays depicted cross at the BFP
4a)parallel rays from points that are closer together will cross behind the BFP
4b)parallel rays from points that further apart will cross in front of the BFP
You want an object at infinity, with the image formed in the BFP. This isn't !
Sorry - again, the diagram may be of some use on the telecentric lens page ?
-- 195.137.93.171 ( talk) 04:09, 7 March 2008 (UTC)
Did I pass? Your turn. Why did the f:64 school of photography not use 35mm cameras ? And why can a very small hawk not see better than a human ? And how small should a pinhole be ? -- 195.137.93.171 ( talk) 06:46, 7 March 2008 (UTC)
I note that you seem to be equating 'focal plane' and 'aperture' in your Fourier 'explanation' - another symptom of a 'telecentric lens' !
Maybe if I put the two diagrams side-by-side you may appreciate why I thought the first one was just as telecentric as the second?
The rays are identical !
You have chosen to plot 'telecentric rays'.
I agree that it could be a simple lens.
A simple lens can be a telecentric lens.
It becomes telecentric when you put the aperture in the focal plane !
Any lens can be a telecentric lens.(citation
[3]?)
I think the term 'telecentric lens' is very misleading. Telecentricity is more a function of the aperture than the glass. Perhaps we should rather speak of a 'telecentric aperture'? 'Telecentric optical system' would be best.
Maybe it's not a weird lens, but the focal plane seems a weird place to put the aperture.
Does this clarify ?
I still think the diagrams are misleading and confusing, due to the telecentricity.
By the way, please don't delete the images - the
telecentric page has a 'diagram request' on it, and I've linked these in the talk page.
Oh - just re-read that page - why do you deny that either lens is telecentric ?
I thought the whole point of the second image was demonstrating telecentricity ?
That page uses the definition :
Telecentric: The chief rays, that is the rays through the center of the entrance or exit pupil, are all parallel to the optical axis, on one or both sides of the lens, no matter what part of the image space or object space they go through.
Isn't that true in the diagrams - the middle one of the three rays from each of the two object points ? Am I missing something ? I don't think I'm being dense - this really isn't clear.
Each different point on the object 'sees' the entrance pupil in a different place, immediately below it, but 'located' infinitely far away.
Not meaning to be personal, but would I be wrong in deducing that you are primarily a microscopist ? That would explain the predilection for telecentricity. WP:NPOV ? WP:UNDUE ? Am I doing it right ?
For my side, I declare working in planar gradient-index optics, optical waveguide, fibre-optics, integrated optics modulators, laser diodes. Then I was sidelined into QA/QC - microscopy, photography, optical metrology etc. Then I got into IT - 7 years as a web-developer, now unemployed. I'm now tickling some dormant grey cells and practicing typing English rather than script languages. (Feel free to delete the last 2 paras - some of this should probably be moved to our personal talk pages when resolved !)
It's been a good meeting of minds. Sorry if I overdid the 'Be bold' Wikipedia philosophy. I'm not really a vandal. Still - it has to beat months or years of inactivity.
-- 195.137.93.171 ( talk) 23:38, 7 March 2008 (UTC)
Would it appear petulant to suggest that vacuum would be a better example ? -- 195.137.93.171 ( talk) 06:31, 7 March 2008 (UTC)
I updated the formerly-blue focal-plane images with SVGs. Now that I can see them clearly, I still don't really like them. As was discussed above, they are telecentric lenses, which is an unusual case. It was only in the last few days that I started to realize that an optical microscope is essentially telecentric, which is why microscopists talk of the back focal plane as the location for the apertue, whereas photographers think of the back focal plane as almost equivalent with the image plane. I'm not sure if this page or photographic lens or optical microscope should make this distinction; perhaps they all should. Just to clarify, am I technically correct about the back focal plane? Unless someone objects, I may start making these clarifications. —Ben FrantzDale ( talk) 01:19, 20 May 2008 (UTC)
It is requested that an optical diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
We could do with a diagram for surface vertex, obvious as it may be. —Ben FrantzDale ( talk) 20:55, 26 May 2008 (UTC)
I'll try again. Sorry for the delay - I let life get in the way of wikipeding for a bit !
The more I think about it, the more I am convinced this section is just plain wrong.
The nodal points are widely misunderstood in photography, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the iris diaphragm of the lens is located there, and that this is the correct pivot point for panoramic photography, so as to avoid parallax error. These claims are all false, and generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. The correct pivot point for panoramic photography can be shown to be the centre of the system's entrance pupil.
For practical lenses, designed to minimise vignetting and distortion, it is not necessary to make the distinction - the front nodal point is the centre of the system's entrance pupil. That is why experiments can show either point to be correct. People that show 'entrance pupil' is correct don't show that 'nodal point' is wrong.
A simple thought experiment will help clear up the confusion. We need to separate the nodal point and entrance pupil, and think about what happens.
Consider a lens which is specially constructed so that the aperture stop has two degrees-of-freedom. Not only can you vary its radius, but also its physical position by moving it parallel to the optical axis. This lets you investigate the more general case of unusual lenses, where the front nodal point is not at the centre of the system's entrance pupil.
Before you move the aperture away from its normal position, you rotate the camera about the agreed common point (front nodal point = centre of the entrance pupil). Why ? Because that is the point at which the lens focuses all light from the object point to the same constant stationary image point on the film even when the camera is rotated. There is no 'parallax'. Near objects do not move relative to distant objects. The camera's 'point-of-view' does not move. The image on film is not blurred by motion.
Note that it is not the aperture stop that is focussing the light, it is the refractive (glass) part of the lens. The front nodal point is a property of the glass, not of the aperture. The aperture only determines whether a ray passes through the lens to the film or not - not where it lands on the film, nor where it intersects other rays.
Now move the aperture along the optical axis. The entrance pupil is where the aperture appears to be, so it has to move along the optical axis, too. The glass hasn't moved, so the front nodal point has not moved, so it is no longer at the centre of the entrance pupil.
OK Now what happens when the camera is rotated about the same point as before (the front nodal point, no longer at the centre of the entrance pupil)? Nothing that contributes to the mapping of points in image space to points on film has changed. The glass hasn't been moved so it must focus the light exactly as it did before - to the same point on the film.
Therefore moving the aperture stop axially does not affect the motion, or lack of motion, of the image on the film. The aperture doesn't affect the focussing (bending of rays). It plays no part in the mapping of points in object space to points in image space.
If you follow the Wikipedia article quote above and change the panoramic-pivot-point to follow the motion of the entrance pupil instead, what happens? If you had rotated about that new point before moving the aperture, then the image would have moved across the film. The movement is determined by the focussing properties of the lens - by the refraction - by the glass - not by the aperture. Therefore the image will be blurred now.
QED ?
I do not find responses of the form "That is meaningless" or "You are confused" to be useful. They may lead me to question whether you understand what I say, or what is happening physically. I believe that the above is perfectly clear and meaningful.
-- 195.137.93.171 ( talk) 01:23, 3 July 2008 (UTC)
in simple terms [...] the aperture determines the perspective of an image by selecting the light rays that form it. Therefore the center of perspective and the no-parallax point are located at the apparent position of the aperture, called the “entrance pupil”. Contrary to intuition, this point can be moved by modifying just the aperture, while leaving all refracting lens elements and the sensor in the same place.
In general, when we impose a small aperture, the in-focus image stays the same, except for getting dimmer as we make the aperture smaller. The out-of-focus image also gets dimmer, by the same amount on average, but this is accomplished by leaving intact the portion of the blur that corresponds to having the center of perspective at the aperture, while eliminating all other portions of the blur.
Is there a good reason why the object point, image point, object plane, image plane, object distance and image distance are not defined in this article ? If not here, where do they belong ? Redbobblehat ( talk) 23:51, 8 August 2009 (UTC)
1. By ray-tracing : (I quote Malacara pp.25-26 [9] verbatim because my grasp is not sufficient to paraphrase) "By tracing two paraxial rays, the six cardinal points for a lens may be found... Figure 19 shows the six cardinal points of a lens when the object index of refraction is no and the image side index of refraction is nk. The points F1, F2, P1, P2 are located by tracing a paraxial ray parallel to the optical axis at a height of unity. A second ray is traced parallel to the optical axis but from right to left. The incoming rays focus at F1 and F2 and appear to refract at the planes P1 and P2. This is why they are called principal planes. These planes are also planes of unit magnification. The nodal points are located by tracing a ray back from C parallel to the ray direction F1A. If this later ray is extended back towards the F2 plane, it intersects the optical axis at N1. This construction to locate N1 and N2 shows that a ray which enters the lens headed towards N1 emerges on the image side from N2 making the same angle with the optical axis."
2. Experimentally : "Figure 14-8 illustrates a procedure by which the focal points and principal points for a thick lens may be experimentally determined." (Concepts of Classical Optics, John Strong, 2004, pp.311-312 [10].) Redbobblehat ( talk) 12:12, 10 August 2009 (UTC)
In the subsection Cardinal point (optics)#Nodal points it said that "If the medium on both sides of the optical system is the same (e.g., air), then the front and rear nodal points coincide with the front and rear principal planes, respectively." I changed "planes" into "points" here, as having points coincide with planes sounds a bit like sorcery...
I did not change another statement in the same sentence, as it is not wrong but only incomplete. Fot the nodal points to coincide with the corresponding principal points, it is not necessary that the medium on either side is the same, but the refractive index. If the media are different but happen to have the same refractive index, the nodal points will also coincide with the corresponding principal points.
-- HHahn (Talk) 12:57, 15 January 2010 (UTC)
I restored some material that was deleted by another editor today, trying to merge his new material into the old. His edits added some good explanation, but deleted too much valuable information and left the article with a poor lead section. A good lead always starts by explaining what the subject of the article is. You can't start an encyclopedia article with a qualification like "Strictly speaking the concept of cardinal points applies only to..."
There may be differences in perspective at work here. For nearly all real optical systems, the cardinal points allow useful approximate modelling of the true performance of the system. Modern optical design is done primarily by ray tracing and other computational techniques, using cardinal points and other paraxial properties only as a rough first approximation to the system's performance. I applaud the effort to introduce some information on the important concept of transformations between optical spaces in an ideal system, however. Hopefully this can be expanded further.
I'm not comfortable with including peripheral definitions such as those for "optical space", "optical axis", and "Rotationally symmetric optical system" as subsections, especially not so high in the article. Generally, material like that should be in other articles that we can link to. I removed optical axis since there is already an article on that. For the others I'm not sure yet whether the definitions should be moved into new articles, or whether the material can be dealt with some other way. As it is, it breaks the flow of the article too much and pushes the definitions of the cardinal points themselves down where the reader is less likely to see them.-- Srleffler ( talk) 05:06, 19 August 2010 (UTC)
TedEyeMD ( talk) 21:48, 19 August 2010 (UTC)
I took a look at Greivenkamp's book, which is a reference I have used in the past when writing material for this article. He does refer to "cardinal points and planes", on page 6. He does not refer to vertices as cardinal points, and I am fine with not referring to them as such in the article.
Information on practical application of the cardinal points in the analysis of real optical systems is at least as important as explanation of their theoretical importance to idealized systems. We need both in the article. It may well be best to explain the theoretical/idealized case first.
Your point about the incompleteness of the section on ideal optical systems is well taken. I actually fell asleep before finishing this sorry I will fix it today. TedEyeMD ( talk) 13:19, 20 August 2010 (UTC)
As far as whether or not only IRSFOS systems have cardinal points or all rotationally symmetric focal optical systems (RSFOS) have cardinal points is a question of viewpoint. To me, only ideal systems can have cardinal points. When taken as a whole non ideal systems do not have cardinal points, but certainly the paraxial regions of such systems do have cardinal points. If you want to say the "system" has cardinal points becasue its paraxial region has cardinal points well I suppose you could say that. However, I have found that many people are unclear on the difference between the entire system and the paraxial region. It is perhaps a fine distinction but to me some degree of clarity is added when one distinguishes between the system as a whole and the system's paraxial region. I am basically following the approach taken by Welford in Aberrations of Optical Systems. First, Welford establishs the properties of ideal optical systems even though he states a priori that such systems do not exist in practice (except for a plane mirror). Then he shows that this is useful because real optical systems do behave ideally in the paraxial region which can have a significant size in some cases.
I agree that the application of cardinal points to optical design is an important feature, but first I think we should be clear on what the cardinal points are before going on to applications. TedEyeMD ( talk) 13:19, 20 August 2010 (UTC)
I expanded the introduction and renamed it to what I thought was a more appropriate and informative title for the paragraph. I expanded the discussion on optical spaces. I added a section explaining the difference between afocal systems that even if ideal and rotationally symmetric lack cardinal pionts and focal systems which have cardinal points. This also seemed a good place to introduce the notion of focal points. TedEyeMD ( talk) 19:17, 21 August 2010 (UTC)
Hi I noticed some of your changes today. You added some links to other wikipedia pages which is helpful but I have a few concerns. For instance the link to rotational symmetry goes to a page that describes n-fold rotational symmetry. The problem is that the type of rotational symmetry I am referring to here is not n-fold so I think the link may be more confusing than helpful. Similarly the link to optical system goes to a general page on optics and the reader has to go along way to find optical system. The link to ray defines ray in terms of physical optics and this is counter to a decades long trend to make geometrical optics as free of physical optics as possible. The point about usage of conjugate is well taken.
When you talk about writing for a high school audience you raise a very important point. At what level should the article be directed to? Certainly I have found many Wikipedia pages that are well above high school even undergraduate level. Could you provide some link that would provide guidance on this point?
Also, I would like to add some illustrations could you provide some guidance on how to add drawings and illustrations? TedEyeMD ( talk) 01:19, 24 August 2010 (UTC)
By the way thanks so much for helping with the reference to Welford's book. Also, I don't think the wikipedia page on the paraxial approximation is very good. The paraxial approximations are really three specific approximations and the wiki page simply talks about the small angle approximation. So, again I have removed the link to that page since I am going to go into that subject in some detail on this page. So, I took all references to paraxial out and will discuss paraxial rays later in detail. TedEyeMD ( talk) 01:37, 24 August 2010 (UTC)
Well yes and no. Sure 'ideally we should link to other articles, and certainly such links do keep articles from becoming bloated. On the other hand when the linked to article is not just uninformative, but has a high potential to mislead then I think a link should be removed otherwise the reader may not simply ignore the linked to article, the reader may be confused by the linked to article. While the ideal solution is to edit the linked to article may not be practical because of time constraints. So I think there is something to be said for omitting links in certain cases.
Could you provide some guidance on how to generate and insert diagrams? Thanks TedEyeMD ( talk) 18:55, 24 August 2010 (UTC)
I noticed that a couple of times srleffler has restored something to the effect of exact calculation requires the application of Snell's law and the law of reflection each time the ray reaches an interface between two media. I have several problems with this sentence. First, it implies that both the laws of reflection and refraction are used every interface. In fact at any one interface only one or the other is used not both. Second, the law of reflection is just a special case of Snell's law so you technically don't need to mention it. Third, in addition to Snell's law and the law of relection there is the law of rectilinear propagation that is just as important in exact ray ttracing. Forth, there is no need to be so detailed here. This section deals with the concept of treating an optical system as a physical device for achieveing a mathematical transformation. the details of ray tracing need not be mentioned here. so I deleted it. TedEyeMD ( talk) 01:09, 25 August 2010 (UTC)
The fact that one is a special case of the other does not preclude mentioning both, however the fact that it has no place in an introductory level article on cardinal points does preclude mentioning. If you want to trace multiple rays then for each ray going into the optical system multiple rays come out. None of your illustrations show this and it would really confuse introductory level readers (the high school students you referred to earlier). Moreover it would take things to a higher level of approximation and as you note we are dealing with the lowest level of approximation so multiple reflections do not belong here. I find it very difficult to justify a discussion of fresnel's laws and multiple reflections in this article. I am aware of no textbook that introduces multiple reflections at this stage except perhaps to mention that they should be ignored at this point. 75.33.34.83 ( talk) 00:08, 27 August 2010 (UTC)
Do not read too much into my wording "optical system as a physical device for achieveing a mathematical transformation" I debated over how to word it and considered doing it the other way around, but I chose this wording for pedagogical reasons. By wording it this way my intent was to surprise the reader since we usually think as you do that the physics is primary and the math secondary. Pedagogically by wording it the other way around I wanted to catch the reader off guard and make them really think about this. Our differences are due not to a difference in technical background but rather to a difference in pedagogy. I too am a physicist and an optical engineer that has taught optics at the post graduate and post doctoral level. As an engineer I am well aware of the approximations made in applying paraxial optics to real world optical systems. However, as an educator I am also quite aware that there is a great deal of confusion between first order optics, paraxial optics, and Gaussian optics. The three are clearly related but in fact different. Worse, often the literature confuses the three using them synonymously which is inappropriate. It was my intention to do a complete rewrite of this article. I am doing that rewrite bit by bit for a few reasons. First, when I started editing this article there was some serious misinformation such as including lens vertices as cardinal points. Also, there was a lot of extraneous information about stops and pupils that was very interesting but not about cardinal points. So, I thought some changes were immediately necessary. Second, it will take some time to do a full rewrite so I was trying to do it piecemeal.
I realized immediately from all the discussion of stops and pupils and the inclusion of vertices into the cardinal ponts that you are definitely interested in the practical applications and I think that's great. However, there is no need to sacrifice rigor for practicallity. My plan was to start with theoretical rigor. Which is why I started by using the word ideal. If you begin with only ideal optial systems have cardinal points then no approximation is necessary. I planned later to introduce approximations. I would explain each approximation as it was introduced and why. The reader would finish with a very clear understanding not only that the cardinal points only approximate the behavior of real world optical systems they would also know precisely what the approximations were and what the implications of those approximations are. My approach is first let's explain exactly what the cardinal points are without approximation which means with ideal systems then show how by using approximations we can apply the concept to real optical systems. However, I would put the approximation lower in the article. I certainly realize that you want people to know that the cardinal points approximate the behavior of real systems. I have absolutely no intention of "glossing over" that point. Indeed, I want the reader not only to know that the cardinal points approximate the behavior of real world systems but also to know why the cardinal points approximate the behavior of real world systems. However, you keep redoing the changes I make so I have to re-edit and don't have time to introduce new material. Please be assured I will bring in approximations quite explicitly. Indeed to do so I would really appreciate it if you could help me find out how to introduce my own illustrations that would help a lot thanks. 75.33.34.83 ( talk) 00:08, 27 August 2010 (UTC)
A specific comment: In this edit you moved the list of the three cardinal points back down to where it was (and made some other changes in the wording). This is a problem, because as the intro stands you use the specific cardinal points in discussion before you have introduced them to the reader. You have to say what the cardinal points are before you say something like "only four points are necessary: the focal points and either the principal or nodal points". It just doesn't flow right the way it is.-- Srleffler ( talk) 03:31, 28 August 2010 (UTC)
I moved the more mathematical material discussed above lower in the article, because it is less approachable than some of the other material, and because it was left incomplete by the editor who added it. It didn't actually get around to explaining how the cardinal points are related to the mapping between optical spaces.-- Srleffler ( talk) 23:28, 7 September 2013 (UTC)
The recommended file format for drawings and diagrams on Wikipedia is SVG. Inkscape is a free editor for these files. For more info, see How to draw a diagram with Inkscape. You upload the image at Wikipedia:Upload. Be sure to read and follow the prompts. When uploading images, you have to specify the license under which they are released. The upload page's prompts try to help you with this. For an image you drew yourself common choices would include the CCbySA license, or just releasing the image to the public domain.-- Srleffler ( talk) 06:25, 28 August 2010 (UTC)
There are numerous names for this addition to the gaussian model, IMO "Toepler points" is the most distinctive :
AFAIK (from citation) they originate in Toepler, A. Bemerkungen ueber die Anzahl der Fundamentalpuncte eines beliebigen Systems von centrirten brechenden Kugelflaechen: Pogg. Ann., cxlii. (1871), pp.232-251.
The main use of toepler points (AFAIK) is to actually measure the focal length of a lens, using the conjugate distances at unit magnification. This method is implicit in Newton's conjugate equation, but for a full description of the method (and his contraption "the focometer") see Thompson, S.P. 1912 The Trend of Geometrical Optics : "Proceedings of the Optical Convention 1912" p.297-307. -- Redbobblehat ( talk) 01:11, 11 February 2011 (UTC)
(BTW: Gauss, C.F. Dioptrische Untersuchungem Goettingen, 1841. The "nodal points" were proposed/added by Listing, J.B. Beitrag zur physiologischen Optik Goettinger Studien, 1845 ( in german). Apparently the term "cardinal points" was coined by Felice Casorati (mathematician) and Galileo Ferraris - but I haven't found chapter and verse for that one.) -- Redbobblehat ( talk) 01:11, 11 February 2011 (UTC)
Section: Principal planes and points
This section and the accompanying diagram “Various lens shapes...” do not explain the concept clearly. The diagram shows a random collection of arrows impinging on lenses from all directions, signifying nothing. I respectfully suggest that this section be rewritten with a more meaningful diagram. -- Prof. Bleent ( talk) 14:41, 24 April 2015 (UTC)