:: My favorite part about that essay is the pictures. That is the essay that convinced me that the pupil position is really what matters. One realization that helped me understand it is this: by putting the entrance pupil in a strange place, as Littlefield does, the small aperture he adds doesn't make different rays hit the film, it just cuts off some rays that ''would'' have gotten to the film. That is, the f/# has gone up and so the depth of field has gone up so he's removing some of the rays of the defocus blur. You can get a similar odd effect with your eye. If I hold a pencil tip a few inches in front of my eye, backlit by the screen, it is out of focus. If I then move my finger between the pencil and my eye, it too is out of focus, but as the blurry image of my finger gets near the blurry image of pencil tip, the pencil appears to bend toward my finger. It isn't that the light rays are bending, it's that the blur is being selectively removed geometrically. [[User:BenFrantzDale|—Ben FrantzDale]] ([[User talk:BenFrantzDale|talk]]) 10:51, 3 July 2008 (UTC)
:: My favorite part about that essay is the pictures. That is the essay that convinced me that the pupil position is really what matters. One realization that helped me understand it is this: by putting the entrance pupil in a strange place, as Littlefield does, the small aperture he adds doesn't make different rays hit the film, it just cuts off some rays that ''would'' have gotten to the film. That is, the f/# has gone up and so the depth of field has gone up so he's removing some of the rays of the defocus blur. You can get a similar odd effect with your eye. If I hold a pencil tip a few inches in front of my eye, backlit by the screen, it is out of focus. If I then move my finger between the pencil and my eye, it too is out of focus, but as the blurry image of my finger gets near the blurry image of pencil tip, the pencil appears to bend toward my finger. It isn't that the light rays are bending, it's that the blur is being selectively removed geometrically. [[User:BenFrantzDale|—Ben FrantzDale]] ([[User talk:BenFrantzDale|talk]]) 10:51, 3 July 2008 (UTC)
:::OK, maybe rotating about the entrance pupil may reduce the increased-blurring-due-to-rotation for object points that form blurry discs in the image because they are out-of-focus. I wasn't really considering elongation of a circle-of-confusion - that is certainly a possible second-order effect. I was just concerned with the mapping of object-space points to image-space points for simplicity- if it's blurred anyway, parallax is probably a very small contribution to blur. Considering image-space rather than image-plane is more general, but avoids the confusion of "when you talk about parallax you are dealing with objects that are not exactly in focus" If you have a rotating lens or film, then objects may go in and out of focus during the duration of the exposure - see [[Scheimpflug principle]]--[[Special:Contributions/195.137.93.171|195.137.93.171]] ([[User talk:195.137.93.171|talk]]) 17:31, 6 July 2008 (UTC)
:::Welcome to the debate, Ben! OK, maybe rotating about the entrance pupil may reduce the increased-blurring-due-to-rotation for object points that form blurry discs in the image because they are out-of-focus. I wasn't really considering elongation of a circle-of-confusion - that is certainly a possible second-order effect. I was just concerned with the mapping of object-space points to image-space points-of-focus for simplicity- if it's blurred anyway, parallax is probably a very small contribution to blur. The lateral movement of the point of view will be small compared to the aperture diameter. Considering image-space rather than image-plane is more general, but avoids the confusion of "when you talk about parallax you are dealing with objects that are not exactly in focus" If you have a rotating lens or film, then objects will go in and out of focus during the duration of the exposure. For simplicity, consider an isoceles triangle (ray diagram of object space plane of focus), with the lens as a point at the vertex on the axis of symmetry, and the other vertices at the edges of the field of view. Now rotate the triangle about the lens vertex. The line in the object plane sweeps out an area. All points in object space in the swept area will have passed through focus. For complexity - see [[Scheimpflug principle]] --[[Special:Contributions/195.137.93.171|195.137.93.171]] ([[User talk:195.137.93.171|talk]]) 17:31, 6 July 2008 (UTC)
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I believe the principal planes are actually principal surfaces (curved) unless you're using the paraxial approximation. Worth mentioning, or leave that to another article?
The nodal points are coincident with the principal points if the lens the same medium on both sides. Probably worth adding.
What diagrams do we want? I was thinking of basically redrawing Hecht (2nd ed.) figure 6.1. Would fig 6.2 & 6.3 be useful also, or too much?
Any preferred labelling scheme? Hecht uses F1, F2, V1, V2, H1, H2, etc., whereas Jenkins & White use F, F', A, A', H, H'.
Yes, the principal surfaces are actually curved, if you're not using the paraxial approximation. Perhaps that could be mentioned. The article (and most of the rest of geometric optics on Wikipedia) assumes the paraxial approximation though. I'm not sure how useful it is to consider the cardinal points at all, once one moves beyond paraxial optics.
It's in there already.
Hecht's 6.1 and 6.2 look good. I'm not so sure about 6.3.
No preference on numbers vs. primes. I prefer V to A for the vertices, for obvious reasons. Greivenkamp uses F, F', P, P', V, V', and N, N', which seems nice and simple. Any idea why the more conventional symbol for the principal planes is H? One of those things inherited from German, perhaps?
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)[reply]
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)[reply]
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)[reply]
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)[reply]
Nodal points ~ entrance pupil ?
"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 ...
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.
Your message above illustrates exactly why the article needs to say that there is a misconception here. The nodal point is not at the center of the entrance pupil. Pretty much everything you wrote after the first paragraph is wrong or irrelevant, because you're assuming something that is not true.
In general, it's important to explicitly address misconceptions in Wikipedia articles, both for the purpose of educating the reader, and to ensure that editors do not insert incorrect information drawn from sources that are themselves incorrect.
Now, about your first paragraph: you are of course correct that the ray doesn't pass through the nodal points. The article's description glosses over this issue. I'll try to rephrase it.--Srleffler (talk) 03:56, 7 March 2008 (UTC)[reply]
so these are 'authoritative sources' ?
"Pumpkin" doug.kerr.home.att.net - an electrical engineer, specialising in telecomms
vanwalree.com "I am not professionally involved in photography, optics ... I work as an underwater acoustician. This website is just a hobby "
"Rik Littlefield" 19 pages of PDF tl:dr looks impressive but he seems to be a computer guy, not an optics guy ! eg he talks as though there were just one nodal point, rather than two - front & rear. (I skimmed it - he knows.) Basically he shows that the Entrance pupil works. He doesn't show that the front nodal point is distinct from the pupil, or that the front nodal point doesn't work. I think the verbosity just indicates confusion and the truth is simple - they are the same ! See below.
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)[reply]
This is why we have a rule against original research on Wikipedia—so we don't have to deal with edits based on an editor's own opinion. You're right that the nodal points normally coincide with the principal planes. This is only true, however, if the surrounding medium is the same on both sides of the lens. See Greivenkamp's book, page 11 (full reference in the article). Where you go really wrong is in assuming that the entrance pupil must coincide with the front principal plane. They do not in general coincide. Page 26 of the book shows a schematic example where the entrance pupil is in front of the lens group, and the principal planes are both inside the lens. If you want a simple example, consider a plano-convex lens used flat side first. The front principal plane is located t/n from the front vertex, where t is the thickness and n is the refractive index. This places the principal plane inside the lens. The rear principal plane is at the rear vertex. The entrance pupil is coincident with the flat front surface of the lens.
Yes, some of us here have studied optics. You're not the only one here with a physics degree. --Srleffler (talk) 17:22, 7 March 2008 (UTC)[reply]
Nodal point = entrance pupil ! Proof ?
"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.
N, N' The front and rear nodal points of a thick lens.
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)[reply]
Hope this helps explain, and defuses the controversy.
"Rotate about the nodal point or the entrance pupil ?"
"Both - they are the same !"
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.
I see a couple of problems with the "proof" above. The first is that it presumes the camera lens is designed with the aperture at the nodal point to minimize vignetting. I don't know much about camera lens design, but it seems to me that there might be other constraints that affect where the aperture is placed. Indeed, you noted some examples of lenses that don't put the aperture at the nodal point.
The second and more critical problem: In 10 you are proposing rotating about an image of the nodal point that coincides with the center of the entrance pupil. This is not the nodal point itself, which is located at the aperture. Rotating about the actual nodal point certainly would move the center of the entrance pupil. Note also that the nodal point is not a physical object and does not form an image. It is meaningless to say that the nodal point is "seen at" the center of the entrance pupil. --Srleffler (talk) 17:32, 8 March 2008 (UTC)[reply]
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 ?
That illustration really isn't about the lens design. It's just a diagram with a lens and a few rays to illustrate a principle that applies generally to all lenses.
In general, articles on technical topics like optics need to cover the general information for non-experts, and information suitable for people who need more technical detail. Usually the general information comes first. Even in the general-reader material, though, it's important to ensure that all information presented is accurate. This article is legitimately more slanted to the technical reader than most, because it is covering a topic that is mainly a matter of technical detail. We do need to ensure that the nontechnical reader who comes here looking for info is not excluded, though.--Srleffler (talk) 17:43, 8 March 2008 (UTC)[reply]
Filter rays by angle - removed
I deleted this section.
Angle filtering with an aperture at the rear focal plane.
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.[1] 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 ?
You seem to be deleting material based on personal speculation rather than knowledge or external sources. This is not a good editing practice. Your points 3 and 4 are speculative. The issue with detectors is that CCD detectors are sensitive to the angle of incidence of the light, so cameras based on them may require a narrower cone of rays at the detector than a film camera would. See Vignetting#Pixel vignetting for more discussion of this. I'm not sure offhand if this angle sensitivity is due to a physical well as the article implies (which would be in addition to the quantum well), or if the description of this angle sensitivity as a "well" is metaphorical.
Your point 2 seems to be based on misunderstanding. The article discusses a general geometric optics effect, and the image illustrates that. The article then goes on to give a specific example of where that effect is used, which happens to involve keeping the angle of incidence of light on a detector close to perpendicular. The image doesn't illustrate that application. --Srleffler (talk) 04:28, 7 March 2008 (UTC)[reply]
I've just read telecentric - does my head in - convinces me these are poor examples.
Is adding speculative material (shape of photon well) not also poor editing practice ?
Maybe I should have just flagged it 'citation needed' or something !
4 is not speculative - I think it's called snell's law or fresnel effect - had a quick look for source - will continue.
I'm about to add to my comment on the other image below ....
Raising your concern on the talk page was a good idea. Deleting a big chunk of text without discussing it here first was not. You are deleting material based on your own misunderstanding of it.--Srleffler (talk) 04:47, 7 March 2008 (UTC)[reply]
I don't have time for edit wars - I challenge you, or anyone to find reliable sources for/against 4) --195.137.93.171 (talk) 05:00, 7 March 2008 (UTC)[reply]
Don't bother - 4) is based on Fresnel equations. OK - I ignored polarised light !
Or you can avoid the maths and graphs by just looking at the reflection of a window(no - blue sky is polarised!) lamp in something shiny, while you tilt it to vary the angle ! The reflection is dimmest at 90 deg. Even something black & polished will do. It's more common experience than speculation. --195.137.93.171 (talk) 05:58, 7 March 2008 (UTC)[reply]
The issue is not whether Fresnel reflection increases with angle of incidence. Of course it does. The issue is that you were speculating that this is the reason why CCD-based cameras are designed to limit the angle of incidence at the sensor. There could be an additional angle-sensitivity in this type of sensor, which is what the article implies. I don't personally know one way or another, but I know that your speculation is not sufficient grounds to change the article.
I am thinking now that the paragraph on DSLR cameras should probably be deleted for another reason, though: the angle filtering described in the diagram is object-space angle filtering: the aperture in the rear focal plane limits the range of angles in object space which are accepted by the lens. The DSLR cameras clearly need image-space angle filtering. This is related to your point abou the rays not being perpendicular at the detector. --Srleffler (talk) 17:34, 7 March 2008 (UTC)[reply]
Since the sensors generally have RGB colour filter arrays (exceptfoveon) it's a fair bet that there's a pretty complex stack of many thin layers of materials of different refractive index acting as an anti-reflection coating as well. I was considering a simple case. The coating is probably not just optimised for normal perpendicular incidence, so that its reflectance-as-a-function-of-angle helps reduce pixel vignetting, working in tandem with the telecentric lens design.
The telecentric article explains DSLR pixel vignetting purely in terms of the RGB sensor filter - no mention of the underlying CCD/CMOS photon wells.
Yes, if you swap the words 'object' and 'image' and reverse the arrows, your front-telecentric diagram becomes rear-telecentric. My main point: "Does it really relate to 'cardinal points' at all ?" They are on-axis: telecentricity is off-axis.--195.137.93.171 (talk) 21:41, 7 March 2008 (UTC)[reply]
back focal plane - image removed
I deleted this image
File:BFP.pngRays with the same angle cross at the back focal plane.
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 ?
I reverted your deletion. The image correctly illustrates the point being made in the text. You just didn't understand the optics here. Your point 3 is exactly the point: parallel rays from different parts of the object cross at the back focal plane. This is not a coincidence, contrary to your point 4. Your points 4a and 4b are simply wrong. --Srleffler (talk) 04:14, 7 March 2008 (UTC)[reply]
I improved the caption to better reflect what is going on. As to the size of the image: click on the image to see it full-scale. The image on the page is a thumbnail, which provides a link to the full picture. Logged-in users can set the default size for thumbnails so they can have them appear bigger if they wish.--Srleffler (talk) 04:17, 7 March 2008 (UTC)[reply]
Regarding your point 2: the image is a diagram illustrating the specific point being made in the text. The property described is true of all lenses, telecentric or not. The lens depicted is, in fact, not telecentric.--Srleffler (talk) 04:19, 7 March 2008 (UTC)[reply]
The 'co-incidence' is that you happen to have illustrated a telecentric lens ! I therefore withdraw 4a) & 4b) above !
I give up ! I only have an honours degree in physics, albeit 23 years ago and 13 years in optics & electro-optics research. No more time to waste - what does the community think ? --195.137.93.171 (talk) 04:47, 7 March 2008 (UTC)[reply]
The image really is no coincidence. The phenomenon depicted would be true of any lens (in the limit where geometric optics is a good approximation, of course). Ray diagrams are tricky to interpret correctly. --Srleffler (talk) 04:56, 7 March 2008 (UTC)[reply]
Let me see if I can jog your memory: would it sound more familiar to say that a lens maps angle in the far field to position at the focal plane? Parallel rays entering the lens always come to a point in the appropriate focal plane, in geometric optics. It doesn't matter what kind of lens it is, or where the object and image planes are located. This is related to Fourier optics, and is based on the fact that each position in the focal plane corresponds to a plane wave component in the incident light, with a particular direction of propagation. --Srleffler (talk) 05:07, 7 March 2008 (UTC)[reply]
Ah, now you're testing me. Lol! Even my favourite pinhole 'lens' will translate angle in far field to position in the 'focal plane' - you don't even need to invoke 'simple lens', let alone 'geometric optics' for that - 'Fourier optics' are overkill, if not barely relevant! Fourier optics is more to do with the 14-point starburst when you stop down a 7-blade iris diaphragm, although I suspect that the iris blades also contribute, due to reflection off rounded edges, which are an imperfect knife-edge ! Fourier optics is more to do with angle in the far field mapping to spatial frequency in the near field - ie the aperture plane, not the focal plane. And phase in the near field determines amplitude in the far field, and vice-versa! And small features in the aperture affect the large or wide parts of the far-field, while the small features in the far-field are determined by the large features of the aperture.
Great. Now we're on the same wavelength. Every lens translates angle in the far field to position in the focal plane. That is all that is involved here. The lens doesn't know whether a ray comes from infinitely far away or from a nearby object. Rays arriving at the lens with a given angle of incidence map to a particular point in the focal plane, therefore rays that leave the object parallel to one another cross at the rear focal plane, as the article says. The image illustrates this by tracing a few selected rays, showing that rays that leave different object points with the same angle pass through identical points (cross) in the focal plane.
You complained above that this is a weird lens. It's actually not. The lens illustrated is just an ideal thin converging lens. Such a lens cannot be telecentric, since the entrance pupil coincides with the plane of the lens. What is throwing you off is that the rays shown are not the typical ones one would use to analyze a camera lens. None of the rays shown is a chief ray or marginal ray. Rather, the rays shown are chosen to illustrate the effect being discussed. The chief rays would go through the center of the lens, and would not be parallel to the axis.--Srleffler (talk) 17:54, 7 March 2008 (UTC)[reply]
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)[reply]
Lol. I'll have to think about those. Offhand, the second and third appear to involve the diffraction limit, but perhaps there is more going on. No time for this now.--Srleffler (talk) 17:54, 7 March 2008 (UTC)[reply]
That's fine - "diffraction limit" as a two-word answer will score 100% for the first two and > 80% for the third. The pinhole diameter causes a circle of confusion in ray optics which works with diffraction to produce an airy disk. it's surprisingly insensitive to hole size, so a bigger hole than determined by max sharpness is probably worthwhile for the sake of speed. Answers depend on object/film distances.
I resisted the question about the speed of an unladen swallow - you might not know the answer is 'African or European swallow?' - it's a Monty Python thing.
I knew you were just testing me by mentioning fourier optics as an explanation of the ray diagram. Ray diagrams are fundamentally incompatible with fourier optics - that uses gaussian beams instead. There is no such thing as a 'ray' in fourier optics! Lol!--195.137.93.171 (talk), 7 March 2008
I didn't intend it as a test, but perhaps did mean for it to grab your attention. What I had in mind is that Fourier optics is based on the fact that one can decompose any optical field on a basis set of plane waves. (Pardon me if I'm going over stuff you know—others may read this too.) See Fourier optics#Origin of plane wave spectrum representation of the electric field. When a plane wave is incident on a lens, the lens focuses that plane to a single point in the focal plane. Any light distribution incident on the lens can be represented as a sum of plane waves with different angles, each of which maps to a different point at the focal plane. The lens thus maps angle of incidence to position in the focal plane just as is represented in geometric optics. Fourier optics is not "incompatible" with geometric optics; it is a superset of it. Any physics that is correctly described by ray optics can also be described by Fourier optics or by a diffraction integral model. The reverse is not true, because ray optics is a simplification of the underlying physics.--Srleffler (talk) 19:53, 8 March 2008 (UTC)[reply]
I note that you seem to be equating 'focal plane' and 'aperture' in your Fourier 'explanation' - another symptom of a 'telecentric lens' !
No, see just above. Fourier optics predicts the mapping of angle to position in the focal plane, and this is fundamentally the basis of Fourier optics.--Srleffler (talk) 19:53, 8 March 2008 (UTC)[reply]
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?
File:BFP.pngRays with the same angle cross at the back focal plane.Angle filtering with an aperture at the rear focal plane.
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 [2]?)
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.
You're right that the lens with the apeture is telecentric; I missed that. For that lens the middle ray in the cone from the edge of the object is the chief ray. The same ray in the other drawing is not the chief ray, because the aperture stop is in a different place. The actual chief ray in that case is not shown, but would go diagonally from the edge of the object through the center of the lens (since the aperture stop of a simple lens is the boundary of the lens itself).
I stand by my claim that simple lenses cannot be telecentric, but with the qualification that adding an aperture displaced from the lens makes the optical system no longer just a simple lens. Telecentric lenses are pretty weird. I agree with most of your comments on telecentricity above.
Wrong guess. I'm a laser physicist. I didn't draw the images used in this article, although I'm responsible for a lot of other text here. --Srleffler (talk) 19:53, 8 March 2008 (UTC)[reply]
refractive index of 1 (e.g., air)
Would it appear petulant to suggest that vacuum would be a better example ? --195.137.93.171 (talk) 06:31, 7 March 2008 (UTC)[reply]
Not at all. Air (treated with the approximation n≈1) is a pretty important case in classical geometric optics, though, and needs to be addressed. I tried rephrasing the article a bit. See if you like the new text better.--Srleffler (talk) 18:00, 7 March 2008 (UTC)[reply]
It might be worth making it clear that nAIR is never exactly 1. The differences are non-trivial even to naked eye - twinkling stars, mirages, heat-haze, squashed setting sun. I recently came across a Nikon FAQ about why a lens focus-ring will turn beyond the infinity mark - mountaineers work in a lower refractive index due to altitude. Cynically I had thought it was due to sloppy manufacture, or a marketing ploy ("... infinity and beyond ...") akin to the guitar amps that 'go to 11'. Plus we always noted the daily barometer reading in our optics lab notebook - I can't remember the experiment for context, but it wasn't just a token gesture. --195.137.93.171 (talk) 01:15, 8 March 2008 (UTC)[reply]
Focal plane images
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)[reply]
The lenses are not really the point. These are just simple ray diagrams that illustrate several principles that are discussed in the text. They are not camera lenses. They are not microscope lenses. The first diagram illustrates that the image plane is distinct from the focal plane when the object is a finite distance away, and shows that rays that leave the object parallel to one another cross at the back focal plane. These two principles are true of any optical system, but it would be hard to illustrate them in a small raytrace diagram of a conventional lens. The second diagram illustrates object-space angle filtering (i.e. telecentricity). Of course we use a diagram of a telecentric system to illustrate the principle that is responsible for telecentricity!
One correction: only the system shown in the second diagram is telecentric. The first is not. The lenses and rays illustrated are identical, but telecentricity (angle-filtering) is determined by the placement of the aperture. This might seem strange, but it really shouldn't. The rays illustrated happen to be the same, but not every ray through each system is shown. Diagrams showing the chief and marginal rays of each lens would make it clear that only one of the two systems is telecentric, but that wouldn't serve the purpose for which these diagrams were made.
If photographers think of the back focal plane as equivalent to the image plane they are mistaken in general, and need to be corrected. The two planes only coincide when the lens is focused at infinity.--Srleffler (talk) 03:55, 20 May 2008 (UTC)[reply]
I made a tweak to the wording. The article used the word "aperture" when it probably should have said "stop". The bfp is not in general the location for the aperture stop. If you want to filter rays by object space angle, however, you want a stop at the rear focal plane. It could be a field stop in a camera, for example. If that angle-filtering aperture is the aperture stop, then the system is object-space telecentric. --Srleffler (talk) 04:29, 20 May 2008 (UTC)[reply]
Thanks. At very least you clarified some things for me. —Ben FrantzDale (talk) 11:18, 20 May 2008 (UTC)[reply]
Reqdiagram
We could do with a diagram for surface vertex, obvious as it may be. —Ben FrantzDale (talk) 20:55, 26 May 2008 (UTC)[reply]
Rotating Lens for panorama - wrong
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.
Welcome back. Before I get to your main argument, a couple of points:
I'm still not sure about your assertion that the nodal point coincides with the entrance pupil in a well-designed lens. Do you have a reference to support this claim? Your attempted proof above fails for the reasons I already pointed out. The nodal points coincide with the principal planes for a lens in air. It's not at all obvious that the entrance pupil must coincide with the first principal plane, and I suspect you are mistaken on this point.
Showing mathematically or geometrically that the entrance pupil is the correct choice is sufficient, unless the argument implicitly or explicitly assumes that the nodal point coincides with it. You have argued that the nodal point normally coincides with the entrance pupil in a good camera lens. That might or might not be true, but it is clearly not true for a completely general optical system. A correct and general optical analysis will therefore either show that the correct center of rotation is the nodal point, or that it is the entrance pupil, regardless whether they happen to coincide in certain selected optical systems. There are only three possibilities here:
The analyses in the references contain errors.
The analyses assume (perhaps implicitly) that the nodal point coincides with the entrance pupil.
Your analysis contains an error.
Not having dug through any of the analyses in detail yet, I find #3 at least as likely as #1. I'll think about your argument in more detail and expand this reply.--Srleffler (talk) 03:33, 3 July 2008 (UTC)[reply]
Still thinking about the arguments, but a couple lines from the Littlefield essay[3] jump out at me:
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.
The aperture stop's effect on an optical system is subtle, and easily overlooked. I think you have erred in assuming that the location of the no-parallax point had to be determined by the refractive elements alone. This is starting to remind me of the discussion above about telecentric lenses—telecentricity is related to parallax, and is determined solely by the placement of the aperture. --Srleffler (talk) 03:47, 3 July 2008 (UTC)[reply]
The Littlefield essay is quite instructive. The key point is that when you talk about parallax you are dealing with objects that are not exactly in focus (because only one distance can be exactly in focus at a time). Objects that are not at the exact optimum distance are slightly blurred. When rays are clipped by an aperture, the blurring of the out-of-focus image is altered, and its center can be shifted. This shouldn't really be surprising—it is only the action of the aperture stop that allows the not-exactly-in-focus parts of the image to be reasonably sharp in the first place. A very large aperture causes objects away from the correct object distance to form very blurred images. Selecting a more limited ray fan with an aperture sharpens the out-of-focus image, but affects its position in the image plane. Littlefield summarizes this:
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.
Littlefield also directly contradicts your claim that the nodal point coincides with the entrance pupil, and shows a detailed raytrace of a camera lens illustrating this. He writes, "In real lenses, there is no particular relationship between locations of the entrance pupil and front nodal point."--Srleffler (talk) 04:54, 3 July 2008 (UTC)[reply]
My favorite part about that essay is the pictures. That is the essay that convinced me that the pupil position is really what matters. One realization that helped me understand it is this: by putting the entrance pupil in a strange place, as Littlefield does, the small aperture he adds doesn't make different rays hit the film, it just cuts off some rays that would have gotten to the film. That is, the f/# has gone up and so the depth of field has gone up so he's removing some of the rays of the defocus blur. You can get a similar odd effect with your eye. If I hold a pencil tip a few inches in front of my eye, backlit by the screen, it is out of focus. If I then move my finger between the pencil and my eye, it too is out of focus, but as the blurry image of my finger gets near the blurry image of pencil tip, the pencil appears to bend toward my finger. It isn't that the light rays are bending, it's that the blur is being selectively removed geometrically. —Ben FrantzDale (talk) 10:51, 3 July 2008 (UTC)[reply]
Welcome to the debate, Ben! OK, maybe rotating about the entrance pupil may reduce the increased-blurring-due-to-rotation for object points that form blurry discs in the image because they are out-of-focus. I wasn't really considering elongation of a circle-of-confusion - that is certainly a possible second-order effect. I was just concerned with the mapping of object-space points to image-space points-of-focus for simplicity- if it's blurred anyway, parallax is probably a very small contribution to blur. The lateral movement of the point of view will be small compared to the aperture diameter. Considering image-space rather than image-plane is more general, but avoids the confusion of "when you talk about parallax you are dealing with objects that are not exactly in focus" If you have a rotating lens or film, then objects will go in and out of focus during the duration of the exposure. For simplicity, consider an isoceles triangle (ray diagram of object space plane of focus), with the lens as a point at the vertex on the axis of symmetry, and the other vertices at the edges of the field of view. Now rotate the triangle about the lens vertex. The line in the object plane sweeps out an area. All points in object space in the swept area will have passed through focus. For complexity - see Scheimpflug principle --195.137.93.171 (talk) 17:31, 6 July 2008 (UTC)[reply]
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