Discussion in 'Large Format' started by david_flockhart, Aug 11, 2002.
What or where is the nodal point of a lens? Thanks.
Someone else can tell you the exact story of what, as to where I'm not sure either. I had a situation some time back where I needed to know the exact distance from the nodal point. To determine this I put a clear plastic ruler in the negative stage of my enlarger and adjusted the focus and height until I had exact magnifications from 1:1 on up. By measuring the a distance from the easel to a point on the lens I determined where the nodal point was ( multiple magnifications to eliminate errors). Is there an easier way to determine the nodal point?
The nodeal point of a lens is the point where different rays from the same point cross each other. If you were looking at the ariel image, it is the point from which the image rays appear to be emanating. The simplest way to determine the nodal point is probably what was alluded to earlier i.e., set up the camera accurately to obtain exactly a 1:1 image on the GG. Now measure the total distance from the ground glass to the surface of the object (which will be four focal lengths) and divide that by 4. You can also obtain the nodal point with a fair degree of accuracy by autocollimating with a shaving mirror. If you need greater accuracy than these methods, you will probably need access to a nodal slide. Cheers, DJ
In optics a Nodal slide is used. An artifical star is observed; and the lens is rotated. The aerial image of the star the film plane will move either to the left or the right; if the rotational point is not the same as the nodal point. There are two nodal points typically with a multi element lens. There is one when viewed normally; and one when the lens is reversed. The distance between the nodal points is the nodal sometimes many millimeters. In a telephoto lens design; many times the nodal points are outside the physical body of the lens. <BR><BR> Grab any old lens and hold it one foot away from your eye and rotate the lens; while viewing a room lamp across the room. If magically rotated about the nodal point; the image will not move.
Yet another definition: the nodal points of a lens are the intersection of the optical axis with the principal planes. For a current lens, the manufacturer's datasheet usually indicates the locations of the principal planes.
As already mentioned, there are two nodal points, as there are two principal planes. Only in the "thin lens" approximation of optics both nodal points coincide. The one of interest for the photographer is usually the back nodal point, e.g. for panoramics when combining several images. When the camera is rotated, the rotation axis should coincide with the back nodal point to allow perfect overlap. The positions of the nodal points depend entirely on the construction of the lens - in telephoto lenses it is in front of the lens (it has to, since by definition the distance from the back nodal point to the focal plane at infinity is the focal length). This is noticeable when applying front tilts or swings, which lead to image movement, since the rotation axis is far away from the back nodal point. Note that the back nodal point can actually be in front of the front nodal point - so when checking technical lens drawings (they usually indicate the nodal point positions) make sure that you use the right one.
So, for the purpose of Scheimphlug focusing: focus at infinity and the back nodal point is the focal length forward of the focal plane.
The moon is probably near enough to infintity for first approximations.
Dick, that is correct. The problem is, one does usually not know the _exact_ focal length of the individual lens. The actual focal length can differ from the engraved one by several percent. How to find both the focal length and the nodal point position has been described several times by Richard Knoppow on usenet. Make a search for "principle point" and his name on
The moon is fine for infinity but not necessary. Think of it in terms of multiples of the focal length. If you focus on an object at a distance 100x times the focal length and use it as "infinity", your error is about 1%. For a 210mm lens, that is only 21m (about 70 ft) away. Any reasonably distant building, tree, mountain is fine.
Professional lenses for specialized applications many times have the exact focal length for that serial number lense marked on the lens itself.
My Apo Ronar Process lenses are marked to the nearest 0.05 mm focal length on each lens. My Kodak 10 inch F4.5 is marked 253.5mm .
My Fastax high speed movie cameras 16mm lenses are marked to the nearest thousands of an inch. The 50mm/2" F2 is also engraved/marked 1.992"; the 152mm/6" is also engraved/marked 6.063"; the 254mm/10" is also engraved/marked 9.969" The exact focal length is used to figure the exact scale of the photo. This is required for testing of machinery; explosions, etc..
Some of the earlier leica 35mm lenses have semi hidden codes which tell the focal length to within about 0.2 to 0.5 mm; depending on the lens model
Kelly, this is of course true. Graphic applications (like your Ronars), photogrammetry etc. need to know the exact focal length.
For general photography, however, this is different. My Apo-Ronar, which came as a photographic lens in a shutter, says 300mm and nothing else. I think this is due to the fact that people have gotten used to "standardized" focal length like 150mm, 210mm, 300mm etc. Take 210mm for example. In this range, Schneider has/had the Apo-Symmar, the G-Claron, and the Xenar. All of these are engraved 210mm. The technical data sheets from Schneiders web site list 209.6mm, 208.2mm, and 215.7mm, respectively, for these lenses. Thats a difference of 3.6% between the last two. And these are just the calculated ideal values and do not account for any individual fluctuations in production (which should be lower, probably only tenths of millimeters).
To keep it in perspective, in normal photography this doesn't matter at all. Only if one goes to "specialized applications", it might matter. Stereo photography (with a two-lens system) is one where the two lenses have to be matched closely in focal length.
My two euro-cents about nodal points :
* in (fully-) symmetrical lenses (such as Schneider G-Claron or Schneider Makro-Symmar) the front and rear nodal points share the same location, at the center of the lens
* with a conventional camera (ie not a rotary panoramic camera), when you shoot multiple pictures that will be stitched into a panoramic view, you have to rotate around an axis crossing the entrance pupil center, not the front nodal point [of course when there are only distant objects in the frame, this is quite needless]. See for example the "Lens FAQ" by David Jacobson. This topic has also been discussed at great length with Emmanuel Bigler on the French site www.galerie-photo.org (search "Point nodal" in the upper frame when it is loaded). Remark : in symmetrical lenses the entrance pupil won't be at the center of the lens, because the aperture stop is at the center of the lens and the entrance pupil is the (virtual) image of the stop made by the front lenses.
* In a rotary panoramic camera, the lens rotates around its rear nodal point because this makes the image almost stationary (so there is no blur when the "light slit", which has a finite width, goes across the film). In return for which, the "point of view" will change across the image, because the center of the entrance pupil will move (unless it coincides with the rear nodal point). This is not a problem because no stitching is needed.
Yves, I stand corrected on the panoramic stitching issue. It is the entrance pupil position that should coincide with the rotation axis. I mixed that up with the rotating lens case. Thanks for correcting that.
As for symmetric lenses, the nodal points don't have to be positioned at the lens center. They are, of course, symmetric about the center. Check, for instance, the G-Claron specs:
The distance HH' in the specs is the distance between the front and rear nodal points (1.7mm in this case), which means they do not coincide at the center.
With regard to lens lettering: I found a quote that DIN 4522 allows rounding of the actual focal length for the lettering on the lens up to 6%, i.e. anything between 197.4mm and 222.6mm could be labeled 210mm.
Arne; On my Kodak 10" F4.5; the focal length is hand scribed into the rear flange area; which was found well after I bought the lenses. The APO Ronars came with data sheets for our 3 different lenses; the exact tested focal length was done by Acti Camera; which set up our process camera decades ago. The 16mm lenses actually have the Nominal and exact focal lengths engraved in white letters; on the lenses grey bodies.
The rotational points brought up for panaramic photos is interesting; THANKS.
Yes you are right Arne, my mistake. What I had somewhere in my mind was that in a symmetrical lens the front nodal point coincides with the center of the entrance pupil, and the rear nodal point coincides with the center of the exit pupil... (easily seen with a ray going physically through the center of the lens)
This is all getting very technical, but I think that the simple method for distortion-free stitching is to use shift, and not rotate the lens at all.
Monorail cameras with MF backs are usefull tools, and on a 54 you can scan @ 4,000 ppi, and stitch together a virtual neg about 25 X 18 cm.
Then with a 617 back...
Thank you for the many and varied responses to the question.
Perhaps I should have stated that the purpose behind the
question was a practical application: shooting triptychs usually
with a 5X7 and sometimes an 8X10. While it is not difficult to
match edges when rotating the camera I'm sure the technique
could be improved for more natural appearing perspetive, thus
the question. While I appreciate the beauty of technical
explanations and theory, I am hoping for practical instructions in
this case. Many thanks.
your application is very similar to the panoramic stuff Yves and I discussed. Provided you want to do this by rotating the camera and not shifting, what you have to do is to position the entrance pupil of the lens over the rotating axis of your tripod head. I don't know what type of camera and/or tripod connector you have. If it is a flatbed and you just use the 3/8" thread for connecting, that means after attaching the camera to the tripod you move the front standard until that position is reached and then do all the focussing with the back standard. If you use a monorail or an Arca-swiss type quick connector you may be able to slide the whole camera back and forth to position the entrance pupil over the axis. Horizontal shifts of the front standard are of course not allowed. How do you know where the entrance pupil is? Schneider gives this information in their data sheets. The symbol they use is "SEP", which is the distance from front glass vertex to the entrance pupil. Don't scratch the lens trying to measure it that way - from all the other measures given there you can infer the distance from the flange plane. I don't have a Rodenstock catalog at hand but its probably also in there. If not, either Rodenstock or Bob Salomon of HP marketing can probably give you the numbers. In the Nikon catalog I have (in German) SEP is marked on the drawings for each lens. For Fuji or older lenses you may be out of luck to get an exact value. My guess is that at least for plasmat type lenses you're not too far off if you assume its a few mm in front of the aperture itself.
The simple answer is that for almost all LF lenses, rotating
about the physical centre of the aperture iris (and not, say, the
tripod socket of your field camera) will reduce parallax errors to
insignificance. The exceptions are 'asymmetric' lenses such as
telephotos or if you are using a single group of a convertible lens
like the old Symmars. Even then, the problem is almost always
irrelevant if your panorama is an infinity landscape, but if you
want to do macro panoramas you may need to be more
Yves, thanks for the pointer to Emmanuel's description of his
conversion to the true faith -0). My French is better than
Babelfish's, but still not that fluent, so I would be grateful if you
could confirm a couple of points.
First, that the reason to rotate about the centre of the entrance
pupil is so that an in-focus object is always centred on the circle
of confusion of an out of focus object behind or in front of it.
Second, that Kingslake and Ray mention the problem but don't
discuss it in detail for the specific case of stitched panoramas. (I
know I should look them up, but both books are expensive, and
our library here is completely useless when it comes to optical
Hi Struan (nice STM pictures!)
first - yes, that's it exactly. In a more common discussion - but Emmanuel wanted to see and explain exactly what happens - one could forget about the fact that only one plane of the object space is imaged sharply, and simply state that the relative positions of objects from the foreground to the background, as recorded on film, remain unaltered during this rotation.
second - your French is perfect! Kingslake and Ray merely state that the entrance pupil is the center of perspective of the picture (regarding the object space; the center of perspective for the image space is the center of the exit pupil), without thrusting into a more detailed study.
Thanks Yves. I know several teachers, a butcher and at least
two vintners who disagree with your assessment of my French,
but it's nice to know it gets the job done
I need to sit down and draw some rays. My first attempt
concurred with the nodal point rotation, but I may be doing
something wrong (it has been known . For an example
inspired by my penchent for coke bottle optics, see here:
I'd appreciate any nits you might spot, but no hurries - I already
have promised the group a DOF analysis, and it seems they can
only take so much geometry before they start to whine and shift
in their seats.
I've seen your drawings. Well, maybe I was wrong about your French... - kidding. They just show the mistake almost everybody makes (including me before being interested in this issue). You should draw (even grossly) the positions of the two image points. Only one will be on the film (because the other corresponds to a subject that is out-of-focus). Then you draw the rays that * actually * go through the lens (and the aperture stop) and hit the film. These rays are not only determined by the positions of the image points - these positions can be found with the nodal points alone, so the entrance pupil would play no role. To draw these rays, you will have to consider the entrance pupil... then you will get it.
[I will be away for some days]
The nodal point is simply the point where the rays passing through the lens cross eachother.
If you are doing panoramic with multiple shots stitched together, then you want to position your camera so that it turns around the axis that goes vertically through the nodal point. Otherwise, you'll experience parallax errors/problems.
Parallax: Close your left eye, and stretch out your hand and hold up a finger. Then close the left and open the right eye. Note that the background behind the finger jumps a bit to the side.
This causes pictures not to line up exactly on the edges, for example, if you stood still with a 35mm camera an snapped off a 360degree roll of pictures while turning.
However, if you turn your camera on the axis of the nodal point, the edges should match up much better and make stitching the pictures together much easier.
Well Yves, I'm a convert. This isn't the first time I've had a mental
block, and I'm sure it won't be the last. Thanks for making me
The simplest way on paper for me to see that Yves (and others)
was right was to dispense with thick lenses and nodal points
altogether and go back to an ideal thin lens or a singlet like a
Sherlock Holmes magnifying glass. Here the rule is that rays
aimed at the centre of the lens pass straight through - i.e. the
lens behaves as if both nodal points are together at its centre.
Now put a pinhole or other small aperture a short distance front
of the lens and see what happens as you rotate it about the
centre of the lens and the centre of the pinhole. It's the latter
which prevents parallax.
It is worth reiterating: in practice turning a view camera around
the physical centre of the iris will in almost all cases eliminate
parallax errors, or at least reduce them to insignificance. I tried
this with my 180/315 mm convertible Symmar, and even in the
converted state, where the entrance pupil is some centimeters
from the nodal point, you have to include a very close up object
before parallax becomes noticeable when you simply turn about
the vertical axis of the lensboard. Get that lot in focus without tilts
and you will have other problems besides parallax.
Finally, the process described on many websites that moves the
rotation point forward until parallax dissapears does work
perfectly. It's just that it finds the centre of the entrance pupil and
not, as usually claimed, the front nodal point. Why this error is
so widely propagated I don't know, but I've done my part in the
past so it's time to munch on some humble pie.
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