Nodal Point Shift When Tilting the Camera - Solved

[dwswager]

If one attempts to do horizontal multi-shot images with the camera tilted down/up, the problem becomes placing the nodal point at the vertical axis of rotation.  We all experimentally find the nodal point for out seutps, but that is with the whole thing horizontally leveled.  I am personally dealing with this issue and have seen numerous posts on various boards so I thought I would post my solution. bjanes on this board recommended the following setup as in inexpensive way to do it.



The one issue with this setup is that as the camera is tilted back and forth the nodal point will shift away from the axis of rotation.  This is relatively easy to solve with a little math.  Assuming you already determined the nodal point for the lens/camera combination when horizontally level and we designate the tilt of the head from 90° (forward) to 0° (Vertical) to -90° (backward) then given the image below(note: my tilt head has degree markings on it...not sure how accurate):



A = Nodal Point
B = Point where horizontal line through nodal point meets sensor plane
C = Point of rotation of the tilt head
T = Tilt of head 90° to -90° (Pi/2 to -Pi/2 Radians)

x = Horizontal normal nodal distance
y = Vertical distance from tilt head axis of rotation to nodal point axis
z = Hypotenuse of our right triangle

We can calculate theta = arctan(y/x)

When we tilt the head we are increasing or decreasing theta by adding or subtracting so

Theta' = Theta - T

Now the new nodal distance x' = cos(Theta') * SQRT(x^2 + y^2) = cos(arctan(y/x) - T)* SQRT(x^2 + y^2)

Depending on your x and y distances, you will notice different rates of shift tilting forward and back.  I would do this ahead of time just like you did with finding your nodal points for your lenses.  I made a spreadsheet and then keep a cheat sheet for a few angles of tilt.  You can check your work by setting Tilt = 90°, -90° and Theta which should result in your answers being the value of y, -y and the length of the hypotenuse of the original triangle respectively.  This makes sense since rotated pointing straight down or up, the nodal point is always going to be the distance of the rotation out in front or back.  And, of course, the longest point forward has to be the length of the hypotenuse as you rotate around 360° you are just subscribing a circle with the nodal point.

Of course, this is somewhat esoteric depending on the setup and what you are shooting. 
 

[Ellis Vener]

You have just proven why ideally you should use a rig that allows you to adjust the vertical vertically, horizontally, and fore/aft displacement of the camera and lens so that the exit pupil remain centered in both a vertical and horizontal axes  while changing tilting and swinging  the camera/lens.

Think about  it this way: You are putting the nodal point or exit pupil of the lens at the center of an evenly lit   solid color sphere that has no reference points to tell you when  the camera platform of a tripod  head is level with the earth's horizon.  The world we are photographing is outside and separate from the camera's frame of reference. that sphere. This is what Bart meant when he said the that the camera exists in one spatial frame and the subject is in another that is  independent of the first.

[fdisilvestro]

Hi, just a note, I think the correct term is the "entrance pupil"

[dwswager]

Hi, just a note, I think the correct term is the "entrance pupil"

Yeah, but they don't call it an Entrance Pupil Slide and we all know what we mean.

[dwswager]

You have just proven why ideally you should use a rig that allows you to adjust the vertical vertically, horizontally, and fore/aft displacement of the camera and lens so that the exit pupil remain centered in both a vertical and horizontal axes  while changing tilting and swinging  the camera/lens.

Think about  it this way: You are putting the nodal point or exit pupil of the lens at the center of an evenly lit   solid color sphere that has no reference points to tell you when  the camera platform of a tripod  head is level with the earth's horizon.  The world we are photographing is outside and separate from the camera's frame of reference. that sphere. This is what Bart meant when he said the that the camera exists in one spatial frame and the subject is in another that is  independent of the first.

First, don't do that to me before coffee!

In reality, I agree.  But there is absolutely nothing 'wrong' with this setup as far as single row horizontal multi-shot images is concerned.  It is relatively light weight and inexpensive to achieve what I am attempting. The math is actually more accurate than the precision in the manufactured components or my ability to adjust them to the 'exact' positions I intend. 

I selected the following components for this exercise

• RRS PC-LR Panning Clamp
• RRS MPR-CLII Nodal Slide
• Sunwayfoto DT-01D50 Tilt Head (Clamp can rotate lateral or longitudinal positions)

While all are high quality components, I went with premium panning clamp and nodal slide as they are likely long term components.  If and when, I decide to really go this direction and move to multi row shooting, I will likely add a camera bar to the panning clamp or replace it with a leveling base and RRS PG-02 HB: Pano-Gimbal Horizontal Base and the RRS  PG-02-VA-LR upright.  Just not there yet!

[allegretto]

the Trig isn't really that difficult, but another way would be to simply experiment with horizontal lines instead of vertical ones in advance and not the radii and tilt involved

as a practical matter I just used the horizontal nodal point default and shifted vertically with T/S lenses in the cold/dark of Yellowstone last week

But lacking T/S, this is quite accurate, as you say.

[dwswager]

Of course, if you mount the tilt head centered into the panning clamp so the axis of rotation goes through the center of the clamp and mount the nodal slide into the tilt head, it now just requires knowing that single nodal point on the slider.  At 0° tilt you just set as normal or skip the tilt head all together.  At any other tilt angle all you need to do is position that same known nodal point for the camera/lens combo at the center axis of the tilt head.  About as much precision as any other method in the field.

[OldRoy]

I had no idea this was so difficult. It makes me wonder how I've managed to successfully stitch so many panos. On reflection maybe they weren't actually successful. I'll have to go back, check and delete any that don't meet the mathematical requirements.
It never ceases to amaze me how much people over-complicate stitching.
Roy

[Bart_van_der_Wolf]

It makes me think Bernard and Bart and all; make better composites, much much faster and more reliably than I can -- to a large degree because they use the best technology to avoid problems when they make the exposures. (There's also the small matter of skill and knowledge, but let's not get into that.)

There is also the matter of how one composes one's images. Personally I do not need a camera to see the composition. Only when I see a subject worth capturing, after maneuvering myself in the best perspective position, will I pull out the camera from the bag (or leave it where it is), and usually set up the tripod. That of course also depends on the type of subject, action photography rarely offers enough time for reflection.

It is then a liberating experience to not be restricted by the aspect ratio of the sensor, but let the subject dictate what to include or exclude. I also get to decide on the resolution by choosing a longer or shorter focal length (or even a mix). When I use the Pano setup, I'll also have the peace of mind that the stitching operation will not present time-consuming challenges, which is especially nice when deadlines need to be met, or when re-shooting is not an option.

Stitching has become a way of life, rather than a challenge. And it is also fun when a single image suffices, so I don't view stitching as a hammer looking for a nail ..., just another tool in the toolkit.

Cheers,
Bart

[Bart_van_der_Wolf]

Unfortunately I do like to compose (vertical) near & far, so there will be problems, and the most I'm likely to buy is Panosaurus not RRS or Nodal Ninja.

Shooting both near and far will benefit from a proper No-Parallax Point (NPP) setup, to avoid parallax issues if there are overlapping features/occlusions. A dedicated pano-stitcher, such as Hugin or PTGUI, will allow to compensate for image magnification differences of Focus-stacks (especially relevant for near focus). Alternatively a lens with tilt capability can help (tilt often also shifts the entrance pupil a little!).

Many subjects are less critical for far range parallax (especially vertical), so even a single row setup may be usable with a small change of pitch and a lot of overlap, for vertical panos. Just make sure that the near end is well aligned without parallax. It can also help to stitch horizontal strips first, and then stitch these strips vertically together. It's at these things that PTGUI is a great help, if it can't do the job in one go already.

Cheers,
Bart

[allegretto]

Shooting both near and far will benefit from a proper No-Parallax Point (NPP) setup, to avoid parallax issues if there are overlapping features/occlusions. A dedicated pano-stitcher, such as Hugin or PRGUI, will allow to compensate for image magnification differences of Focus-stacks (especially relevant for near focus). Alternatively a lens with tilt capability can help (tilt often also shifts the entrance pupil a little!).

Many subjects are less critical for far range parallax (especially vertical), so even a single row setup may be usable with a small change of pitch and a lot of overlap, for vertical panos. Just make sure that the near end is well aligned without parallax. It can also help to stitch horizontal strips first, and then stitch these strips vertically together. It's at these things that PTGUI is a great help, if it can't do the job in one go already.

Cheers,
Bart

which pano program do you use Bart?

[Bart_van_der_Wolf]

which pano program do you use Bart?

Mostly PTGUI Professional, but I have others as well (like PTassembler, Autopano Giga, Hugin, ICE), just in case. But PTGUI does almost everything I need, and it does it well. Do note that the Pro version offers several additional features that are important for specific workflows.

Pano2VR is another very powerful program for the creation of interactive 360 degree VR scenes/tours, and it takes e.g. equirectangular projection (360x180 degree) output from panostitchers, or based on a partial scene can create large zoomable Web-displays.

Cheers,
Bart

[OldRoy]

FWIW I've been using an NN3 since they first appeared. Totally under-spec for an FF SLR  really but adequate for MFT cameras. For stitching I use PTGui Pro.

As for all the hoo-ha about setup and the geometry of the NPP I don't have a lot of experience of doing conventional multi-row panos off a pano head unless you include 360x180s with a patched nadir using an FE lens, which requires 10 shots (excluding bracketing for hdr). I've done literally hundreds of these: people even pay me for them... For interiors this requires very accurate NPP setup if one's to avoid tedious kludges in post as the depth of field often ranges from a proximity of less than 1m. Parallax errors are very obvious and can completely defeat the stitcher.

But it ain't that difficult!
Roy

[dwswager]

First, as the initiator of this thread, I want to remind that this was about doing multi shot images with the camera tilted.  I tried to stay away from the word panoramic, because that is not the point.

In addition, I am an engineer and the most critical evaluator of my images, and have only just begun doing this so I have little field experience.  I do know that if you don't keep the panning base level, then the horizon will dip and if you don't center the entrance pupil over the axis of rotation, near and far parallax errors will occur and require correction in the stitching.

I find it hilarious that people will buy the most expensive, highest resolution cameras, lenses and gadgets and then cut massive corners in technique.  Now there is something to be said for utilizing field experience to know when it matters and when it doesn't, but it is always better to get the best input images possible.  I live by the motto "The good shot you get is better than the great shot you didn't!"

[NancyP]

You freaked them out dswager. Math! 
Yes you are quite right - GIGO - it is as easy to form good habits as it is to form bad habits. Actually, what amazes me is the relative rarity of tripods in the field. It is not just the absence of motion blur, but the extra time to set up and to evaluate whether you might do things differently.

[dwswager]

You freaked them out dswager. Math! 

For the mathematically challenged (and you really don't want to be doing math in the field anyway), the better arrangement might be pictured below.  In the field all you need to do is center the head in the panning clamp, and center the nodal point over the axis of the tilt head.  Hence, the only number you need to remember is the same one you would need for doing a single row level shot...the distance on the nodal slide to properly position the camera.  The propagation of all errors will overwhelm any 'alignment' errors you might get if you do a decent job positioning everything.

[NancyP]

That will work! Thanks.