How to Find the Correct Lens Pivot for Panoramas

When you shoot multiple shots to stitch into a panorama, you should pivot the lens around what’s often called the entrance pupil. This magical pivot spot is the only location that will eliminate parallax error. This spot is also known as the nodal point.

If you don’t pivot your lens in the correct location, you’ll end up with overlapping shots that don’t match up precisely. Stitching programs try to compensate for this error, but it’s better to get the right shots in the first place.

Unfortunately, lens manufacturers don’t normally provide the information about the lens’ entrance pupil. In this case, you’ll probably have to figure it out for yourself. Believe it or not, sometimes the entrance pupil can be located outside of your lens.

To set up a lens for proper panorama shooting, you’ll need a tripod head that can rotate about the vertical axis, and you’ll also probably need an attachment plate that you use to offset the camera tripod screw from the tripod’s pivot axis. The best attachment plates are Arca-Swiss (your tripod head needs to have an Arca-Swiss clamp). With these plates, you can easily slide the camera/lens and then securely clamp them in place.

There are also special ‘panorama heads’ you can buy to make panoramas, instead of the more generic Arca-Swiss clamps. You still need to locate the pivot-point(s) for your lens to make proper use of them, however. Beware that zoom lenses have a different pivot point for each focal length.

Camera attached to a long Arca-Swiss plate

In the photo above, the camera is attached to a long Arca-Swiss plate on top of a tripod. The long plate allows the camera to be shifted far from the tripod rotation centerline. Now, when the tripod head gets rotated the camera/lens will rotate around the vertical red line instead of the camera tripod socket.

Usually, really long Arca-Swiss plates are a pain and are best avoided. Here’s a case, however, where a long plate is exactly what’s needed. As you’ll see below, sometimes even the hardware shown above isn’t enough to achieve a correct pivot.

Method 1 to Locate Pivot Location

To gather the information about the ideal pivot location, you need to start by taking photos with subjects at medium and long distances that are aligned with each other. Start by aligning the near and far objects in the exact frame center. Your camera should be perfectly level. Now, rotate the tripod head to get those objects on the left-hand side of the frame. Take a shot with the distant detail on the left frame edge and then rotate on the tripod to the right edge of the frame and take another photo.

Repeat the process, but first shift the camera/lens combination in the tripod’s Arca-Swiss clamp by a large amount. Make notes about which shift location was used for each pair of shots.

With a mirrorless camera, you might get away with just switching to a magnified view to check for left/right alignment and skip having to review photos.

The first attempt: pivot around the camera tripod socket

I used an 8-meter-away window frame for the medium object, and a 500-meter-away palm tree for the distant object. I adjusted the camera position until the medium and far objects were right next to each other in the exact frame center.

Next, I pivoted the camera to place those objects on the left side of the frame. I captured the first shot.

Close object aligned with distant detail on the frame left edge

Distant detail appears shifted right from the window frame

Next, I pivoted the camera to place those objects on the right side of the frame and took another shot.

Close object aligned with distant detail on the frame right edge

Distant detail appears shifted left from the window frame

The results from pivoting over the camera’s tripod socket were terrible. The distant object shifted severely, compared to the window frame. It slid from one side of the window to the other, just by photographing it from opposite sides of the frame.

What’s shown above is classic parallax error. The distant object keeps moving, relative to a closer object, when shot from different left-right locations in the frame.

The next test: pivot around the lens as shown

Since I am using a mirrorless camera for the testing, it’s pretty straightforward to just iterate as follows, once I have my near/far objects aligned in the frame center using a magnified viewfinder image:

1)    Pan left or right and observe any shifting of the far object.

2)   Slide the camera/lens forward or backward in the Arca-Swiss clamp by maybe 10mm and lock it down.

3)   Repeat the panning to see if the far object shifting error grows or shrinks. If it is growing, then slide the opposite direction in the clamp. Go to step (1).

In my testing, the trends indicated that moving the pivot point more toward the lens front got better and better results. Finally, I ended up with the configuration shown above. The entrance pupil is roughly between 90 and 100mm from the camera sensor at the 24mm focal length. I couldn’t tell the difference after I got to within a zone of maybe 5mm at this focal length.

Close object aligned with distant detail on the frame left

Distant left-detail appears the same as in the frame center!

Close object aligned with distant detail on the frame right

Distant right-detail location matches the frame center and left!

After I located the proper lens pivot location, I attached the Arca-Swiss plate onto the camera such that one end of the plate exactly aligned with the Arca-Swiss tripod clamp edge. This makes it easy to reliably place the camera onto the tripod with perfect alignment for correct panorama pivots.

I got lucky with this 150mm Arca-Swiss plate. If it were any shorter, then I wouldn’t be able to quite reach the lens nodal point with the plate fully gripped inside the tripod head’s clamp.

The top photograph shows the correct nodal point (entrance pupil) for the Nikkor 24-120mm f/4 S lens when zoomed to 24mm.

Same lens zoomed to 120mm: entrance pupil now located at 59.5mm

I got my smug smile wiped right off of my mouth when I now tried zooming the lens from 24mm out to 120mm. Big-time parallax error had returned. After repeating the panning procedures at this zoom setting, the new nodal point was located as shown above.

Method 2 to Locate Pivot Location

The following technique can at least get you close to finding the lens nodal point (entrance pupil). This technique is more challenging and time-consuming than the first method.

You need to draw the lens horizontal field of view (FOV) angle on paper, with a line splitting that angle exactly in half. In the case of this 24mm setting, that’s 73.7 degrees, with the split line at 36.84 degrees. Use a protractor to measure the angle. Lay this paper on the floor and lay some long straight guides along these lines. You might find that using string taped to the floor will make a good guide line.

Mark the exact field of view angle and lay guides

Next, place your camera on the floor over the intersection of these guides, and shift it forward and backward until both guides are seen just along the vertical frame edges in the viewfinder. Switching to Live View may make this job easier. Be sure to stop down the lens aperture to get a deep depth of focus.

Also, you’ll want your camera to be level. I have a handy little bubble level that I keep in the camera’s hot shoe to check for level.

Align the camera to split the angle

Slide the camera to get the guides parallel to frame edges

Notice that the thin black guide lines are just along the frame edges in the shot above. Where the guides intersect under the camera/lens is the location of the correct pivot point (entrance pupil).

To verify the pivot point, go back to Method 1 using this location as a starting point to see if it's correct. You may need to fine-tune the location a little.

15-frame panorama after pivoting around the ‘entrance pupil’

I stitched the photographs together using Capture One with ‘cylindrical projection’. This editor has several projection options. I like using Lightroom for making panoramas, too.

Nikkor AF-S 24-70 f/2.8 E ED VR at 24mm zoom setting

Shown above is another lens also zoomed to 24mm. Its entrance pupil is quite different than the 24-120mm lens. It should be obvious that the kind of severe offset of the camera and the center of gravity shown above requires a very sturdy tripod. The last thing you want is to have your tripod fall over with your camera and lens.

Entrance Pupil the Easy Way

If he happens to include your lens, Bill Claff’s Photons to Photos database of lens information has already compiled the pivot information you need.

Bill’s wonderful site has many lenses analyzed here, and you need to find the value of ‘P’ (entrance pupil) and ‘I’ (image plane) for your lens at the correct zoom setting. For the 24-70 lens shown above, his site link gives the values of P=34.76mm and I=220.25mm at 24mm.  Just do the subtraction  I-P or (220.25 – 34.76)=185.5mm to find the distance from the camera sensor to the tripod pivot location. At 50mm zoom, the pivot is at 181.25mm, and at 70mm zoom, the pivot is at 172.3mm.

These pivot numbers are pretty huge, requiring hardware with a long range of adjustment. This also requires strong tripod hardware.

I found out that Bill had also analyzed my 24-120 f/4S lens, unfortunately only after I did the experiments mentioned above, and I got essentially the same results as Bill did. Bill got I@24mm = 130.96mm, P@24mm = 30.8 and I@120mm = 185.96mm and P@120mm = 126.43mm. This means the sensor-to-pivot at 24mm = 100.16mm. For the 120mm zoom setting, this means the sensor-to-pivot value is 59.5mm.

Bill has my 24-120mm lens listed as “Nikon 25-117mm f/4 IF”, which is why I didn’t find it at his site initially. He lists it according to the measured focal length versus the actual lens name.

Bill has lots of very nice information on his website, although much of the site is targeted more for scientist types.

Summary

Probably 99% of photographers would simply use the camera tripod socket location on their tripod for making panoramas. As demonstrated above, that would simply produce incorrect results. Don’t be that photographer; you’re better than that.

The procedures shown above could also be done with the camera in portrait orientation, but you better be sure that you have pretty heavy-duty hardware, a camera ‘L’ bracket, and a strong tripod.