How to Take a Photo of the Curve of the Horizon

Mick West

Administrator
Staff member
20170625-121407-meuq4.jpg
4x vertical scaled. Lunada Canyon, Rancho Palos Verdes, California. 33.767482853°, -118.408898009°
Source: https://nobodyhikesinla.com/2010/12/06/lunada-canyon/


The horizon is visual line that separates the earth from the sky. On land this is usually nearby hills and is quite uneven, but if you have a good view of the ocean the horizon appears as an essentially flat line between the sea and the sky.

Image Source: https://commons.wikimedia.org/wiki/File:Sailing_Boat_Horizon.JPG

It looks flat, and in fact the horizon IS geometrically flat. Since all the points on the ocean horizon are the same distance away from you, and the same distance below you, the horizon forms a flat circle with its center some distance below your feet.

But while it's flat, it is a circle, and so the higher above the circle you are the more the curve becomes apparent.

You'd think you could simply go high enough and then take a photo, and show the curve. However the problem here is that the higher you go the further away the horizon is. If you are just 40 feet above sea level then the horizon will be a nice sharp line, as it's only 8 miles away. However it's too flat from this angle to see the curve.
20170625-094505-9g17m.jpg

Image Source: Mick West

But if you go up in a plane to 35,000 feet the horizon is 229 miles away. It's curving a lot more, and would be obvious if there was no atmosphere, but it's too hard to see.
20170625-094816-ki847.jpg

Image Source: Mick West, IMG_6137, North Sea.

So we must seek a happy medium, high enough to detect the curve, but not too high that the horizon is blurry. The sweet spot here seems to be around 400 to 700 feet (around 120 to 210 meters) above sea level.

However caution must be exercised, and there's several other factors to consider. Here I'll list the best advice for getting a photo of the curve of the the horizon. We'll consider:

  1. Location - you need a spot about 400 to 700 feet up, with a view of the the ocean horizon that fills the whole image from left to right.
  2. Time and weather - overcast with good visibly, minimize sun
  3. Equipment - a good camera with a wide angle lens with minimum distortion
  4. Settings. Wide angle, focus on the horizon, underexpose, small aperture, best image quality.
  5. Lens distortion compensation. Keep horizon centered, have a straight edge in the shot. Take photos above, at, and below the center.
  6. Magnification. Stretch image vertically to magnify the curve without changing it. Increase image contrast, use gradient maps.
Location

This is relatively straightforward, just get 400 to 500 feet up. A tall building near the water would do. But the key is having an unbroken horizon from left to right. Now I have 500 feet as the upper end, however you might be able to use a higher location (like the viewing platform of the new World Trade Center). You might find though that when you enhance the image that distant lands will prevent you getting a clear image.

Time and Weather

The sun is not your friend here. Glare can make the ocean blend into the sky and you want a sharp transition. So if it's sunny you should try to get the sun behind you (i.e. looking west in the morning, or east in the evening.

20170625-101134-c2ylx.jpg

Image source: http://millerprosthetics.com/category/inspiring-stories/page/3/

Shooting closer to noon will also ensure there's less reflection from the ocean, especially in summer, as the sun will be high in the sky. Local solar noon varies, but is often around 1PM due to daylight savings time.

You can also get good results when the weather is overcast, but not foggy - the sea will be slate grey against a whiter sky.
20170625-100659-pl61a.jpg

Image Source: http://www.iangarrickmason.com/journal/stolid


Another potentially good time is when the sun is below the horizon.
20170625-100850-xoco4.jpg

Image Source: http://www.freestockphotos.biz/stockphoto/9810

The bottom line though is that you need a clear horizon as is possible.

Equipment

The more of the horizon you can see, and the more pixels you have in the image, the easier it will be to see the curve. So the basic things you want are wide angle and high resolution. You also want to avoid introducing curve via lense distortion. Some distortion is inevitable (and we shall deal with that later), but you want to minimize it was much as possible. So ideally you'd have a rectilinear lens.

Wide angle here means a field of view (FOV) of 60° or more. Lenses typical don't have their FOV written on the side, but 60° is a typical field of view of a modern camera phone. On a full frame DSLR (like a Canon 5D or Nikon D610) you'd want 30mm or wider, with something like 17mm (93°) being ideal.

Crop sensor DSLRs are much more common than full frame, so to get the full 90° you'd need to use something like 10mm.

High resolution is important as the curve can be just a few pixels. The higher the resolution, the easier it will be to see. But any recent DSLR should work, assuming it's set to best quality. What won't work is video. 4K video may come close, but 4K is only 2160 pixel vertically, regardless of the camera. A modern DSLR is generally twice that vertical resolution. So shoot stills, not video.

Rectilinear is a fancy way of saying "straight line". A rectilinear lens will not distort straight lines, so they will appear straight in the image. Similarly if a line is curved (like the horizon) it won't get more or less curved. So we want our lens to be rectilinear.
20170625-104310-61aid.jpg

Image Source: https://en.wikipedia.org/wiki/File:Panotools5618.jpg

Perfectly rectilinear lenses can be hard to find, and expensive. However an obvious thing we can do is don't use fisheye lenses. Fisheye lenses are highly curvilinear. Basically you want to use a lens that is as rectilinear as possible.

Non-DSLR camera
like the Nikon P900 and even the iPhone or other phone camera might work. However you've got a more limited field of view, and lower quality sensors, so you then become more dependent on other factors.

Settings


Point-and-shoot might work, especially if you've got good atmospheric and lighting conditions but there are things you can do to improve the quality of the image.

Best Quality - you want the image setting to be as high resolution as possible. If your camera allow RAW then use RAW. Otherwise set the image size and image quality to the highest it will go - usually this is referred to as fine. You may also have a separate image size setting, again as high as it will go.

Focus on the Horizon
- The horizon is what we want to see, so if the camera focusses on a window, or nearby people, then the horizon might end up blurry. If you need to, then use manual focus to get the horizon as sharp as possible. This image might have been perfect if not for the bad focus.

20170625-125823-qe2cb.jpg

Image Source: https://girlhiker.com/2013/09/03/los-liones-trail-in-pacific-palisades-california/

Underexpose
- glare from the sun, and sometimes haze, can make the horizon hard to see. You can often counteract this by underexposing. This can be done with the Exposure Compensation setting, often expressed as "EV", set it to -1.0EV. But you may need to experiment to get the best result. You can also set the camera to Bracket, where it will take three shots at different exposures.

Small/Medium Aperture
- Smaller apertures give a wider depth of field and so give you more leeway with focus. Large "f" numbers mean smaller apertures. Try for f/8 at least. Going very small like f/22 might help your depth of field, but the overall quality depends on the lens. Lenses have a sweet spot for sharpness, and you should try to find out what it is for your lens and use that. If you don't know then just go for f/8, and make sure you have good focus on the horizon.

Low ISO
- Lower ISO gives a less noisy image. ISO 100 is usually the best. However you need to make sure this is not going to give you a low shutter speed. If so then use a tripod.


Lens Distortion Correction

With a wide angle lens you are probably going to get some distortion. However there are things you can go to minimize this.

Center and Level the Horizon - Distortion happens concentrically around the middle of the image. So if a line goes through the middle of the image it will be lengthened or shortened slightly, but it will not be bent.
20170625-110526-3xhxk.jpg

Image Source: https://millerprosthetics.com/2016/08/25/nancy-settles-in-her-rio-apartment-and-its-amazing/

Use a Straight Edge - If you put a known straight edge very close to the horizon, then you can compare the horizon against the straight edge. If the lense is distorting things then the straight edge will be curved too. Then we can see if the horizon curves more than the straight edge, which will indicate the horizon is actually curved.

(This image discussed in more detail here: https://www.metabunk.org/measuring-the-curvature-of-the-horizon-with-a-level.t7832/ )

Take pictures above and below the center - Move the camera so the horizon is first above the center line, then at the center line, and then below the center line. If it curves in the same direction all three then it's definitely curved. If not then we need to account for this.

Magnification

The curve of the horizon is small at low altitudes. You can use the metabunk curve calculator (in "advanced" mode) to work out just how much you should be looking for. Around 450 feet this is going to be something between 3 and 6 pixels.
Now you can see that in an image with the naked eye - especially if it's against a straight edge, like with the yellow carpenter's level above. However it becomes easier to see if you magnify it.

Just zooming in will help if you are comparing against a straight edge, but does not really make the curve more apparent.

Enhancing Contrast can be very helpful. You can just use the brightness and contrast controls, or use the levels. Basically adjust to make the horizon as clear as possible. Just don't go too far, as you can lose detail.

Magnifying vertically is what you need. This means selecting a narrow strip of the image around the horizon, and then stretching it vertically. The process here is:
  1. Use the original resolution image with enhanced contrast.
  2. Select the strip of the image with the rectangular marquee tool
  3. Copy and Paste that strip
  4. Edit->Free Transform
  5. Drag down the bottom edge of the strip (and maybe raise up the top edge).
Example:
Source: https://www.youtube.com/watch?v=E-RXUa25jPA

via GIPHY

Source: https://giphy.com/gifs/3o7buaAKBcQDnHvSeI/html5


Several more examples can be found here:
https://www.metabunk.org/measuring-the-curvature-of-the-horizon-with-a-level.t7832/

Other Things

If you are really interested there's a variety of things you might try to make things more apparent.

Compare Against Google Earth

Google Earth models the Earth as you'd expect - as a globe. So if you position the Google Earth camera where you took the photo, then take a screenshot, then you should be able to see the curve. Ideally you would fit the image precisely in GE. Like this example from around 550 feet.


You crop the horizon portion of the Google Earth view under the photo, and scale vertically (20x here)


Then compare that against the same portion of the photo scaled by the exact same amount.



The photo is obviously higher resolution than the screenshot, however you can see the same curve in both. This verifies we are photographing the expected curve.
 
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0x90

Closed Account
Nice thinking -- this is probably one of the best proofs I've seen yet, as it is directly recorded in a single moment, and is not susceptible to any misunderstanding about refraction. The "skeptics" do always amaze me with their creativeness, but I struggle to imagine what alternative explanation could possibly be given; anything having to do with the camera can be ruled out simply by capturing several images with the camera upside-down, sideways, and so forth, and you have already covered lens distortion.

[...]
 
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Mick West

Administrator
Staff member
Actually Google has updated the 3D Buildings for that area, allowing me to get a much better fit:
33.766558512°, -118.405555257°
Eye alt 564 feet
See attached KMZ file
20170627-062240-qjr2d.jpg
 

Attachments

Mick West

Administrator
Staff member
So some interesting results here:
Source: https://www.youtube.com/watch?v=fUyChYlSmnk


Basically they took a photo of the horizon from what looks like about 536 feet (slightly lower than the Lanuda pic above). This was done with a P900 at 24mm effective zoom. This should have been enough to show a curve. But it didn't
20170627-102932-9apk7.jpg


In fact it shows a weird upwards bend.

Further investigation with my P900 shows something odd, and basically makes it very hard to get any useful results from the P900 without using a left-to-right straight edge close to the horizon.

I took a video of my slowly panning up over level, so that we get images both above and below.

Source: https://www.youtube.com/watch?v=wElvvze1Bxw


At the start of the frame, the level is below the center of the image, and when magnified 20x vertically you get a downwards curve.
20170627-103607-fxep3.jpg


One second later, still below the center, it's flat!
20170627-103753-c93ja.jpg


At 2 seconds, we are STILL below the center, but now it's curved up
20170627-103825-rj9qv.jpg


Almost exactly at the center, still a smooth upwards curve
20170627-103936-zt4m1.jpg


Well above the center, still an upwards curve
20170627-104016-epj04.jpg


Above the center, and FLAT
20170627-104053-1l5gc.jpg


Finally, still above the center, and it's curving down.
20170627-104132-x17qk.jpg


I suspect the reason for this is the image stabilization. In the P900 this would be done by shifting the sensor, which would then move the effective center of the image, and possible make the mirror no longer perpendicular to the focal axis of the lens.

Compare with a Canon 7D DSLR with a non-IS 10-22mm lens at 17mm.
20170627-104605-u1c1l.jpg


And compare the various random distortions above with the expected curve from about 50 feet higher.
20170627-105057-ljkc1.jpg


Clearly claiming that a curved horizon is or is not visible in a P900 is impossible without a full width straight edge to compare it against.
 

Amber Robot

Member
I suspect the reason for this is the image stabilization. In the P900 this would be done by shifting the sensor, which would then move the effective center of the image, and possible make the mirror no longer perpendicular to the focal axis of the lens.
Can you deactivate the image stabilization? Perhaps it's just a minor optical misalignment resulting in the center of your barrel distortion not being at the center of your sensor.
 

Mick West

Administrator
Staff member
Can you deactivate the image stabilization? Perhaps it's just a minor optical misalignment resulting in the center of your barrel distortion not being at the center of your sensor.
You can. And I also considered it might be from the movement during the video. So I disabled the IS, then took three still photos with the top edge of the level above, at, and below the center.
Three P900 around the center.jpg


All three show a downwards curve, lessening as you get lower. I imagine it would change direction if I kept going, however the "below" shot was already quite a bit below the centerline (see the magenta line, below).
20170627-121027-cugg1.jpg


Perhaps turning off IS just locks the sensor where it last settled?
 

Mick West

Administrator
Staff member
If you took photos of a regular grid you might be able to suss out the amount of distortion and where it is centered.
Yeah, but since it varies randomly that's not really useful. You need to know the distortion for a particular shot.

Basically you need the straight edge in the frame.
 

Amber Robot

Member
Yeah, but since it varies randomly that's not really useful. You need to know the distortion for a particular shot.

Basically you need the straight edge in the frame.
If it's the optical aberration called 'distortion' (i.e., a varying plate scale with field position) then it shouldn't vary randomly. It may vary with focal length and focus setting of the lens, but not randomly.
 

Mick West

Administrator
Staff member
If it's the optical aberration called 'distortion' (i.e., a varying plate scale with field position) then it shouldn't vary randomly. It may vary with focal length and focus setting of the lens, but not randomly.
But as I noted above, it DOES vary randomly, and I suspect the cause is the image stabilization moving the sensor. This is subject to random inputs, and so is random.
 

Amber Robot

Member
But as I noted above, it DOES vary randomly, and I suspect the cause is the image stabilization moving the sensor. This is subject to random inputs, and so is random.
That's why I recommended turning off the image stabilization. These kinds of photos should be done with a tripod anyway.
 

Mick West

Administrator
Staff member
That's why I recommended turning off the image stabilization. These kinds of photos should be done with a tripod anyway.
Yes, but then to seems to stop in a random place, not centered. And if you don't know where the center is you can't tell what's going on with the line. Hence the need for a straight edge (or a better camera).
 

Amber Robot

Member
Yes, but then to seems to stop in a random place, not centered. And if you don't know where the center is you can't tell what's going on with the line. Hence the need for a straight edge (or a better camera).
Indeed. An in-image calibration is always the best.
 

Calluser

New Member
oh wow. i didn't even expected to get so many and so useful tips. thank you very much for them, i will definitely save this post to read for later. are any of those photos above yours? or you've taken them from internet?
 

Mick West

Administrator
Staff member
oh wow. i didn't even expected to get so many and so useful tips. thank you very much for them, i will definitely save this post to read for later. are any of those photos above yours? or you've taken them from internet?
A mixture. I've added source links to all the image in the first post.
 

Rory

Senior Member
Barrel distortion on two phones, a Moto G3 and an iPhone 6:

moto G3.jpg

iphone.jpg


The distortion on the Motorola is so evident I can even see it in the viewfinder.

(iPhone image rotated slightly: this compression technique is also useful in showing how poor I am at aligning a camera perfectly parallel to a target. ;) )
 

Rory

Senior Member
iPhone SE:

iPhone SE test.JPG


Looks good right around the centre of the frame. Interestingly, more of an upward curve in the lower portion, and downward above centre.

Analysing closer, a little over 7% of the horizontal field is showing pretty much perfect straight lines, which equates to pixels 1403-1621 in an original 3024 pixel high image.

Here are three horizons I took the other day. Obviously they'd be better if they didn't have trees in the way, but the curve is pretty evident (y-axis position of horizon in brackets):

horizon 1452-1476.jpg

(1452-1476 ~48px above centre)

horizon 1488-1504.jpg

(1488-1504 ~14px above centre)

horizon 1536-1554.jpg

(1536-1554 ~33px below centre)

Just a trial run. A clearer horizon and a straight edge next time, I think.
 
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Rory

Senior Member
From how high?
1500 feet. It's a pretty sweet spot with 180° views to a horizon and, I discovered, driveable to the top, so easy enough to go up with better gear. I might do the full set of parallel lines, water level, theodolite, curve of the horizon, actual eyes, and the new pipe one that the YouTube crowd have been getting excited about. :)
 

Mick West

Administrator
Staff member
1500 feet.
Nice, seems like I need to revise my "you need a spot about 400 to 700 feet up," in the OP. Based on the clarity of your horizon it seems up to around 2,000 feet should be good. It's going to depend on the atmosphere and the weather.
 

Rory

Senior Member
I've knocked up a frame with some bits I found lying around:

horizonamotic5000.JPG


The idea is that I can locate the horizon in between the two metal bars, so I have a straight edge not only below but above the horizon.

Vertically stretched, it looks like this:

horizonamotic5000_squashed.jpg


Pretty good in the centre of the frame, and a noticeable barrel pincushion distortion moving above and below the centre of the frame, as demonstrated with the grid above (it's the iPhone SE).

My next plan is to use more cable ties to ensure that the two edges are as near as damnit the same distance apart all the way along. And then when it comes to actually photographing the horizon, to measure from the camera to the two ends of the frame, to make sure it's as perpendicular to the line of sight as possible.
 
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Steve S

New Member
I've knocked up a frame with some bits I found lying around:

View attachment 36073

The idea is that I can locate the horizon in between the two metal bars, so I have a straight edge not only below but above the horizon.

Vertically stretched, it looks like this:

View attachment 36074

Pretty good in the centre of the frame, and a noticeable barrel distortion moving above and below the centre of the frame, as demonstrated with the grid above (it's the iPhone SE).

My next plan is to use more cable ties to ensure that the two edges are as near as damnit the same distance apart all the way along. And then when it comes to actually photographing the horizon, to measure from the camera to the two ends of the frame, to make sure it's as perpendicular to the line of sight as possible.
That looks like pincushion distortion to me.
 

Mick West

Administrator
Staff member
Mick, how did you create this gif? Was there a quick way to do it or was it a frame by frame crop and position job?
Animated transform in Photoshop.

  1. Open file
  2. Window/Timeline
  3. Create Video Timeline
  4. Right click on background layer, "Convert to Smart Object"
  5. In timeline expand Layer 0
  6. Add Transform keyframes as needed with vertical stretch (start, pause, stretch, pause, restore)
  7. Export as gif or video
 

Rory

Senior Member
Thanks Mick, that's great. I shall give it a try soon.

Meanwhile, here's a video introducing the Horizonomatic5000, and giving it a test:

Source: https://www.youtube.com/watch?v=YyEfmX2cvOk

Results are promising. About time I took it up the hill and photographed the horizon. Other than weather conditions, the only issue I see is getting both the Horizonomatic and the horizon in a decent enough focus.
 

Mick West

Administrator
Staff member
Meanwhile, here's a video introducing the Horizonomatic5000, and giving it a test:
Nice. What are you using for the straight edges?

For consistent replication, I'd recommend a couple of 48" aluminum I-beam levels, about $25-$40 each. THat way you get the added benefit of having the edge level.
 

Rory

Senior Member
Took some more photos today with two shorter, straighter, narrower windowed frames. Elevation was about 575 feet above sea level. Great clear and crisp horizon. Here's a small selection:

IMG_1968.jpg

IMG_1989.jpg

IMG_2105.jpg


Those images are unrotated, cropped to the centre 124 pixels from an original 4032x3024 image. Pictures are taken with an iPhone SE, which a grid test showed had 200+ pixels undistorted around the centre of the frame.

I quite like this one too, which has the straight edges raised up at one end to create a v-shape in opposition to the downward curve of the horizon:

IMG_2132.jpg


In all the images I took today - there were over 400 in total - the curve of the horizon shows the same, while the straight edges stay straight.

The curve matches both the simulated curve from Walter Bislin's website and the expected pixel difference between the centre of the curve and the edge (~4).
 
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