Fisheye Lens

A fisheye lens is an extremely wide lens that sees about 180 degrees, a whole hemisphere, by curving every straight line that does not pass through the center of the frame. It matters because no ordinary lens can see that much: a normal wide angle has to keep lines straight, and that rule makes 180 degrees impossible. A fisheye drops the rule, and its curved, bubble-like look is the price of that huge view.

Once you know how it maps the world onto the sensor, a fisheye stops being a novelty. You can predict which lines will bend and which will not, keep a horizon flat or curve it on purpose, and decide when the look helps a picture. The photo above shows most of it already: the street across the middle is nearly level, the curb at the bottom bends, and the round image leaves the corners black.

Not sure how a fisheye differs from the wide lens you already own? The ultra-wide lens page covers the straight-line kind, which sees roughly 90 to 120 degrees.

Why it is called a fisheye

The name comes from the physicist Robert W. Wood, who in 1906 built a water-filled pinhole camera to show how the world looks to a fish looking up. Light from the whole sky, horizon to horizon, bends as it enters the water and squeezes into a cone only about 97 degrees wide overhead. A fish looking up sees the entire sky inside one bright circle, with the far edges of the world crowded into a thin ring around it. Divers call that circle Snell’s window.

That picture is the right mental model for the lens. A fisheye takes a half sphere of view and packs it into a circle on a flat sensor, squeezing the outer parts more than the middle. Early fisheyes were scientific instruments built to record the whole sky in one frame, for example to measure cloud cover. Photographers adopted them later for the look.

A fisheye maps angles: how it differs from a wide angle

Every lens has to decide where on the sensor a point in the scene lands. The deciding number is the angle between that point and the lens axis (the straight line out of the middle of the lens). Call it theta. The question is how far from the center of the frame a point at angle theta ends up.

A normal lens, called rectilinear, puts it at the focal length times tan(theta). That formula is what keeps straight lines straight, and it is why your standard zoom, your phone’s main camera and an ultra-wide all show buildings with straight walls. But tan(theta) grows without limit as theta approaches 90 degrees. A point 45 degrees off axis lands one focal length from the center, a point 70 degrees off lands 2.7 focal lengths out, and a point 90 degrees off would need an infinitely large sensor. That is why no rectilinear lens can ever show 180 degrees.

A fisheye uses a gentler curve. The common ones are:

• Equisolid angle: distance = 2f times sin(theta/2). Measurements of real camera fisheyes show that most come close to this one. It also has a useful property for science: equal areas of sky take equal areas of the picture.
• Equidistant: distance = f times theta (theta in radians). Each degree off axis moves the point the same distance outward, which makes angles easy to measure straight off the image.
• Stereographic: distance = 2f times tan(theta/2). It squeezes the edges least and keeps small shapes looking right. It is rare in camera lenses but common in software, where it makes the “little planet” pictures.

Real lenses only approximate these formulas, and that is fine. What matters is the shape of the curves.

The practical result is that focal length alone does not tell you the angle of view of a fisheye. The table compares a 15mm fisheye of the equisolid type with a 15mm rectilinear lens, both on a full-frame (36 by 24mm) sensor.

Want to see how these angles are worked out for ordinary lenses? Angle of view walks through the arithmetic, and field of view turns the angle into how much of the scene fits at a given distance.

The one rule: lines through the center stay straight

If you remember one thing about shooting with a fisheye, make it this: a straight line that passes through the center of the frame stays straight. Every other straight line bows outward, and the further it is from the center, the more it bends.

The reason is in the formulas above. A fisheye only changes how far from the center a point lands, never which direction from the center. Every point on a line running through the center lies along one direction, so it stays on one straight line in the picture. A line off to one side crosses many directions at different angles, and the gentle curve pulls its far ends inward, so it bows.

This rule gives you control. To keep a horizon flat, put it through the middle of the frame. To curve it, move it away from the middle: tilt the camera up so the horizon sits below center, and it bends into a bowl with its ends rising; tilt down so it sits above center, and it bulges into a dome. That dome is where the “curved earth” look comes from, and it is the lens, not the planet. The same goes for walls, door frames and poles. A pole in the middle is straight. A pole at the side of the frame bows outward, its middle pushed toward the edge and its ends curving back toward the center.

Is this the same as the barrel distortion people correct in ordinary lenses? Related, but not the same: barrel and pincushion distortion are small, unintended bends in a lens meant to be rectilinear, while a fisheye bends on purpose and by design.

Circular, diagonal and cropped circle fisheyes

A fisheye forms its 180 degree view as a circle of image. Which kind of picture you get depends on how big that circle is compared with the sensor, a question of image circle and sensor size.

• Circular fisheye: the whole 180 degree circle fits inside the frame, so you see a round picture with black all around it. It records the entire hemisphere in every direction. Nothing is broken; the black is simply where no image falls.
• Diagonal (full-frame) fisheye: the circle is big enough to cover the whole rectangle, so the picture has no black edges. It sees 180 degrees from corner to corner but less across the width and much less top to bottom (about 147 and 94 degrees on full frame).
• Cropped circle: in between. The circle is wider than the frame is tall, so the top and bottom are cut off but black still shows in the corners. The photos on this page look like this.

For an equisolid fisheye, the focal lengths that give each type work out like this (real lenses vary slightly with their exact projection):

This is why a fisheye made for full frame gives a different picture on a smaller sensor. A 15mm diagonal fisheye on an APS-C body only uses the middle of its circle, so you lose the corner to corner 180 degrees and get a milder curve. The crop factor page explains the general idea. Some fisheye zooms cover both types, giving a circle at the short end and filling the frame at the long end.

Edges squeeze on a fisheye; they stretch on a wide angle

A common belief is that a fisheye stretches things at the edges. It is the other way round. Stretched edges are the problem of the rectilinear wide angle, where faces near the corners turn into ovals. A fisheye squeezes things near the edge in the direction toward the center and widens them a little the other way, so they look flattened, not stretched.

You can put numbers on it by asking how big a small round object looks at different angles off axis, compared with the same object in the middle of the frame:

Two things follow. First, a fisheye keeps shapes surprisingly natural well away from the center: at 50 degrees off axis a round object is drawn within about 10 percent of its central size in each direction, while a rectilinear lens would draw it nearly two and a half times too long toward the center. Second, at the far edge an object is drawn about 0.7 times its central size toward the center and about 1.4 times across, so it looks half as deep as it is wide. Its area stays about the same (that is the equal-area property of the equisolid type); edge subjects look small mainly because a fisheye takes in so much of the world that anything not close to the lens is small.

The bulging nose in a close fisheye portrait is not the lens squeezing anything. It comes from being a few centimeters from the face, so the nose is much closer than the ears. That is perspective distortion, and it happens with any lens at that distance; a fisheye simply lets you get that close and still fit the whole head in.

How to shoot with a fisheye

Get much closer than feels right

Because a fisheye takes in so much, anything a few meters away is tiny. The subject that carries the picture usually needs to be within arm’s length, often closer. Most fisheyes focus very close, and the near-far contrast is the point of the lens: a foreground object fills half the frame while the background shrinks into a ring around it.

Place lines on purpose

Decide which lines must look straight and run them through the middle. For a flat horizon, hold the camera level with the horizon through the center. For a curved one, tilt. Verticals at the sides will always bow outward on a fisheye; keep the most important ones near the center line. If you want a plain, uncurved wide picture of a building or room, a rectilinear wide-angle lens is the better tool.

Watch your feet, your shadow and the sun

A view of 180 degrees includes things you never think about. Your feet, the tripod legs, your shadow and your own hands can all appear at the edge of the frame. Look around the whole edge of the viewfinder before you press the shutter. Outdoors the sun is very often in the picture, so expect lens flare and use it, or hide the sun behind something.

Depth of field comes almost free

Short focal lengths give enormous depth of field. For a 15mm lens at f/8 on full frame, the hyperfocal distance is about 0.95 meters, so focusing there keeps everything from about half a meter to infinity acceptably sharp. An 8mm circular fisheye at f/8 is sharp from roughly 15 centimeters to infinity. The hyperfocal distance calculator will give you the figures for your own lens and aperture (these formulas are worked out for the middle of the frame, so treat them as a guide at the edges).

Filters and hoods work differently

The front element bulges out of the barrel, so most fisheyes cannot take a screw-in filter at all. Some have a slot at the back of the lens for a gel or small filter. Diagonal fisheyes usually have a short petal hood built into the barrel, because any normal hood would show up in the frame. A separate lens hood is out of the question, so flare control is mostly a matter of where you point the lens. If filters are central to your work, the filters page explains which effects you can add later instead.

Shooting stars, interiors or a whole room at once? Fisheyes are popular for the night sky because one frame covers it all; photographing stars and the Milky Way covers the settings, and interior photography covers making a small room readable.

Defishing, little planets and other remaps

Because a fisheye follows a known formula, software can move every pixel to where a different projection would have put it. This is called remapping, and it opens three doors:

• Defishing to rectilinear. Software can straighten the lines, but it is bound by the same limits as a rectilinear lens. The edges get stretched enormously and must be cropped away, so a defished 180 degree fisheye usually ends up showing something like 100 to 120 degrees. You keep the middle and give up most of the reason you used the lens.
• Remapping to cylindrical or similar projections. With the camera held level, these keep verticals straight while letting the horizontal view stay very wide, a useful compromise for interiors and street scenes.
• Stitching and little planets. Two or more fisheye frames pointing in different directions can be joined into a full 360 by 180 degree sphere. Rendering that sphere with the stereographic projection makes a “little planet”. The 360 degree photography page walks through it.

Ordinary lens correction profiles in editing software are built to remove small amounts of barrel distortion from rectilinear lenses. A fisheye’s curve is not a defect of that kind, so treat defishing as a deliberate choice, not a fix. Lens corrections explains what the standard profiles do.

Where a fisheye earns its place

• Action up close. Board sports, cycling and climbing photographers put the lens right next to the action. The subject looms large, the background swings around it, and speed and height look exaggerated.
• Tight spaces. Inside a car, a small cabin, a cave or an underwater wreck, a fisheye shows the whole space from one spot. Underwater it pairs well with a dome port, since getting close also cuts down how much water the light passes through; see underwater photography.
• The whole sky. Pointed straight up, a circular fisheye records horizon to horizon in one frame, used for auroras, meteor showers and cloud and light pollution surveys.
• Looking up. Domes, atriums, tree canopies and tall buildings all radiate from the center when the lens points straight up, so their lines run through the middle and stay straight. Scientists use the same trick to measure how much sky shows through a forest canopy.
• Graphic play. Bending a horizon into a dome or wrapping a skyline around the frame can be the whole idea of a picture, as long as it is a choice and not an accident.

Where it does not belong: flattering portraits, product shots that must look true to life, and architecture where the client expects straight walls.

Common mistakes with a fisheye lens

• Treating it as a wider wide angle. It is a different projection. If you want straight lines, use a rectilinear lens; a fisheye will bend anything off center.
• Letting the horizon drift. A horizon slightly off center comes out slightly bent, which looks like a mistake rather than a choice. Either put it exactly through the middle or move it well away so the curve is obviously on purpose. The horizon in photography covers placement more broadly.
• Standing too far back. From normal distances everything ends up small, with lots of empty ground and sky. Get in close so something real fills the foreground.
• Blaming the lens for a big nose. Close faces distort because of distance, not projection. Back off a little, or put the face nearer the center and accept a playful look.
• Not checking the edges. Feet, shadows, straps, tripod legs and fingers creep into a 180 degree frame. Scan the whole border before each shot.
• Expecting a fisheye app or a crystal ball to do the same job. A phone filter can only bend the angle your camera already captured; it cannot add view. A crystal ball shows a wide, upside-down world inside the ball, but the rest of the frame is a normal photo.
• Applying a standard lens correction and wondering why the corners look wrong. Defishing stretches the edges hard and crops a lot. Decide before you shoot whether you want the curve.

Try this: find the straight lines in ten minutes

You need a fisheye (a clip-on fisheye for a phone works for this exercise) and a scene with clear straight lines: a doorway, a long wall, a horizon or a row of windows.

1. Center it. Stand square to a door frame and put its vertical edge exactly through the middle of the frame. Take a picture. The edge should be straight.
2. Move it to the side. Without changing where you stand, turn the camera so the same edge sits near the left side of the frame. Take another. The edge should now bow outward, away from the center.
3. Tilt up and down. Find a horizon or the line where a wall meets the floor. Shoot it level through the middle, then tilt the camera up so it sits low in the frame, then down so it sits high. You should get a straight line, a bowl and a dome.
4. Get close. Hold the lens a hand’s width from something with texture, a fence or a tree trunk, with the background a few meters behind. Then step back two meters and shoot again.

How to judge it: line up the frames side by side. You have it if you could predict, before each shot, which lines would stay straight and which way the others would bend, and if the close frame clearly reads as “foreground plus world” while the distant one looks small and empty. If a line bent the wrong way, check where the center of the frame actually was.

Want the same exaggerated near-far look without the curve? A rectilinear wide angle used close does it with straight lines, at the cost of stretched corners.

Fisheye lens FAQ

Can a fisheye lens see behind itself?

A few specialist designs see more than 180 degrees, around 220 degrees, so they take in a little of what is behind the front of the lens. They are rare, very large and mostly used for surveillance, science and immersive video. Ordinary fisheyes stop at about 180 degrees.

Is a fisheye lens good for landscapes?

Sometimes. With the horizon through the center and nothing tall near the edges, a diagonal fisheye can pass for a very wide landscape lens and take in far more sky and ground. Trees and mountains near the sides will lean and bend, so most landscape work suits a rectilinear wide angle better.

Why are the corners black on some fisheye photos?

The lens forms its image as a circle. With a circular fisheye, or a fisheye on a larger sensor than it was designed for, that circle is smaller than the frame, so the corners get no light. It is how the lens is designed, not vignetting or damage.

Can I turn a fisheye photo into a normal wide-angle photo?

Yes, with software that remaps it to a rectilinear projection, but you lose a lot. The edges stretch so much that the result is usually cropped to around 100 to 120 degrees, with softer corners than a real wide-angle lens would give.

What focal length is a fisheye?

It depends on the sensor and on whether you want a circle or a full frame. On full frame, circular fisheyes are around 8mm and diagonal ones around 15mm; on APS-C the figures are about 5.6mm and 10mm. A fisheye’s focal length does not translate into angle of view the way a normal lens’s does, because the projection is different.

Do phones have fisheye lenses?

A phone’s ultra-wide camera is usually processed to look rectilinear, keeping lines mostly straight at around 120 degrees. A clip-on fisheye attachment adds real angle in front of the phone’s lens. A fisheye filter in an app only bends the picture the camera already took.