How does light bend around my finger tip?

Posted by Pinki | Updated on

This effect is caused by both the foreground and the background objects being out of focus, and occurs in areas where the foreground object (your finger) partially occludes the background, so that only some of the light rays reaching your eye from the background are blocked by the foreground obstacle.

To see why this happens, take a look at this diagram:

Diagram 1: light rays forming a blurred image of a object

The black dot is a distant object, and the dashed lines depict light rays emerging from it and hitting the lens, which refocuses them to form an image on a receptor surface (the retina in your eye, or the sensor in your camera). However, since the lens is slightly out of focus, the light rays don’t converge exactly on the receptor plane, and so the image appears blurred.

What’s important to realize is that each part of the blurred image is formed by a separate light ray passing through a different part of the lens (and of the intervening space). If we insert an obstacle between the object and the lens that blocks only some of those rays, those parts of the image disappear!

Diagram 2: obstacle blocking part of the light rays, resulting in a sharper and shifted image

This has two effects: first, the image of the background object appears sharper, because the obstacle effectively reduces the aperture of the lens. However, it also shifts the center of the aperture, and thus of the resulting image, to one side.

The direction in which the blurred image shifts depends on whether the lens is focused a little bit too close or a little bit too far. If the focus is too close, as in the diagrams above, the image will appear shifted away from the obstacle. (Remember that the lens inverts the image, so the image of the obstacle itself would appear above the image of the dot in the diagram!) Conversely, if the focus is too far, the background object will appear to shift closer to the obstacle.

Once you know the cause, it’s not hard to recreate this effect in any 3D rendering program that supports realistic focal blur. I used POV-Ray, because I happen to be familiar with it:

Render 1: Sphere in front of a grid plane, narrow aperture Render 2: Sphere in front of a grid plane, wide aperture, grid in focus

Above, you can see two renderings of a classic computer graphics scene: a yellow sphere in front of a grid plane. The image on the left is rendered with a narrow aperture, showing both the grid and the sphere in sharp detail, while the one on the right is rendered with a wide aperture, but with the grid still perfectly in focus. In neither case does the effect occur, since the background is in focus.

Things change, however, once the focus is moved slightly. In the image on the left below, the camera is focused slightly in front of the background plane, while in the image on the right, it is focused slightly behind the plane:

Render 3: Sphere in front of a grid plane, focus between grid and sphere Render 4: Sphere in front of a grid plane, focus behind both grid and sphere

You can clearly see that, with the focus between the grid and the sphere, the grid lines close to the sphere appear shifted away from it, while with the focus behind the grid plane, the grid lines shift towards the sphere.

Moving the camera focus further away from the background plane makes the effect even stronger:

Render 5: Sphere in front of a grid plane, focus between grid and sphere Render 6: Sphere in front of a grid plane, focus behind both grid and sphere

You can also clearly see the lines getting sharper near the sphere, as well as bending, because part of the blurred image is blocked by the sphere.

I can even recreate the broken line effect in your photos by replacing the sphere with a narrow cylinder:

Render 7: Narrow cylinder in front of a grid plane, focus between grid and cylinder Render 8: Narrow cylinder in front of a grid plane, focus between grid and cylinder

To recap: This effect is caused by the background being (slightly) out of focus, and by the foreground object effectively occluding part of the camera / eye aperture, causing the effective aperture (and thus the resulting image) to be shifted. It is not caused by:

  • Diffraction: As shown by the computer renderings above (which are created using ray tracing, and therefore do not model any diffraction effects), this effect is fully explained by classical ray optics. In any case, diffraction cannot explain the background images shifting towards the obstacle when the focus is behind the background plane.
  • Reflection: Again, no reflection of the background from the obstacle surface is required to explain this effect. In fact, in the computer renderings above, the yellow sphere / cylinder does not reflect the background grid at all. (The surfaces have no specular reflection component, and no indirect diffuse illumination effects are included in the lighting model.)
  • Optical illusion: The fact that this is not a perceptual illusion should be obvious from the fact that the effect can be photographed, and the distortion measured from the photos, but the fact that it can also be reproduced by computer rendering further confirms this.

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