Parallax – Definition, Examples, Uses


Parallax Effect Definition

Parallax is the apparent shift in the position of an object when observed from different viewpoints. This effect occurs because the perspective from which an object is viewed changes and makes it appear differently against a distant background. Parallax is a fundamental concept in astronomy and photography, plus it plays a significant role in human vision.

Examples of Parallax in Everyday Life

Parallax is a part of everyday life, if you know where to look for it:

  • Driving and Passing Scenery: When you look out the window of a moving car, nearby objects like trees or mailboxes seem to move quickly past your field of vision, while distant mountains or buildings appear to move slowly. This difference in apparent speed is due to parallax. Closer objects have a larger apparent motion compared to farther ones.
  • Finger Experiment: Hold a finger at arm’s length and close one eye. Move your head from side to side. Notice that your finger appears to move against the background. Switch the eye you have open, and the direction of movement changes. The shift in viewing angle results in a change in perceived position.

Types of Parallax

The three types of parallax are positive, zero, and negative parallax. The distinction depends on the relative motion of an object against its background as the observer’s viewpoint changes. Understanding these categories helps in various fields, including astronomy, virtual reality, and 3D imaging.

  • Positive Parallax: Positive parallax occurs when an object appears to move to the right relative to the background as the observer’s viewpoint shifts to the right. If the observer moves to the left, the object appears to move left. This suggests that the object is closer to the observer than the background. In stereo imaging, positive parallax makes objects appear as if they are in front of the screen, enhancing depth perception.
  • Zero Parallax: Zero parallax happens when there is no apparent motion of the object relative to the background as the observer changes position. This occurs when the object is at the focal plane of the camera or at the point where the sight lines from different viewpoints converge. In practical terms, the object appears at the same depth as the screen or the point of convergence. It neither pops out nor recedes into the background.
  • Negative Parallax: Negative parallax occurs when an object appears to move in the opposite direction of the observer’s movement. For instance, if the observer moves to the right, the object shifts to the left, and vice versa. This type of parallax indicates that the object is further away from the observer than the background. In stereo imaging, negative parallax makes objects appear as if they are behind the screen. This adds depth to the background and enhances the viewer’s sense of immersion in the scene.

Instruments and Systems Affected by Parallax

Parallax affects various instruments and systems, including:

  • Cameras: Optical parallax occurs when the viewfinder of a camera gives a slightly different image from what is captured through the lens.
  • Telescopes: Astronomical observations account for parallax to accurately pinpoint the positions of celestial bodies.
  • Surveying Instruments: Devices like theodolites use parallax correction to imrpove the accuracy of distance and angle measurements.

Depth Perception

Parallax plays a role in vision, but how it works depends on whether both eyes have an overlapping field of view or not.

Parallax in Human Vision

Humans and other animals (largely predators) with binocular vision naturally use parallax to perceive depth. The slight difference between the images seen by the left and right eyes provides a stereoscopic view, helping our brains calculate depth and distance.

Motion Parallax in Animals

Prey animals often have monocular vision. This gives them a wide range of view and exceptional peripheral vision, but they use motion parallax, shading, and texture for depth perception. For example, pigeons use motion parallax for depth perception. As they move their heads back and forth, objects at varying distances shift differently in their vision.

Determining Distance Using Parallax

Parallax helps calculate the distance to an object based on the angle of parallax and the distance between observation points. The formula is:

𝑑 = 𝑏/𝜃​

where d is the distance to the object, b is the baseline distance between observation points, and θ is the parallax angle in radians.

Example Calculation:

Suppose the baseline b is 100 meters, and the observed parallax angle θ is 0.005 radians. The distance d is:

𝑑 = 100 / 0.005 = 20,000 meters

Stellar Parallax and Astronomical Distances

Astronomers use stellar parallax to measure the distances to nearby stars. As Earth orbits the Sun, nearby stars shift slightly against the background of more distant stars. However, the greater the distance to an object, the smaller its parallax. Distances as far away as the Galactic Center (around 30,000 light years away) can be measured using parallax to within 10% of their true values.

Parallax Error

Parallax error occurs when the measurement of an object’s position is done from different lines of sight. This is a common issue in precision measurements, such as in:

  • Optical Devices: Error occurs when the viewfinder does not align perfectly with the lens. This is common in cameras, telescopes, and microscopes.
  • Meter Readings: There is error when the angle of viewing a meter scale changes the apparent position of the needle.
  • Weapon Sights: The distance between the sighting device and the launch or bore axis introduces significant aiming errors. The practice of “sighting in” compensates for the error. Some scopes include a parallax compensation mechanism.

References

  • Hirshfeld, Alan W. (2001). Parallax: The Race to Measure the Cosmos. New York: W.H. Freeman. ISBN 978-0-7167-3711-7.
  • Popowski, P.; Gould, A. (1998). “Mathematics of Statistical Parallax and the Local Distance Scale”. doi:10.48550/arXiv.astro-ph/9703140
  • Riess, A. G.; Casertano, S.; Anderson, J.; MacKenty, J.; Filippenko, A. V. (2014). “Parallax Beyond a Kiloparsec from Spatially Scanning the Wide Field Camera 3 on the Hubble Space Telescope”. The Astrophysical Journal. 785 (2): 161. doi:10.1088/0004-637X/785/2/161
  • Steinman, Scott B.; Garzia, Ralph Philip (2000). Foundations of Binocular Vision: A Clinical Perspective. McGraw-Hill Professional. ISBN 978-0-8385-2670-5.
  • Zeilik, Michael A.; Gregory, Stephan A. (1998). Introductory Astronomy & Astrophysics (4th ed.). Saunders College Publishing. ISBN 978-0-03-006228-5.