Persistence of vision

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Short description: Optical illusion


Persistence of vision is the optical illusion that occurs when the visual perception of an object does not cease for some time after the rays of light proceeding from it have ceased to enter the eye.[1] The illusion has also been described as "retinal persistence",[2] "persistence of impressions",[3] simply "persistence" and other variations. A very commonly given example of the phenomenon is the apparent fiery trail of a glowing coal or burning stick while it is whirled around in the dark.[1]

Many explanations of the illusion actually seem to describe either positive afterimages[4] or motion blur.

"Persistence of vision" can also be understood to mean the same as "flicker fusion",[5] the effect that vision seems to persist continuously when the light that enters the eyes is interrupted with short and regular intervals. When the frequency is too high for the visual system to discern differences between moments, light and dark impressions fuse together into a continuous impression of the scene with intermediate brightness.

Since its introduction, the term "persistence of vision" has been believed to be the explanation for motion perception in optical toys like the phenakistiscope and the zoetrope, and later in cinema. However, this theory has been disputed even before cinematography's breakthrough in 1895. If "persistence of vision" is explained as "flicker fusion", it can be regarded as the reason why the dark intervals do not interrupt the continuous impression of a depicted scene. The illusion of motion as a result of fast intermittent presentations of sequential images is a stroboscopic effect, as detailed by inventor Simon Stampfer.[6]

Early descriptions of the illusion often attributed the effect purely to the physiology of the eye, particularly of the retina. Nerves and parts of the brain later became accepted as important factors.

Sensory memory has been cited as a cause.[7]

Natural occurrences and applications

Some natural phenomena and the principles of some optical toys have been attributed to the persistence of vision effect. In 1768, Patrick D'Arcy recognised the effect in "the luminous ring that we see by turning a torch quickly, the fire wheels in the fireworks, the flattened spindle shape we see in a vibrating cord, the continuous circle we see in a cogwheel that turns with speed".[8] Basically everything that resembles motion blur seen in fast moving objects could be regarded as "persistence of vision".

Sparkler's trail effect

The apparent line of light behind a fast moving luminous object is known as the "sparkler's trail effect", since it is commonly known from the use of sparklers.

The effect has occasionally been applied in the arts by writing or drawing with a light source recorded by a camera with a long exposure time.

Color-top / Newton disc

Colors on spinning tops or rotating wheels mix together if the motion is too fast to register the details. A colored dot then appears as a circle and one line can make the whole surface appear in one uniform hue.

The Newton disc optically mixes wedges of Isaac Newton's primary colors into one (off-)white surface when it spins fast.

Thaumatrope

In April 1825 the first Thaumatrope was published by W. Phillips (in anonymous association with John Ayrton Paris).[9] The fact that the pictures on either side of the twirling disc seem to blend together into one image has often been used to illustrate the concept of persistence of vision.

Kaleidoscopic colour-top

In April 1858 John Gorham patented his Kaleidoscopic colour-top.[10] This is a top on which two small discs are placed, usually one with colors and a black one with cut-out patterns. When the discs spin and the top disc is retarded into regular jerky motions the toy exhibits "beautiful forms which are similar to those of the kaleidoscope" with multiplied colours. Gorham described how the colours appear mixed on the spinning top "from the duration of successive impressions on the retina". Gorham founded the principle on "the well-known experiment of whirling a stick, ignited at one end" (a.k.a. the sparkler's trail effect).[11]

Rubber pencil trick

A pencil or another rigid straight line can appear as bending and becoming rubbery when it is wiggled fast enough between fingers, or otherwise undergoing rigid motion.

Persistence of vision has been discarded as sole cause of the illusion. It is thought that the eye movements of the observer fail to track the motions of features of the object.[12]

This effect is widely known as an entertaining "magic" trick for children.[13]

Sequential Wave Imprinting Machine (S.W.I.M.)

An early (June 1974) sequence of photographs of a S.W.I.M. (linear array of computer-controlled lamps) being waved back-and-forth while imprinting content upon the naked eye (e.g. human vision) as well as the photographic media (photographic film) used to capture it. Here image content (a graticule) is displayed superimposed on top of a real-time graph (plot) of an electromagnetic radio wave received at the output of a radio receiver phase-coherently to plot in coordinates in which the radio wave appears to be sitting still.[14]
GIF animated photograph sequence depicting a modern version of S.W.I.M..
Modern version of S.W.I.M. made with light-emitting diodes, here displaying the electromagnetic radio wave emitted from a cellular telephone in real-time

In the 1960s and 1970s a row of computer-controlled light sources attached to a stick was waved back-and-forth or spun (by hand or on a motor) to sequentially "imprint" upon the naked eye (or cameras) images, text, graphics, and graphs (plots of mathematical or recorded or live functions), originally using incandescent lamps at high voltage for quick response, and this system was called S.W.I.M. (Sequential Wave Imprinting Machine).[15][16][17] Originally a radar system was used to track the position of the S.W.I.M. to appropriately index into the content so that if it was waved backwards the content played backwards, and if it was waved faster the content played faster, etc., such as to create "virtual" content overlayed in near perfect alignment with physical reality.[18][19] More modern versions of S.W.I.M. use SDR (Software-Defined Radio) combined with inertial measurement units to track position.[20]

Rotary S.W.I.M.

When the S.W.I.M. is waved in a circular motion rather than reciprocally waved back-and-forth, the tracking system only needs to determine speed, but not direction, and is therefore much easier to implement, not requiring a quadrature detector or direction detector or the like. Such rotary S.W.I.M. is often mounted onto the shaft of a motor, so that it does not need to be waved back-and-forth by hand. In this configuration it can continuously display images, text, graphics, and graphs, such as a plot of the rotating magnetic field in the motor, or its rotor current, in coordinates in which the rotary motion of the motor is cancelled out, so as to make visible various functional aspects of the motor in real-time.[21] Rotary S.W.I.M. is also used for realtime visualization of audio, brain activity, and meditation.[22]

This technology is used commercially so that designers and engineers can visualize and understand a complete electric vehicle powertrain, and not just the motor to which the S.W.I.M. is attached.[23]

LED S.W.I.M.

Early S.W.I.M. sometimes used colored bulbs, but in 1980, L.E.D.-based versions of the S.W.I.M. were made for both hand-held and wearable use to display images, text, graphics, and graphs in color, while the lower voltages made it safer and easier to use in teaching labs as well as near water and even underwater.[24][25][26]

Such displays are often attached to individual drones (e.g. rotors of drones) or make use of drone swarms.[27][28]

A spinning LED display.
Spinning (rotor) LED display

The term "persistence of vision display" or "POV display" has been used for LED display devices that compose images by displaying one spatial portion at a time in rapid succession, (for example, one column of pixels every few milliseconds).[29] A two-dimensional POV display is often accomplished by means of rapidly moving a single row of LEDs along a linear or circular path.[citation needed] The effect is that the image is perceived as a whole by the viewer as long as the entire path is completed during the visual persistence time of the human eye. A further effect is often to give the illusion of the image floating in mid-air. A three-dimensional POV display is often constructed using a 2D grid of LEDs which is swept or rotated through a volume.[30] POV display devices can be used in combination with long camera exposures to produce light writing.[31]

A common example of this can be seen in the use of bicycle wheel lights that produce patterns.[32]

History

Phenomena related to flicker fusion and motion blur have been described since antiquity. Film historians have often confused flicker fusion with afterimages that arise after staring at an object, while mostly ignoring the importance of the stroboscopic effect in their explanations of motion perception in film.

Historical references to afterimages

Aristotle (384–322 BC) noted that the image of the sun remained in his vision after he stopped looking at it.

The discovery of persistence of vision is sometimes attributed to the Roman poet Lucretius (c. 15 October 99 BC – c. 55 BC), although he only mentions something similar in connection with images seen in a dream.[33]

Around 165 AD Ptolemy described in his book Optics a rotating potter's wheel with different colors on it. He noted how the different colors of sectors mixed together into one color and how dots appeared as circles when the wheel was spinning very fast. When lines are drawn across the axis of the disc they make the whole surface appear to be of a uniform color. "The visual impression that is created in the first revolution is invariably followed by repeated instances that subsequently produce an identical impression. This also happens in the case of shooting stars, whose light seems distended on account of their speed of motion, all according to the amount of perceptible distance it passes along with the sensible impression that arises in the visual faculty."[34][35]

Porphyry (circa 243–305) in his commentary on Ptolemy's Harmonics describes how the senses are not stable but confused and inaccurate. Certain intervals between repeated impressions are not detected. A white or black spot on a spinning cone (or top) appears as a circle of that color and a line on the top makes the whole surface appear in that color. "Because of the swiftness of the movement we receive the impression of the line on every part of the cone as the line moves."[36]

In the 11th century Ibn al-Haytham, who was familiar with Ptolemy's writings, described how colored lines on a spinning top could not be discerned as different colors but appeared as one new color composed of all of the colors of the lines. He deducted that sight needs some time to discern a color. al-Haytam also noted that the top appeared motionless when spun extremely quickly "for none of its points remains fixed in the same spot for any perceptible time".[37]

Leonardo da Vinci wrote in a notebook: "Every body that moves rapidly seems to colour its path with the impression of its hue. The truth of this proposition is seen from experience; thus when the lightning moves among dark clouds the speed of its sinuous flight makes its whole course resemble a luminous snake. So in like manner if you wave a lighted brand its whole course will seem a ring of flame. This is because the organ of perception acts more rapidly than the judgment."[38]

In his 1704 book Opticks, Isaac Newton (1642–1726/27) described a machine with prisms, a lens and a large moving comb with teeth causing alternating colors to be projected successively. If this was done quickly enough, the alternating colours could no longer be perceived separately but were seen as white. Newton compared its principle to the sparkler's trail effect: a gyrating burning coal could appear as a circle of fire because "the sensation of the coal in the several places of that circle remains impress'd on the sensorium, until the coal return again to the same place."[39]

In 1768 Patrick d'Arcy (1725-1779) reported how he had measured a duration of 0.13 seconds for one full rotation of a burning coal while it was seen as a full circle of light. He registered multiple rotations with a purpose-built machine in his garden and with the collaboration of an observer who had superior eyesight (D'Arcy's own eyesight had been damaged in an accident). D'Arcy suspected that the duration may differ between different observers, light intensities of spinning objects, colours and viewing distances. He planned further experiments to determine such possible differences,[8] but no results seem to have been published.

1820–1866: Revolving wheel

Wood-cut illustration of An Optical Deception (1821)
Illustration plate for Peter Mark Roget's Explanation of an Optical Deception in the Appearance of the Spokes of a Wheel Seen through Vertical Apertures (1825)
Illustrations of Michael Faraday's experiments with rotating wheels with cogs or spokes (1831)

In 1821 the Quarterly Journal of Science, Literature, and The Arts published a "letter to the editor" with the title Account of an Optical Deception. It was dated Dec. 1, 1820 and attributed to "J.M.", possibly publisher/editor John Murray himself.[40] The author noted that the spokes of a rotating wheel seen through fence slats appeared with peculiar curvatures (see picture). The letter concluded: "The general principles on which this deception is based will immediately occur to your mathematical readers, but a perfect demonstration will probably prove less easy than it appears on first sight".[41] Four years later Peter Mark Roget offered an explanation when reading at the Royal Society on December 9, 1824. He added: "It is also to be noticed that, however rapidly the wheel revolves, each individual spoke, during the moment it is viewed, appears to be at rest." Roget claimed that the illusion is due to the fact "that an impression made by a pencil of rays on the retina, if sufficiently vivid, will remain for a certain time after the cause has ceased." He also provided mathematical details about the appearing curvatures.[42]

As a university student Joseph Plateau noticed in some of his early experiments that when looking from a small distance at two concentric cogwheels which turned fast in opposite directions, it produced the optical illusion of a motionless wheel. He later read Peter Mark Roget's 1824 article and decided to investigate the phenomenon further. He published his findings in Correspondance Mathématique et Physique in 1828[43] and 1830.[44] In 1829 Plateau presented his then unnamed anorthoscope in his doctoral thesis Sur quelques propriétés des impressions produites par la lumière sur l'organe de la vue.[45] The anorthoscope was a disc with an anamorphic picture that could be viewed as a clear immobile image when the disc was rotated and seen through the four radial slits of a counter-rotating disc. The discs could also be translucent and lit from behind through the slits of the counter-rotating disc.

On 10 December 1830, scientist Michael Faraday wrote a paper for the Journal of the Royal Institution of Great Britain, entitled On a Peculiar Class of Optical Deceptions. Two instances of rotating wheels that appeared to stand still had been pointed out to him and he had read about the somewhat similar palisade illusion in Roget's article. Faraday started experimenting with rotations of toothed cardboard wheels. Several effects had already been described by Plateau, but Faraday also simplified the experiment by looking at a mirror through the spaces between the teeth in the circumference of the cardboard disc.[46] On 21 January 1831, Faraday presented the paper at the Royal Institution, with some new experiments. He had cut concentric series of apertures nearer to the center of a disc (representing smaller cogwheels) with small differences in the amount of "cogs" per "wheel". When looking at the mirror through the holes of one of the wheels in the rotating disc, that wheel seemed to stand still while the others would appear to move with different velocities or opposite direction.[47]

Plateau was inspired by Faraday's additional experiments and continued the research. In July 1832 Plateau sent a letter to Faraday and added an experimental circle with apparently abstract figures that produced a "completely immobile image of a little, perfectly regular horse" when rotated in front of a mirror.[48][49] After several attempts and many difficulties Plateau managed to animate the figures between the slits in a disc when he constructed the first effective model of the phénakisticope in November or December 1832 . Plateau published his then unnamed invention in a January 20, 1833 letter to Correspondance Mathématique et Physique.[50]

Simon Stampfer claimed to have independently and almost simultaneously invented his very similar Stroboscopischen Scheiben oder optischen Zauberscheiben (stroboscopic discs or optical magic discs) soon after he read about Faraday's findings in December 1832.[6]

Stampfer also mentioned several possible variations of his stroboscopic invention, including a cylinder (similar to the later zoetrope) as well as a long, looped strip of paper or canvas stretched around two parallel rollers (somewhat similar to film) and a theater-like frame (much like the later praxinoscope).[6] In January 1834, William George Horner also suggested a cylindrical variation of Plateau's phénakisticope, but he did not manage to publish a working version.[51] William Ensign Lincoln invented the definitive zoetrope with exchangeable animation strips in 1865 and had it published by Milton Bradley and Co. in December 1866.[52]

Other theories for motion perception in film

In his 1833 patent and his explanatory pamphlet for his stroboscopic discs, Simon Stampfer emphasized the importance of the interruptions of the beams of light reflected by the drawings, while a mechanism would transport the images past the eyes at an appropriate speed. The pictures had to be constructed according to certain laws of physics and mathematics, including the systematic division of a movement into separate moments. He described the idea of persistence of vision only as the effect that made the interruptions go unnoticed.[6]

The idea that the motion effects in so-called "optical toys", like the phénakisticope and the zoetrope, may be caused by images lingering on the retina was questioned in an 1868 article by William Benjamin Carpenter. He suggested that the illusion was "rather a mental than a retinal phenomenon".[53]

Early theories of persistence of vision were centered on the retina, while later theories preferred or added ideas about cognitive (brain centered) elements of motion perception. Many psychological concepts of the basic principle of animation suggested that the blanks in between the images were filled in by the mind.[citation needed]

Max Wertheimer proved in 1912 that test subjects did not see anything in between the two different positions in which a figure was projected by a tachistocope at frequencies that were ideal for the illusion of one figure moving from one position to the next. He used the Greek letter φ (phi) to designate illusions of motion. At higher speeds, when test subjects believed to see both positions more or less simultaneously, a moving objectless phenomenon was seen between and around the projected figures. Wertheimer supposed this "pure phi phenomenon" was a more direct sensory experience of motion.[54] The ideal animation illusion of motion across the interval between the figures was later called "beta movement".

A visual form of memory known as iconic memory has been described as the cause of persistence of vision.[55] Some scientists nowadays consider the entire theory of iconic memory a myth.[citation needed]

When contrasting the theory of persistence of vision with that of phi phenomena, an understanding emerges that the eye is not a camera and does not see in frames per second. In other words, vision is not as simple as light registering on a medium since the brain has to make sense of the visual data the eye provides and construct a coherent picture of reality.[citation needed]

Although psychologists and physiologists have rejected the relevance of the theory of retinal persistence film viewership, film academics and theorists generally have not, and it persists in citations in many classic and modern film-theory texts.[56][57][58][59]

Joseph and Barbara Anderson argue that the phi phenomena privileges a more constructionist approach to the cinema (David Bordwell, Noël Carroll, Kirstin Thompson) whereas the persistence of vision privileges a realist approach (André Bazin, Christian Metz, Jean-Louis Baudry).[59]

See also

References

  1. ↑ 1.0 1.1 Nichol, John Pringle (1857). A Cyclopædia of the Physical Sciences. Richard Griffin and Company. https://books.google.com/books?id=MCtbAAAAcAAJ&q=persistence+of+impressions&pg=PA571. Retrieved 29 October 2017. 
  2. ↑ "The Fortnightly". Chapman and Hall. 29 October 1871. https://books.google.com/books?id=bPsdAQAAIAAJ&q=retinal+persistence&pg=PA335. 
  3. ↑ Tyndall, John (1870). Notes of a Course of Nine Lectures on Light: Delivered at the Royal Institution of Great Britain, April 8-June 3, 1869. Longmans, Green. p. 26. https://archive.org/details/notesacoursenin00tyndgoog. "persistence of impressions." 
  4. ↑ Bill Nichols; Susan J. Ledermann (1980). Flicker and motion in film. ISBN 9781349164011. https://books.google.com/books?id=mcLtCwAAQBAJ&q=%22We%20can%20only%20guess%20that%20film%20writers%20are%20referring%20to%20what%20psychologists%20call%22%20'positive%20after%20images'&pg=PA96. 
  5. ↑ Buchan, Suzanne (2013-08-22). Pervasive Animation. ISBN 9781136519550. https://books.google.com/books?id=ZeiAAAAAQBAJ&q=pervasive%20animation&pg=PT77. 
  6. ↑ 6.0 6.1 6.2 6.3 Stampfer, Simon (1833) (in de). Die stroboscopischen Scheiben; oder, Optischen Zauberscheiben: Deren Theorie und wissenschaftliche anwendung, erklärt von dem Erfinder. Vienna and Leipzig: Trentsensky and Vieweg. p. 2. https://books.google.com/books?id=xUk0AQAAMAAJ&pg=PA2. 
  7. ↑ Goldstein, B. (2011). Cognitive Psychology: Connecting Mind, Research, and Everyday Experience--with coglab manual. (3rd ed.). Belmont, CA: Wadsworth: 120.
  8. ↑ 8.0 8.1 (in fr) Histoire De L'Academie Royale Des Sciences. Année ... Avec les Memoires de Mathematique & de Physique, pour la même Année. Tirés des Registres de cette Academie. Boudot, Jean. 1768. https://books.google.com/books?id=cL5eAAAAcAAJ&pg=RA1-PA439. 
  9. ↑ Herbert, Stephen. "Wheel of Life - The Taumatrope". http://www.stephenherbert.co.uk/thaumatropeTEXT1.htm. 
  10. ↑ [1][|permanent dead link|dead link}}]
  11. ↑ Gorham, John (January 1859). The Rotation of Coloured Discs. https://books.google.com/books?id=ZrdbAAAAcAAJ. 
  12. ↑ Thaler, Lore; Todd, James T.; Spering, Miriam; Gegenfurtner, Karl R. (1 April 2007). "Illusory bending of a rigidly moving line segment: Effects of image motion and smooth pursuit eye movements". Journal of Vision 7 (6): 9. doi:10.1167/7.6.9. PMID 17685792. 
  13. ↑ "Easy Magic Tricks for Kids: The Rubber Pencil". https://www.thespruce.com/rubber-pencil-kids-magic-tricks-2267012. 
  14. ↑ Steve Mann (2016). "Surveillance (Oversight), Sousveillance (Undersight), and Metaveillance (Seeing Sight Itself)". IEEE. pp. 1–10. https://www.cv-foundation.org//openaccess/content_cvpr_2016_workshops/w29/papers/Mann_Surveillance_Oversight_Sousveillance_CVPR_2016_paper.pdf. 
  15. ↑ S. Mann, Campus Canada, ISSN 0823-4531, p55 Feb-Mar 1985, pp58-59 Apr-May 1986, p72 Sep-Oct 1986.
  16. ↑ Wavelets and Chirplets: Time-Frequency Perspectives With Applications, S. Mann, 1992, DOI: 10.1142/9789814355841_0006 in "Advances in Machine Vision, Strategies and Applications", editors Archibald and Petriu, World Scientific, Singapore . New Jersey . London . Hong Kong, World Scientific Series in Computer Science - Vol. 32, ISBN 981-02-0976-2, Vol. 32.
  17. ↑ Intelligent Image Processing, S. Mann, 2001, John Wiley and Sons textbook, Wiley Interscience Series.
  18. ↑ Wavelets and Chirplets: Time-Frequency Perspectives With Applications, Steve Mann, 1992
  19. ↑ Mann, S. (2018, August). Phenomenological augmented reality with the sequential wave imprinting machine (swim). In 2018 IEEE Games, Entertainment, Media Conference (GEM) (pp. 1-9). IEEE.
  20. ↑ Mann, S., Do, P. V., Lu, Z., & Lau, J. K. (2020, April). Sequential wave imprinting machine (SWIM) implementation using SDR (software-defined radio). In 2020 seventh international conference on software defined systems (SDS) (pp. 123-130). IEEE.
  21. ↑ Mann, S., Garcia, D. E., Do, P. V., Lam, D., & Scourboutakos, P. (2020, November). Moveillance: Visualizing electric machines. In 2020 22nd Symposium on Virtual and Augmented Reality (SVR) (pp. 420-424). IEEE.
  22. ↑ Bhargava, A., O’Shaughnessy, K., & Mann, S. (2020, October). A novel approach to eeg neurofeedback via reinforcement learning. In 2020 ieee sensors (pp. 1-4). IEEE.
  23. ↑ Mann, S., Bhimani, J., Leaver-Preyra, C., Simons, K., & Tjong, J. (2022, November). Powertrain photography and visualization using SWIM (Sequential Wave Imprinting Machine) for veyance safety. In 2022 IEEE International Conference on Vehicular Electronics and Safety (ICVES) (pp. 1-8). IEEE.
  24. ↑ Intelligent Image Processing
  25. ↑ "Extended Reality", S. Mann and C. Wyckoff, MIT 4-405, 1991.
  26. ↑ Mann, S., Sadrzadeh-Afsharazar, F., Khaki, S., Lu, Z., Mann, C., & Bhimani, J. (2022, March). Waterhci part 1: Open water monitoring with realtime augmented reality. In 2022 IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems (SPICES) (Vol. 1, pp. 49-54). IEEE.
  27. ↑ Mann, S., Lu, Z., Sadrzadeh-Afsharazar, F., Mann, C., Khaki, S., & Bhimani, J. (2022, March). WaterHCI Part 2: Open water sensing, meta-sensing, and observing with drones and augmented reality. In 2022 IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems (SPICES) (Vol. 1, pp. 378-383). IEEE.
  28. ↑ Mann, S., Khaki, S., Bhimani, J., Verges, G., & Sadrzadeh-Afsharazar, F. (2021, October). Drone-based sensing and exploration of overhead electric power lines. In 2021 IEEE 4th International Conference on Power and Energy Applications (ICPEA) (pp. 76-81). IEEE.
  29. ↑ "POV - The Persistence of Vision Principle". 2015. https://tobibu.github.io/POV/pov/. 
  30. ↑ Ruggeri, Luca (2017-06-14). "DIY an Amazing 3D POV Holographic Display!". https://www.open-electronics.org/diy-an-amazing-3d-pov-holographic-display/. 
  31. ↑ Sierzputowski, Kate (2015-07-29). "Photographer Stephen Orlando Captures the Movement of Musicians Through Light Painting". https://www.thisiscolossal.com/2015/07/music-through-light-stephen-orlando/. 
  32. ↑ Bushwick, Sophie (2014-10-24). "DIY: How To Light Up Your Bike Wheels [Video"]. Camden Media. https://www.popsci.com/article/diy/diy-how-light-your-bike-wheels-video/. 
  33. ↑ Herbert, S. (2000). A history of pre-cinema. London. Routledge. p 121
  34. ↑ Smith, A. Mark (29 October 1999). Ptolemy and the Foundations of Ancient Mathematical Optics: A Source Based Guided Study. American Philosophical Society. ISBN 9780871698933. https://books.google.com/books?id=ASILAAAAIAAJ&q=ptolemy+potter's+wheel&pg=PA43. Retrieved 29 October 2017. 
  35. ↑ Smith, A. Mark (29 October 1996). "Ptolemy's Theory of Visual Perception: An English Translation of the "Optics" with Introduction and Commentary". Transactions of the American Philosophical Society 86 (2): iii–300. doi:10.2307/3231951. 
  36. ↑ Porphyry's Commentary on Ptolemy's Harmonics: A Greek Text and Annotated Translation. Cambridge University Press. 15 September 2015. ISBN 9781316239681. https://books.google.com/books?id=c6QKDgAAQBAJ&q=ptolemy+spinning+top&pg=PA137. Retrieved 29 October 2017. 
  37. ↑ Alhazen; Smith, A. Mark (29 October 2017). Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn Al-Haytham's Kitab Al-Manazir. American Philosophical Society. ISBN 9780871699145. https://books.google.com/books?id=3x0LAAAAIAAJ&q=ptolemy+optics+color+rotating+wheel&pg=PA444. Retrieved 29 October 2017. 
  38. ↑ Leonardo da Vinci (2008-04-17). Notebooks. ISBN 9780191608896. https://books.google.com/books?id=xeaqDsktcc8C&q=%22every%20body%20that%20moves%20rapidly%20seems%20to%22&pg=PA132. 
  39. ↑ Newton, Sir Isaac (29 October 2017). "Opticks:: Or, A Treatise of the Reflections, Refractions, Inflections and Colours of Light". William Innys at the West-End of St. Paul's.. https://books.google.com/books?id=GnAFAAAAQAAJ&q=newton+Theory+about+Light+and+Colors&pg=PA123. 
  40. ↑ Schuler, Romana Karla (15 January 2016). Seeing Motion: A History of Visual Perception in Art and Science. Walter de Gruyter GmbH & Co KG. ISBN 9783110422993. https://books.google.com/books?id=npFlCwAAQBAJ&q=%22john+murray%22+wheel+roget&pg=PP31. Retrieved 29 October 2017. 
  41. ↑ J.M. (1820-12-01). Account of an optical deception. https://archive.org/stream/quarterlyjournal10roya#page/282/mode/2up. 
  42. ↑ Roget, Peter Mark (1824-12-09). "Explanation of an optical deception in the appearance of the spokes of a wheel when seen through vertical apertures". Philosophical Transactions of the Royal Society of London 115: 131–140. doi:10.1098/rstl.1825.0007. http://rstl.royalsocietypublishing.org/content/115/131.full.pdf+html. 
  43. ↑ (in fr) Correspondance mathématique et physique. 4. Brussels: Garnier and Quetelet. 1828. p. 393. https://books.google.com/books?id=ezcDAAAAQAAJ&pg=PA393. 
  44. ↑ (in fr) Correspondance mathématique et physique. 6. Brussels: Garnier and Quetelet. 1830. p. 121. https://books.google.com/books?id=wDcDAAAAQAAJ&pg=PA121. 
  45. ↑ Plateau, Joseph (1829) (in fr). Sur quelques propriétés des impressions produites par la lumière sur l'organe de la vue. http://orbi.ulg.ac.be/bitstream/2268/501/1/Plateau_phd.pdf. 
  46. ↑ Faraday, Michael (February 1831). On a peculiar Class of Optical Deceptions. https://archive.org/stream/journalofroyalin01roya#page/204/mode/2up. 
  47. ↑ Royal Institution of Great Britain (1831). Journal of the Royal Institution of Great Britain. London Natural History Museum Library. London : Royal Institution of Great Britain. http://archive.org/details/journalofroyalin01roya. 
  48. ↑ Plateau, Joseph (1833-03-08). letter to Faraday. ISBN 9780863412493. https://books.google.com/books?id=9lknVoNGj30C&q=%22Annales%20de%20physique%20et%20de%20chimie%22%20faraday%20plateau&pg=PA71. 
  49. ↑ Plateau, Joseph (1832-07-24). letter to Faraday. ISBN 9780863412493. https://books.google.com/books?id=9lknVoNGj30C&q=%22Annales%20de%20physique%20et%20de%20chimie%22%20faraday%20plateau&pg=PA107. 
  50. ↑ (in fr) Correspondance mathématique et physique. 7. Brussels: Garnier and Quetelet. 1832. p. 365. https://books.google.com/books?id=RxNbAAAAYAAJ&pg=PA365. 
  51. ↑ The London and Edinburgh Philosophical Magazine and Journal of Science. 1834. p. 36. https://books.google.com/books?id=XmrkAAAAMAAJ&q=On+the+Properties+of+the+Daedaleum,+A+New+Instrument+of+Optical+Illusion&pg=PA36. 
  52. ↑ Herbert, Stephen. (n.d.) From Daedaleum to Zoetrope, Part 1. Retrieved 2014-05-31.
  53. ↑ Carpenter (1868). On the Zoetrope and its Antecedents. https://books.google.com/books?id=H0FHAAAAcAAJ&q=Student%20and%20Intellectual%20Observer&pg=PA428. 
  54. ↑ Wertheimer (1912). Experimentelle Studien über das Sehen von Bewegung. Zeitschrift für Psychologie 61. pp. 161–265. http://gestalttheory.net/download/Wertheimer1912_Sehen_von_Bewegung.pdf. Retrieved 2019-04-02. 
  55. ↑ Coltheart, M (Jul 1980). "The persistences of vision". Philos Trans R Soc Lond B Biol Sci 290 (1038): 57–69. doi:10.1098/rstb.1980.0082. PMID 6106242. Bibcode: 1980RSPTB.290...57C. 
  56. ↑ Bazin, André (1967) What is Cinema?, Vol. I, Trans. Hugh Gray, Berkeley: University of California Press
  57. ↑ Cook, David A. (2004) A History of Narrative Film. New York, W. W. Norton & Company.
  58. ↑ Metz, Christian (1991) Film Language: A Semiotics of The Cinema, trans. Michael Taylor. Chicago: University of Chicago Press.
  59. ↑ 59.0 59.1 Anderson, Joseph; Anderson, Barbara (1993). "The Myth of Persistence of Vision Revisited". Journal of Film and Video 45 (1): 3–12. 

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