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Steoreoscopic displays: Stereoscopic vision of humans

2023-02-14

Functioning of the human eye

The human eye has a lens system consisting of cornea, fluid-filled anterior chamber, lens and vitreous body (see Fig. 1 ), which altogether functions as a variable converging lens (also convex lens) to always image objects of different distances with a focal point on the retina 8 / 9 . The latter contains a large number of sensory cells for perceiving the visible wave spectrum in the form of electrical stimuli that are transmitted to the brain for processing 8 / 9 . This spectrum ranges from about 700 nm wavelength (≙ red) to about 400 nm wavelength (≙ violet) 8 / 10 (see Fig. 2 ).

The sensory cells of the retina are divided into the so-called rods, which generate stimuli even at low light intensity but can only distinguish between light and dark, and the so-called cones, which only become active with significantly more light but, depending on the subspecies, cover the red, green or blue range of the visible light spectrum (see Fig. 2 ) and thus enable color perception 8 / 11 / 12 . In the center of the retina, opposite the lens system, is the so-called macula (see Fig. 1 ), in which the accumulation of these sensory cells is particularly high and which thus represents the place of sharpest vision 11 / 12 .

In order to hit this ideal point as precisely as possible, the focal length of the lens system should always correspond to its distance from the retina, which is on average about 20 mm 8 / 9 . For the correct representation of different focal planes, i.e. objects at different distances that are to be displayed sharply, there is therefore a constant adjustment of the lens curvature and thus also of the focal length of the optical aparatus by the so-called ciliary muscle (see Fig. 1 ) in a process known as accommodation 8 / 13 .

Since the object distance, i.e. the distance of the object to be focused from the lens system, is always significantly greater than the average focal length of 20 mm, a greatly scaled-down real image is produced on the retina, which is inverted in height and width, although this is compensated for by the brain in real time 9 / 11 / 14 .

Creation of the stereoscopic visual impression

The fact that humans have two eyes that are on average 6.3 cm apart 8 / 15 (see Fig. 3 ) results in slightly different perspectives and thus also slightly different monocular images, i.e. images originating from one eye, which is described by experts as transverse disparity 16 / 17 . In the brain, these individual images are combined to form a coherent binocular perception, i.e. perception originating from both eyes, with spatial and depth information obtained from the difference in perspective 11 / 16 / 18 / 19 .

However, the transverse disparity alone does not cause the partial impression, but the information of each eye is processed to an independent image shape and the differences between the shapes of the two eyes generate the depth impression 16 / 17 / 19 . Thus, even 2 transversely disparate images, one of which is drawn black on white and one white on black (see Fig. 4 ), generate a correct stereoscopic impression, although the pure stimulus complexes should actually balance each other out 17 . The cognitive, qualitative component thus plays a major role in our perception in addition to quantitative aspects 16 / 17 / 19 .

In order to be able to reliably estimate distances and movements of objects, the perspective deviations must be within a natural range, since too large differences destroy the effect or lead to confusion 7 / 11 / 16 / 19 and too small differences do not produce any perceptible effect.

In addition, stereoscopic vision requires a minimum distance of a few centimeters and the correct alignment of objects, if possible, in the center of the 120-degree-wide binocular field of view, i.e. the field of view covered by both eyes (see Fig. 5 ), because otherwise there is not enough overlap of the monocular images and, depending on the focal plane, one perceives only erroneous ghost images 7 / 8 / 11 / 17 / 19 .

The correction of the numerous structure-related optical errors of our eyes can also be traced back to the cognitive component of vision and only breaks down when looking specifically at these very defects 14 .

Appendix

Fig. 1: The human eye

The human eye
Fig. 1: The human eye 33

Fig. 2: The visible wave spectrum

The visible wave spectrum
Fig. 2: The visible wave spectrum 34

Fig. 3: The stereoscopic eye pair of humans

The stereoscopic eye pair of humans
Fig. 3: The stereoscopic eye pair of humans 35

Fig. 4: Symbolic drawing of complementary figures

Symbolic drawing of complementary figures
Fig. 4: Symbolic drawing of complementary figures 36

Fig. 5: The horizontal field of view

The horizontal field of view
Fig. 5: The horizontal field of view 37

Sources

Text

  1. Tauer, Holger: Stereo 3D. Grundlagen, Technik und Bildgestaltung, Berlin 2010, p. 1 – 35.
  2. Joachim Herz Stiftung: Das menschliche Auge - Aufbau und scharfes Sehen, https://www.leifiphysik.de/optik/optische-linsen/grundwissen/das-menschliche-auge-aufbau-und-scharfes-sehen , 14.02.2023.
  3. Joachim Herz Stiftung: Sichtbares Licht, https://www.leifiphysik.de/optik/elektromagnetisches-spektrum/grundwissen/sichtbares-licht , 14.02.2023.
  4. Dörner, Ralf, and Steinicke, Frank: Wahrnehmungsaspekte von VR, in: Dörner, Ralf, Broll, Wolfgang, Grimm, Paul, and Jung, Bernhard: Virtual und Augmented Reality (VR/AR). Grundlagen und Methoden der Virtuellen und Augmentierten Realität, 2. edition, Berlin 2019, p. 46 – 49.
  5. Joachim Herz Stiftung: Das menschliche Auge - Aufbau und Funktion einzelner Teile, https://www.leifiphysik.de/optik/optische-linsen/ausblick/das-menschliche-auge-aufbau-und-funktion-einzelner-teile , 14.02.2023.
  6. Joachim Herz Stiftung: Das menschliche Auge - Akkomodation und Sehfehler, https://www.leifiphysik.de/optik/optische-linsen/grundwissen/das-menschliche-auge-akkomodation-und-sehfehler , 14.02.2023.
  7. Grasnick, Armin: 3D ohne 3D-Brille. Handbuch der Autostereoskopie, Berlin 2016, p. 34.
  8. Grasnick, Armin: 3D ohne 3D-Brille. Handbuch der Autostereoskopie, Berlin 2016, p. 43 ff..
  9. Lau, Ernst: Versuche über das stereoskopische Sehen, in: Psychologische Forschung no. 2 (1922), p. 1 – 4.
  10. Lau, Ernst: Über das stereoskopische Sehen, in: Psychologische Forschung no. 6 (1924), p. 121 – 126.
  11. Eckert, Bodo, Stetzenbach, Werner, and Jodl, Hans-Jörg: 3D-Kino: Doppelbildprojektion, and: Eckert, Bodo, Stetzenbach, Werner, and Jodl, Hans-Jörg: 3D-Kino: Polarisationszustände von reflektiertem Licht, in: Eckert, Bodo, Stetzenbach, Werner, and Jodl, Hans-Jörg: Low Cost – High Tech. Freihandversuche Physik: Praktische Anregungen für einen zeitgemäßen Unterricht, 3. edition, Berlin 2018, p. 54 – 57.
  12. Tauer, Holger: Stereo 3D. Grundlagen, Technik und Bildgestaltung, Berlin 2010, p. 53 – 76.

Appendix

  1. Based on: Joachim Herz Stiftung: Das menschliche Auge, https://www.leifiphysik.de/sites/default/files/images/a4f8c0f6a14f38987eac9913e1331528/992Das_menschliche_Auge_Aufbau.svg , 14.02.2023.
  2. Based on: Joachim Herz Stiftung: Einordnung des sichtbaren Lichts in elektromagnetische Spektrum, https://www.leifiphysik.de/sites/default/files/images/f82d8382735026f503641ccfccfd4457/992Sichtbare_Wellenlaenge_0.svg , 14.02.2023.
  3. Based on: JoePhin: D5pndst-8eef53ff-42ad-4c7a-be7e-13a003992cd6.png, https://commons.wikimedia.org/wiki/File:D5pndst-8eef53ff-42ad-4c7a-be7e-13a003992cd6.png , 14.02.2023.
  4. Based on: LosHawlos: Mh stereogramm halbbilder.png, https://commons.wikimedia.org/wiki/File:Mh_stereogramm_halbbilder.png , 14.02.2023.
  5. Based on: Zyxwv99: FOV both eyes.svg, https://commons.wikimedia.org/wiki/File:FOV_both_eyes.svg , 14.02.2023.

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