Chromostereopsis refers to a phenomenon of binocular stereopsis that depends on binocular disparity due to the difference in color [1, 2, 3, 4]. For example, red and blue on the same surface can appear to lie in different depth planes.
When the background is black (Fig. 1), the majority of observers see red objects closer to them than blue ones (red-in-front-of-blue observers), while a minority of observers see the reversal (blue-in-front-of-red observers) and the rest do not experience the phenomenon. On the other hand, when the background is white (Fig. 2), the perceived depth order is reversed, and the effect is weaker than when the background is black.
Goethe  may deserve to be the first person who proposed the notion of advancing color (red) versus receding color (blue), but he did not notice the binocular aspect of chromostereopsis. According to Thompson et al.’s review , the history of chromostereopsis goes back at least to the work of Donders in 1864 , while Vos’ review  suggested that Donders first reported this effect in 1868, followed by Bruecke  in the same year. According to Dengler and Nitschke’s review , however, Brewster  reported in 1851 that owing to the chromatic aberration of the lens, short-wavelength colors are seen stereoscopically as more distant.
Both Donders and Bruecke attributed chromostereopsis to accommodative feeling, which was translated to the perception of distance . Blue or short-wavelength light has a larger refractive index than the red or long-wavelength one. This makes the color rays run in a different way as shown in Fig. 3. This is called “longitudinal chromatic aberration” . This idea suggests that red should be closer than blue even if both colors are placed in the same depth plane because a closer object comes into focus at the posterior part. Moreover, this idea suggests that chromostereopsis should be seen monocularly. Yet, these two suggestions are not the cases, and this idea is not regarded as a plausible explanation of chromostereopsis [3, 11].
It was Bruecke  in 1868 who found the binocular nature of the phenomenon . The optical axis of an eyeball is slightly (about 5° = angle gamma or angle alpha) shifted in the outward direction from the visual axis. Red light is thus projected to a more temporal part of the retina than does blue light (Fig. 4) because of the difference in refractive index of both colors. This physiological optics is called “transverse chromatic aberration” . This idea suggests that red should be perceived in front of blue through binocular stereopsis based upon the binocular disparities of both colors. More specifically, a closer object projects to a more temporal part in the retina and so does red light. This suggestion, however, made Bruecke immediately reject his hypothesis because some of his observers reported red receding with respect to blue.
According to Vos , Einthoven discovered in 1885 that chromostereopsis is enhanced or reversed by using a simple method as shown in Fig. 5 [11, 12]. Covering the temporal parts of both pupils forces observers to see blue in front of red (upper image of Fig. 5). On the other hand, covering the nasal parts of both pupils makes observers see red in front of blue (lower image of Fig. 5). This method was also demonstrated by Kishto . He cited Kohler’s article  in 1962, which did not mention any other literature, though.
Subsequently, Einthoven’s covering method was simplified to the method using artificial pupils. Nasally placed artificial pupils gave blue in front of red (upper image of Fig. 6), while temporally placed ones rendered red in front of blue (lower image of Fig. 6) [15, 16, 17, 18, 19, 20, 21, 22, 23]. Vos [4, 16, 18] attributed chromostereopsis to interactions between each individual pupil decentralization (angle gamma) and the Stiles-Crawford effect. The Stiles-Crawford effect is a phenomenon that the rays entering the eye through the peripheral regions of the pupil are less efficient than those through the central region . This two-factor model, which Vos  called the “generalized Bruecke-Einthoven explanation,” has been widely accepted, while a few authors did not approve it .
Many studies suggested that pupil size affects chromostereopsis [19, 21, 22, 23], which supports the generalized Bruecke-Einthoven explanation. Simonet and Campbell , however, did not find any consistent relationship between pupil size and chromostereopsis.
Einthoven’s original finding was explained by the center-of-gravity model (Fig. 7) . It is hypothesized that the position of color is determined at the center of gravity in the range of each projected light onto the retina. For example, when the temporal half is occluded, the center of gravity of red light shifts in the relatively nasal direction, while that of blue light deviates in the temporal direction (upper image of Fig. 7). These shifts give binocular disparities to produce the blue-in-front-of-red stereopsis. When the nasal half is occluded, the center of gravity of red light shifts in the relatively temporal direction, while that of blue light deviates in the nasal direction (lower image of Fig. 7). These shifts give binocular disparities to produce the red-in-front-of-blue stereopsis.
In 1965, Kishto reported a tendency that red appears to be in front of blue at high levels of illumination, while blue appears to be in front of red at low levels of illumination, i.e., 17 of 25 observers (68 %) reported so . This finding was influential and drew much attention , though it was questioned by some studies [9, 26]. For example, Simonet and Campbell  reported a reversal in the direction of the chromostereopsis for 16 of 30 observers (53 %) when the ambient illumination was increased, but six of them (38 %) reported a change toward the blue-in-front-of-red chromostereopsis. Moreover, at low illuminance, there was lack of correlation between the direction of chromostereopsis and transverse chromatic aberration, which may indicate that there may be a supplementary binocular factor in chromostereopsis .
In 1928, Verhoeff reported that the perceived depth order between red and blue is reversed by changing the background from black to white (Fig. 2) [9, 28, 29, 30]. One account is that red surrounded by white lacks blue, while blue surrounded by white lacks red, suggesting that there are virtually blue and red edges, respectively . According to Faubert , Hartridge described in his 1950s textbook  that “when both black and white pattern lie on a uniformly coloured background a stereoscopic effect is frequently noticed” (Fig. 8).
With respect to this luminance-dependent reversal, Faubert [31, 33] proposed a new demonstration of chromostereopsis in which colors are bordered with each other (Fig. 9) and pointed out the critical role of luminance profiles caused by transverse chromatic aberration in subsequent binocular stereopsis. The luminance-profile-dependent binocular stereopsis is thought to correspond to the one which Gregory and Heard showed in 1983 as shown in Fig. 10 [34, 35], though Faubert did not mention it. If the luminance order is reversed between the two colors, the apparent depth is reversed as shown in Fig. 11. When two colors are isoluminant, two depth planes are simultaneously observed (rivaldepth) with luster where two colors meet (Fig. 12) . In addition, actually a century ago, Einthoven  had pointed out the role of luminance profiles caused by transverse chromatic aberration, but he had assumed the perception of convex or concave objects depending on where illuminated light comes from and made a monocular explanation like the crater illusion (Fig. 13).
Faubert’s luminance-profile-based model [31, 33] can be extended to explain the luminance-dependent reversal (Fig. 14). Suppose that white consists of red, green, and blue. Given transverse chromatic aberration when the background is black, and suppose that red appears to shift in one direction, blue appears to shift in the opposite direction (upper panel of Fig. 14), and green does not change the apparent position. Then, when the background is white, red appears to slightly shift in the opposite direction, with yellow leading to and magenta (color mixture of red and blue) following red. On the other hand, blue appears to slightly shift in the same direction as that of red when the background is black, with cyan (color mixture of blue and green) leading to and magenta following blue (lower panel of Fig. 14). Figure 15 shows the pictorial explanation of how transverse chromatic aberration induces the positional shifts of colors.
It was reported that the effect of chromostereopsis is large when observers see the image at a distance [13, 27, 31], whether observers are of the red-in-front-of-blue type or the blue-in-front-of-red type . This issue remains open. In addition, there is no literature to suggest any involvement of myopia or hyperopia in chromostereopsis.
The majority of observers see red in front of blue with the black background in a light environment. How many people see blue in front of red? In Luckiesh , 11 % (1 of 9 observers) did so. The proportion was 4 % (1 of 25 observers) in Kishto , 30 % (9 of 30 observers) in Simonet and Campbell , 7 % or 14 % (1 or 2 of 14 observers) in Dengler and Nitschke , 20 % (4 of 20 observers) in Kitaoka et al. , and 21 % (16 of 75 observers) in Kitaoka .
Color anomaly people also see chromostereopsis. Kishto  examined three color anomaly observers, one being a strong protanope, one being a mild deuteranope, and the third having too poor color discrimination to read any of Ishihara plates. They all saw red in front of blue with the black background in a light environment.
It is thought that some part of the effect is due to luminance differences or contrast differences (Fig. 16), with bright objects appearing closer than dim ones  or high-contrast objects appearing closer than low-contrast ones . Saturation also affects chromostereopsis [11, 13]. Desaturation decreased the depth effect, though desaturation is inevitably accompanied by changes in luminance, contrast, or spectrum.
Moreover, if an image consists of the inset and surround, there seems to be a tendency that the inset appears to be behind the surround (Fig. 17). This phenomenon seems to be observed with achromatic images, too (Fig. 18).
Neural correlates of chromostereopsis were investigated using visually evoked potentials . Results demonstrate that the depth illusion obtained from contrast of color implicates similar cortical areas as classic binocular depth perception.
It is summarized that chromostereopsis is a phenomenon of binocular stereopsis based upon binocular disparity produced by some interaction between optic properties of color rays and further neural processing. Chromostereopsis is a ubiquitous phenomenon and has a considerable pile of observations gained in its long research history.
Sundet, J.M.: The effect of pupil size variations on the colour stereoscopic phenomenon. Vision Res. 12, 1027–1032 (1972)CrossRefGoogle Scholar
Sundet, J.M.: Two theories of colour stereoscopy. An experimental investigation. Vision Res. 16, 469–472 (1976)CrossRefGoogle Scholar
Owens, D.A., Leibowitz, H.W.: Chromostereopsis with small pupils. J. Opt. Soc. Am. 65, 358–359 (1975)ADSCrossRefGoogle Scholar
Ye, M., Bradley, A., Thibos, L.N., Zhang, X.: Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils. Vision Res. 31, 1787–1796 (1991)CrossRefGoogle Scholar
Ye, M., Bradley, A., Thibos, L.N., Zhang, X.: The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles-Crawford effect and chromatic aberrations. Vision Res. 32, 2121–2128 (1992)CrossRefGoogle Scholar
Stiles, W.S., Crawford, B.H.: The luminous efficiency of rays entering the eye at different points. Proc. R. Soc. Lond. 112B, 428–450 (1933)ADSCrossRefGoogle Scholar
Bodé, D.D.: Chromostereopsis and chromatic dispersion. Am. J. Optom. Physiol. Opt. 63, 859–866 (1986)CrossRefGoogle Scholar
Simonet, P., Campbell, M.C.: Effect of illuminance on the directions of chromostereopsis and transverse chromatic aberration observed with natural pupils. Ophthalmic Physiol. Opt. 10, 271–279 (1990)CrossRefGoogle Scholar
Kitaoka, A., Kuriki, I., Ashida, H.: The center-of-gravity model of chromostereopsis. Ritsumeikan J. Human Sci. 11, 59–64 (2006)Google Scholar
Verhoeff, F.H.: An optical illusion due to chromatic aberration. Am. J. Ophthalmol. 11, 898–900 (1928)CrossRefGoogle Scholar
Hartridge, H.: The visual perception of fine detail. Phil. Trans. R. Soc. 232, 519–671 (1947)CrossRefGoogle Scholar
Winn, B., Bradley, A., Strang, N.C., McGraw, P.V., Thibos, L.N.: Reversals of the optical depth illusion explained by ocular chromatic aberration. Vision Res. 35, 2675–2684 (1995)CrossRefGoogle Scholar
Faubert, J.: Seeing depth in colour: more than just what meets the eyes. Vision Res. 34, 1165–1186 (1994)CrossRefGoogle Scholar
Hartridge, H.: Recent Advances in the Physiology of Vision. J & A Churchill, London (1950)Google Scholar
Faubert, J.: Colour induced stereopsis in images with achromatic information and only one other colour. Vision Res. 35, 3161–3167 (1995)ADSCrossRefGoogle Scholar
Gregory, R.L., Heard, P.F.: Visual dissociations of movement, position, and stereo depth: some phenomenal phenomena. Q. J. Exp. Psychol. 35A, 217–237 (1983)CrossRefGoogle Scholar
Kitaoka, A.: Configurational coincidence among six phenomena: a comment on van Lier and Csathó (2006). Perception 35, 799–806 (2006)CrossRefGoogle Scholar
Adams, W.J., Graf, E.W., Ernst, M.O.: Experience can change the “light-from-above” prior. Nat. Neurosci. 7, 1057–1058 (2004)CrossRefGoogle Scholar
Kitaoka, A.: A new development of studies on advancing and receding colors: modified longitudinal chromatic aberration model. KAKEN report 15330159, pp. 1–45 (2007)Google Scholar
Mount, G.E., Case, H.W., Sanderson, J.W., Brenner, R.: Distance judgments of colored objects. J. Gen. Psychol. 55, 207–214 (1956)CrossRefGoogle Scholar
Cauquil, A.S., Delaux, S., Lestringant, R., Taylor, M.J., Trotter, Y.: Neural correlates of chromostereopsis: an evoked potential study. Neuropsychologia 47, 2677–2681 (2009)CrossRefGoogle Scholar