In a 1925 paper in Die Naturwissenschaften, Erwin Schrödinger analyzed the subjective colors of stars and proposed to explain the well-known mismatch between stellar temperatures and perceived star colors by combining (i) chromatic contrast against the prevailing rod-mediated 'twilight sensation' of the dark-adapted eye and (ii) the Bezold-Brücke hue shift at very low luminance. The explanation rests on his own determinations of the quality of that twilight sensation: for normal trichromats a desaturated reddish-violet matching wavelengths below about 430 nm, conditionally shifting toward indigo near 445 nm; for one deuteranomalous observer a green-blue hue varying with field brightness between about 484 and 495 nm. The paper leaves open the conditions of the indigo shift, whether the retina's intrinsic light (Eigenlicht, perceived as the Eigengrau of the completely dark-adapted eye) carries the same color as the twilight sensation, the difference between normal and anomalous observers, and whether the observed brightness dependence is intrinsic to the rod sensation or a Bezold-Brücke artifact of the comparison field. The precise hue of the fully dark-adapted rod sensation in normal and anomalous trichromats, the intrinsic-versus-artifact status of its brightness dependence, and whether the Eigengrau shares the rod sensation's color remain open.

Background

Human vision rests on a duplex receptor system. Cone photoreceptors mediate daylight (photopic) vision and, in people with normal color vision (trichromats, who have three cone types), carry the three-dimensional color percept; rod photoreceptors are far more sensitive and mediate dim-light (scotopic) vision. In the classical duplicity theory of the late nineteenth and early twentieth centuries, the qualitative character of the scotopic sensation was called the Dämmerungsempfindung, the 'twilight sensation', and a standing question of physiological optics was whether this rod-mediated sensation is essentially achromatic or has a determinate chromatic quality of its own — 'the color of the rods'. The Purkinje shift, the displacement of spectral sensitivity toward short wavelengths as light level falls, already showed that the dim-eye sees the world differently, and early observers reported that dim extended fields look faintly blue.

The occasion of Schrödinger's paper was an astronomical puzzle recently publicized by Bottlinger: the subjective colors of stars disagree with their physical colors as blackbody radiators. White stars like the Sun appear yellowish to the dark-adapted naked eye, while cool stars of 2000-3000 K appear deep red, far redder than a terrestrial glowing source of the same temperature looks. Schrödinger proposed a two-factor explanation: (i) simultaneous chromatic contrast against the prevailing twilight sensation of the dark-adapted visual field yellows white stars; (ii) the Bezold-Brücke phenomenon, the empirical change of perceived hue when luminance is drastically reduced (hues migrate toward the perceiver's dominant fundamental colors), turns the weak reddish-yellow light of cool stars into saturated red. Factor (i) made the actual hue of the twilight sensation a measurable load-bearing quantity, so Schrödinger re-measured it. The earlier determinations he cites were inadequate in his view: one was obtained on a deuteranope (a red-green dichromat whose two-dimensional color space makes the match untransferable to normals), giving about 480-485 nm; another, obtained with a pre-adaptation technique that left dark adaptation incomplete, gave about 457-465 nm for three normal subjects. Using long dark adaptation and interocular matching — one eye fully dark-adapted and stimulated at scotopic levels, the other acting as the color-measuring instrument — he found for normal trichromats a desaturated reddish-violet corresponding to spectral wavelengths below about 430 nm (a hue at the short-wavelength, violet end of the spectrum), shifting under circumstances he could not yet pin down toward indigo near 445 nm, and never greenish; for one deuteranomalous observer (an anomalous trichromat whose red-green matching is displaced because the middle-wave cone sensitivity is shifted) he found a green-blue twilight color whose matching wavelength varied with the subjective brightness of the rod field, about 484 nm for a very bright field and 495 nm for a very dark one.

The paper closes with the unresolved issues that define this problem: the conditions governing the indigo shift of the normal twilight color were unclarified; whether the Eigenlicht — the self-excitation of the dark-adapted retina, perceived as the intrinsic 'grey light' (Eigengrau) of a completely dark visual field, today understood as retinal dark noise — has a color genuinely matching the twilight sensation was judged probable but unproven; the striking difference between the normal and the anomalous observer's twilight colors was deferred to a future discussion that Schrödinger never published (his work turned to wave mechanics); and the brightness variation of the anomalous observer's matches might reflect either an intrinsic change of the rod sensation or a Bezold-Brücke hue shift of the photopic comparison field. Because the white-star half of the astronomical explanation leans on the contrast between starlight and the twilight color of the surrounding dark field, the identity between the Eigengrau and the measured twilight hue is itself a load-bearing premise.

Modern vision science has reorganized this territory. Rods are known to feed signals into all post-receptoral cone pathways (the neural channels beyond the photoreceptors that carry the cone signals); a scotopic successive-contrast experiment — successive contrast being the aftereffect left by a preceding stimulus — shows rod-triggered contrast colors resembling cone-triggered ones, displaced toward blue; rod activation biases the hue of concurrent cone-mediated percepts in a light-level- and adaptation-dependent manner; and under rod-only illumination of everyday surfaces, observers report variegated relational color percepts — higher scotopic reflectance surfaces look blue-green-grey, lower ones red-orange — while isolated scotopic patches look blue-green, in tension with Schrödinger's reddish-violet determination. Reviews conclude that hue perception is possible under pure rod-mediated conditions with cortical involvement, but that scotopic hue is spatially contextual and modulated by memory, which qualifies the classical construct of a single 'twilight color' without settling the source's determinations.

Problem Statement

For fully dark-adapted human observers, with rod mediation verified and cone participation excluded, determine the chromatic quality of the twilight (rod) sensation and its relation to the eye's intrinsic light, as left open by Schrödinger (1925): (i) the hue of the normal trichromat's dark-adapted twilight sensation — determined by Schrödinger as a desaturated reddish-violet matching wavelengths below about 430 nm, shifting under conditions he could not pin down toward indigo near 445 nm — together with the conditions (dark-adaptation duration, field brightness, adaptation state of the comparison eye) under which it shifts; (ii) whether the intrinsic excitation of the completely dark-adapted retina, perceived as the Eigengrau, has a chromatic quality genuinely matching the twilight sensation or is achromatic grey; (iii) whether the twilight-hue difference Schrödinger reported for his single deuteranomalous observer holds generally across anomalous trichromats rather than being peculiar to that observer; and (iv) whether any brightness dependence of the rod hue, as found for the anomalous observer (matches drifting from about 484 to 495 nm as the rod field darkens), is an intrinsic property of the rod sensation or a Bezold-Brücke hue shift of the comparison stimulus. All four determinations are required, each is stated independently, and a partial result on any single component does not resolve the problem. The twilight hue and its identity with the Eigengrau are the load-bearing premises of the contrast-plus-Bezold-Brücke explanation of subjective star colors, while the normal-versus-anomalous comparison and the intrinsic-versus-artifact question concern the coherence of the twilight-sensation construct itself; in modern terms the four determinations ask whether the rod system contributes a lawful, context-independent hue to perception and whether the dark-adapted visual field's intrinsic percept shares it. (The origin-of-rods remark in the source is a passing concession of priority regarding Schrödinger's 1924 note, not a question posed by the 1925 paper, and is excluded from this problem.)

References

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