Polarization arising from light scattering within the earth’s atmosphere. Unpolarized sunlight (upper left panel) remains unpolarized if it reaches the observer directly (scattering angle 0°, right panel), but is linearly polarized if it is scattered by atmospheric O2 and N2 molecules. Within a theoretical (Rayleigh) atmosphere, the degree of polarization reaches 100%, if the scattering angle is 90° (lower left panel). Other scattering angles yield smaller degrees of polarization (lower right panel). The light is then said to be partially linearly polarized. In the real atmosphere, the degree of polarization – even in full blue skies – is almost always less than 70% (see Horvath and Wehner, 1999). Background landscape: Naukluft gravel plain desert, north of Gobabeb, Namibia.
Polarization arising from the reflection of light by a water surface. Unpolarized sunlight (left panel) becomes linearly polarized when it is reflected by water surfaces. The reflected light is horizontally polarized (right panel). Maximum polarization is reached at a particular angle of incidence (Brewster’s angle; 53° for the air/water interface). Background landscape: Sabkhat al Muh, south-east of Tadmur, Syria.
Experimental paradigm to test an animal’s ability to detect the angle of polarization (e-vector orientation, χ) independently of radiant intensity (I) and to determine the animal’s sensitivity to different values of χ. In the first discrimination paradigm, the animal is trained to an unpolarized stimulus, which it later has to discriminate from linearly polarized stimuli (χ1−χ5) that are varied in intensity (abscissa). The resulting family of response curves (choice frequency versus logI; one for each value of χ) allows one to define combinations of χ/I that are discriminated equally well, e.g. by 75% responses, from the unpolarized training stimulus. Hence, the animal perceives them as equally bright. If, in a second training and discrimination paradigm, the animals are able to discriminate these χ/I combinations from each other, this ability must be due exclusively to the stimulus differences in χ. In addition, the family of response/logI characteristics allows one to compute the animal’s sensitivity to various values of χ. This is because the sensitivity to χ is proportional to the reciprocal of the intensity values that elicit equal responses for all values of χ (see orange arrowheads and black dotted lines in the upper part of the graph). [Actually the response/logI functions have been taken from an analogous study on colour vision in fish. The latter data can be restored by replacing the unpolarized stimulus by an uncoloured (grey) stimulus, and the χ1−χ5 values by λ1=461nm, λ2=555nm, λ3=434nm, λ4=599nm and λ5=719nm (Neumeyer, 1986).] Note that the rationale behind the experimental paradigm described for detecting different values of χ is strictly valid only for a stationary (rather than scanning) detector system. Such restrictions are not necessary in tests on colour vision.
Experimental paradigm in which desert ants, Cataglyphis fortis, were trained to walk in a particular compass direction while a partial e-vector pattern (a strip-like aerial window) was displayed to them. Examples are given for three earthbound orientations of the slit-like window (αw) shown in training. The training directions were 180°, 210° and 270° (blue arrowheads in inset figures). During the course of the day, the sun (yellow disc) and concomitantly the entire e-vector pattern (blue bars) moved across the sky (see abscissa, which is calibrated linearly with respect to time of day). In the subsequent tests performed immediately after training, the ants were presented either with a full e-vector pattern (paradigm A) or, in one case, with the same aerial window that they had seen during training (paradigm B). Systematic navigation errors, αe, occur in the former case (paradigm A; black data points, means ± s.d., N=433), but not in the latter (paradigm B; green data point, mean ± s.d., N=34). Technically, it is much more difficult to carry out paradigm B tests rather than paradigm A tests. Therefore, the former tests are represented by only one series of experiments. The orange lines depict the errors to be expected theoretically (the mean of the errors induced in paradigm A tests by the presentation of individual e-vectors in isolated pixels of sky). The open arrowheads in the upper parts of the figures mark the zero crossings of the theoretical curves. Paradigm A tests are based on Wehner (Wehner, 1997).
The insect’s polarization channel for the e-vector compass. Hypothetical scheme based on neurophysiological data. (A) The e-vector pattern in the sky. The orientation and size of the blue bars indicate the angle and degree of polarization, respectively. 0°, azimuthal position of the sun; open disc, zenith. In the particular case shown here, the elevation of the sun (yellow disc) is 60°. (B) Array of polarization detectors (L and R, left and right visual field, respectively). The e-vector tuning axes of only a few of the total of 55–75 polarization (POL) detectors per eye (in Cataglyphis bicolor) are shown. Each detector consists of a pair of orthogonally arranged analyzers (photoreceptors), which interact antagonistically. The dashed line depicts the animal’s longitudinal body axis. To simplify matters, the array of detectors shown here is symmetrical with respect not only to the animal’s longitudinal but also to its transverse (L–R) body axis and, thus, introduces a 180° ambiguity in the compass responses. The latter symmetry does not hold in the animal. (C) Response ratios of three large-field POL neurons. The response ratios are schematically translated into false colours. If the animal rotates relative to the skylight pattern (see filled arrow in B), different false colours show up (see white arrow in C). (D) Circular array of hypothetical compass neurons. Each fine-tuned compass neuron encodes a particular response ratio of the broadly tuned POL neurons. The compass neuron marked by the filled red circle is maximally excited when the animal faces the solar azimuth. (Owing to the 180° ambiguity mentioned above, in this artificial case the 180° circle should be coloured red, too).