Apparent Zenith Research Articles

Les développements de Radau et leur divergence : commentaire historique

In an award-winning 1882 article, Radau (1835–1911) takes stock of various expressions of refraction, including the power series of the tangent of the apparent zenith distance. We focus on the integral expression of its coefficients, on the fundamental approximation used to calculate them, and on the subsequent introduction (1906) for this purpose of multiple families of characteristic heights of the atmosphere. We comment on the divergence, due to the fundamental approximation, of the series obtained in the case of the isothermal atmosphere (therefore unlimited).

Influence of multisensory graviceptive information on the apparent zenith

We studied the contribution of vestibular and somatosensory/proprioceptive stimulation to the perception of the apparent zenith (AZ). Experiment 1 involved rotation on a centrifuge and settings of the AZ. Subjects were supine on the centrifuge, and their body position was varied in relation to the rotation axis so that the gravitoinertial resultant force at the otoliths was 1 or 1.2 g with the otolith organs positioned 50 or 100 cm from the axis of rotation. Their legs were also positioned in different configurations, flexed and elevated or extended, to create different distributions of blood and lymph. Experiment 2 involved (a) settings of the AZ for subjects positioned supine with legs fully extended or legs flexed and elevated to create a torsoward shift of blood and (b) settings of the subjective visual vertical for subjects horizontally positioned on their sides with legs extended or bent. Experiment 3 had subjects in the same body configurations as in Experiment 2 indicate when they were horizontal as they were rotated in pitch or roll about an inter-aural or naso-occipital axis. The experimental results for all three experiments demonstrated that both visual localization and apparent body horizontal are jointly determined by multimodal combinations of otolithic and somatosensory/proprioceptive stimulation. No evidence was found for non-overlapping or exclusive mechanisms determining one or the other. The subjective postural horizontal and AZ were affected in similar ways by comparable manipulations.

Effect of low gravitational stimulation on the perception of target elevation: Role of spatial expertise

To examine the interindividual differences in the judgment of the visually perceived eye level (VPEL-upright position) and of the visually perceived apparent zenith (VPAZ-supine position) when the subject is subjected to low gravitational-inertial force (GIF), we independently altered GIF in two different populations: control subjects and spatial experts. Subjects were instructed to set a luminous target to the eye level while they were in total darkness and motionless or undergoing low radial acceleration with respect to the threshold of the otolithic system (0.015-1.67 m/sec2 for the VPEL and 0.55-2.19 m/sec2 for the VPAZ, respectively). Results showed that (1) low GIFs, close to those met during daily life, induced an eye level lowering in the upright and supine positions for the control group, and (2) the spatial expertise modified the influence of low GIF. Whereas an oculogravic illusion was found for the control group, this phenomenon was absent (VPAZ) or weaker (VPEL) for the spatial experts. Thus, the relations that the subjects maintain with their spatial environment and the knowledge acquired through experience modify the processing of sensory information and the perceptive construction resulting from it. The interindividual differences in sensitivity to the oculogravic illusion are discussed in terms of sensory dominance and of a better efficiency in the use of the available sensory information.

Effects of supine body position and low radial accelerations on the visually perceived apparent zenith.

The visually perceived eye level (VPEL) has been shown to shift toward the lower part of the body in upright subjects facing toward the axis of rotation on a centrifuge. This shift occurs in the same direction as the shift in the gravito-inertial forces (Gis) produced by very low radial acceleration (centrifugation) combined with gravity. The purpose of this study was to determine whether the same phenomenon affects the visually perceived apparent zenith (VPAZ) in subjects in a supine position. Twelve supine subjects were instructed to set a luminous target to the VPAZ, either while they were in total darkness and motionless or while undergoing very low centrifugation. Data showed that Gis induced a VPAZ shift similar to that observed for the VPEL. Thus, as is the case for the VPEL, the corresponding logarithmic psychophysical function of the VPAZ may be considered to be a type of oculogravic illusion phenomenon with differences in the subjects' that differs from subject to subject, depending on the subject's sensitivity to low radial accelerations. Data on VPEL and VPAZ support the notion that the subjective perception of eye level in total darkness takes into account changes--even if extremely slight-in the direction of the gravito-inertial forces produced by the combination of gravity and low radial accelerations, although subjects are unaware of the Gi shift. However, depending on the intensity of the radial acceleration and the angular deviation of Gi relative to G, the shift of the VPEL and the VPAZ can be either amplified or attenuated. Moreover, differences between VPEL and VPAZ responses suggest two explanatory assumptions--namely, that this is (1) a peripheral phenomenon dependent on the neurophysiological anisotropy of the otolithic system or (2) a central phenomenon dependent on the relevance assigned to the peripheral information by the integrative sensory functions and the associative processes.

Effects of Observer Orientation on Perception of Ego- and Exocentric Spatial Locations

Perceived eye position and/or the perceived location of visual targets are altered when the orientation of the surrounding visual environment (Cohen et al, 1995 Perception & Psychophysics571 433) or that of the observer (Cohen and Guzy, 1995 Aviation, Space, and Environmental Medicine66 505) is changed. Fourteen subjects used biteboards as they lay on a rotary bed that was oriented head-down −15°, −7.5°, supine, head-up +7.5°, and +15°. In the dark, subjects directed their gaze and set a target to the apparent zenith (exocentric location); they also gazed at a subjective ‘straight ahead’ position with respect to their head (egocentric location). Angular deviations of target settings and changes in vertical eye position were recorded with an ISCAN infrared tracking system. Results indicated that, for exocentric locations, the eyes deviate systematically from the true zenith. The gain for compensating changes in head orientation was 0.69 and 0.73 for gaze direction and target settings, respectively. In contrast, ‘straight ahead’ eye positions were not significantly affected by changes in the subject's orientation. We conclude that subjects make systematic errors when directing their gaze to an exocentric location in near-supine positions. This suggests a systematic bias in the integration of extra-ocular signals with information regarding head orientation. The bias may result from underestimating changes in the orientation of the head in space. In contrast, for egocentric locations, where head orientation information can potentially be discarded, gaze directions were unaffected by head orientation near supine.

AN ACCURATE METHOD FOR COMPUTING ATMOSPHERIC REFRACTION

ABSTRACT This paper describes a method for computing atmospheric refraction that is simple, highly accurate, and usable for wavelengths lambda-lambda-3000 - 10,000A. When compared with the REfraction Tables of Pulkovo Observatory (Abalakin 1985), the computed and Pulkovo refractions are in extremely good agreement (~10 mas or better) for zenith distances under 65 degrees, and at a zenith distance of 75 degrees, the agreement degrades to about ~150 mas. Moreover, this refraction is easy to compute, since only knowledge of the meterological conditions at the observing site (e.g., ambient temperature, atmospheric pressure, and dew point or relative humidity), the apparent zenith distance of the object being observed, and the location of the observing site relative to the Earth's geoid are needed for its calculation. Because of its simplicity and high accuracy, the refraction presented in this paper is well suited for programs where huge amounts of data needs to be processed quickly to star positions or for accurately setting automated telecopes. In addition, the refraction for a given telescope passband will differ in a way dependent on the spectrum of the object being observed. This paper describes how a mean refraction, weighting the selective refraction over the passband, can be computed.

Precision in determination of astronomical refraction from aerological data

AbstractVarious errors in determination of the local pure astronomical refraction are evaluated versus the apparent zenith distance z0. Numerical integration with the step imposed by heights of an aerological sounding brings the error smaller than 0″01 until z0 = 70°. For larger zenith distances integration with a more dense step is possible after fitting the data to a five‐parameter functional dependence of the refractive index on height. The fitting is simultaneously a good equalization of aerological data reducing considerably their experimental error as well as short‐term local fluctuations of the atmosphere. After equalization, the error in the refraction originating from the error in the aerological data is found to approach 0″01 at z0 = 72°, 0″1 at z0 = 82°, 1″ at z0 = 87°, and 10″ at the horizon. This has to be taken into account when considering systematic deviations of the local pure refraction from that determined in a standard way. The purely stochastic error in the refraction originating in the error of the refractive index at the observation site is discussed within the context of local fluctuations of the atmosphere. It is evaluated that until z0 = 85° the precision in determining the astronomical refraction in a single observation is limited by refraction anomalies (image motion) and only above 85° the error in aerological data becomes more important.

Velocity Aberration and Atmospheric Refraction in Satellite Laser Communication Experiments

The effects of satellite velocity aberration and atmospheric refraction on the direction of propagation of lagser radiation reflected from a satellite back to an observer on the earth are examined. A velocity aberration analysis for the two-dimensional case where the satellite passes directly overhead at velocity v is presented to first order in v/c in order to illustrate the method. The equations for the more general threedimensional case are then given to first order in v/c, and it is indicated that higher order treatments are normally unnecessary in typical experimental considerations. Following this, a simple approximate equation giving the atmospheric refraction to an accuracy of a few microradians is developed; it is indicated that greater accuracy is not important because of laser pointing limitations imposed by atmospheric scattering and turbulence. The atmospheric refraction equation depends only on the apparent zenith angle of the satellite reflector relative to the earth-based laser, on the satelli-te altitude, and on the index of refraction of the laser radiation in the atmosphere at the earth's surface. Both of these developments should be useful in the design and interpretation of satellite laser-communication experiments.