Albertian errors in head-mounted displays: I. Choice of eye-point location for a near- or far-field task visualization

Jannick Rolland; Yonggang Ha; Cali Fidopiastis

doi:10.1364/JOSAA.21.000901

Journal of the Optical Society of America A
Vol. 21,
Issue 6,
pp. 901-912
(2004)
•https://doi.org/10.1364/JOSAA.21.000901

Albertian errors in head-mounted displays: I. Choice of eye-point location for a near- or far-field task visualization

Jannick Rolland, Yonggang Ha, and Cali Fidopiastis

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Jannick Rolland, Yonggang Ha, and Cali Fidopiastis, "Albertian errors in head-mounted displays: I. Choice of eye-point location for a near- or far-field task visualization," J. Opt. Soc. Am. A 21, 901-912 (2004)

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Abstract

A theoretical investigation of rendered depth and angular errors, or Albertian errors, linked to natural eye movements in binocular head-mounted displays (HMDs) is presented for three possible eye-point locations: the center of the entrance pupil, the nodal point, and the center of rotation of the eye. A numerical quantification was conducted for both the pupil and the center of rotation of the eye under the assumption that the user will operate solely in either the near field under an associated instrumentation setting or the far field under a different setting. Under these conditions, the eyes are taken to gaze in the plane of the stereoscopic images. Across conditions, results show that the center of the entrance pupil minimizes rendered angular errors, while the center of rotation minimizes rendered position errors. Significantly, this investigation quantifies that under proper setting of the HMD and correct choice of the eye points, rendered depth and angular errors can be brought to be either negligible or within specification of even the most stringent applications in performance of tasks in either the near field or the far field.

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Equations (28)

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Parameter	Near-Field Visualization	Far-Field Visualization
$D (m)$	1	10
$z_{g} (m)$	1	10
Rendering depth $z_{p} (m)$	$0.73 \sim 1.32$	$5.08 \sim 329.0$
Vertical FOV $ϕ_{g},$ $ϕ_{B} (°)$	±15
Horizontal FOV $θ_{g}^{L},$ $θ_{B}^{L} (°)$	±20
$r_{p} (mm)$	9.25

$θ_{g}^{L} (°)$	$ϕ_{g} (°)$	Maximum Magnitude of Angular Error (arc min)		Condition When Angular Error Reaches Minimum
$θ_{g}^{L} (°)$	$ϕ_{g} (°)$	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points
0	0	1	0.01	$θ_{B}^{L} = 0$ or $z_{p} = 10$	$z_{p} = 10$
0	15	0.8	0.7
10	0	1.4	0.5	$θ_{B}^{L} = 10$ or $z_{p} = 10$
10	15	1.4	0.9
-10	0	1.4	0.5	$θ_{B}^{L} = - 10$ or $z_{p} = 10$
-10	15	1.4	0.9
20	0	2.0	1.1	$θ_{B}^{L} = 20$ or $z_{p} = 10$
20	15	2.0	1.3
-20	0	2.0	1.1	$θ_{B}^{L} = - 20$ or $z_{p} = 10$
-20	15	2.0	1.3

$θ_{g}^{L} (°)$	$ϕ_{g} (°)$	Maximum Magnitude of Angular Error (arc min)		Maximum Magnitude of Depth Error (mm)
$θ_{g}^{L} (°)$	$ϕ_{g} (°)$	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points
0	0	4	0.4	1	4.2
0	15	4	3	0.8	4.2
10	0	5.4	1.7	1.1	4.2
10	15	5.4	3.4	1.0	4.2
-10	0	5.4	3.0	1.1	4.2
-10	15	5.4	4.0	1.0	4.2
20	0	7.2	4.0	1.0	4.2
20	15	7.2	5.0	1.0	4.2
-20	0	7.2	4.4	1.2	4.2
-20	15	7.2	5.0	1.0	4.2

$ϕ_{g} (°)$	α (°)	Maximum Magnitude of Angular Error (arc min)		Condition When Angular Error Reaches Minimum
$ϕ_{g} (°)$	α (°)	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points
0	-15	1.2	0.024	$z_{p} = 10$	$z_{p} = 10$
0	-10	1.2	0.016
0	-5	1.2	0.008
0	0	1.2	0
10	-25	1.5	0.5
10	-10	1.1	0.54
10	0	1	0.53
10	5	1	0.52
15	-30	1.6	0.75
15	-20	1.4	0.8
15	-10	1.2	0.8
15	0	1.0	0.78

$ϕ_{g} (°)$	α (°)	Maximum Magnitude of Angular Error (arc min)		Maximum Magnitude of Depth Error (mm)
$ϕ_{g} (°)$	α (°)	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points	$C_{L}$ and $C_{R}$ as Eye Points	$P_{L}$ and $P_{R}$ as Eye Points
0	-15	4.8	0.05	1.0	4.2
0	-10	4.4	0.04	1.0	4.2
0	-5	4.2	0.037	1.0	4.2
0	0	4.2	0.07	1.0	4.2
10	-25	5.6	2.0	1.0	4.2
10	-10	4.6	2.2	1.0	4.2
10	0	4.2	2.1	1.0	4.2
10	5	4.2	2.0	1.0	4.2
15	-30	6.4	2.8	1.0	4.2
15	-20	5.4	3.0	1.0	4.2
15	-10	4.6	3.0	1.0	4.2
15	0	4.0	2.9	1.0	4.2

Abstract

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Equations (28)

Journal of the Optical Society of America A