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Retinal image quality in near-eye pupil-steered systems

Kavitha Ratnam, Robert Konrad, Douglas Lanman, and Marina Zannoli

Open Access Open Access

Abstract

State-of-the-art near-eye displays often compromise on eye box size to maintain a wide field of view, necessitating a means for steering the eye box to maintain alignment with a moving eye. The design space of such pupil-steered systems is not well defined and the implications of imperfect steering on the perceived image are not well understood. To better characterize the pupil steering design space, we introduce a generalized taxonomy of pupil-steered architectures that considers both system and ocular factors that affect steering performance. We also develop an optical model of a generalized pupil-steered system with a wide-field schematic eye to simulate the retinal image. Using this framework, we systematically characterize retinal image quality for different combinations of design parameters. The results of these simulations provide an overview of the pupil steering design space and help determine relevant psychophysical experiments for further evaluation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (9)
Fig. 1.
Fig. 1. Pupil steering of a small exit pupil (or eye box). In the real world ("overfilled pupil"), the pupil is always filled regardless of eye rotation. With a small eye box, even small eye rotations clip the cone of light, resulting in a vignetted or entirely-obscured image on the retina. The goal of pupil steering is to continuously move the eye box so that it aligns with the ocular pupil. Steering degrees of freedom can be restricted to translation (2D, 3D) or also tip/tilt (5D) to compensate for misalignment. Retinal image quality depends not only on exit-ocular pupil alignment but also the size of the exit pupil relative to the ocular pupil ("underfilled" vs "critically-filled"). Schematic retinal vignetting profiles are shown for moderate rotations of the eye.

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Fig. 2.
Fig. 2. The Zemax setup and Arizona eye model (AZEye15 [17]). A display, aperture, and set of paraxial lenses form an exit pupil at the entrance pupil of the eye. In the on-axis configuration, the eye is unrotated and the exit pupil and ocular entrance pupil are aligned. The eye is rotated around the y-axis to simulate saccades and vergence up to 35°. For each rotated configuration, an optimization procedure is performed to determine the optimal exit pupil position for 2D ($x,y$) and 3D ($x,y,z$) steering. 5D steering performance is simulated by reverting the system to the on-axis, aligned configuration. The vignetting profile and on-axis modulation transfer function (MTF) at the retinal plane are then used to compare image metrics for the different steering modes. The eye’s pupil plane is apodized to simulate the Stiles-Crawford effect [18].

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Fig. 3.
Fig. 3. Global percent transmission as a function of eye rotation over a 100° FOV. Rows correspond to pupil-fill; columns correspond to ocular entrance pupil diameter. Colors correspond to different modes of steering (2D, orange; 3D, green; 5D, red); the no steering condition (gray) refers to when the exit pupil position is fixed regardless of eye rotation. The overfilled case (not shown) would have 100% transmission for all eye rotations. For the underfilled cases, 3D and 5D steering performed similarly except for extreme eye rotations. 2D and 3D performance degraded for the critically-filled cases, although performance always exceeded $\sim$30% and $\sim$90% transmission for 2D and 3D steering respectively.

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Fig. 4.
Fig. 4. Local percent transmission by field position for the 3 mm ocular entrance pupil. Percent transmission for the 1 mm ("underfilled") and 3 mm ("critically-filled") pupils were calculated for varying eye rotations. Percent transmission for the 0°, 25° temporal, and 50° temporal retinal locations are denoted by the solid, dashed, and dashed-dotted lines respectively.

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Fig. 5.
Fig. 5. Global percent transmission tolerance analyses for underfilled and critically-filled ocular pupils. The colormap represents the percent transmission of rays over a 100° FOV for varying combinations of pupil-fill, eye rotation, steering modes, and $x$ or $z$ stop displacements. Stop displacements are plotted relative to the optimal steering position (displacement = 0 mm) for a given amount of eye rotation.

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Fig. 6.
Fig. 6. The spatial frequency cutoff of the modulation transfer function (SFcMTF) is an image quality metric denoted by the intersection of the retinal MTF and neural contrast threshold function (CTF). The visual strehl metric is derived by finding the area under the MTF weighted by the neural contrast sensitivity function (CSF). CSF = 1/CTF.

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Fig. 7.
Fig. 7. $SFcMTF$ (left) and $VS_{[0,60]}$ (right) as a function of eye rotation. Values for the 1 mm ("underfilled", top row) and critically-filled pupils (bottom row) were calculated for varying eye rotations. Data for the 2 mm and 3 mm ocular pupils are presented for the cases of no steering (gray), 2D steering (orange), 3D steering (green), 5D steering (red), and the overfilled pupil (black). Data is shown for $\lambda$ = 555 nm.

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Fig. 8.
Fig. 8. $SFcMTF$ (top) and $VS_{[0,60]}$ (bottom) tolerance analyses. The colormap represents values for varying combinations of pupil-fill, eye rotation, steering modes, and $x$ or $z$ stop displacements. Stop displacements are plotted relative to the optimal steering position (displacement = 0 mm) for a given amount of eye rotation.

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Fig. 9.
Fig. 9. Maximum displacement between steering position and ocular pupil along the $x$ (left) and $z$ (right) axes for different saccadic amplitudes and steering latencies. Analysis assumes saccadic and steering motion profiles are identical except for a temporal offset in steering onset. Contour lines represent maximum $x$ or $z$ displacement between the steered pupil and ocular pupil over the course of the eye movement.

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Equations (5)

Equations on this page are rendered with MathJax. Learn more.

T ( f ) = ∑ n = 1 s r a y n ( f , p n ) s
Δ z = 13.5 − 13.5 ∗ cos ⁡ ( θ r o t )
θ r o t = arccos ⁡ ( 13.4 / 13.5 ) = 7.0 ∘
S F c M T F = max ( f )   |   M T F ( f ) > C T F ( f )
V S [ m i n , m a x ] = ∫ m i n m a x C S F ( f ) ⋅ M T F ( f ) d f
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