Perceived brightness and resolution of holographic augmented reality retinal scan glasses

Maximilian Rutz; Pia Neuberger; Simon Pick; Torsten Stra{\ss}er

REVIEW 3 major objections 5 minor 11 references

Perceived brightness and resolution of holographic augmented reality retinal scan glasses

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper derives an equivalent luminance for retinal-scan AR glasses that scales inversely with pupil area, and supports it with a perceived-resolution study.

desk verdict Useful derivation and dataset for retinal scan display metrology, but the practical brightness benefit is conditional on perfect beam-pupil alignment and the resolution thresholds lack error bars. read the letter →

arxiv 2412.00831 v1 pith:DMXLAM4U submitted 2024-12-01 physics.optics physics.bio-ph

Maximilian Rutz , Pia Neuberger , Simon Pick , Torsten Stra{ss}er This is my paper · ORCID

classification physics.opticsphysics.bio-ph

keywords retinalscandisplayholographicopticalelementaugmentedrealityequivalentluminanceambientcontrastratioperceivedresolutionpupildiameterpsychophysics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the brightness of laser-scanning augmented reality glasses can be quantified by an equivalent luminance, defined as the luminance of a standard Lambertian display that would produce the same retinal illuminance. The formula depends on laser powers, wavelengths, field of view, and pupil diameter, and it implies that as the pupil shrinks in bright light, the virtual image gets relatively brighter. If true, retinal-scan displays have a self-compensating brightness advantage over conventional displays, which matters for designing AR glasses used outdoors. The paper also measures perceived resolution of a working prototype and finds thresholds around 7 cycles per degree, limited by the display optics rather than the eye.

What carries the argument

The load-bearing object is the equivalence $ L_{\mathrm{RS}} $: the luminance of a hypothetical Lambertian display that would create the same retinal illuminance as the scanned laser beam. Only emitted flux, field-of-view angles, and pupil area enter; the eye's focal length cancels, so no assumptions about eye geometry are needed beyond pupil size. The companion quantity $ \mathrm{ACR}_{\mathrm{RS}} = L_{\mathrm{RS}}/(\tau_C L_A) $ then lets virtual-image contrast with the real world be computed in the same photometric units as ordinary displays.

What would settle it

Measure the equivalent luminance of a retinal-scan display while controlling pupil size independently, for example with artificial apertures of different diameters placed at the eye or with pharmacologically dilated pupils, and compare the result with Equation (14): if the luminance that matches a Lambertian reference does not scale as $ 1/$d_P^{2}$ $, the derivation is wrong. A simpler check is that, in a dark room with a dilating pupil, a retinal-scan display should appear dimmer rather than brighter, opposite to a Lambertian display.

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Extended reading notes

Core claim

The central claim is that a retinal scan display's brightness can be written as $ L_{\mathrm{RS}} = \dfrac{K_m \sum V(\$\lambda$) \Phi}{4 A_P \tan(\$\alpha$/2) \tan(\$\beta$/2)} $, with $ K_m $ the luminous efficacy constant, $ V(\$\lambda$) $ the luminosity function, $ \Phi $ the radiant powers of the RGB lasers, $ A_P $ the pupil area, and $ \$\alpha$, \$\beta$ $ the field-of-view angles. This is derived by equating the retinal illuminance from the scanned beam with the retinal illuminance from a Lambertian display and noting that the eye's focal length cancels. Because $ A_P = \pi (0.001\, d_P)^2 / 4 $ appears in the denominator, the same display looks brighter when the pupil is smaller. Combined with a published pupil-diameter-versus-ambient-luminance model, $ L_{\mathrm{RS}} $ rises by a factor of about five from mesopic to bright photopic surroundings. The paper further defines $ \mathrm{ACR}_{\mathrm{RS}} = L_{\mathrm{RS}}/(\tau_C L_A) $ and argues that standard ambient contrast ratio, rather than one including the ambient transmission term in the numerator, is the right way to characterize these displays. In a 20-participant staircase study with a fully functional prototype, perceived resolution thresholds clustered around 7.1–7.4 cycles per degree, independent of background conditions, and well above the 3.4 cycles per degree measured by an IEC optical-resolution standard, indicating that the display optics limit what users can resolve.

Load-bearing premise

The derivation assumes the narrow scanning beam (diameter under 0.5 mm) always passes completely through the pupil, so all emitted light enters the eye and the flux does not depend on pupil size; if a small or misaligned pupil clips the beam, the inverse-pupil-area scaling breaks down.

Editorial extensions

If this is right

Retinal-scan displays can be specified with a luminance value that is directly comparable to ordinary Lambertian displays, provided the pupil diameter is known or modeled.
In bright ambient light, the pupil shrinks and the equivalent luminance rises, so virtual content stays visible outdoors without extra laser power.
The ambient contrast ratio $ \mathrm{ACR}_{\mathrm{RS}} $ can be used as a design target, since it stays well above the contrast level needed for reliable resolution perception even on bright backgrounds.
The perceived resolution threshold of roughly 7 cycles per degree is limited by the display optics, so future prototypes should first improve optical resolution and field of view before expecting users to see more detail.
IEC-style optical resolution measurements underestimate what users can actually resolve in retinal-scan glasses, so perceived-resolution testing is a useful addition to display metrology.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: If $ L_{\mathrm{RS}} $ is accepted as a metric, a direct brightness-matching experiment between a retinal-scan display and a calibrated Lambertian display should show that the retinal-scan display matches a luminance scaling as $ 1/d_P^2 $ when the pupil diameter is changed; the paper does not run such a test.
Editorial inference: The luminance-versus-ambient boost suggests an energy-budget design strategy where laser power is reduced in dark scenes while maintaining perceptually constant contrast outdoors, but the paper does not demonstrate such an adaptive power scheme.
Editorial inference: Because the human eye was not the resolution bottleneck up to about 7 cycles per degree, a retinal-scan display could potentially reduce its pixel density or holographic combiner area without a noticeable loss in perceived detail, until the optical resolution is improved.
Editorial inference: The proposed distinction between a standard ambient contrast ratio and an additive ambient contrast ratio could help unify comparisons across AR display types, but it would require industry consensus before becoming a standard measurement.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read it. The useful core is a clean derivation of an equivalent luminance for retinal scan displays, L_RS = K_m Σ V(λ) Φ / (4 A_P tan(α/2) tan(β/2)), with pupil area in the denominator. That is genuinely useful photometry for a display class that luminance cameras misreport, and it makes the ambient contrast ratio definition for RS displays explicit. The perceived-resolution experiment on a functional holographic RS prototype is a real addition; the field has very little human-in-the-loop data on this architecture. The staircase design is standard, and thresholds clustering around 7 c/d across fifteen conditions is a creditable measurement.

The soft spots are real but not fatal. First, the headline 'brighter in bright environments' depends on the beam fully passing through the pupil. The formula assumes RS flux is pupil-independent; the paper's own Discussion concedes the single-eyebox prototype loses visibility if the beam is clipped, and the psychophysical study used a chinrest plus a five-minute fitting. Without a tolerance analysis or eye-tracking data, the practical claim for wearable use is not established. The derivation itself is fine in the ideal static-alignment regime.

Second, the perceived-resolution thresholds come without confidence intervals or statistical tests. The comparison between the IEC optical resolution (3.4 c/d) and the perceived 7.4 c/d is left unexplained; the paper mentions the 30% modulation cutoff but does not quantify how it maps to perceptibility. That undercuts the conclusion that perceived resolution is limited by the optics.

Third, minor: Eq. (5) has a typographical slip in the written area expression, though the final formula is correct.

The citation pattern is honest; prior ACR definitions are discussed and the standard-vs-additive ACR distinction is sensible. No circularity: the Stanley-Davies pupil model is an input, not a fitted parameter.

This paper deserves a serious referee. It is a solid, useful contribution to near-eye display metrology, not a paradigm shift. A referee should ask for error bars and a direct treatment of the clipping condition; the core derivation and the dataset are worth publishing after revision.

Referee Report

3 major / 5 minor

Summary. This paper addresses brightness and resolution metrology for retinal scan (RS) augmented-reality glasses. The authors derive an equivalent luminance L_RS for an RS display by equating its retinal illuminance with that of a Lambertian display, obtaining L_RS = K_m Σ V(λ)Φ / (4 A_P tan(α/2)tan(β/2)) (Eq. 12), where A_P is the pupil area. They then use a Stanley–Davies pupil model to express L_RS and an ambient contrast ratio ACR_RS as functions of ambient luminance, and argue that pupil constriction in bright environments increases the equivalent luminance—a property they call beneficial for AR. In the experimental part, 20 participants performed a 3-down-1-up staircase discrimination task on a holographic RS glasses prototype, yielding perceived resolution thresholds of about 7 cyc/deg across different line orientations, colors, brightnesses, and backgrounds. The study also reports an IEC 61947-2 optical resolution of 3.4 cyc/deg for green and discusses why the perceived threshold exceeds it.

Significance. The derivation in Eqs. (3)–(14) is a genuinely parameter-free analytic result: the only inputs are measured optical powers, wavelengths, field of view, and pupil diameter, and the eye's focal length fe cancels. This gives RS displays a falsifiable, human-centric brightness metric that is directly comparable with conventional displays, and the predicted inverse scaling of L_RS with pupil area is a clear quantitative claim that can be tested. The psychophysical design is a reasonable and clearly described first step for bringing the human visual system into AR display metrology. The main caveats are that the practical brightness benefit depends on the full-beam pupil transmission assumption, which is not validated for realistic eyebox tolerances, and that the resolution comparisons are reported without statistical uncertainty.

major comments (3)

[§2.1.1, Eq. (12); §4 (Discussion)] The derivation of Eq. (12) is internally consistent, but the claim that pupil constriction is beneficial for AR use cases rests on the assumption that the entire RS beam flux ΦVScan enters the eye independently of pupil area (§2.1.1, Fig. 2). The paper's own Discussion states that the prototype has a small exit pupil and that the RS display is only visible if the narrow beam fully passes through the pupil. In realistic wearable use, head and eye movements and the smaller pupil diameters typical of bright environments (2–4 mm) make partial clipping likely; once clipping occurs, ΦVScan depends on A_P and on lateral alignment, and the inverse-pupil scaling in Eq. (12) breaks down. No tolerance analysis, eye-tracking data, or bench measurement of transmitted flux versus pupil position is provided, and the psychophysical study used a chinrest with a 5-minute fitting procedure that maintains the full-beam condition. The paper should either add a clipping factor (or measured tolerance curve) to Eq. (12), or restrict the 'beneficial pupil dependence' claim to the ideal static-alignment regime.
[§3.2, Table 1, Figs. 6–9] The perceived-resolution results are reported as point estimates (7.1 cyc/deg horizontal, 7.4 vertical; 6.7 red, 7.4 green, 7.3 blue; etc.) without confidence intervals or any inferential test. Because the staircase data are dichotomous pass/fail counts per level, the statements that background conditions 'did not have a notable influence' and that red stimuli were 'slightly worse' are not statistically supported. A mixed-effects logistic regression or a bootstrap over participants would quantify the uncertainty and should be added before the cross-condition comparisons are claimed.
[§4 (Discussion), IEC 61947-2 comparison] The comparison between the perceived resolution threshold (7.4 cyc/deg for green) and the IEC 61947-2 optical resolution (3.4 cyc/deg) is used to conclude that the optical resolution of the glasses, not human visual perception, was the limiting factor. This inference is not immediate, because the IEC cutoff is defined at 30% modulation rather than at the contrast detection threshold; a display can convey perceptible modulation beyond the 30% point. Without reporting the display's modulation transfer at the perceived threshold (or the spatial frequency at which modulation reaches the human contrast threshold), the data do not establish that the optical resolution is the limiting factor. The conclusion should be softened or supported by additional MTF/contrast measurements.

minor comments (5)

[Eq. (5)] The intermediate expression in Eq. (5), 'fe^2 tan(α/2) fe^2 tan(β/2)', is not the correct area product; it should read (2 fe tan(α/2))(2 fe tan(β/2)). The final equality and the subsequent formulas are correct, but the written line is confusing.
[Eqs. (15)–(16)] Equations (15) and (16) contain garbled notation for the Stanley–Davies model ('LA 3600 846' without explicit operators); please typeset the formula with clear parentheses and state the units of LA (cd/m²).
[§2.2] The anti-guessing rule 'a line pattern was always presented after two correct responses' is not fully explained; please clarify how this interacts with the 3-down-1-up staircase.
[References] The reference 'Dressier and Rassotv (1981)' appears to contain misspelled author names (likely Dressler and Rassow); please correct.
[§2.2 and §4] The manuscript states that the study had a 'gamified design', but no gamification is described in Methods; please either describe the gamification or remove the term.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the luminance formula is derived from measured inputs and standard photometry, with the pupil model imported from external literature.

full rationale

The derivation chain is self-contained. Equation (12) is obtained by equating retinal illuminance from a Lambertian display (Eq. 10, derived from standard luminance definitions and the lens formula) with retinal illuminance from the RS display (Eq. 6, computed from measured radiant flux, V(λ), and geometric field of view), followed by algebraic rearrangement. The focal length fe cancels in Eq. (11), so no unmeasured ocular parameter enters the final formula. The inputs Φi, wavelengths, α, β, and dPmm are measurements, not fitted parameters, and the Stanley-Davies pupil model used to express dPmm as a function of ambient luminance is an external published model, not derived from or fitted to this paper's data. The perceived-resolution experiment is evaluated against the IEC 61947-2 optical measurement and yields thresholds that are not used as inputs to the luminance derivation. The paper's stated limit that the beam must fully pass through the pupil is an alignment or assumption caveat about when Eq. (12) applies, not a circular reuse of the result.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The only free parameter inherited from the literature is the Stanley-Davies pupil model. The derivation itself is parameter-free apart from measured values. The main domain assumptions concern beam-pupil geometry, the pupil model, the neglect of combiner effects on pupil size, and the contrast criterion for resolution measurements.

free parameters (1)

Stanley-Davies pupil model coefficients = 7.75, 5.75, 846, 0.41, field size (60 deg)^2
Empirical coefficients from the Stanley-Davies pupil model in Eq. (15), fitted to population data in the cited source. They control how L_RS and ACR_RS vary with ambient luminance and are not fitted in this paper.

assumptions (6)

domain assumption The RS laser beam (diameter < 0.5 mm) fully passes through the human pupil, so total luminous flux entering the eye is independent of pupil size.
Stated in Section 2.1.1 and Fig. 2; if beam clipping occurs, L_RS no longer scales as 1/A_P.
standard math Lambertian display retinal illuminance is E_R = L A_P / f_e^2, from standard photometry and geometrical optics.
Used in Eq. (10) to equate Lambertian and RS retinal illuminance; assumes small-angle paraxial imaging.
domain assumption Stanley-Davies pupil model with adaptive field size (60 deg)^2 describes average observer pupil diameter as a function of ambient luminance.
Used in Eq. (15) to replace pupil measurement with ambient luminance; model choice affects the quantitative L_RS(LA) curve but not the inverse-pupil scaling.
domain assumption The combiner transmittance tau_C does not affect pupil diameter because the HOE is small and monocular.
Stated in Section 3.1 after Eq. (17); if the combiner covered a large binocular field, tau_C would enter Eq. (15).
domain assumption Perceived resolution depends only on spatial frequency when ACR_RS > 0.5.
Cites Dressier and Rassotv (1981) and Pelli and Bex (2013); used to justify ignoring contrast effects in the staircase results.
domain assumption Participants' visual acuity of at least 24 c/d means the measured 7 c/d threshold is not limited by the eye.
Used in the Discussion to conclude that the display optics, not visual perception, limit the perceived resolution threshold.

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Cite this review

Pith. "Pith review of Perceived brightness and resolution of holographic augmented reality retinal scan glasses." pith.science (2026). https://pith.science/paper/DMXLAM4U

@misc{pith2026241200831,
  author       = {Pith},
  title        = {Pith review of: Perceived brightness and resolution of holographic augmented reality retinal scan glasses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DMXLAM4U}},
  note         = {Machine review of arXiv:2412.00831}
}

read the original abstract

Augmented reality display performance depends strongly on features of the human visual system. This is especially true for retinal scan glasses, which use laser beam scanning and transparent holographic optical combiners. Human-centered approaches allow us to go beyond conventional optical metrology and evaluate display performance as it is perceived in actual augmented reality use cases. Here, we first present a theoretical formula for the retinal scan luminance and ambient contrast ratio calculated from optical powers, wavelengths, field of view, and human pupil diameter. As a promising insight we found that the pupil diameter dependence is beneficial in assimilating the virtual image luminance to the ambient luminance. Second, we designed and performed a psychophysical experiment to assess perceived resolution in augmented reality settings using a fully functional retinal scan glasses prototype. We present the results of the trials and illustrate how this approach can be useful in the further development of augmented reality smart glasses.

Figures

Figures reproduced from arXiv: 2412.00831 by the authors.

**Figure 9.** Sigmoidal psychometric curves for perceived resolution with different stimulus and background color [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

11 extracted references · 10 canonical work pages

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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and Lakshminarayanan, V

Bass, M., Enoch, J.M. and Lakshminarayanan, V. (2010) Handbook of optics. Volume III, Vision and vision optics. 3rd ed. New York: McGraw-Hill. Bayle, E. et al. (2019) ‘Binocular rivalry in monocular augmented reality devices: a review’, in J. (Jack) N. Sanders-Reed and J. (Trey) J. Arthur (eds) Situation Awareness in Degraded Environments

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work page doi:10.1117/12.2589102 2021

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work page doi:10.1117/12.2518928 2024

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Thibos, L.N., Lopez-Gil, N

Available at: https://doi.org/10.1117/12.2295751. Thibos, L.N., Lopez-Gil, N. and Bradley, A. (2018) ‘What is a troland?’, Journal of the Optical Society of America A, 35(5), p

work page doi:10.1117/12.2295751 2018

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Maimone, A., Georgiou, A

Available at: https://doi.org/10.3389/fneur.2019.00129. Maimone, A., Georgiou, A. and Kollin, J.S. (2017) ‘Holographic near -eye displays for virtual and augmented reality’, ACM Transactions on Graphics , 36(4), pp. 1 –16. Available at: https://doi.org/10.1145/3072959.3073624. Park, J.-H. and Lee, B. (2022) ‘Holographic techniques for augmented reality an...

work page arXiv 2017