# Perceived Brightness and Resolution of Holographic Augmented Reality Retinal Scan Glasses
## 4 Discussion  
RS glasses use an optical architecture that is different from conventional display technologies. We explained how the human pupil influences the perceived brightness of an RS display and presented a physical derivation for the RS luminance \(\mathrm{L_{RS}}\). Since the pupil adapts to ambient luminance, RS glasses appear darker in dark environments and brighter in bright environments. For an observer with standard pupil dynamics, the RS display luminance multiplies fivefold from mesopic to bright photopic environments. For conventional displays, Troland is commonly used to describe retinal illuminance as a function of pupil size [18]. Although Troland accounts for the pupil area \(\mathrm{A_{P}}\) in Equation (10), one still needs to make an assumption about the eye's focal distance \(\mathrm{f_{e}}\) (i.e., use a value for a standard eye) to calculate an actual Troland value [13]. In our derivation, however, \(\mathrm{f_{e}}\) cancels out in Equation (11) after setting \(\mathrm{E_{R_{lam}}}\) equal to \(\mathrm{E_{R_{Scan}}}\). This means that \(\mathrm{L_{RS}}\) is independent from any assumptions about the eye apart from the pupil size. We picked the model from [PERSON] and [PERSON] [17] to express pupil size as a function of ambient luminance. Using another model with additional parameters such as age [16] could further increase the accuracy but would also increase the complexity. The fundamental relationship between pupil size and RS luminance holds independently from this model choice. Using the ambient luminance \(\mathrm{L_{A}}\) and combiner transmittance \(\mathrm{\tau_{C}}\), we defined the ambient contrast ratio for RS glasses as \(\mathrm{ACR_{RS}}=\frac{\mathrm{L_{RS}}}{\mathrm{T_{C}}\,\mathrm{L_{A}}}\). In some previous research [4, 5], the ambient contrast ratio has been defined as \(\mathrm{ACR}=\frac{\mathrm{L_{on}}+\mathrm{T_{L_{A}}}}{\mathrm{L_{off}}+ \mathrm{T_{L_{A}}}}\), where \(\mathrm{L_{on}}\) and \(\mathrm{L_{off}}\) are the luminance of on and off pixels, \(\mathrm{\tau}\) is the see-through transmittance, and \(\mathrm{L_{A}}\) is the ambient luminance. RS displays do not project light into dark pixel areas. \(\mathrm{L_{off}}\) is always zero, so the denominator of the two formulas does not differ. More thought must be put into the ambient light term \(\mathrm{\tau\,L_{A}}\) in the numerator. If the term is included, the ambient contrast ratio would equal 1 for an off display. This seems in conflict with the conventional notion of a contrast ratio. We therefore propose to make a distinction between a standard \"ambient contrast ratio\" that does not include the background term \(\mathrm{\tau\,L_{A}}\) in the numerator, and a second quantity, potentially called the \"additive ambient contrast ratio\", that does include it. In this paper, we use the standard ambient contrast ratio. With the derivation for the brightness and contrast of visual stimuli, we were finally able to design and evaluate our psychophysical study for the perceived resolution. Overall, we found consistent results across 15 trials with different stimulus parameters. This study had a gamified design, but we provided no reward for correct answers. Instead, we instructed the participants to give accurate feedback according to their perception. Several participants reported after the study that they did not find any visual cues to manipulate the results even if they had wanted to, hinting toward a robust experimental design. From the field-of-view size and the number of digital pixels, we can infer that the pixels were not perfectly quadratic. This led to different spatial frequencies for horizontal and vertical staircase levels (Table 1). The fact that the correct response ratios in Figure 6 still follow the trend of a common overall sigmoidal function further speaks to the validity of our measurement approach. The 0.8 decimal (0.097 logMAR) minimum visual acuity that participants needed to achieve to be included in the study corresponds to a visual resolution of 24.0 cyc/deg [19].