# Image Quality Assessment of Augmented Reality Glasses as Medical Display Devices (HoloLens 2)
## 2 Materials and Methods
### Methods
#### 2.2.3 Evaluation of Luminance-to-Grayscale Conformance  
To evaluate the luminance-to-grayscale conformity, the luminance levels of the 18 TG18-LN12 series test patterns (Figure 2) were measured and compared against the GSDF. Each test pattern corresponds to a specific gray level, defined by a digital input level (P) ranging from 0 (pattern -01) to 255 (pattern -18). The test patterns were uniformly distributed across this range to encompass the entire brightness spectrum.  
Initially, the darkest (\(L_{min}\)) and brightest (\(L_{max}\)) test patterns were measured and assigned a just noticeable difference (JND) index following DICOM guidelines. This index accounts for the nonlinear perception of the eye and represents the number of brightness differences detectable by the human eye within a luminance range [24].  
The difference between \(JND_{\min}\) (for \(L_{min}\)) and \(JND_{\max}\) (for \(L_{max}\)) indicates the number of gray levels the display device can distinguish. Subsequently, JND indices for all other test patterns were calculated using Equation (1):  
\[JND_{i}=JND_{min}+\frac{P_{i}\,*\,JND_{max}-JND_{min}}{P_{max}-P_{min}} \tag{1}\]  
Here, \(JND_{i}\) represents the index to be determined, \(P_{i}\) denotes the digital input level of the test pattern, and \(P_{max}\) or \(P_{min}\) corresponds to the input levels of the brightest or darkest test patterns, respectively.  
Figure 4: Test setup for measuring minimum and maximum luminance and for investigating luminance-to-grayscale conformance.  
The measured luminance values were compared to those of the GSDF. In Figure 5, the measured luminance values are plotted on the \(y\)-axis against calculated JND indices on the \(x\)-axis.  
To assess whether transitions between individual gray levels are perceived uniformly, the luminance response (\(\Delta L/L\)) was calculated. This metric quantifies the brightness difference between two successive test patterns based on their mean luminance and the difference in their JND indices. The calculations followed Equation (2),  
\[\frac{\Delta L}{L}=\frac{2\ *(L_{i}-L_{i-1})}{(L_{i}+L_{i-1})\ *(JND_{i}-JND_{i-1})} \tag{2}\]  
where \(L_{i}\) and \(L_{i-1}\) denote the luminance values of two consecutive test patterns, while \(JND_{i}\) and \(JND_{i-1}\) represent their respective indices.  
The luminance response of the display device was compared to the GSDF, as plotted in another graph. In Figure 6, the calculated contrast response is shown on the \(y\)-axis, plotted against the JND indices.  
For primary displays, a maximum deviation of 10% from the GSDF contrast response is permissible, while secondary displays may diverge by up to 20% from the GSDF [4]. Because HoloLens 2 does not produce measurable luminance for entirely black images, measurements were limited to test patterns TG18-LN12-03 through TG18-LN12-18 (Figure 3). Luminance values were recorded following the procedure detailed in the previous section.  
Figure 5: Comparison of the luminance measured values of a display device (measured values) with the GSDF [5].