## 5 Measurements and Evaluation
### Hologram Image Resolution  
Since the hologram image is rendered in free space as a volumetric image, simple pixel resolution does not properly represent the resolution or quality of optically reconstructed hologram image. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Metrics** & **Definition/Description** \\ \hline \multirow{2}{*}{Image volume size} & 3-dimensional volume & Maximally representable image size measured in \\  & (width \(\times\) height \(\times\) depth) & lateral and depth direction, or equivalent \\ \hline Viewing angle (VA) & Horizontal/vertical VA & Lateral or circular viewing range measured in angle \\ \hline \multirow{4}{*}{Image quality} & 3D-MTF (image resolution) & MTF measured through depth range of image \\  & volume, which represents image resolution \\ \cline{2-3}  & Color fidelity & Color distortion measured for standard color chart \\ \cline{2-3}  & Speckle noise & Speckle contrast measured \\ \cline{2-3}  & Brightness & Perceptive brightness level of the image \\ \hline Support of accommodation & Degree of Depth of Focus (DOF) & The smaller the DOF, the better the capability of supporting accommodation \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Metrics and their definitions for holographic performance measure. Figure 10: Image volume space. We defined a new metric for representing the image resolution, which we named 3D-MTF. The modulation transfer function (MTF) is usually used to measure the performance of an optical device like lens in terms of how well it conveys the contrast of an object to the image. MTF is modulation depth denoted as a function of frequency of the test pattern as shown in Equation (2). A 3D-MTF is defined as an extension of conventional MTF by adding depth as another parameter, which is defined as in Equation (3):  
\[M=\left[\frac{I_{max}-I_{min}}{I_{max}+I_{min}}\right],\quad MTF=\left[\frac{M_ {image}(\xi)}{M_{object}(\xi)}\right] \tag{2}\]  
\[3D\ MTF=\left\{MTF_{k}\right\}_{k=1}^{k=N\Delta D} \tag{3}\]  
where, \(M\) is modulation depth, \(I_{max}\) and \(I_{min}\) are the maximum and minimum signal intensity of signal, respectively, \(M_{a}(b)\) is the modulation depth of \(a\) as a function of \(b\), \(\Delta D\) is depth resolution, and \(N\) is the number of depth layers used in the measurement. \(MTF_{k}\) is the MTF value measured at the \(k\)-th depth plane. Defined as such, 3D-MTF is a collection of conventional MTF measured for images at different depth. We measured 3D-MTF value of the implemented display system as shown in Figure 11. For the purpose of accurate measurement, hologram image is captured directly by CCD (Sony ICX834) placed at different depth plane for a fixed viewpoint (Figure 11a). A linear stage and a green laser with a 532 nm wavelength are used in the experiment. An example black and white stripe pattern used in the measurement is shown in Figure 11c, in the order of original shape, its CGH fringe pattern, and reconstructed hologram image. For each stripe pair of the test pattern, modulation depth value is measured and average value of whole stripe pairs is plotted for each depth in Figure 11d. The ranges of measured values for whole stripe pairs at each depth are denoted by vertical bars. MTF changes with image depth, and the average value of MTF is 35.9%@1.2 cycles/mm test pattern. More details of measurement and evaluation are given in Appendix A. In reference [26], a holographic stereogram is analyzed for MTF modeling, showing the effect of phase error arising from approximating the wavefront of a 3D image with a wavefront of a projected image at stereogram plane. While a holographic stereogram can be analyzed as a diffraction-limited imaging system with some aberrations, our display system relies on the diffraction to make a real or virtual image, which requires different analysis. Furthermore, binary encoding of computed fringe pattern results in distortions of frequency spectrum, which should be taken care of. This is remained for further study.