From Pixels to Patterns: Decoding Smartphone Display Properties through Diffraction, Reflection, and Refraction

TL;DR

The paper addresses how everyday smartphone displays can be interrogated optically to reveal pixel density, glass thickness, and lensing behavior using accessible methods. It employs three complementary experiments: diffraction of reflected light to deduce pixel pitch via a derived 2D diffraction pattern with principal maxima spaced by $\lambda D / c$, reflection-based thickness estimation with Snell's law and a linear fit, and a water-drop refraction model that accounts for three interfaces and yields a closed-form magnification $M = M_1 M_2 M_3$ and $\frac{1}{M} = 1 - \left(1-\frac{\mu_a}{\mu_w}\right)\frac{1}{r_c}\left(h_d + \frac{\mu_w}{\mu_g} t + \mu_w s\right)$. The small-drop limit $\frac{1}{M} = \frac{3+\cos{\phi}}{4} - \frac{1}{3 r_o}(s + \frac{2}{3} t)$ is derived, and measurements of drop radius $r_o$ and contact angle $\phi$ are used to validate the model against data, with deviations for larger drops explained by gravity-driven shape changes via a gravity–surface-tension differential equation. The results provide accessible, hands-on optical insights into pixel technology and demonstrate a concrete educational workflow for physics and engineering teaching.

Abstract

In this paper we show how students can measure optical features of smartphone displays through three experiments. Observing diffraction patterns from smartphone displays allows students to determine the Pixels Per Inch (PPI). Observing reflections within a smartphone display provides information about touch glass thickness and pixel layer properties. Finally, water drops are used as miniature lenses to see the magnified image of the pixels beneath. An enhanced theoretical model that covers both small and large droplets is provided.

Figures (23)

• Figure 1: (a) Schematic diagram of the display assembly of a phone consisting of a touch screen glass and RGB pixels. (b) magnified view of the pixel display.
• Figure 3: Schematic diagram of the diffraction experiment set up (Sec. II).
• Figure 4: Schematic representation of the pixel array. Two arrays of RGB pixels are tilted at an angle $\alpha$ with respect to each other. The individual subpixels are labeled numerically (1 to 6). The spacing between adjacent subpixels is small and negligible compared to the subpixel thickness $t$ and the centre-to-centre distance between repeating pixel units or the pixel pitch $g$. The inter-pixel separation between two neighbouring pixel units is $h$. The arrays are separated by a distance $b$ along the $y$-direction. All the subpixels have the same thickness $t$.
• Figure 5: Simulated diffraction pattern due to a single red subpixel 1.
• Figure 6: Simulated diffraction pattern due to pixels 1 to 6 of Fig. \ref{['fig:Diffraction_schematic_figure']}.