Optoelectronic LED Display Panel Average Irradiance (Entertainment & Electrical Engineering)

An entertainment and electrical systems engineer at the UNLV Howard R. Hughes College of Engineering is designing a modular, high-dynamic-range LED stage display panel for an interactive performance venue on the Las Vegas Strip.

The modular rectangular panel measures $0.5\text{ m}$ in width along the $x$-axis and $0.4\text{ m}$ in height along the $y$-axis, occupying the closed rectangular domain:

Because of resistive thermal heating along the internal power busbars and localized LED driver clustering, the emitted radiant surface irradiance $E(x, y)$ is non-uniform across the panel surface and is characterized by the empirical polynomial model:

where $E_0$ is the baseline radiant irradiance measured at the origin corner $(0, 0)$ in watts per square meter ($\text{W/m}^2$).

To prevent visible optical brightness banding (hotspots) and to calibrate the overall electrical power supply feeding the stage wall, the engineering team must determine:

1. The total surface area $\text{Area}(R)$ of the modular display panel.
2. The total radiant luminous flux $\Phi = \iint_R E(x, y) \, dA$ emitted across the active face of the panel, evaluated as an iterated double integral using Fubini's Theorem.
3. The spatial average irradiance $E_{\text{avg}}$ across the entire panel expressed as a multiple of the baseline irradiance $E_0$.
4. The physical engineering interpretation of the ratio $E_{\text{avg}} / E_0$ and how it informs optical diffuser film selection.