The Noise Equivalent Power (NEP) is an instrumental metric used to characterize sensitivity of detectors and quantify impact of noise sources across domains like optics, electrical circuits, thermodynamics among others. It represents the equivalent input noise power that generates a signal-to-noise ratio (SNR) of unity at the detector output.

However, extensive usage across domains has given rise to multiple ambiguous interpretations of NEP in literature over the years. **This article aims to provide an unified perspective on the physical meaning and mathematical derivation of NEP by tracing the origin and propagation of noise signals through different internal stages of a detector.**

Fundamentally, noise stems from random fluctuations in the quantity being measured by the detector. Thus, a stochastic framework based on statistical signal processing is necessary to characterize such random processes.

For a stationary process with ergodic power variations, the Power Spectral Density (Sxx(f)) represents the mean square fluctuations as a function of frequency. The function linking the value of x to the real power dissipated into the system is the sensitivity (or power response) of the system to the measured property:

NEP is then defined as:

Where, Power Response refers to the detector sensitivity, i.e. units of power dissipation per unit magnitude of input process fluctuations. This general definition leads to two distinct physical interpretations:

- Electrical NEP: The actual noise power measured at the detector output terminals
- Optical NEP: The equivalent noise power at the detector input terminals

The article specifically focuses on a quantum mechanical treatment of photon noise NEP in optical detectors. Photon detection is modeled by accounting for dual wave-particle aspect – photon number statistics and electromagnetic mode analysis. Critical factors incorporated include:

- Detector area, photon wavelength distribution
- Spatial and temporal coherence of optical waves
- Polarization specific losses and efficiencies
- Optical transmission / absorption efficiencies

By tracking the photon number fluctuations through multiple beam splitting and attenuation stages, the article derives a generalized formula for photon NEP in terms of measurable physical parameters. Simplified expressions quoted in existing literature are recovered as special cases under assumptions of detector size, diffraction limits, coherence beam factors etc.

For communication receiver systems and optical/radio astronomical instrumentation, key system sensitivities are characterized by equivalent input Noise metrics:

- Noise Equivalent Flux Density (NEFD)
- Noise Equivalent Temperature (NET)

These can be mathematically related to NEP metrics using detector bandwidth and collection area by appropriately converting units of flux, power and temperature.

In summary, the article develops an unified perspective on the various interpretations of NEP by methodically tracing the signal and noise paths through different stages of the detector. In the process, mathematical relationships between the many domain-specific NEP variants are established while elucidating subtle assumptions. This clarifies sensitivity definitions and provides a foundation for comparing benchmarks across optical, electrical and thermal systems.

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