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The Calculation of Total Power Density Emitted from a Light Source

Introduction

The total power density emitted from a light source can be calculated by integrating the spectral irradiance over all wavelengths or energies.

Calculation Formula

The total power density emitted from a light source (H) can be calculated using the formula:
[H = int_{0}^{infty} F(lambda) dlambda]
where:
– H is the total power density emitted from the light source in W m^-2,
– F(λ) is the spectral irradiance in units of Wm^-2 μm^-1, and
– dλ is the wavelength.

Practical Calculation

In practice, a closed form equation for the spectral irradiance for a light source often does not exist. Instead, the measured spectral irradiance must be multiplied by the wavelength range over which it was measured and then calculated over all wavelengths. The following equation can be used to calculate the total power density emitted from a light source:
[H = sum_{i} F(lambda) Deltalambda]
where:
– H is the total power density emitted from the light source in W m^-2,
– F(λ) is the spectral irradiance in units of Wm^-2 μm^-1, and
– Δλ is the wavelength.

Consideration of Spectral Data

Measured spectra are typically not smooth as they contain emission and absorption lines. The wavelength spacing is usually not uniform to allow for more data points in the rapidly changing parts of the spectrum. The spectral width is calculated from the mid-points between two adjacent wavelengths. The power in each segment can be calculated as:
[H_i = Deltalambda cdot F(lambda_i)]

Conclusion

By summing all the segments calculated using the above formula, the total power density emitted from a light source can be determined accurately. This calculation method is essential in various fields such as optics, spectroscopy, and photonics for understanding the power characteristics of light sources.

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