Description
Convert density per angular frequency to density per hertz.
Spectral and radiation quantities depend on their denominator coordinates, reference levels and physical definitions. A density per wavelength changes by a Jacobian when expressed per frequency, and photon counts, radiant energy, exposure and absorbed dose remain different quantities.
Convert density per angular frequency to density per hertz.
When to use this tool
Use Spectral Angular Frequency Frequency Density when checking the stated spectral, photon, attenuation or radiometric conversion.
How to use the tool and how it works
- Enter perRadianFrequency. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read perHertz. Use the output convention below.
Convert density per angular frequency to density per hertz. perHertz = 2*pi*perRadianFrequency using angular frequency omega = 2*pi*f.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| perRadianFrequency | Spectral density per unit angular frequency omega; multiply by 2*pi for density per Hz. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| perHertz | Per Hertz | Required. Finite number. |
{
"input": {
"perRadianFrequency": 2
},
"output": {
"perHertz": 12.566370614359172
}
}Limitations and assumptions
- This is a density Jacobian, not the inverse coordinate conversion; one/two-sided spectra must already use the same convention.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete spectrum, measurement calibration and appropriate physical interaction model for integration, uncertainty or exposure interpretation.
References
Similar or alternative tools
- Conversion: Spectral Bin Energy To Density
Return mean spectral density over a wavelength bin.
- Spectral Flux Frequency Wavelength Jacobian
Convert spectral density per frequency to per wavelength.