Description
Return solid angle of a cosine-polar-coordinate bin.
Survey geometry combines solid angle, radial distance and a stated coordinate or selection basis. A sky fraction, bin midpoint or thin-shell term is a local geometric quantity rather than an integrated survey volume, observed population or selection-corrected estimate.
Return solid angle of a cosine-polar-coordinate bin.
When to use this tool
Use Angular Bin Solid Angle Weight when checking the stated survey-area, bin or comoving-volume term.
How to use the tool and how it works
- Enter azimuthWidthRadians, lowerCosPolar, upperCosPolar. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read solidAngleSteradians. Use the output convention below.
Return solid angle of a cosine-polar-coordinate bin. Require azimuth width in [0,2*pi], cosine bounds in [-1,1] and upperCosPolar <= lowerCosPolar; solid angle = azimuthWidth*(lowerCosPolar-upperCosPolar).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| azimuthWidthRadians | Azimuth Width Radians | Required. Finite number; minimum 0. |
| lowerCosPolar | Cosine at the lower polar-angle edge; numerically at least upperCosPolar. | Required. Finite number; minimum -1; maximum 1. |
| upperCosPolar | Cosine at the upper polar-angle edge; numerically no greater than lowerCosPolar. | Required. Finite number; minimum -1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| solidAngleSteradians | Solid Angle Steradians | Required. Finite number. |
{
"input": {
"azimuthWidthRadians": 2,
"lowerCosPolar": 1,
"upperCosPolar": 0.5
},
"output": {
"solidAngleSteradians": 1
}
}Limitations and assumptions
- Bounds are cosines rather than polar angles; ordering follows those input names and no sky mask or overlap is inferred.
- 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
Integrate the appropriate cosmological volume element and actual survey mask/selection function for complete coverage or number-count analysis.
References
Similar or alternative tools
- Survey Solid Angle Fraction
Return surveyed sky fraction from solid angle.
- Angular Comoving Scale Factor Tool
Apply the small-angle transverse comoving relation using an explicitly supplied distance.