Description
Solid angle of an ideal centered rectangular angular patch versus its small-angle product, without a visual-field test interpretation.
Vision research uses stimulus angles, chart notations, image scales, viewing distances, coordinate origins, and observation windows. These quantities have different denominators and measurement conventions. A conversion or support share does not independently establish a visual measurement or its clinical interpretation.
Solid angle of an ideal centered rectangular angular patch versus its small-angle product, without a visual-field test interpretation.
When to use this tool
Use Visual Field Solid Angle Small Angle Term when you need this image, stimulus, notation, coordinate, or observation component for supplied research data.
How to use the tool and how it works
- Enter horizontalRadians, verticalRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read smallAngleSteradians, rectangularPyramidSteradians. Use the output convention below.
For horizontalRadians and verticalRadians in [0,pi] return smallAngleSteradians=horizontal*vertical and rectangularPyramidSteradians=4*asin(sin(horizontal/2)*sin(vertical/2)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| horizontalRadians | Full horizontal angular width in radians, in [0,pi]. | Required. Finite number; minimum 0. |
| verticalRadians | Full vertical angular width in radians, in [0,pi]. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| smallAngleSteradians | Small Angle Steradians | Required. Finite number. |
| rectangularPyramidSteradians | Rectangular Pyramid Steradians | Required. Finite number. |
{
"input": {
"horizontalRadians": 1.5707963267948966,
"verticalRadians": 1.5707963267948966
},
"output": {
"smallAngleSteradians": 2.4674011002723395,
"rectangularPyramidSteradians": 2.094395102393195
}
}Limitations and assumptions
- Inputs are full angular widths of a centered rectangular pyramid, not half angles. The product is a small-angle approximation; neither quantity measures an actual visual field or establishes a clinical test's coverage.
- 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 calibrated acquisition and a documented visual or imaging protocol for complete interpretation. Confirm the reporting notation, viewing geometry, image scale, and support of the underlying observations.
References
Similar or alternative tools
- Visual Angle Stimulus Size
Return the exact centered planar stimulus angular width from supplied compatible dimensions, without an acuity score.
- Retinal Image Angle Length Factor
Supplied reduced-eye planar scale times angle or tangent, without an individual eye biometry or retinal magnification model.