Description
Return signed magnification from convergence and two shear components.
Gravitational lensing changes a local angular mapping through its Jacobian. Its determinant controls signed magnification and image parity, while a zero determinant marks a singular local mapping; those terms require a lens model rather than establishing one from a single supplied point.
Return signed magnification from convergence and two shear components.
When to use this tool
Use Lensing Convergence Shear Magnification Term when checking a supplied local lensing determinant, parity or magnification convention.
How to use the tool and how it works
- Enter convergence, shearFirst, shearSecond. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read jacobianDeterminant, signedMagnification. Use the output convention below.
Return signed magnification from convergence and two shear components. Require nonzero determinant D = (1-convergence)²-shearFirst²-shearSecond²; signedMagnification = 1/D.1
Lensing magnification and parity depend on the local mapping Jacobian; a signed reciprocal determinant is distinct from an unsigned flux magnification.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| convergence | Convergence | Required. Finite number. |
| shearFirst | Shear First | Required. Finite number. |
| shearSecond | Shear Second | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| jacobianDeterminant | Jacobian Determinant | Required. Finite number. |
| signedMagnification | Reciprocal determinant; negative means reversed parity, not negative observed brightness. | Required. Finite number. |
{
"input": {
"convergence": 0.5,
"shearFirst": 0,
"shearSecond": 0
},
"output": {
"jacobianDeterminant": 0.25,
"signedMagnification": 4
}
}Limitations and assumptions
- Inputs are dimensionless local lens terms; the sign encodes parity and is not an unsigned brightness factor.
- 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 lens model and observational uncertainty analysis for source reconstruction or physical lensing inference.
References
-
Calculation and input contract: cosmology/lensing-convergence-shear-magnification-term — tool.io
-
Weak Gravitational Lensing — Matthias Bartelmann and Peter Schneider
Similar or alternative tools
- Lensing Parity Determinant Sign
Return a two-dimensional lensing Jacobian determinant and parity.
- Weak Lensing Reduced Shear Scalar
Calculate one signed reduced-shear component gamma/(1-kappa) for explicit convergence other than one.