Parabolic Pulse Fit
Fit intensity as a linear function of squared time and report parabolic-fit R squared.
Description
A centered parabolic-pulse fit regresses intensity on squared time.
A centered parabolic-pulse fit regresses intensity on squared time. It fits an intercept and quadratic coefficient, with no linear time term.1
Fit intensity as a linear function of squared time and report parabolic-fit R squared.
When to use Parabolic Pulse Fit
Use this tool to fit intensity as a linear function of squared time and report parabolic-fit R squared.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Parabolic Pulse Fit and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter timeCoordinates, intensities using the field table and calculation rules, then run the tool.
- Read quadraticIntercept, quadraticCoefficient, rSquared. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| timeCoordinates | Time coordinates | list of number | Required |
| intensities | Measured intensities | list of number | Required |
Enter at least two aligned finite time/intensity lists whose squared times vary. Return ordinary-least-squares parameters and intensity-space R². Constant intensity with exact zero residual yields R²=1.
intensity=intercept+coefficient×time² Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| quadraticIntercept | Fitted parabolic intercept | number |
| quadraticCoefficient | Fitted squared-time coefficient | number |
| rSquared | Fit R squared | number; maximum: 1 |
{
"input": {
"timeCoordinates": [
-1,
0,
1
],
"intensities": [
0,
1,
0
]
},
"output": {
"quadraticIntercept": 1,
"quadraticCoefficient": -1,
"rSquared": 1
}
}Limitations and assumptions
No requirement enforces downward curvature, positivity or time ordering. Pulse-center shift and uncertainty are not fitted.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Transient-Absorption Lifetime Fit: Fit a positive transient-absorption trace to a single exponential using log-linear regression. For a complementary task, use Q-Switch Peak Power: Calculate triangular-pulse peak power and pulse-train average power.
References
-
Parabolic Pulse Fit — tool.io
Similar or alternative tools
- Transient-Absorption Lifetime Fit
Fit a positive transient-absorption trace to a single exponential using log-linear regression.
- Q-Switch Peak Power
Calculate triangular-pulse peak power and pulse-train average power.