Ernst Flip Angle
Calculate the spoiled steady-state Ernst angle for supplied TR/T1; contrast optimization, B1 inhomogeneity and preparation pulses are excluded.
Description
The Ernst angle maximizes the ideal spoiled steady-state signal for a given TR and T1.
The Ernst angle maximizes the ideal spoiled steady-state signal for a given TR and T1. It follows from balancing recovery and excitation depletion.
The tool returns ernstAngleDegrees (ernst angle degrees). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Ernst Flip Angle
Use Ernst Flip Angle when you already have trMs, t1Ms and want ernstAngleDegrees. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Ernst Flip Angle and understand its results
- Enter trMs, t1Ms using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read ernstAngleDegrees. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| trMs | Tr ms | number | Required |
| t1Ms | T1 ms | number | Required |
Require positive TR and T1 in matching units, then return the angle in degrees.
angleDegrees = acos(exp(−TR/T1))×180/π The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"trMs": 100,
"t1Ms": 1000
},
"output": {
"ernstAngleDegrees": 25.19860510178534
}
}Limitations and assumptions
The optimum is for the ideal spoiled model, not a general contrast or sequence optimization. B1 errors and multi-tissue objectives are excluded.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
SPGR Signal Intensity: Evaluate ideal fully spoiled gradient-echo steady-state signal with explicit T2* attenuation; receiver gain is included in caller equilibrium amplitude. Spin Echo Signal Intensity: Evaluate an ideal saturation-recovery spin-echo signal M0(1−e^(−TR/T1))e^(−TE/T2); refocusing imperfections and stimulated echoes are excluded.
Methodological background: Basic steady-state free-precession sequences and the Ernst equation.1
References
-
Basic steady-state free-precession sequences and the Ernst equation — ISMRM educational proceedings
Similar or alternative tools
- SPGR Signal Intensity
Evaluate ideal fully spoiled gradient-echo steady-state signal with explicit T2* attenuation; receiver gain is included in caller equilibrium amplitude.
- Spin Echo Signal Intensity
Evaluate an ideal saturation-recovery spin-echo signal M0(1−e^(−TR/T1))e^(−TE/T2); refocusing imperfections and stimulated echoes are excluded.