Echo Time TE

Audit ideal Hahn-echo center timing against a supplied ADC echo center; finite pulse widths, gradient echoes and off-resonance phase are not solved.

Description

For an ideal spin echo, the echo center follows refocusing by the same interval that separates excitation and refocusing.

For an ideal spin echo, the echo center follows refocusing by the same interval that separates excitation and refocusing. Center timing is distinct from pulse duration.

The tool returns idealEchoTimeMs (ideal echo time ms); observedEchoTimeMs (observed echo time ms); centerMismatchMs (center mismatch ms); withinTolerance (within tolerance). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Echo Time TE

Use Echo Time TE when you already have excitationCenterMs, refocusingCenterMs, adcEchoCenterMs, absoluteToleranceMs and want idealEchoTimeMs, observedEchoTimeMs, centerMismatchMs, withinTolerance. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Echo Time TE and understand its results

Enter excitationCenterMs, refocusingCenterMs, adcEchoCenterMs, absoluteToleranceMs 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 idealEchoTimeMs, observedEchoTimeMs, centerMismatchMs, withinTolerance. 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
excitationCenterMs	Excitation center ms	number	Required
refocusingCenterMs	Refocusing center ms	number	Required
adcEchoCenterMs	Adc echo center ms	number	Required
absoluteToleranceMs	Absolute tolerance ms	number	Required

Require excitation < refocusing < ADC center. Compare absolute mismatch with a nonnegative tolerance; equality passes.

ideal TE = 2(refocusing−excitation); mismatch = observed TE−ideal TE

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "excitationCenterMs": 0,
    "refocusingCenterMs": 40,
    "adcEchoCenterMs": 81,
    "absoluteToleranceMs": 0.5
  },
  "output": {
    "idealEchoTimeMs": 80,
    "observedEchoTimeMs": 81,
    "centerMismatchMs": 1,
    "withinTolerance": false
  }
}

Limitations and assumptions

This audits supplied center times, not a pulse sequence’s RF profiles, gradient moments or acquisition feasibility.

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

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. Echo Spacing: Budget echo-center spacing from explicitly nonoverlapping readout, turnaround and settling intervals; waveform overlaps require a different timing model.

Methodological background: RAD229: MRI signal and sequence lecture notes.^[1]

References

RAD229: MRI signal and sequence lecture notes — Brian Hargreaves and colleagues, Stanford University

Similar or alternative tools

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.
Echo Spacing
Budget echo-center spacing from explicitly nonoverlapping readout, turnaround and settling intervals; waveform overlaps require a different timing model.