Larmor Frequency
Calculate signed nuclear Larmor frequency and angular frequency with caller-supplied γ in Hz/T, rather than embedded isotope tables.
Description
Larmor frequency is proportional to field strength and a nucleus’s gyromagnetic ratio.
Larmor frequency is proportional to field strength and a nucleus’s gyromagnetic ratio. Retaining the ratio’s sign preserves precession convention.
The tool returns frequencyHz (frequency hz); angularFrequencyRadiansPerSecond (angular frequency radians per second). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Larmor Frequency
Use Larmor Frequency when you already have fieldTesla, gyromagneticHzPerTesla and want frequencyHz, angularFrequencyRadiansPerSecond. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Larmor Frequency and understand its results
- Enter fieldTesla, gyromagneticHzPerTesla 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 frequencyHz, angularFrequencyRadiansPerSecond. 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 |
|---|---|---|---|
| fieldTesla | Field tesla | number | Required |
| gyromagneticHzPerTesla | Gyromagnetic hz per tesla | number | Required |
Require positive field strength and a nonzero signed gyromagnetic ratio in Hz/T. Return both cyclic and angular frequency.
fHz = fieldTesla×signedGammaHzPerTesla; omega = 2πf The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"fieldTesla": 3,
"gyromagneticHzPerTesla": 42577478.92
},
"output": {
"frequencyHz": 127732436.76,
"angularFrequencyRadiansPerSecond": 802566569.9006777
}
}Limitations and assumptions
The nucleus is not selected automatically. Local field shifts and gradients are not included.
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
Chemical Shift PPM to Hz Converter: Invert a signed chemical shift into a frequency offset using reference frequency in MHz; this is distinct from existing sample/reference frequency-to-ppm tools. B0 Inhomogeneity PPM: Summarize a measured B0 offset map in ppm with peak-to-peak and RMS about the frequency reference, not a fitted shim solution.
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
- Chemical Shift PPM to Hz Converter
Invert a signed chemical shift into a frequency offset using reference frequency in MHz; this is distinct from existing sample/reference frequency-to-ppm tools.
- B0 Inhomogeneity PPM
Summarize a measured B0 offset map in ppm with peak-to-peak and RMS about the frequency reference, not a fitted shim solution.