Spatial Integrity Depth Scans

MRI Affine Address Three-Row Scan

An MRI address rule has both an offset and a slope; three rows show which part moved. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Base one tesla gives four, eight, twelve hertz

With base field 1 tesla and gradient 1 tesla per metre, positions 0, 1, 2 metres give frequencies 4, 8, 12 hertz.

f=4(Bbase+Gx)=4,8,12f=4(B_{\mathrm{base}}+Gx)=4,8,12
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase

Raising only the base field shifts every frequency

Keeping gradient 1 and raising base field to 2 tesla changes the frequency row to 8, 12, 16 hertz.

f=4(Bbase+Gx)=8,12,16f=4(B_{\mathrm{base}}+Gx)=8,12,16
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase

Raising only the gradient spreads the addresses

Returning base field to 1 and using gradient 2 makes the frequency row 4, 12, 20 hertz.

f=4(Bbase+Gx)=4,12,20f=4(B_{\mathrm{base}}+Gx)=4,12,20
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase