Spatial Map Cross Scans

MRI Gradient Three-Row Scan

Holding position fixed while the gradient changes shows the address formula as a line of exact cases. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One-tesla-per-metre gradient makes an eight-hertz address

At position 1 metre, base field 1 tesla and gradient 1 tesla per metre make field 2 tesla and frequency 8 hertz.

1+1⋅1=2,4⋅2=81+1\cdot1=2,\quad 4\cdot2=8
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasezero phase

Doubling the gradient raises the same address to twelve hertz

At the same position 1 metre, gradient 2 tesla per metre makes field 3 tesla and frequency 12 hertz.

1+2⋅1=3,4⋅3=121+2\cdot1=3,\quad 4\cdot3=12
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasezero phase

A three-tesla-per-metre gradient gives sixteen hertz

Gradient 3 tesla per metre gives field 4 tesla at position 1 metre, so the frequency address is 16 hertz.

1+3⋅1=4,4⋅4=161+3\cdot1=4,\quad 4\cdot4=16
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasezero phase