Biomedical Engineering Reference
In-Depth Information
Transformation ratio
α
Unknown parameters
V
i
n
s
r
s
Sensor position
Sensor direction
In liquid helium
n
c
i
Known parameters
C
i
a
r
c
i
Circular current array
j
Fig. 3.22.
Calibration of sensor parameters by using a circular current array
Calibration and Alignment
Calibration of the Sensitivity and the Position of the Sensors.
The bioma-
gnetic measurement system is an instrument to measure a magnetic field, so
it is important that the value is correctly measured in the sense of “traceabi-
lity”. The sensitivity, position, and direction are calibrated with a multi-coil
set which is machined precisely and fed with current using a generator-of-
standard instrument. The coils are fed with a known current and emit a
known magnetic field at a known position in a known direction. The output
voltage of the FLL circuit is represented by
V
=
h
(
I
,x,y,z,
n
,b
;
g
s
,x
s
,y
s
,z
s
,
n
s
), where
is the current in the calibration coil,
x
,
y
,and
z
are the position
of the calibration coil,
I
is the unit vector (
n
x
,n
y
,n
z
)ofthedirectionofthe
coil,
b
is the baseline between the sensing coil and the reference coil,
g
s
is the
magnetometer or gradiometer sensitivity,
x
s
,
y
s
,and
z
s
are the position of the
sensor, and
n
s
is the unit vector (
n
sx
,n
sy
,n
sz
) of the direction of the sensor
(Fig. 3.22). The detailed expression is described by an integral of the Biot-
Savar equation. Six variables,
g
s
,
x
s
,
y
s
,
z
s
,
n
sx
,and
n
sy
, are unknown. (The
variable
n
sz
is a dependent value of
n
sx
and
n
sy
.) This means that measure-
ments by the five different calibration coils yield five different equations to be
solved using the five answers to these variables. It is desirable to do the cali-
bration using 10-20 coils in order to obtain better precision. The procedure
is carried out for all sensors installed in the cryostat. With this calibration
procedure, the magnetic field can be precisely identified and the source of
the field can be estimated through an inverse problem. To demonstrate that
the calibration has been carried out correctly, we have done the following.
We have prepared another coil and measured the magnetic field produced by
this coil (Fig. 3.23). With this measurement result, we have estimated the
n
