Instrumentation & Measurement Magazine 25-7 - 22

artifact; and (2) simultaneous measurements of the same object
by different instruments [8]. The first type was used: the
two calibration methods were repeated several days, and the
recorded irradiance levels' standard deviation (STDEV) were
calculated to evaluate which method was more stable than the
other.
One of the well-known control chart methods utilized for
Fig. 2. The automated filter wheel.
reference detector (Si-Trap detector) was used at Radiometry
Department, NIS and was traceable to TÜBITAK UME.
Both the reference and the test detector were mounted vertically
next to each other on a controlled motorized translation
stage, allowing an exchange of position of two detectors in the
x-axis to reduce any personal errors as a source of uncertainty
in repeatability. In addition, the source and each optical tool
were vertically installed parallel to the optical axis between the
source and the two detectors. The system was aligned in x-y
positions by an alignment laser. The test and reference detector
received a direct homogenous and zero tilt beam, as optimally
possible. The irradiance readings were recorded n times periodically
as a repeatability source of uncertainty.
This study used two well-known calibration methods: the
ND- filters and the diaphragm. The irradiance levels from the
lamp source were varied, either by an iris diaphragm, which
automatically widened or narrowed the iris diameter to control
the width of the light patch of area incident on the test and
reference detectors, or by placing neutral density filters (ND)
with different opacities [7]. The ND filters were held in an automated
filter wheel (Fig. 2) designed by the author, installed
in the optical path directly to the lamp source to replace between
the filters automatically and more safely.
evaluating stability in measurements is the x and R. These
control charts are used with variables data when sub-measured
groups are between 20 and 30 numbers of data [9]. The x
and R control charts were applied on the two calibration methods
and the data were collected along twenty days (N=20 day);
each day has n=5 irradiance measurements for each calibration
method, and the average values' central line (CL) were calculated.
The formula of the range R for irradiance measurements
of every day is as follows:
RX (max) (min)X


(1)
where X(max) and X(min) are the highest and lowest values in
a one-day irradiance measurements. The mean value
X   xi

N
i 1
N
(2)
x  
where: x = the average for everyday measurement, and
N = the number of days. The average of all days' measurements
2
R   Ri
N
i 1
N

(3)
where: Ri = the individual range from (1), and N = the number
of days. The upper control limit (UCL) and lower control limit
(LCL) for the average 2
UCL X A R
x  
UCL X A R
x  
LCL X A R
x  
Stability Measurement
The path of measurements' stability was calculated for the
two calibration methods, ascending and descending, to verify
whether the recorded irradiance levels were the same in
the two paths or not, and hence, to try to estimate the change
value. As for calibration method 1, the diaphragm diameter
was adjusted to pass definite nominal values known to the
reference detector, and accordingly, the test detector results
were compared. In the case of calibration using ND filters, the
transmittance of the filter controls neutrally the change in irradiance
values received by the reference and test detectors,
whether the experiment was performed in ascending order
from small to large irradiance values and vice versa.
Reproducibility has two possible types: (1) measurements
at different times, locations, etc., of a stable radiometric
22
2
were determined (x control limit) by:
2
(4)
(5)
where A2 is a constant dependent on the number of measurements
within a subgroup (n), and its value is given in most
textbooks on statistical process control [10]. The upper control
limit for the ranges was determined according to the
following:
UCLR D R
4
LCLR D R
3
(6)
(7)
where D4 and D3 are constants depending on the number of
measurements within a measurement day n. The x and R
charts were plotted, and all values of them were added between
the two control limits and data points in the plotting
area.
IEEE Instrumentation & Measurement Magazine
October 2022
X   of all 1i xi

N
the individual measurements days was calculated using (2),
and the x (mean average) becomes the centerline:
N
UCL X A R was calculated using (3), becoming the centreline for
the R chart area:
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