Page 562 - Sensors and Control Systems in Manufacturing

SpectRx NIR Technology
This algorithm can be extended to more than three points using 515
statistical regression analysis on the polynomial much in the same
way as was done for the linear case.

10.10 Radiometric Accuracy
Radiometric accuracy is the deviation of the measured spectral radi-
ance from the actual object view radiance. This is illustrated sche-
matically in Fig. 10.16.
2
However, even if noise affects the radiometric accuracy, it is
treated as a separate parameter, the NESR, which is not included in
the radiometric accuracy.
In general, radiometric accuracy is an arbitrary function, as shown
in Fig. 10.16, but is usually described in two parts, one absolute, the
other relative. Radiometric error is absolute, if it does not vary with
the object view radiance, or it is relative, if the error does vary with
object view radiance. Absolute errors are more difficult to estimate
than relative ones. In the following paragraphs, we will only discuss
relative radiometric errors, converting absolute errors into relative
equivalents. This is a more convenient way to predict the system
accuracy for a given object view.
Three types of errors influence radiometric accuracy. The first type
of calibration source errors are deviations in the production of a perfect
(i.e., perfectly known) calibration source. These errors include the
accuracy of blackbody temperature and the accuracy of its emissivity
over the operational spectral range. The second type of error is cali-
bration drift. Calibration drift includes everything that changes the
radiometric gain and offset during the time interval between per-
forming calibration measurements and object view measurements.
Calibration drift is influenced by many factors, including the ambient
temperature, the stability of the electrical gain, the stability of detec-
tor responsivity, and optomechanical stability. Finally, the third type
of error that influences radiometric accuracy is the spectrometer
intrinsic linearity. This includes system parameters such as detector
linearity, channel spectrum, and spectral aliasing.
Because they are uncorrelated, the contributions from all pre-
dicted errors add up in a root-sum-square fashion.
10.10.1 Calibration Source Errors
Calibration source errors are misevaluations of the spectral radiance
supplied by the calibration source. The effect of calibration source

2 The distinction between noise and radiometric error is somewhat arbitrary. It
is assumed that noise is the spectral-element-to-spectral-element uncorrelated
intensity variations, which statistically average out with time. Radiometric errors
stem from system imperfections and stay in the calibrated spectra even after all
visible noise has been washed out.