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ated real-
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mpensate
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AETER
t-squares
d as:
(4) ()
ixel),
ns/pixel)
It might be noted that in the case of M-WIP, Eq. (1)
calls for minimization of the weighted sum of squares of
differences between the theoretical and experimental
values of the detected signal, where the points with higher
values of the rms shot noise are given less weight.
Used in Eq. (1) radiometric model for the output
signal of the IR imager was developed based on the
reference wavelength [7] approach and is given by [2]:
S(A.T)=k(AT) (A) R(A)- Li, (AT) o
where L, (A, T) is the blackbody spectral radiance,
R(M) is the spectral responsivity of the imager, and K(A,
T) is the correction coefficient, which depends on the
effective transmission of the camera optical system,
T(A),the geometry of the detector and the optical
integration time.
It can be shown that the accuracy of the least squares
based M-WIP temperature measurement strongly depends
on the selected emissivity model [2]. In order to correctly
determine the temperature of the target with unknown
emissivity, it is necessary to provide a sufficiently
complex and flexible emissivity model that is capable of
accurately approximating the target spectral emissivity.
On the other hand, a too complex, overdetermined model,
will lead to a decrease in the resulting temperature
accuracy of the measurement due to the redundant degrees
of freedom which it introduces in the fitting algorithm.
Analysis of the published data on the spectral emissivity
of various materials [8] shows that in most cases the
spectral emissivity can be adequately represented by a
polynomial function of wavelength:
eA)=ap +a; A+ ay A +... 3)
where a, a, a,-are the parameters of the emissivity
model.
However, our theoretical and experimental studies [9]
of the spectral emissivity of silicon using Fourier
Transform Infrared (FTIR) Spectroscopy (that may also
apply to other semiconductor and metallic surfaces)
indicate that the emissivity is most accurately
approximated by polynomial functions of wavenumber as:
/ ’
e(A) - ao ime (4)
EXPERIMENTAL M-WIP SYSTEM
As illustrated by the schematic diagram in Fig. 1,
the experimental M-WIP system consists of an IR camera
with associated electronics, an IR filter assembly, and an
image data processing system.
79
Emissivity
Lens
IR Filters (1,22, ...., An) Model
FPA Fragt ayl+azd2 +...
Image Data
IR /D Jr Output
Camera Processing e Temperature (T)
Target - Profiles
(e, T) * Emissivity (£)
- ag, aj , a pee
Fig. 1. Multi-wavelength imaging pyrometer (M-WIP)
IR Camera
The experimental multi-wavelength imaging
pyrometer uses a Samoff 320x244 PtSi IR-CCD camera
[5]. For the purpose of radiometric imaging, the camera is
operated in a non-interlaced mode with 320x122 pixels
and automatically selectable optical integration times in
the range from 120us to 12s or longer [4,10]. The
operation of the camera with variable optical integration
time increases its effective dynamic range and allows to
accommodate a wide range of optical signal levels.
Subframe integration time control was achieved by
employing a double detector readout. To facilitate this
operation, camera circuitry was developed for
automatically controlling the CCD waveforms to operate
at the required integration time. This imager was also
operated in a multi-frame integration mode with a single
detector readout for optical integration times in multiples
of 33ms. The analog video signal was digitized to 12-bits
resolution. Circuits were also developed to embed critical
information in the video signal to facilitate radiometric
post-processing. An optoelectronically buffered digital
interface was developed to connect the camera system to a
DATACUBE image processing system.
M-WIP Filters
The experimental M-WIP presented here is based on
a line-sensing filter assembly with 7 narrow-band filters
mounted on FPA packaging. The line-sensing assembly
uses f/1.4 spherical lens in order to focus the image of the
radiant target on the narrow horizontal slit. The image of
the target area defined by the slit aperture is then refocused
on FPA in horizontal direction using cylindrical lens as
illustrated in Fig. 2. As a result the image of the
horizontal line on the target surface is "spread" across all
M-WIP filters in vertical direction while preserving
horizontal resolution.
Focus Focus
Filter
Jf Assembly
Horizontal rays
ES Magnification=-Q/P
Vertical Rays f
Target Spherical Slit Cylindrical Lens 320X244
Lens IR-CCD FPA
Fig. 2. Filter optics for M-WIP (shaded areas represent
optical images)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
