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A Simple Stray-light Correction Matrix for Array Spectrometers
Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno
National Institute of Standards and Technology, Gaithersburg, Maryland, USA.
Abstract. A stray-light correction matrix has been
developed for array spectrometers. By using the correction
matrix, measurement errors arising from stray light are
corrected by a simple, fast matrix multiplication.
Validation measurements demonstrate that stray-light
errors are reduced by one to two orders of magnitude, to a
level less than 10 -5 of the measured signal of broad-band
sources, equivalent to less than one count of the
15-bit-resolution instrument. By applying the stray-light
correction, the error in a spectroradiometer calibration was
significantly reduced in the UV region, and the error in a
LED color measurement was reduced by 0.01 in
chromaticity coordinates (x, y).
Introduction
Array spectrometers are used in a wide range of
applications in the fields of spectroradiometry,
spectrophotometry, colorimetry, photometry, and optical
spectroscopy due to the benefits of measurement speed,
sensitivity, portability, and affordability. Array
spectrometers, however, are single grating instruments, and
there are intrinsic limitations to their measurement
accuracy. Among several sources of errors, stray light is
often the dominant source of measurement error in these
instruments. Because of stray light inside the instrument,
significant errors can occur when measuring light sources
having dissimilar spectra from the standard source. Stray
light error is serious when measuring a very low level
spectral component at some wavelength while there are
high level components in other wavelength regions.
Currently, reliable standard sources other than tungsten
lamps (and deuterium lamps for UV) are not available and
errors due to stray-light are inevitable.
Brown, et al., developed an iterative algorithm
previously that corrects stray-light errors in a
spectroradiometer's spectral responsivity calibration and a
test source’s spectral distribution measurement in separate
steps. In this paper, we describe a simpler and faster
method using a matrix called the stray-light correction
matrix. In this approach, the stray-light errors in measured
signals are corrected by a simple matrix multiplication.
The correction is applied to all measured raw output
signals, and no distinction is made for the source being
measured; i.e. whether the source is a calibration source or
a test source.
The stray-light correction matrix
The array spectrometer is first characterized for the
stray-light distribution function (SDF): the ratio of the
stray-light signal to the total signal within the bandpass of
a spectrometer when measuring a monochromatic spectral
line source. By measuring a set of line sources covering the
spectral range of the instrument, and interpolating between
these line spectra, a SDF matrix is obtained. The SDF
matrix is used to derive the stray-light correction matrix,
and the instrument’s response for stray light is corrected by
Y IB = C · Y meas , (1)
where C is the stray-light correction matrix, Y meas is a
column vector with the measured signals, and Y IB is a
column vector with stray-light corrected signals. Note
that development of matrix C is required only once, unless
the imaging characteristics of the instrument change.
Using Eq. 1, the stray-light correction becomes a single
matrix multiplication operation, and the correction can be
performed in real-time with minimal impact on acquisition
speed.
The results of stray-light correction
The effectiveness and robustness of this stray-light
correction matrix has been validated. Stray-light correction
matrices have been developed for several different array
spectrometers. Figure 1 shows an example validation
measurement. This array spectrometer has a stray light of
10 -4 for a narrow-band source measurement. The
spectrometer was used to measure a green broad-band
bandpass filter illuminated by a tungsten incandescent
lamp. The transmittance of the filter below 420 nm is less
than 10 -9 . Figure 1 shows that the stray-light contribution
to the measured raw signal is significant: 10 -3 below
420 nm. After applying the stray-light correction, the
signal below 420 nm is reduced by 2 orders of
magnitude.
Relative Signal
1.0E+01
1.0E+00
1.0E-01
1.0E-02
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
200 300 400 500 600 700 800
Wavelength (nm)
Measured Sig Corrected Sig 1 count level
Figure 1. Validation result of the stray light correction for a
broad-band source with a bandpass filter. Thick solid line:
measured raw signals from the spectrograph; thin symbol line:
stray-light corrected signals; horizontal dashed line: one-count
level of the 15-bit spectrograph.
The stray-light correction matrix C can also be used to
correct stray-light errors in narrow-band source
measurements. Figure 2 shows an example of the
stray-light correction for a laser source measurement. The
stray-light errors are reduced by one to two orders of
magnitude in this case as well.
Proceedings NEWRAD, 17-19 October 2005, Davos, Switzerland 191