Optimizing a Three-Channel Sensor Spectral Sensitivity Using A
Genetic Algorithm
Dorukalp Durmus*
Pennsylvania State University, University Park, PA, USA 16802
*alp@psu.edu
Abstract: Previous spectral error estimation studies are
focused only on daylight. Spectral sensitivity of three sensors are
optimized for electric light sources using genetic algorithm, which
resulted in reduced errors between actual and estimated spectra.
OCIS codes: 120.0280, 280.4788.
1. Introduction
A multi-channel spectrum imaging system enables accurate spectral
measurement across changes in illumination and ensures color matches for
all observer types [1]. Multi-channel imaging is important for areas
that require high-end color reproduction and spectral data collection,
such as artwork reproduction and conservation [2], archeology
[3], telemedicine [4], agriculture [5], study of minerals
and gems [6], and integrative lighting systems [7]. Research on
multi-channel imaging systems also impacts filter design [8] and
target analysis [9], where spectral mismatches are considered
detrimental for the optical systems. However, previous studies comparing
and evaluating the mismatches in spectral power distributions (SPDs) are
daylight oriented [10–13]. Optical imaging systems that are aimed
to detect spectra during night time (i.e., sky glow, ecological impacts
of lighting) require spectral analysis of electric light sources
[14]. Here, the optimal spectral sensitivity of a three-channel
sensing system is described using electric and natural light sources
(i.e., one standard illuminant and ten commercially available electric
light sources).
2. Methods
The spectral properties of three theoretical sensors were optimized
using a genetic algorithm (GA) to minimize the error between
reconstructed (estimated) and actual light source spectra. A GA is a
computational tool inspired by the natural selection [15], and it is
widely used in engineering and lighting research to find optimal
solutions for a given problem [16,17]. The spectral sensitivity of
each sensor was generated using a Gaussian distribution and
characterized by their peak wavelengths and bandwidths (i.e., the full
width at half maximum (FWHM)).
The differences between reconstructed (estimated) and measured spectrum
were analyzed using spectral curve difference metrics. Root mean square
error (RMSE) is a simple, but widely used, metric for spectral
estimation evaluation [18,19]. In addition to RMSE, two other
metrics (integrated irradiance error (IIE) [10] and goodness-of-fit
(GFC) coefficient [11]) were also considered for spectral analysis.
While RMSE and IIE range between 0 and 1 (a smaller value denotes
smaller error), a spectrally accurate estimation requires a GFC
> 0.995 (“acceptable” fit), a “good” spectral fit
requires a GFC > 0.999, and GFC > 0.9999 is
needed for an “excellent” fit [11, 12]. Instead of a mean absolute
average, the root-mean-square of three metrics was used, which is found
to be more sensitive to distance differences and more appropriate when
the error distribution is expected to be Gaussian [20].
3. Results and discussion
The optimal peak wavelength and bandwidth of the three sensors are
λsens1 = 380 nm, FWHMsens1 = 160 nm,
λsens2 = 563 nm, FWHMsens2 = 194 nm,
λsens3 = 750 nm, FWHMsens3 = 166 nm. The
resulting error for each light source and error measures are summarized
in Table 1. The highest RMSE was found for daylight illuminant and the
smallest error was recorded for low-pressure sodium. There was one
“excellent” fit for GFC (LPS), eight “good” fits, and two
“acceptable” fits. None of the light sources were below the
“acceptable” level for GFC. The reconstructed spectra for tri-phosphor
fluorescent and phosphor-coated LED with additional red peak performed
the best according to IIE.
The results obtained here are comparable to other spectral mismatch
studies, where values for daylight ranged between IIE = 0.032 [10],
GFC = 0.9900 [11], RMSE = 0.3715, GFC = 0.9997, IIE = 0.0133
[14], and GFC = 0.9985, IIE = 0.70 [13]. Although some of the
GFC values in these previous studies are marginally better than results
presented here, the RMSE and IIE scores found in previous studies are
lower compared to data gained through GA.
Table 1. Spectral properties of the reference light sources and the
error between the estimated and measured spectra according to three
spectral mismatch metrics.