Spectrometer bandwidth correction for generalized bandpass functions

Abstract

The bandpass of spectrometers can cause appreciable errors when making radiometric measurements. This paper describes a practical method for correcting a set of equispaced measured values provided by a spectrometer with a finite bandwidth, an arbitrary bandpass function and at an arbitrary wavelength step. The paper reviews the limits of the approach for real spectra in the presence of measurement noise and suggests ways of reducing the effect of noise.

A new approach to bandpass correction in spectrometer measurements using the Richardson-Lucy method

“…That the uncertainties associated with the errors of the Richardson-Lucy estimate enclose zero implies that it these uncertainties are a reliable statement of the estimation accuracy. In the previous study [5] the proposed Richardson-Lucy method for bandpass correction turned out to be rather insensitive to measurement noise in contrast to the classical approach as described in [4]. To illustrate this result we considered the reconstruction of the measured spectrum for different noise levels, i.e.…”

“…where b denotes the bandpass function characterizing the measurement device [4]. We restrict ourselves to the often relevant case where the bandpass function depends on the difference λ − λ only, in contrast to the more general case of wavelength dependent bandpass function considered, for instance, in [13].…”

“…different signal-tonoise ratios (SNR). We applied the proposed Richardson-Lucy method and the classical approach with 4th order derivatives [4] to the above simulated measurement and calculated the root-mean-squared error. In order to reduce the effect of the randomness of the noise processes, we repeated these calculations 1e4 times and calculated the mean of the rms errors.…”

“…However, this reduces the spectral resolution and can cause spectral distortions. The mathematical model for the observed spectral responsivity is typically the convolution of the spectrum of the light source with the instrument's line spread function (the mirrored bandpass function), multiplied by the detector's spectral responsivity [1][2][3][4]. A deconvolution, based on the monochromator bandpass function, is therefore often applied to reconstruct the underlying spectrum of the light source from the measured data.…”

Stray light correction of array spectroradiometer measurement in ultraviolet

“…Since compact array spectroradiometer has a fast acquisition speed and is portable, it is widely used in photometric and radiometric measurement in recent years. The characteristic of the array spectroradiometer was investigated during the past ten years, such as the bandwidth, the stability and the stray light [1][2][3][4][5][6][7][8][9]. However, report on the UV spectroradiometer application in direct use is not much due to the significant stray light in UV band.…”