An array spectroradiometer can rapidly measure spectra and is widely used in fields such as aerospace, remote sensing, photovoltaics, and environmental monitoring. Currently, the dynamic range of array spectroradiometers is increasing. When measuring light sources at different radiation levels, it is crucial to determine whether the spectroradiometer’s responsivity remains constant. Due to the low stray light suppression ratio of array spectroradiometers, a spectrally stable, wide-band, adjustable light source with a large dynamic range must be designed for linearity testing. Traditional dual-beam superposition methods can only provide a relatively spectrally invariant light source over about three orders of magnitude, while cascaded integrating sphere superposition with dual light sources and neutral density filter methods both alter the relative spectral distribution. To accurately assess the measurement capability of the array spectroradiometer, a spectral radiance linearity measurement facility has been designed.

The linearity measurement facility integrates an integrating sphere light source, interchangeable apertures, a diffuse reflective whiteboard, and a linear guide rail. Different apertures (20, 6, or 2 mm) are used to adjust the exit surface size of the integrating sphere light source, and the radiation from the aperture irradiates the whiteboard at normal incidence. The distance between the aperture and the whiteboard can vary from 30 to 100 cm. The aperture size is small compared to the distance between the aperture and the whiteboard, so the irradiance at the center of the whiteboard is approximately proportional to the aperture area and inversely proportional to the square of the distance. The whiteboard exhibits excellent spectral flatness characteristics and demonstrates Lambertian reflectance behavior over a 2π steradian solid angle. By changing the aperture area and the distance between the aperture and the whiteboard, it is possible to achieve a 6-order-of-magnitude variation from the spectral radiance of the integrating sphere light source to the reflective radiance of the whiteboard. The consistency of the whiteboard’s reflectance factor verifies that the relative spectrum of the facility is nearly constant from 380 to 780 nm. Table 1 lists the theoretical spectral radiance ratios under different measurement conditions for the linearity measurement facility. The nonlinearity of the spectroradiometer is defined as the deviation between the measured ratio and its theoretical counterpart under each specified condition.

Before characterizing the nonlinearity of the array spectroradiometer, we first evaluate the stability of the light source and the differences in aperture changes of the linearity measurement facility. Experimental results show that the drift rate of the light source is less than 0.07% per hour, and the back-reflections to the light source as well as diffraction errors during size changes are negligible. As shown in Fig. 7, when the distance between the aperture and the whiteboard is fixed at 30 cm and the aperture diameter is reduced from 20 to 2 mm, the experimental results exhibit wavelength-dependent nonlinearity. The nonlinearity reaches 5.6% at 380 nm, and the maximum nonlinearity from 550 to 780 nm is about 0.5%. When the array spectroradiometer is calibrated at the intermediate level (r=10 mm, d=300 mm as in Table 1) and the measurement range is extended by three orders of magnitude toward both higher and lower intensity levels, the nonlinearity reaches a maximum of approximately 10%, as shown in Fig. 8. The nonlinearity remains predominantly within ±1.0% for wavelengths above 450 nm. The measurement uncertainties of the facility when extended towards both small and large values are 0.50% (k=2) and 0.72% (k=2), respectively. When the linear measurement system performs a six-order-of-magnitude downward extension from the integrating sphere source radiance level, the measurement uncertainty of the system is evaluated as 0.76% (k=2). Results show that the nonlinearity around 380 nm exceeds 15%.

The designed linearity measurement facility is used to characterize the nonlinear response of an array spectroradiometer. Measurement results indicate that the nonlinearity of the spectroradiometer exhibits a significant dependence on both wavelength and integration time. When performing measurements across a broad range of magnitudes, the nonlinearity of the spectroradiometer must be corrected. Furthermore, the dynamic range of the linearity measurement facility can be extended by using a much longer linear guide rail and a high-temperature blackbody matched to the integrating sphere’s correlated color temperature. When employing a 3-m linear guide rail, the dynamic range can be increased to seven orders of magnitude. By using a blackbody instead of the integrating sphere light source, the facility can be used to calibrate spectroradiometers with a much higher measurement limit.