In this issue, we will introduce a very important concept in the field of remote sensing - the spectral response function .
There are three types of cone cells (L, M, S) in the human eye, which have different sensitivities to light in different bands. The combination of the signals of the three types of cone cells constitutes the colorful world in our eyes. As shown in the figure below, although green vegetation such as spinach (Spinach) has the strongest reflection in the red band, the cone cells of the human eye are not sensitive to near-infrared light, and the green light band with strong reflection is in the cone cells. Sensitive band, so spinach appears green to the human eye.
Source: https://medium.com/hipster-color-science/a-beginners-guide-to-colorimetry-401f1830b65a
The spectral response function of the satellite sensor is also similar. The spectral response function (Spectral Response Function, SRF) refers to the ratio of the received radiance to the incident radiance of the sensor at each wavelength, and describes the response intensity of a sensor at different wavelengths. Due to hardware limitations of the sensor filter, it is not possible for the sensor to respond 100% within a predetermined wavelength range.
The figure below shows the spectral response function of the well-known GOCI.
Also due to the limitation of the filter manufacturing process, the energy of a certain band and other than the channel can also enter the channel (as shown in the complete spectral response function of the two sensors of HY 1-C in the figure below), which affects the radiation calibration accuracy. Out-of-band response is also one of the indicators for evaluating satellite performance.
来源：Cui T , Ding J , Jia F , et al. Out-of-Band Response for the Coastal Zone Imager (CZI) Onboard China's Ocean Color Satellite HY-1C: Effect on the Observation Just above the Sea Surface[J]. Sensors, 2018, 18(9).
Example of Spectral Response Function— Measured Equivalent Reflectance of Hyperspectral Simulated Satellite
The spectral response function plays a very important role in the processes of radiation correction and spectral resampling, one of which is the simulation of equivalent reflectivity.
In order to evaluate the accuracy of the atmospheric correction results/surface reflectance products of satellite images, the ground-synchronously measured true surface reflectance is indispensable. For this reason, people generally use hyperspectral radiometers (such as ASD FieldSpec 4, HyperSas, etc.) to measure the hyperspectral reflectance of ground objects when satellites pass by and compare them with the remote sensing reflectance of processed satellite images.
ASD FieldSpec4 Portable Ground Object Spectrometer
However, because ① the satellite sensor with low spectral resolution records the water-leaving radiance in a band, it is the integral of the radiance recorded in a wavelength range; ② due to the sensor hardware settings (filters, etc.) The responsivity is not all 1. The radiance/reflectivity at the central wavelength of satellite images after atmospheric correction is different from the real radiance/reflectivity at this wavelength, and cannot be directly compared with the measured hyperspectral data.
Comparison of measured/equivalent/satellite Rrs of a water body
Therefore, it is necessary to convert the measured remote sensing reflectance into the satellite band equivalent remote sensing reflectance through the spectral response function according to the following formula:
来源：Luo, W.; Li, R.; Shen, F.; Liu, J. HY-1C/D CZI Image Atmospheric Correction and Quantifying Suspended Particulate Matter. Remote Sens. 2023, 15, 386. https://doi.org/10.3390/rs15020386
Among them, Rrs(bandi) is the equivalent remote sensing reflectivity of the i-band of the satellite, λ1 and λ2 are the band ranges of this band, Rrs(λ) is the measured hyperspectral remote sensing reflectivity, and SRF(λ) is the spectrum at λ wavelength response rate. I have packaged the MATLAB code and examples to realize the conversion, and you can receive it without routine by replying " SRF " in the background.
