Spectral and Radiometric Calibration Methods for Acousto-Optic Spectrometer
Objective Imaging spectrometers based on acousto-optic tunable filters(AOTFs)are widely recognized for their rapid tuning,reliability,repeatability,and ability to change spectral channels with ease.These instruments have been extensively studied in space remote sensing and reconnaissance.Meanwhile,the spectrometers should be capable of functioning accurately over a broad temperature range to deliver precise spectral information across various operating environments.However,the spectral data accuracy is compromised by ambient temperature fluctuations,which affects the AOTF's spectral tuning and the spectrometer's response to radiation.The tuning relationship shift is predominantly the result of refractive index changes in the acousto-optic crystal and the velocity of acoustic waves as temperature varies,altering the acousto-optic interaction within the crystal.Similarly,the spectrometer's radiation response drifts due to alterations in the AOTF's diffraction efficiency and temperature-dependent changes in the performance of both electronic and optical components.Although previous studies have taken account of the temperature drift in radiation response during the radiometric calibration,it is necessary to first ensure the spectral wavelength stability in the output images,and otherwise,radiometric calibration cannot be achieved.Therefore,implementing temperature corrections during spectral calibration is essential to prevent wavelength deviations in the output images during temperature shifts,which would result in erroneous radiometric calibration.Methods We propose a spectral and radiometric calibration method for correcting temperature effects.Firstly,an AOTF tuning model that incorporates a temperature variable is built.Within this model,the relationship between the drive frequency and the optical wavelength,acoustic wave velocity,refractive index,angle of incidence,and acoustic cut angle is derived.The effect of acoustic wave velocity on the drive frequency is considered independently,and a temperature increase brings about rising acoustic wave velocity,leading to a higher drive frequency(Fig.2).Then the effect of the refractive index on the drive frequency is considered separately,and a temperature rise leads to increasing refractive index,which also results in a higher drive frequency.Meanwhile,both crystal physical parameters are considered concerning their influence on the drive frequency and compared with the actual measured frequency.At different temperatures,the response of the AOTF's driving frequency at different wavelengths is measured.The central driving frequencies at various temperatures and wavelengths are extracted,and then a polynomial fitting is employed to deduce the tuning relationship between the central driving frequency,temperature,and optical wavelength.This allows for the correction of temperature-induced tuning drifts during the spectral calibration.During the radiometric calibration,the spectrometer is loaded with adjusted driving frequencies to ensure that the system response can track the required wavelengths at all temperatures.The system responses at different temperatures and wavelengths are collected to obtain the spectral radiometric calibration coefficients that include the temperature variable.By adopting interpolation methods,the spectral radiometric calibration coefficients at any temperature are obtained to realize temperature-corrected radiometric calibration(Fig.3).Results and Discussions Multiple wavelengths within the range of 3.7 to 4.5 μm are selected to measure the frequency response of the spectral imaging system at various temperatures between-30 and 50 ℃[Figs.4(a)and 4(b)].As the temperature increases,the central driving frequency shifts towards higher frequencies.For the spectral channel with a central wavelength of 4.0 μm,the central driving frequency is 20.05 MHz at a working temperature of-30 ℃,and 20.14 MHz at a working temperature of 50 ℃.It is evident that when there is an approximate temperature difference of 80 ℃ in the working conditions,the driving frequency needs an adjustment of 0.09 MHz to ensure the output wavelength stability.If a fixed driving frequency is applied at different temperatures,the central wavelength of the output from each spectral channel of the system drifts(Table 3),with the wavelength drifting by 0.0015-0.0025 μm per 10 ℃.After completing spectral calibration,the driving frequency accuracy at each wavelength is significantly improved[Fig.4(d)],and the average driving frequency deviation at different temperatures is reduced(Table 4).The response of the spectral imaging system drifts with temperature,and the spectral data obtained at different temperatures will show variations with temperature.When the temperature rises from-20 to 30 ℃,the system response decreases and then the calculated spectral radiance decreases[Fig.5(a)].After radiometric calibration corrected for temperature,the spectral radiance accuracy improves at lower temperature ranges(Table 5).Conclusions To enhance the temperature stability of spectrometer data,we propose a method for correcting the temperature influence on spectral and radiometric calibration.Firstly,a tuning model of the AOTF incorporating temperature variables is built.We analyze the mechanism by which temperature variations affect the characteristics of AOTFs via altering the physical parameters of the crystal material,with the most significant effect of acoustic wave velocity.This model corrects the spectral drift caused by temperature in spectral calibration,achieving wavelength tracking during the variable-temperature radiometric calibration and ensuring wavelength stability in subsequent radiometric calibrations.Thereafter,the spectral radiometric calibration coefficients that include temperature variables are determined to complete the radiometric calibration.Relying on a laboratory setup,we construct a mid-wave infrared(3.7-4.5 μm)calibration verification system for AOTF spectral imaging temperature correction to validate the calibration method over the temperature range from-30 to 50 ℃.The results indicate that the average driving frequency deviation at a low temperature of-30 ℃ is reduced from 41.1 to 0.29 kHz,effectively suppressing the spectral radiance deviation from theoretical values.
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