Calculation algorithm for spectral irradiance using broad-band optical filter data

Abstract

A disposable miniature radiometer has been developed using optical filters for spectral separation. Limitations in accurately retrieving irradiance from the broad-band measurement results can be attributed to the broad-band filters. This paper proposes an algorithm for spectral irradiance using broad-band optical filter data (SIBOF algorithm) to achieve precise retrieved irradiance through four correction steps. First, the algorithm uses an energy ratio method to adjust the broad-band data to narrow-band data. The energy ratio is derived from the reference lamp spectrum and measured optical filter transmissivities. Second, the algorithm corrects for filter transmissivity differences by multiplying the normalized spectral transmissivities by calibration coefficients. The third step involves polarization correction, compensating for additional transmissivity caused by polarization effects from the film overlying on the cosine collector, thus eliminating errors due to film polarization. The fourth step involves radiative heating correction, where fitting curves and coefficients are used to analyze the relationship between irradiance deviation and actual irradiance to correct the data. Standardized tests indicate that, after applying the four corrections, the results are highly consistent with the irradiance from the reference radiometer, demonstrating that these correction steps constitute a reliable algorithm for spectral irradiance using broad-band optical filter data. In April 2024, a 20-day sea fog sounding observation was conducted at the Qianliyan Ocean Station. The irradiance data from the miniature radiometers before launch were corrected and compared with those measured by the reference radiometer on the ground. Results indicate that the irradiance retrieved through the algorithm was in good agreement with the measurements from the reference radiometer, validating its performance across various weather conditions.

References

[1] AkhmanovSA, NikitinSY. Physical optics, 1997New YorkOxford University Press

[2] Bird RE, Riordan C (1986) Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the Earth’s surface for cloudless atmospheres. J Appl Meteorol Climatol 25(1):87–97. https://doi.org/10.1175/1520-0450(1986)025%3c0087:SSSMFD%3e2.0.CO;2

[3] BornM, WolfE. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 1999CambridgeCambridge University Press

[4] Bruegge CJ, Stiegman AE, Rainen RA, Springsteen AW (1993) Use of Spectralon as a diffuse reflectance standard for in-flight calibration of Earth-orbiting sensors. Opt Eng 32(4):805–814. https://doi.org/10.1117/12.132373

[5] Du BW (2023) Research on key techniques of multi-beam interference micro spectrometer. PhD thesis, University of Chinese Academy of Sciences

[6] DunkelmanL, ScolnikR. Solar spectral irradiance and vertical atmospheric attenuation in the visible and ultraviolet. J Opt Soc Am, 1959, 49(4): 356-367

[7] EltbaakhYA, RuslanMH, AlghoulMA, OthmanMY, SopianK, RazykovTM. Solar attenuation by aerosols: an overview. Renew Sust Energy Rev, 2012, 16(6): 4264-4276

[8] EpsteinLI. The design of optical filters. J Opt Soc Am, 1952, 42(11): 806-810

[9] ErmolliI, MatthesK, Dudok de WitT, KrivovaNA, TourpaliK, WeberM, et al. . Recent variability of the solar spectral irradiance and its impact on climate modelling. Atmos Chem Phys, 2013, 13(8): 3945-3977

[10] Fan BX, Nie YX, Yang GZ (2009) Encyclopedia of China · Physics (2nd ed). Encyclopedia of China Publishing House, Beijing (in Chinese)

[11] GirishBS, SrivaniKS, SubrahmanyanR, Udaya ShankarN, SinghS, Jishnu NambissanT, et al. . SARAS CD/EoR radiometer: design and performance of the digital correlation spectrometer. J Astron Instrum, 2020, 9(2): 2050006

[12] GrayLJ, BeerJ, GellerM, HaighJD, LockwoodM, MatthesK, et al. . Solar influences on climate. Rev Geophys, 2010, 48(4): RG4001

[13] HahnDW. Light Scattering Theory, 2009GainesvilleUniversity of Florida

[14] KhalilSA, ShaffieAM. Attenuation of the solar energy by aerosol particles: a review and case study. Renew Sust Energy Rev, 2016, 54: 363-375

[15] Kleinman RE, Senior TBA (1986) Rayleigh scattering. In: Mechanics and mathematical methods–series of handbooks, vol 2. Elsevier, Amsterdam, pp 1–70

[16] LiJF, LinGY, WuH, DuanMZ, CaoDS, WangLQ. Design and verification of a double-grating spectrometer system (DGSS) for simultaneous observation of aerosols, water vapor and clouds. Remote Sens, 2022, 14(10)

[17] LouisnathanSJ, BlossFD, KordaEJ. Measurement of refractive indices and their dispersion. Am Miner, 1978, 63(3–4): 394-400

[18] LuoHY, ShiHL, LiZW, LiS, XiongW, HongJ. Study on the spectral characteristics of narrow-band filter in SHS. Spectrosc Spectr Anal, 2016, 35(4): 1116-1119(in Chinese with English abstract)

[19] MaL. Measurement of aerosol size distribution function using Mie scattering–mathematical considerations. J Aerosol Sci, 2007, 38(11): 1150-1162

[20] McCartneyEJ. Optics of the atmosphere: scattering by molecules and particles, 1976ChichesterWiley

[21] MeftahM, BolséeD, DaméL, HauchecorneA, PereiraN, IrbahA, et al. . Solar irradiance from 165 to 400 nm in 2008 and UV variations in three spectral bands during solar cycle 24. Sol Phys, 2016, 291: 3527-3547

[22] MercadoLM, BellouinN, SitchS, BoucherO, HuntingfordC, WildM, et al. . Impact of changes in diffuse radiation on the global land carbon sink. Nature, 2009, 458(7241): 1014-1017

[23] MichaelPR, JohnstonDE, MorenoW. A conversion guide: solar irradiance and lux illuminance. J Meas Eng, 2020, 8(4): 153-166

[24] MuGG, LiRY. General physics: optical part, 1965Beijing (in Chinese)Higher Education Press

[25] MuellerH. On the theory of scattering of light. Proc R Soc London A, 1938, 166(926): 425-449

[26] Mueller JL, Fargion GS (2003) Ocean optics protocols for satellite ocean color sensor validation, revision 4, volume III: radiometric measurements and data analysis protocols. In: Technical report. NASA, Goddard Space Flight Space Center, Maryland, pp 1–63. https://doi.org/10.25607/OBP-62

[27] Murgai V, Klein S, Arnold W, Durell C, Bowers S, Russell B et al (2020) Low degradation Spectralon selection. In: Earth Observing Systems XXV. SPIE, pp 171–180. https://doi.org/10.1117/12.2568774

[28] OkhoninS, GureevM, SallinD, AppelJ, KoukabA, KvasovA, et al. . A dynamic operation of a PIN photodiode. Appl Phys Lett, 2015, 106(3)

[29] PaganoTS, JohnsonDL, McGuireJP, SchwochertMA, TingDZ. Technology maturation efforts for the next generation of grating spectrometer hyperspectral infrared sounders. IEEE J Sel Top Appl Earth Observ Remote Sens, 2022, 15: 2929-2943

[30] RaoSM. Spectrographic technique for determining refractive indices. Opt Eng, 1997, 36(1): 162-166

[31] RichardE, HarberD, CoddingtonO, DrakeG, RutkowskiJ, TriplettM, et al. . SI-traceable spectral irradiance radiometric characterization and absolute calibration of the TSIS-1 spectral irradiance monitor (SIM). Remote Sens, 2020, 12(11)

[32] RiihimakiLD, FlynnC, McComiskeyA, LubinD, BlanchardY, ChiuJC, et al. . The shortwave spectral radiometer for atmospheric science: capabilities and applications from the ARM user facility. Bull Am Meteorol Soc, 2021, 102(3): E539-E554

[33] ShirleyJW. An early experimental determination of Snell's law. Am J Phys, 1951, 19(9): 507-508

[34] SunCL, ChenZQ, YinYX, YeYT, LuoY, MaH, et al. . Broadband and high-resolution integrated spectrometer based on a tunable FSR-free optical filter array. ACS Photonics, 2022, 9(9): 2973-2980

[35] TatsiankouV, HinzerK, HaysomJ, SchriemerH, EmeryK, BealR. Design principles and field performance of a solar spectral irradiance meter. Sol Energy, 2016, 133: 94-102

[36] ThuillierG, ZhuP, SnowM, ZhangP, YeX. Characteristics of solar-irradiance spectra from measurements, modeling, and theoretical approach. Light-Sci Appl, 2022, 11(1): 1-5

[37] Wang WB (2014) Exploring the variation of solar spectral characteristic in atmosphere and ocean principal wavelength. PhD thesis, Ocean University of China

[38] WiscombeWJ. Improved Mie scattering algorithms. Appl Opt, 1980, 19(9): 1505-1509

[39] YangZY, Albrow-OwenT, CaiWW, HasanT. Miniaturization of optical spectrometers. Science, 2021, 371(6528): eabe0722

[40] YoungAT. Rayleigh scattering. Appl Opt, 1981, 20(4): 533-535

[41] ZhangL, LiJH, LiHS, ZhangPF, ZhouAM, LiB, et al. . A high resolution prism-grating panoramic imaging spectrometer based on occultation observations. Opt Commun, 2024, 560

[42] ZhangYS, WangK, YueW, LiuSK, YuJL, YeX. Optical design and stray light analysis of underwater spectral radiometer. Appl Sci, 2024, 14(8)

[43] ZimmerL, DomannR, HardalupasY, IkedaY. Simultaneous laser-induced fluorescence and Mie scattering for droplet cluster measurements. AIAA J, 2003, 41(11): 2170-2178