Seven-Point Correction Approach for Spectrum Measurement of Light Source with a Narrow Bandwidth
WANG Yan-fei1, DAI Cai-hong1, WU Zhi-feng1, CHEN Bin-hua1, 2
1. Division of Optics, National Institute of Metrology China, Beijing 100029, China 2. School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China
Abstract：The finite bandwidth of spectroradiometers always causes significant errors when the measured light source has a narrow bandwidth compared to that of spectroradiometers. In order to solve this problem, an improved correction approach which is called seven-point correction approach is proposed. Firstly, the seven-point correction formula is obtained with Taylor’s series and related derivative formula. Secondly, the effect of seven-point formula is validated through a simulated spectrum with a sine function shape. Considering the sine function as true spectrum, we calculate the measured spectrum with the bandpass function of spectroradiometers. We also correct the measured spectrum with the seven-point formula. At last, we validate the seven-point formula experimentally with a LED lamp whose center wavelength is 365 nm. Using a double grating monochromator, we measure the irradiance of LED lamp when the bandwidth of spectroradiometer is 5 and 0.5 nm. We also obtain the corrected spectrum by applying seven-point formula to measured spectrum. The simulated results show that, the corrected value at the center wavelength could be above 99% of the true value. The experimental results show that, the corrected value at the center wavelength could reach above 95% of the true value. Above all, the proposed seven-point approach has an improved correction effect compared with three-point and five point approach. This correction approach could be widely applied in the field of spectrum measurement.
Key words：Spectroradiometer;Bandwidth function;Seven-point correction approach;Spectrum distribution
[1] Maija Ojanen, Petri Krh, Erkki Ikonen. Applied Optics, 2010, 49(5): 880. [2] Dong Joo Shin, Chul Woung Park, Svetlana S Kolesnikova, et al. Metrologia, 2010, 47(1A): 02005. [3] Boivin L P, Gaertner A A. Applied Optics, 1992, 31(28): 6082. [4] WANG Yan-fei, ZHANG Sheng-nan, WANG Dong-ying, et al. Optics Letters, 2012, 37(19): 4059. [5] WANG Yan-fei, ZHANG Xiao-gang, WANG Dong-ying, et al. Optics Express, 2012, 20(23): 25817. [6] JIN Wei-qi, HU Wei-jie(金伟其，胡威捷). Radiometry, Photometry, Colorimetry Theory and Measurement(辐射度 光度与色度及其测量). Beijing: Beijing Institute of Technology Press(北京： 北京理工大学出版社), 2011. 166. [7] Henry J Kostkowski, Arnold M Bass. Journal of the Optical Society of America, 1956, 46(12): 1060. [8] Stearns E I, Stearns R E. Color Research & Application, 1988, 13(4): 257. [9] Louis Philippe Boivin. Applied Optics, 2002, 41(10): 1929. [10] James L Gardner. Color Research & Application, 2006, 31(5): 374. [11] Emma R Woolliams, Réjean Baribeau, Agnieszka Bialek, et al. Metrologia, 2011, 48(3): 164. [12] Saulius Nevas, Gerd Wubbeler, Armin Sperling, et al. Metrologia, 2012, 49(2): S43. [13] Eichstdt S, Schmhling F, Wübbeler G, et al. Metrologia, 2013, 50(2): 107. [14] Nautical Almanac Office, Interpolation and Allied Tables. London: HMSO, 1956. 54. [15] WANG Yan-fei, DAI Cai-hong, WU Zhi-feng, et al. Proceedings of SPIE, 2014, 9298: 92980V. [16] WANG Yan-fei, DAI Cai-hong, WU Zhi-feng, et al. Proceedings of 28th CIE Session 2015, 167. [17] WANG Yan-fei, DAI Cai-hong, WU Zhi-feng, et al. Mathematical Problems in Engineering, 2015, 378302. [18] DAI Cai-hong, WU Zhi-feng, YU Jia-lin. Proceedings of SPIE, 2013, 8910: 89100D.
