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With the advantages of high precision and great environmental adaptability, laser heterodyne interferometry has been successfullyused in some areas, such as measuring distance and angle and other point detection. The Hertz-level frequency-shifting technology greatly improves the accuracy and stability of surface measurement and extends its application to the areas of array detection, such as three-dimensional topography measurement, smooth surface measurement, digital holography, speckle measurement, etc. The frequency difference of heterodyne interferometry is realized by acousto-optic frequency shifter under the control of two radio frequency signals each with a fixed frequency value. However, a deviation of the real value from the design value of frequency always exists, which is referred to as frequency difference deviation. It causes the heterodyne frequency and the frame rate of the array detector to be unable to be strictly matched, thus affecting the improvement of measurement accuracy. According to the theory of full-field heterodyne measurement, we derive the relationship between frequency difference deviation and measurement accuracy of the heterodyne measurement instrument, and analyze the effects of relevant parameters including the value of frequency difference, frequency deviation, initial sampling time, initial phase, sampling frequency, and sampling cycles on measurement accuracy. A method of improving the measurement accuracy is proposed by reasonably selecting the sampling time and frame number. Analysis shows that the initial sampling time and initial phase have the same effect on the measurement accuracy. With the reasonable choosing of measurement parameters and processing methods, the measurement accuracy of the instrument could be greatly improved. In addition, the peak value of full-field heterodyne measurement error is linearly related to the frequency difference deviation. In the case of a certain frequency difference deviation, the instrument could achieve a higher measurement accuracy with greater frequency difference, but requires a higher frame rate of detector at the same time. As a result, designers should choose an appropriate value of frequency difference for measurement instrument. Furthermore, increasing the sampling frequency could also improve the measurement accuracy. Actually, if sampling frames are more than fifteen in a single cycle, the improvement of measurement accuracy would be limited. Multi-period sampling has little effect on measurement error caused by frequency difference deviation, and the measurement error is the limiting value of measurement accuracy that the instrument could reach. Therefore, this study could be used as a theoretical basis of the design and parameter selection and also the measurement accuracy analysis for full-field heterodyne measurement instrument development.
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Keywords:
- full-field heterodyne /
- interference measurement /
- frequency difference deviation /
- accuracy analysis
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[6] Kong X X, Xiang L B, Zhang W X, Wu Z, Li Y, L X Y 2017 Proc. SPIE 10329 103292E-2
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[8] Patrick E, Michael J C, Fereydoun L, Maurice P W 2006 Opt. Lett. 31 070912
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[10] Clerc F L, Collot L, Gross M 2000 Opt. Lett. 25 100716
[11] Gross M, Goy P, Forget B C, Atlan M, Ramaz F, Boccara A C, Dunn A K 2005 Opt. Lett. 30 111357
[12] Atlan M, Gross M 2007 Opt. Lett. 32 111456
[13] Michel G 2016 Appl. Opt. 55 0300A8
[14] Michel G 2017 Appl. Opt. 56 071846
[15] Dario D, Alexey B, Daniel A, Michel G 2016 Opt. Express 24 26887
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[17] Liao L, Yi W M, Yang Z H, Wu G H 2016 Acta Phys. Sin. 65 140601 (in Chinese)[廖磊, 易旺民, 杨再华, 吴冠豪 2016 物理学报 65 140601]
[18] Li C Q, Wang T F, Zhang H Y, Xie J J, Liu L S, Guo J 2016 Acta Phys. Sin. 65 084206 (in Chinese)[李成强, 王挺峰, 张合勇, 谢京江, 刘立生, 郭劲 2016 物理学报 65 084206]
[19] He Y Z, Zhao S J, Wei H Y, Li Y 2016 Acta Phys. Sin. 65 084206 (in Chinese)[贺寅竹, 赵世杰, 尉昊赟, 李岩 2016 物理学报 65 084206]
[20] Holmes R B, Ma S, Bhowmik A, Greninger C 1996 J. Opt. Soc. Am. A 13 351
[21] Zhang W X, Xiang L B, Kong X X, Li Y, Wu Z, Zhou Z S 2013 Acta Phys. Sin. 62 164203 (in Chinese)[张文喜, 相里斌, 孔新新, 李杨, 伍洲, 周志盛 2013 物理学报 62 164203]
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[1] Wu G, Takahashi M, Arai K, Inaba H, Minoshima K 2013 Sci. Rep. 3 1894
[2] Torre R, Taschin A, Sampoli M 2001 Phys. Rev. E 64 061504
[3] Wang G C, Yan S H, Yang J, Lin C B, Yang D X, Zou P F 2013 Acta Phys. Sin. 62 070601 (in Chinese)[王国超, 颜树华, 杨俊, 林存宝, 杨东兴, 邹鹏飞 2013 物理学报 62 070601]
[4] Yuichi K, Daisuke, Tomohiro K, Toyohiko Y 2010 Opt. Lett. 35 101548
[5] Tomasz T, Romuald J 2001 Proc. SPIE 4190 123
[6] Kong X X, Xiang L B, Zhang W X, Wu Z, Li Y, L X Y 2017 Proc. SPIE 10329 103292E-2
[7] Mark C P, Chung W S, Michael G S 2004 Opt. Lett. 29 111200
[8] Patrick E, Michael J C, Fereydoun L, Maurice P W 2006 Opt. Lett. 31 070912
[9] Wu Z, Zhang W X, Xiang L B, Kong X X 2017 Proc. SPIE 10329 1032905
[10] Clerc F L, Collot L, Gross M 2000 Opt. Lett. 25 100716
[11] Gross M, Goy P, Forget B C, Atlan M, Ramaz F, Boccara A C, Dunn A K 2005 Opt. Lett. 30 111357
[12] Atlan M, Gross M 2007 Opt. Lett. 32 111456
[13] Michel G 2016 Appl. Opt. 55 0300A8
[14] Michel G 2017 Appl. Opt. 56 071846
[15] Dario D, Alexey B, Daniel A, Michel G 2016 Opt. Express 24 26887
[16] Mauro V A, Fereydoun L, Maurice P W, Michael J C 2007 Optics and Lasers in Engineering 45 677
[17] Liao L, Yi W M, Yang Z H, Wu G H 2016 Acta Phys. Sin. 65 140601 (in Chinese)[廖磊, 易旺民, 杨再华, 吴冠豪 2016 物理学报 65 140601]
[18] Li C Q, Wang T F, Zhang H Y, Xie J J, Liu L S, Guo J 2016 Acta Phys. Sin. 65 084206 (in Chinese)[李成强, 王挺峰, 张合勇, 谢京江, 刘立生, 郭劲 2016 物理学报 65 084206]
[19] He Y Z, Zhao S J, Wei H Y, Li Y 2016 Acta Phys. Sin. 65 084206 (in Chinese)[贺寅竹, 赵世杰, 尉昊赟, 李岩 2016 物理学报 65 084206]
[20] Holmes R B, Ma S, Bhowmik A, Greninger C 1996 J. Opt. Soc. Am. A 13 351
[21] Zhang W X, Xiang L B, Kong X X, Li Y, Wu Z, Zhou Z S 2013 Acta Phys. Sin. 62 164203 (in Chinese)[张文喜, 相里斌, 孔新新, 李杨, 伍洲, 周志盛 2013 物理学报 62 164203]
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