通过傅里叶变换测量多表面面形
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摘要
为了更简便、准确地测量透明平行板,提出了一种基于区域生长算法与傅里叶变换的单幅三表面干涉条纹相位恢复方法。通过傅里叶变化将三表面干涉条纹图由空域变化到频谱域。不同表面的干涉条纹在频谱域中对应的位置不同,通过改变区域生长算法中的参数,提取出合适的区域,最终得到面形。该方法可以由单幅三表面干涉条纹图同时得到透明平行板前后两个表面的面形。分析了由算法求得的表面面形的误差,通过叠加分离的双表面干涉图与原三条纹图进行比较,得到相应的误差分布图,通过误差分布图可以改善算法的精度。将得到的面形与Zygo干涉仪得到的面形进行对比,发现该方法测量精度较高,其相位提取误差PV值小于0.12λ,RMS值小于0.065λ;重复性得到验证,其重复率可靠度优于λ/100。测量到的面形与物体真实面形接近,测量方法更加简便。
To measure transparent parallel plates more easily and accurately,aphase recovery method based on the region growing algorithm and Fourier transform for single three-surface interference fringes was proposed.Through the Fourier transform,the three-surface interference fringe pattern was changed from the spatial to the spectral domain.Because the interference fringes of different surfaces have different positions in the spectral domain,the appropriate regions were extracted by changing the parameters in the region-growing algorithm,and the final surface was obtained.By this method,the planar shapes of the front and rear surfaces of the transparent parallel plate can be simultaneously obtained from a single three-surface interference fringe pattern.From an error analysis of the surface shapes obtained by the algorithm,a superimposed and separated double-surface interferogram was compared with the original three-striped graph to obtain the corresponding error distribution graph.The accuracy of the algorithm was improved through the error distribution graph.A comparison of the obtained surface shapes with that obtained by a Zygo interferometer reveals that the method had high measurement accuracy with a phase extraction error PV value of less than 0.12λand a Root Mean Square(RMS)value of less than 0.065λ.A verification of the repeatability shows that the repetition rate is reliable,and the degree is better thanλ/100.The measured surface shape approximated the real surface shape of the object,and the measurement method proved to be simpler than the original method.
To measure transparent parallel plates more easily and accurately,aphase recovery method based on the region growing algorithm and Fourier transform for single three-surface interference fringes was proposed.Through the Fourier transform,the three-surface interference fringe pattern was changed from the spatial to the spectral domain.Because the interference fringes of different surfaces have different positions in the spectral domain,the appropriate regions were extracted by changing the parameters in the region-growing algorithm,and the final surface was obtained.By this method,the planar shapes of the front and rear surfaces of the transparent parallel plate can be simultaneously obtained from a single three-surface interference fringe pattern.From an error analysis of the surface shapes obtained by the algorithm,a superimposed and separated double-surface interferogram was compared with the original three-striped graph to obtain the corresponding error distribution graph.The accuracy of the algorithm was improved through the error distribution graph.A comparison of the obtained surface shapes with that obtained by a Zygo interferometer reveals that the method had high measurement accuracy with a phase extraction error PV value of less than 0.12λand a Root Mean Square(RMS)value of less than 0.065λ.A verification of the repeatability shows that the repetition rate is reliable,and the degree is better thanλ/100.The measured surface shape approximated the real surface shape of the object,and the measurement method proved to be simpler than the original method.
引文
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[12]REN H,MA L,LIU X,et al..Optical element test with multiple surface interference[J].Opt.Precision Eng.,2013,21(5):1144.
[13]徐建程,石琦凯,柴立群,等.三表面干涉条纹空域傅里叶分析[J].中国激光,2006,33(9):1260-1264.XU J CH,SHI Q K,CHAI L Q,et al..Threesurface interference fringe spatial Fourier analysis[J].Chinese Journal of Lasers,2006,33(9):1260-1264.(in Chinese)
[14]QIAN.Applications of windowed Fourier fringe analysis in optical measurement:A review[J].Optics &Lasers in Engineering,2015,66:67-73.
[15]单小琴.单幅载波条纹图相位提取方法的研究[D].南京:南京理工大学,2011.SHAN X Q.Research on Phase Extraction Method of Single Carrier Stripe Pattern[D].Nanjing:Nanjing University of Science and Technology,2011.(in Chinese)
[2]粟银,范琦,王云飞,等.干涉条纹的高准确度傅里叶变换分析[J].光子学报,2015,44(11):94-99.SU Y,FAN Y,WANG Y F,et al..High accuracy fourier transform analysis of interference fringes[J].Acta Photonica Sinica,2015,44(11):94-99.(in Chinese)
[3]YAMAMOTO A,YAMAGUCHI I.Profilometry of sloped plane surfaces by wavelength scanning interferometry[J].Optical Review,2002,9(3):112-121.
[4]TAKEDA M,INA H,KOBAYASHI S.Fourier-transform method of fringe-pattern analysis for computerbased topography and interferometry[J].Review of Scientific Instruments,1982,72(1):156-160.
[5]BONE D J,BACHOR H A,SANDEMAN R J.Fringe-pattern analysis using a 2-D Fourier transform[J].Applied Optics,1986,25(10):1653.
[6]张望平,吕晓旭,刘胜德,等.基于时域傅里叶变换的广义相移相位恢复方法[J].中国激光,2015,42(9):262-268.ZHANG W P,LUX Y,LIU SH D,et al..Generalized phase shift phase recovery method based on time domain Fourier transform[J].Chinese Journal of Lasers,2015,42(9):262-268.(in Chinese)
[7]田爱玲,刘婷,刘剑,等.单幅干涉条纹图的高精度波面重建技术[J].红外与激光工程,2015,44(4):1203-1207.TIAN A L,LIU T,LIU J,et al..High precision wavefront reconstruction technique for single interference fringe pattern[J].Infrared and Laser Engineering,2015,44(4):1203-1207.(in Chinese)
[8]OKADA K,SAKUTA H,OSE T,et al..Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry[J].Apply Optics,1990,29(22):3280.
[9]KIM Y,HIBINO K,HANAYAMA R,et al..Multiple-surface interferometry of highly reflective wafer by wavelength tuning[J].Optics Express,2014,22(18):21145-211456.
[10]SCHMIT J,CREATH K.Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry[J].Applied Optics,1995,34(19):3610-3619.
[11]DECK L L.Fourier-transform phase-shifting interferometry[J].Applied Optics,2003,42(13):2354-2365.
[12]REN H,MA L,LIU X,et al..Optical element test with multiple surface interference[J].Opt.Precision Eng.,2013,21(5):1144.
[13]徐建程,石琦凯,柴立群,等.三表面干涉条纹空域傅里叶分析[J].中国激光,2006,33(9):1260-1264.XU J CH,SHI Q K,CHAI L Q,et al..Threesurface interference fringe spatial Fourier analysis[J].Chinese Journal of Lasers,2006,33(9):1260-1264.(in Chinese)
[14]QIAN.Applications of windowed Fourier fringe analysis in optical measurement:A review[J].Optics &Lasers in Engineering,2015,66:67-73.
[15]单小琴.单幅载波条纹图相位提取方法的研究[D].南京:南京理工大学,2011.SHAN X Q.Research on Phase Extraction Method of Single Carrier Stripe Pattern[D].Nanjing:Nanjing University of Science and Technology,2011.(in Chinese)