3D Hole Inspection Using Lens with High Field Curvature

Transcription

1 /msr MEASUREMENT SCIENCE REVIEW, Volume 15, No. 1, D Hole Inspection Using Lens wit Hig Field Curvature Petr Zavyalov Tecnological Design Institute of Scientific Instrument Engineering, Siberian Branc of te Russian Academy of Sciences 41, Russkaya str., Novosibirsk, , Russia One of te actual 3D measurement problems is te optical inspection of various oles. In tis respect, te task of plane image formation of oles as extended 3D objects using optical metods turns out to be of primary importance. We ave developed specialized lenses tat perform suc transformations due to specially increased aberrations (field curvature, astigmatism) for te formation of extended objects plane images. Te calculations of te lens parameters are presented. Te detail analysis of te imaging properties was carried out. Te presented ole inspection lens as been designed, constructed and used for inspection of te fuel assembly spacer grids. Keywords: Hole inspection lens, 3D imaging, field curvature, distortion, fuel assembly, spacer grid INTRODUCTION D INSPECTION of various oles is te actual measurement problem. Among te noncontact metods for inspection of suc objects, te most promising are te optical ones due to ig informativeness. Tey allow inspecting bot te geometric parameters of oles and te quality (i.e. appearance) of te surfaces. In tis respect, te task of plane images formation of oles as extended 3D objects using optical metods turns out to be of primary importance. Various metods of mecanical scanning and unfolding are traditionally used for tis purpose, but tey ave significant disadvantages, first of all low speed and elaborate design [1-5]. Earlier we ave proposed te use of specialized lenses wit specially increased aberrations (field curvature, astigmatism) for formation of extended oles plane images [6]. Using suc lenses seems a rater promising solution tat allows one to simplify te optical scemes for macine vision systems substantially and to expand teir performance capabilities. It sould be noted tat recently te ole inspection lenses appear on te optical systems market [7, 8]. As an example we can note te PCHI-lens from te Opto Engineering Company for inspecting te oles wit a diameter from 10 to 120 mm wit a ratio of teir lengt to diameter about unity. However, te information about te operation principle of suc lenses, teir optical caracteristics and metods of calculation is absent in te scientific literature. Te calculations of te lens parameters are presented in te given article. Tis ole inspection lens (HIL) as been designed, constructed and used for inspection [9] of te fuel assembly spacer grids. Te metod for calculating and designing suc lens wit te elp of ZEMAX [10] software package is presented and te imaging properties of tis lens are estimated. 2. A THIN LENS APPROACH FOR A HOLE IMAGE FORMATION Firstly, let us analyze te imaging properties of an ideally tin lens for a cylindrical ole formation (Fig.1.). Tis approac will elp us to demonstrate te difference between HIL and conventional lenses. Te lens wit focal lengt f is located outside te ole wit diameter D and lengt L, wile an object is a longitudinal extra-axial segment AB. Fig.1. Te image formation of te cylindrical ole by a tin lens (f = 5 mm, D = 10 mm φ = 45 ). As one can see from Fig.1., te longitudinal segment AB is projected by a tin lens into an inclined segment A B. Essentially, te image of a cylindrical surface will be conical. According to te tin lens formula, te segment image configuration is described in tis case by te expression: 2f' z( y) = y + f' = tg( ϕ ) y + f' (1) D It can be seen tat te conical image curvature depends on te ratio f /D. And te cone angle (π-2φ) increases wit te increase of te ratio f /D. It means tat te tin lenses (really standard lenses) may be used for formation of ole images in detector plane P under condition f <<D, i.e. wen large oles, for instance, wit a diameter about 100 mm and more, are inspected. In tis case te conical image of a ole tends to plane P (φ 0). Tis metod for oles or closed cavity image formation is used in endoscopes of various purposes were te focal lengt of objectives is about some millimeters. However, using tis approac is not feasible for products wit smaller diameter oles (less tan 100 mm) due to te fact tat tere are considerable difficulties in te production of ultra-sort-focus lenses (less tan 5 mm) and tere are no 52

2 matrix potodetectors of suitable sizes (te size of most sensors is about 5-15 mm). Anoter approac for forming te ole images is based on te use of conic mirror [1-5], tat is located inside te inspected ole. In tis case to obtain te image of te entire object te mecanical scanning is usually used, wic is unacceptable in case of ig inspection productivity. 3. THE FORMATION OF HOLE PLANE IMAGE BY THE SPECIALIZED INSPECTION LENS It is evident tat using a standard lens tat projects a plane image on a plain surface does not allow forming te ig quality image of an extended ole wit a small diameter. For tis purpose it is necessary to design a specific lens, tat could be described as a lens for ole or inner surfaces inspection. Te essence of te transformation performed by tis lens is illustrated by Fig.2. Te lens projects te cylindrical surface of te ole wit te diameter D into te plane of a potodetector sensor. Tat means te lens as to project te longitudinal segment AB (wit coordinates z min and z max ) into a transversal segment A B (wit coordinates R min and R max ). So te task is to design a specialized lens wit a ig field curvature. By introducing tis aberration, te lens corrects te curvature of te conical image of te ole. Evidently, te value of own field curvature of lens sould be te iger, te greater te ratio f /D will be. Tus, te most callenging problem is to design a HIL wit a small (5-10 mm) diameter and ig L /D ratio (L /D > 1). 4. LENS DESIGN FOR INSPECTION OF THE FUEL ASSEMBLY SPACER GRID CELLS One of te problems were similar lenses are required is te inspection of te geometrical parameters of te spacer grid cells for nuclear reactor fuel assembly on te base of multiple-ring focusers. In general, solving tis problem as been described in papers [6, 9]. Te main aspects of designing a HIL for solving tis problem will be listed below. Te metod suggested is scematically described in Fig.4. Fig.2. Te formation of ole plane image by te specialized inspection lens. Apparently te R max /R min ratio tat caracterizes te efficiency of potodetector use is approximately equal to β max /β min ratio, were β min and β max are te principal ray angles for points A and B correspondingly. Tat is wy to increase tis ratio it is desirable tat te HIL is placed closer to te ole or tat it as te entrance pupil sifted frontwards. Te ole inspection lens operation can be explained easier, if we consider its operation in te return trace mode. In tis case, as well as in te traditional one, tere is an ordinary plane object, but its image is strongly incurved (see Fig.3.). Wen designing wit traditional lenses tis image curvature is decreased by any means. By contrast, in our example it is necessary to increase te image curvature, so tat te curve segment of A B image is placed (situated) as close to te ole surface as possible. Fig.3. Te operation of a ole inspection lens in te return trace mode. Fig.4. Te spacer grid cell inspection metod on te base of multiple-ring focusers: 1 multiple-ring focuser; 2 cell; 3 ligt rings; 4 HIL; 5 camera; 6 image. Tis metod is based on structural illumination of te cell surface as a set of ligt circles wit te use of a multiplering focuser. A plane image of te cell is formed by te specialized lens wit strong curvature. Te most important problem wen using tis metod is te design of a lens to form te plane cell images. Since te diameter of an inspected cell is rater small (D 9 mm) and its lengt is rater long (L 15 mm), te application of standard lens does not seem possible. For tis reason, a specialized HIL was designed for spacer grid cells inspection. Te calculation of a lens was made using te ZEMAX software. Te calculation procedure is based on optimization algoritms of optical system parameters. As a quality criterion at te initial stage we ave used a root-mean-square minimum of geometrical spot from te points trougout te lengt of te ole. Te following additional requirements were: maximal image size R max (see Fig.4.) is 3.5 mm, te potodetector operation efficiency R max /R min 2, te lens F-number 12, te angle of ray incidence on potodetector sould not exceed 10 (tis restriction spreads upon te most existing image sensor types). 53

3 Moreover, tere are some restrictions for design parameters of optical elements. Taking into account simplicity and low cost production considerations, te number of lenses witin te HIL was no more tan tree. Since te lens is supposed to be dealing wit laser irradiation, it does not ave any requirements on cromatic aberration. Consequently, te glasses optimization was not made under calculations. All te lenses were produced wit te use of N-BK7 glasses (te Scott catalogue). After te first attempts to optimize te system it became clear tat image aberration tends to be compressed in te tangential plane (along te Y-coordinate) and extended in sagittal plane (along te X-axis). Ten to simplify te optimization process it as been decided to cange te optimization criteria from te RMS - Spot Radius to RMS - Spot Radius Х+Y, wile te weigt of te X-component operators was significantly decreased (by five - ten times). Suc allowance can be made since te lens is used for registering te bands of structural irradiation, i.e. tere are no strict requirements to resolution along te X-axis. After te corrections were made, te lens caracteristics were substantially improved. Te calculation results are presented in Fig.5. a) b) Te optical sceme of te HIL is presented in Fig.5.a). It can be seen tat it consists of a double-convex lens and two positive meniscuses. Te effective focal lengt is f = 10.4 mm. Beind te lens group in a distance of approximately 100 mm tere is a standard objective wit a focal lengt of 50 mm (in ZEMAX it is represented by a tin lens). Te standard objective aperture diapragm is te aperture for te entire optical system, and its object-side image - te entrance pupil - is sifted 8 mm towards te inspected object and as a diameter of 0.8 mm. In so doing te standard objective projects te ole image (formed near te tird lens) on te potodetector of te camera wit a magnification of an order 1. Te spot diagrams for various points along te ole axis Z (z = 0 is te point of te ole te most distant from te HIL) are demonstrated in Fig.5.b). Apparently, most of te spot diagrams are extended in sagittal direction (ave significant astigmatism). Te modulation transfer function (MTF) of an HIL for z = 7.5 mm in tangential (along te Y-axis) and sagittal (along te X-axis) directions is presented in Fig.5.c). Denoted by a full-line on te upper part of te figure is te MTF for diffraction-limited system (te diffraction limit for tis aperture ratio). It is evident tat te MTF in tangential direction tends to te diffraction limit. Te tangential resolution on te level of 0.5 constitutes 46 cycles per mm. 5. THE DETAIL ANALYSIS OF THE IMAGING PROPERTIES FOR THE DEVELOPED LENS Let us analyze in detail te properties and te operation principle of te obtained optical sceme and try to understand wy te correction (compensation) of te ole image curvature occurs (in case of standard lens te ole is supposed to be conical). For tis purpose, let us consider te operation of tis kind of lens in te return trace mode. Te image can now be presented as an even asperical surface and its parameters can be optimized (te first tree asperical coefficients). Te optimization criteria cosen will be te same as wen te lens was calculated - Spot X+Y wit te Х-component weigt of 0.1. Te result of tis optimization is presented in Fig.6. It can be seen tat in tis case te image is a noticeably extended surface (in te figure it is not fully sown), te sape of wic tends to a cylinder one near te inspected ole. Fig.6. Te analysis of HIL operation in te return trace mode. c) Fig.5. Te caracteristics of te calculated HIL: a) te optical sceme, b) te spot diagrams from different points along Z-axis: 0, 3.75, 7.5, 13.25, 15 mm; c) te modulation transfer function (for ole center z = 7.5 mm). Te designed lens possesses ig distortion, as well as significant image curvature and astigmatism. Te distortion is te consequence of te sifted frontwards entrance pupil (later we will consider te influence of distortion). Te described effect of te lens is te result of great astigmatism and image curvature. 54

4 Now let us define te contribution of wic aberration is te principal. Te image surface sape presented in Fig.6. is, in fact, te image for tangential beams, because due to optimization te weigt of te X-component was minimal. If we optimize te image sape using te criteria of minimal spot radius (or wit equal weigts of X and Y components), ten we can define te true image curvature (Fig.7.). Fig.7. Te image curvature for developed HIL. Tus, comparing Fig.6. and Fig.7., we can see tat te own curvature of lens image is not sufficient to observe te ole surface. At te same time, ig astigmatism makes a great contribution to te curvature, so te image of tangential beams becomes almost cylindrical. Let us consider wat lenses ave influence on astigmatism and image curvature. For descriptive purposes we will present te Seidel coefficients on te lens surfaces as a diagram (see Fig.8., distortion is not sown on te diagram). te term magnification along te generatrix (see Fig.9.a)) wic for eac point of te ole equals: dr M t = (2) dz Te diagram of M t against Z-coordinate is presented in Fig.9.c). It is evident tat te magnification along te generatrix, and, correspondingly, te resolution of two extreme points z = 0 mm and z = 15 mm differ more tan by two times. It is also wort noting tat from resolution increase considerations it is rational to use te astigmatic beams. In fact, if R max /R min 2, wile te ole lengt is greater tan te diameter: L /D 2, so it can be sown tat te resolution in te meridional direction sould be muc iger tan in te sagittal one. For example, te mean magnification value along te ole: M t R R L R L max min = min = (3) a) b) Fig.8. Te Seidel diagram of te calculated HIL. Te contribution of eac of six surfaces into te four coefficients of te Seidel sum, as well as te overall aberrations of total objective, is demonstrated on te diagram. It is evident from te diagram tat te first two lenses form te astigmatism and te image curvature: double-convex lens and a converging meniscus. Te last lens te negative meniscus decreases insignificantly te coma and increases te astigmatism. Let us pay some attention to te impact of te distortion penomenon. As an example we will take nine points, situated wit te same intervals between tem along te ole, and ten we will construct te footprint diagram on te detector (Fig.9.b)). Apparently, te intervals between points on te image become smaller as we get closer to te image center. To estimate te imaging properties we will introduce c) Fig.9. Te HIL distortion. a) to te illustration of term «magnification along te generatrix», b) te footprint diagram of te points situated wit same intervals between tem along te ole, c) te diagram of M t along Z-coordinate. 55

5 At tat, for te ole center a circular curve wit a lengt of πd is imaged into a circular curve wit a lengt of 2π(R max +R min )/2, and te magnification in sagittal direction is equal to: [ R + R ] 2π max min R M 2 min s = = 6 = 6M πd L t (4) Tus, it is evident tat wen calculating suc lenses it is essential to consider te significant distortions of ole images and to use various weigt coefficients for tangential and sagittal quality criteria (especially for ratio L /D >1). Te image of a spacer grid fragment is sown in Fig.10. An image of a cell of tis spacer in wite ligt (a) and wit structural illumination (b), obtained wit te use of te designed HIL is presented in Fig.11. Tree bumps close to te image center are te so called protrusions, olding te fuel elements togeter. It can be seen tat te image of te cell trougout te dept (~20 mm) is clearly displayed. And at te same time te cell image looks as everted because of te HIL large distortion. Te lens calculation results also demonstrate tat it can be used to inspect oles witin a rater great range of diameters from 8 mm to 20 mm. Moreover, te larger te ole diameter, te iger te image quality. Te readjustment of te HIL for oter ole diameters consists of canging te distances between te ole and te HIL and between te potodetector and te HIL. Fig.10. Spacer grid fragment. One of te disadvantages of te designed lens is its small aperture, tat is sligtly reduced (working F-number 12) due to rater ig aberration level. It migt be explained by te simplicity of te HIL construction: only tree lenses are used and no asperical surfaces. Under furter development of HIL wit greater number of lenses tis disadvantage migt be eliminated. It also sould be noted tat te development of lenses wit several (i.e. two or more) intermediate images will allow reacing better image quality for oles wit small diameter and/or great L /D ratio. In tis case, it is possible to acieve greater cumulative field curvature witout te substantial beam astigmatism. a) b) Fig.11. Te images of spacer grid cell, obtained wit te use of te designed HIL: a) in wite ligt, b) wit structural illumination. CONCLUSION Te metod for calculating te ole inspection lens wit ig field curvature (as a triple lens) is presented. Te ole inspection lens forming of plane images of te 3D inner surfaces of te spacer grid cells was calculated and te corresponding lens type was produced. Te analysis of te imaging properties of calculated HIL was performed. Unlike standard lenses, tis kind of lens as a greater field curvature in te object space, wic is acieved at te expense of greater astigmatism. Due to increased aberrations te lens forms a plane image of te oles inner surfaces witin a broad range of teir diameters D (8 20 mm) and lengts L (1 2) D wit spatial resolution in tangential and sagittal directions on 45 and 8 cycles/mm correspondingly. Using tis lens makes it possible to simplify te spacer grid inspection sceme significantly, to increase te measurement accuracy wile measuring te geometrical parameters of cells, and, lastly, to substantially broaden te nomenclature of te measured spacer grids as compared to te inspection system designed earlier, were standard lenses ad been applied [11, 12]. ACKNOWLEDGMENTS Tis material is based upon work supported by te Ministry of Education and Science of te Russian Federation under Grant Te autor also wises to tank Prof. Yuri Cugui for is assistance during tis paper writing. 56

6 REFERENCES [1] Wakayama, T., Maci, K., Yosizawa, T. (2012). Small size probe for inner profile measurement of pipes using optical fiber ring beam device. In Optical Metrology and Inspection for Industrial Applications II, Proc. SPIE [2] Bao Hua Zuang, Wenwei Zang, Dong Yin Cui. (1997). Noncontact laser sensor for pipe inner-wall inspection using circular optical cutting metod. In Tree-Dimensional Imaging and Laser-Based Systems for Metrology and Inspection II, Proc. SPIE 2909, 223. [3] Si Yongqiang, Sun Cangku, Ma Yukun, Duan Hongxu, Wang Peng. (2012). Hig-precision automatic online measurement system of engine block top surface oles. Optical Engineering, 51 (5), [4] Cugui, Yu., Finogenov, L., Kiryanov, V., Nikitin, V., Sametov, A., Zavyalov, P. (2004). Inspection of oles parameters using a ring diffractive focuser. In Potonics in Measurement, June Düsseldorf: VDI Verlag, [5] Cugui, Yu.V., Lemesko, Yu.A., Zav'yalov, P.S. (2009). Application of diffractive optical elements for inspection of complicated troug oles. In Fift International Symposium on Instrumentation Science and Tecnology, Proc. SPIE [6] Finogenov, L.V., Lemesko, Yu.A., Zav yalov, P.S., Cugui, Yu.V. (2007). 3D laser inspection of fuel assembly grid spacers for nuclear reactors based on diffraction optical elements. Measurement Science and Tecnology, 18 (6), [7] Vertoprakov, V., Tian Po Yew. (2011). Hole Inspection Metod and Apparatus. Patent US A1. [8] Opto Engineering. Hole inspection optics for 360 inside view in perfect focus. ttp:// [9] Lemesko, Yu.A., Finogenov, L.V., Zav yalov, P.S. (2008). Using te diffractive optics for 3D inspection of nuclear reactor fuel assembly grid spacers. Measurement Science Review, 8 (3), [10] Zemax LLC. Zemax Optical and Illumination Design Software. ttp:// [11] Bityutskii, O.I., Vertoprakov, V.V., Guscina, A.A. et al. (2003). Tree-dimensional noncontact inspection of geometric parameters of grid spacers in nuclear reactors. Optoelectronics, Instrumentation and Data Processing, 39 (5), 4. [12] Bityutsky, O.I., Capaev, I.G., Cernysov, V.M. et al. (2002). Laser measuring macine for 3D noncontact inspection of geometric parameters of grid spacers for nuclear reactors VVER In Sevent International Symposium on Laser Metrology Applied to Science, Industry, and Everyday Life, Proc. SPIE 4900, 202. Received October 7, Accepted February 4,