On Babinet's principle and a diffraction-interferometric technique to determine the diameter of cylindrical wires
| dc.contributor.author | Martínez Antón, Juan Carlos | |
| dc.contributor.author | Serroukh, Ibrahim | |
| dc.contributor.author | Bernabeu Martínez, Eusebio | |
| dc.date.accessioned | 2023-06-20T19:05:19Z | |
| dc.date.available | 2023-06-20T19:05:19Z | |
| dc.date.issued | 2001 | |
| dc.description | © IOP Publishing. The authors gratefully acknowledge the support of the DEFCYL project (SMT 4-CT97-2184) from DG.12-EGAA of the European Community and the ABSODIAM project (TIC 96-1694-CE). | |
| dc.description.abstract | Laser diffraction is a robust and precise technique for measuring wire diameters. However, classical Fraunhofer diffraction formulas are inappropriate for determining the size of three-dimensional objects. Babinet's principle (from classical diffraction theory) allows the use of such formulas only for angles of diffraction tending to zero. In practice diffraction measurements require a finite angular range (about 10°) for good resolution. We show that use of the classical slit-diffraction formula for this extended angular interval introduces significant error. We develop a simple diffraction model valid for cylindrical shapes and a formula to obtain the diameter of cylindrical wires. To validate the diffraction formula we calibrate the diameter of the wires using an independent interferometric technique, which to our knowledge is original for this particular task. We have verified our diffraction formula to within about 0.2 µm for various wire materials and diameters (30 µm to 300 µm) and a wide angular range (±25°). Two different experimental set-ups were implemented to increase the reliability of the results. The calibration procedure revealed a systematic disagreement with Babinet's principle, in particular a systematic overestimation of the diameter by about 0.6 µm, almost independent of the material and the diameter itself. This is particularly relevant to metrological applications involving diffraction phenomena and based on classical diffraction theory. | |
| dc.description.department | Depto. de Óptica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea (UE) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/26794 | |
| dc.identifier.citation | [1] Nussenzveig H M 1992 Diffraction Effects in Semiclassical Scattering (Cambridge, Cambridge University Press) 17-20. [2] Greenler R G, Hable J W and Slane P O 1990 Am. J. Phys. 58 (4) 330-331. [3] Keller J B 1962 J. Opt. Soc. Am. 52 (2) 116-130. [4] Schmidt S 1976 PTB-Mitteilungen 86 (4) 239-247. [5] Serroukh I, Martínez-Antón J C and Bernabeu E 1999 Proc. Conf. Wire Association International, Inc. 531-535 [6] Martínez-Antón J C, Serroukh I and Bernabeu E Proc. EOS/SPIE Symposium: Optical Measurements Systems for Industrial Inspection, 14-18 June 1999, Munich. [7] Lebrun D, Belaid S, Özkul C, Ren K F and Gréhan G 1996 Opt. Eng. 35 (4) 946-950. [8] Azzam R M A and Bashara N M 1977 Ellipsometry and Polarized Light (Amsterdam, North-Holland). [9] Millard T K and Herchenreder T A 1991 Wire J. Int. 24 (12) 61-69. [10] Fardeau J F 1989 Wire J. Int. 22 (1) 42-51. [11] Lipinski G, Priel M and Vailleau G P 1997 Metrologia 34 235-240. [12] Xie J, Qiu Y, Ming H and Li C 1991 J. Appl. Phys. 69 (10) 6899-6903. [13] Martínez-Antón J C and Bernabeu E 1994 Appl. Opt. 33 (25) 6059-6061. | |
| dc.identifier.doi | 10.1088/0026-1394/38/2/4 | |
| dc.identifier.issn | 0026-1394 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/0026-1394/38/2/4 | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59230 | |
| dc.issue.number | 2 | |
| dc.journal.title | Metrologia | |
| dc.language.iso | eng | |
| dc.page.final | 134 | |
| dc.page.initial | 125 | |
| dc.publisher | Bureau International des Poids et Mesures (BIPM) | |
| dc.relation.projectID | DEFCYL (SMT 4-CT97-2184) | |
| dc.relation.projectID | ABSODIAM (TIC 96- 1694-CE) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 535 | |
| dc.subject.keyword | Instruments and Instrumentation | |
| dc.subject.keyword | Applied Physics | |
| dc.subject.ucm | Óptica (Física) | |
| dc.subject.unesco | 2209.19 Óptica Física | |
| dc.title | On Babinet's principle and a diffraction-interferometric technique to determine the diameter of cylindrical wires | |
| dc.type | journal article | |
| dc.volume.number | 38 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 1baf6769-50bc-4dcd-9479-8de2d65eec19 | |
| relation.isAuthorOfPublication.latestForDiscovery | 1baf6769-50bc-4dcd-9479-8de2d65eec19 |
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