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Although several theoretical frameworks have been developed to address this situation, relatively few studies have directly compared these models with experimentally measured spectra. In this study, Lekner\u2019s formalism, which is applicable when the principal axes are not confined to the measurement plane, was applied to crystalline quartz. The reliability of this method for three-dimensional orientation analysis of uniaxial crystals was evaluated by comparing calculated reflection spectra with experimental measurements. The results showed that large frequency dispersion produces orientation-dependent spectral features. These features arise from the mixing of the optical responses along the principal axes when out-of-plane orientations are present. The potential and limitations of this approach for determining crystal orientation angles are also discussed.<\/jats:p>","DOI":"10.1177\/00037028261438158","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T08:05:57Z","timestamp":1776758757000},"page":"499-515","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Infrared Reflection Spectra of Quartz at Out-of-Plane Orientations: Validating Lekner\u2019s Expression for Anisotropic Materials"],"prefix":"10.1177","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1335-2000","authenticated-orcid":false,"given":"Yuko","family":"Amaki","sequence":"first","affiliation":[{"name":"Industrial Research Institute of Niigata Prefecture, 1-11-1 Abumi-Nishi, Chuo-ku, Niigata 950-0915, Japan"},{"name":"Graduate School of Science and Technology, Niigata University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0176-7954","authenticated-orcid":false,"given":"Naoto","family":"Nagai","sequence":"additional","affiliation":[{"name":"Graduate School of Science and Technology, Niigata University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takeshi","family":"Yamauchi","sequence":"additional","affiliation":[{"name":"Graduate School of Science and Technology, Niigata University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2026,4,21]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0924-2031(95)00036-4"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0032-3861(95)99440-6"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1021\/ma011492i"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1021\/ac070676d"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpca.9b05316"},{"issue":"579","key":"e_1_3_2_7_2","first-page":"10","article-title":"Alternative Face-on Thin Film Structure of Pentacene","volume":"9","author":"Shioya N.","year":"2019","unstructured":"Shioya N., Murdey R., Nakao K., Yoshida H., et al. \u201cAlternative Face-on Thin Film Structure of Pentacene\u201d. 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