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This work was supported by the Ministerio de Ciencia e Innovacion de Espana (grant PID2019-107391RB-I00) and by Generalitat Valenciana (grant PROMETEO/2019/048), Spain.

Analysis of institutional authors

Garmendia-Martinez, AdrianCorresponding AuthorGimenez, FernandoAuthorCastro-Palacio, Juan CAuthorMonsoriu, Juan AAuthorFerrando, VicenteAuthor

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Comparative Study of Numerical Methods for Solving the Fresnel Integral in Aperiodic Diffractive Lenses

Publicated to:Mathematics. 11 (4): 946- - 2023-02-01 11(4), DOI: 10.3390/math11040946

Authors: Garmendia-Martinez, Adrian; Munoz-Perez, Francisco M; Furlan, Walter D; Gimenez, Fernando; Castro-Palacio, Juan C; Monsoriu, Juan A; Ferrando, Vicente

Affiliations

Univ Politecn Tulancingo, Div Posgrad, Lab Fibra Opt, Tulancingo 43629, Hidalgo, Mexico - Author
Univ Politecn Valencia, Ctr Tecnol Fis, Valencia 46022, Spain - Author
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain - Author
Univ Valencia, Dept Opt, Valencia 46100, Spain - Author

Abstract

In this work, we present a comparative analysis of different numerical methods to obtain the focusing properties of the zone plates based on Fibonacci and Cantor sequences. The Fresnel approximation was solved numerically in order to obtain the axial irradiance provided by these diffractive lenses. Two different methods were applied. The first one is based on numerical integration, specifically the Simpson integration method and the two-dimensional Gaussian quadrature. The second consisted in the implementation of the Fast Fourier Transform in both one and two dimensions. The axial irradiance of the lenses, the relative error with respect to the analytical solution, and the calculation time required by each method are analyzed and compared. From this analysis it was concluded that the Gauss method presents the best balance between accuracy and computation time. This analysis could be useful to decide the most convenient numerical method to be used for the study of more complex diffractive structures.

Keywords

Diffractive lenseDiffractive lensesFast fourier transformFresnel integralNumerical integration methods

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2023, it was in position 21/490, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 3.92. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.21 (source consulted: FECYT Feb 2024)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-15, the following number of citations:

  • WoS: 6
  • Scopus: 7
  • OpenCitations: 4

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-15:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 6 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

    Leadership analysis of institutional authors

    This work has been carried out with international collaboration, specifically with researchers from: Mexico.

    There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Garmendía Martínez, Adrián) and Last Author (Ferrando Martín, Vicente).

    the author responsible for correspondence tasks has been Garmendía Martínez, Adrián.