Author Correction: Comprehensive Modeling of Multimode Fiber Sensors for Refractive Index Measurement and Experimental Validation

Author Correction: Comprehensive Modeling of Multimode Fiber Sensors for Refractive Index Measurement and Experimental Validation Haris Apriyanto, Gautier Ravet, Olivier D. Bernal, Michel Cattoen, Han Cheng Seat, Valérie Chavagnac, Frederic Surre & James H. Sharp Correction to: Scientific Reports https:// doi. org/ 10. 1038/ s4159801824153-0, published online 12 April 2018 The original version of this Article contained errors in Equation 7, which was incorrectly given as:

Correction to: Scientific Reports https:// doi. org/ 10. 1038/ s41598-018-24153-0, published online 12 April 2018 The original version of this Article contained errors in Equation 7, which was incorrectly given as: The correct Equation 7 appears below.
As a result of the changes to Equation 7, the Abstract, "The sensors can be employed over a very wide dynamic RI range from 1.316 to over 1.608 at a wavelength of 1550 nm, with the best resolution of 2.2447 × 10 −5 RI unit (RIU) obtained in Zone II for a 1-cm sensor length. " now reads: "The sensors can be employed over a very wide dynamic RI range from 1.316 to over 1.608 at a wavelength of 1550 nm, with the best resolution of 2.2406 × 10 −5 RI unit (RIU) obtained in Zone II for a 1-cm sensor length. " Additionally, in Figure 5a, the unit of fiber diameter "μm" was incorrectly given as "mm".
The original Figure 5 and accompanying legend appear below.
In the final paragraph of the Discussion, "It is also in this Zone that the 2.5-cm and 4-cm sensors have the best relative resolutions of 2.9919 × 10 −5 RIU and 3.2634 × 10 −5 RIU, respectively, compared to the other two Zones. For Zone I, the best resolution is achieved by the 4-cm long sensor with a minimum detection level of 1.5438 × 10 −3 RIU while the 1-cm and 2.5-cm sensors are capable of resolutions of 5.1952 × 10 −3 RIU and 1.7462 × 10 −3 RIU, respectively. " now reads: www.nature.com/scientificreports/ "It is also in this Zone that the 2.5-cm and 4-cm sensors have the best relative resolutions of 2.9847 × 10 −5 RIU and 3.2517 × 10 −5 RIU, respectively, compared to the other two Zones. For Zone I, the best resolution is achieved by the 4-cm long sensor with a minimum detection level of 1.6116 × 10 −3 RIU while the 1-cm and 2.5-cm sensors are capable of resolutions of 5.5905 × 10 −3 RIU and 1.7528 × 10 −3 RIU, respectively.
In the second paragraph of the Conclusions, "For Zone II, the best sensor resolution of 2.2447 × 10 −5 RIU is achieved for the 1-cm sensor. " now reads: "For Zone II, the best sensor resolution of 2.2406 × 10 −5 RIU is achieved for the 1-cm sensor. " Lastly, as a result of the changes to Equation 7, the data in Table S1, S2, S3, S5, S6 and S7 in the Supplementary Information was incorrect.
The original Supplementary Information file is available below.
The original Article and accompanying Supplementary Information file has now been corrected.

Supplementary Information
The online version contains supplementary material available at https:// doi. org/ 10. 1038/ s41598-021-99941-2. Figure 5. Evolution of optical power and intensity in the MMF RI sensor for various values of n sm by modification of the critical angle, θ csm , for n cl < n sm < n co . (a) increasing n sm will increase θ csm which reduces the acceptance angle of the propagating beam, (b) power in transversal plane decreases for increasing n sm , and (c) illustrates decreasing optical intensity over different a' obtained by Equation (14). www.nature.com/scientificreports/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.