Defocus curve and vergence related to viewing distance : Journal of Cataract & Refractive Surgery

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Defocus curve and vergence related to viewing distance

Galvis, Virgilio MD, PhD; Tello, Alejandro MD, PhD; Carreño, Néstor I. MD; Berrospi, Ruben D. MD; Niño, Camilo A. MD; Serna, Víctor H. MD

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Journal of Cataract & Refractive Surgery 46(5):p 803, May 2020. | DOI: 10.1097/j.jcrs.0000000000000158
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We read with interest the article by Böhm et al. on visual results of intraocular lenses (IOL) for the correction of presbyopia.1

The authors evaluated the monocular distance-corrected defocus curve, with a chart located at a viewing distance of 4 m. They explained that −1.00 diopter (D) defocus simulated 1 m distance of the object, and that −2.50 D defocus corresponded to 40 cm distance of the object. These calculations of the simulated viewing distance after placing a negative defocus in front of the eye are established for an object located 6 m away. In geometrical optics, vergence is calculated as the reciprocal of the distance of the object in meters. The rays that come from real objects, located at a distance less than infinity, will always have negative vergences.2,3 Therefore, an object located 50 cm from the observer will have a vergence corresponding to 1/0.50 m, that is −2.00 D. Then, the object 6 m away will still have a vergence of 1/6 = −0.17 D. This last magnitude of negative vergence is considered clinically nonsignificant. However, when the object is brought closer to the eye, the negative vergence increases. The light rays coming from an object located 4 m away will reach the eye with a vergence of −0.25 D. This magnitude, although low, may already have some effect on optical measurements and visual performance. Therefore, when making measurements as precise as those required when analyzing defocus curves of multifocal IOL, it is necessary to take this detail into account (as explained by Gundersen and Potvin).4

That is, when a defocus curve is constructed with the distance of the chart at 4 m, if a −2.00 D lens is placed in front of the eye, it does not really generate a total divergence of −2.00 D, but −2.25 D. Therefore, the simulated distance of the “virtual” near object will not be 50 cm but 44 cm.

On another note, the fundamental purpose of defocus curves is the simulation of the visual performance of IOLs in daily life, in which patients see objects at different distances in a binocular manner. Therefore, defocus curves should always include the binocular approach. Monocular approach, especially in patients in whom the same type of IOL has been implanted in both eyes, which was the case of the study by Böhm et al., could be considered optional. Now, performing 2 defocus curves, both in a monocular and binocular manner, is more demanding for the patient, more time-consuming, and can lead to patient fatigue, which in turn will affect the results. Therefore, we consider that the best approach is to perform the defocus curve only in a binocular approach.5 The results of binocular defocus curves were not included in the mentioned article.

Finally, we do not find utility in including positive defocus when analyzing defocus curves. We consider that the information yielded by positive lens-stimulated defocus is not only futile but also confusing. However, it lengthens the time required for the examination, which is an additional inconvenience.


1. Böhm M, Petermann K, Hemkeppler E, Kohnen T. Comparative analysis of defocus curves of four presbyopia-correcting intraocular lenses with four designs: diffractive panfocal, diffractive trifocal, segmental refractive and extended depth of focus. J Cataract Refract Surg 2019;45:1625–1636
2. Katz M. Introduction to Geometrical Optics. Toh Tuck Link, Singapore: World Scientific Publishing Co. Pte. Ltd; 2002:11
3. Galvis V, Tello A, Blanco O, Laiton AN, Dueñas MR, Hidalgo PA. The Ametropías: Updated review for non-ophthalmologists physicians [in Spanish]. Rev Fac Cien Med Univ Nac Cordoba 2017;74:150–161
4. Gundersen KG, Potvin R. Trifocal intraocular lenses: a comparison of the visual performance and quality of vision provided by two different lens designs. Clin Ophthalmol 2017;11:1081–1087
5. Galvis V, Escaf LC, Escaf LJ. Visual and satisfaction results with implantation of the trifocal Panoptix® intraocular lens in cataract surgery. Rom J Ophthalmol. In press.
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