×

References

2001 Gatinel D, Hoang-Xuan T, Azar DT. Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model. Invest Ophthalmol Vis Sci. 2001 Jul;42(8):1736-42. PMID: 11431436.
2002 Gatinel D, Haouat M, Hoang-Xuan T. Etude des paramètres permettant la description mathématique de l'asphéricité cornéenne. J Fr Ophtalmol. 2002 Jan;25(1):81-90. PMID: 11965125.
2002 Gatinel D, Malet J, Hoang-Xuan T, Azar DT. Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity. Invest Ophthalmol Vis Sci. 2002 Apr;43(4):941-8. PMID: 11923232.
2004 Gatinel D, Malet J, Hoang-Xuan T, Azar DT. Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding Zernike expansions. Invest Ophthalmol Vis Sci. 2004 May;45(5):1349-59. doi: 10.1167/iovs.03-0753. PMID: 15111588.
2009 Nam J, Thibos LN, Iskander DR. Describing ocular aberrations with wavefront vergence maps. Clin Exp Optom. 2009 May;92(3):194-205. doi: 10.1111/j.1444-0938.2009.00358.x. PMID: 19302675.
2011 Gatinel D, Malet J, Hoang-Xuan T, Azar DT. Corneal elevation topography: best fit sphere, elevation distance, asphericity, toricity, and clinical implications. Cornea. 2011 May;30(5):508-15. doi: 10.1097/ICO.0b013e3181fb4fa7. PMID: 21107250.
2012 Amigo A, Bonaque S, López-Gil N, Thibos L. Simulated effect of corneal asphericity increase (Q-factor) as a refractive therapy for presbyopia. J Refract Surg. 2012 Jun;28(6):413-8. doi: 10.3928/1081597X-20120518-04. PMID: 22692523.
2014 Gatinel D, Azar DT, Dumas L, Malet J. Effect of anterior corneal surface asphericity modification on fourth-order zernike spherical aberrations. J Refract Surg. 2014 Oct;30(10):708-15. doi: 10.3928/1081597X-20140903-10. PMID: 25291755.
2015 Xu R, Bradley A, López Gil N, Thibos LN. Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus. Ophthalmic Physiol Opt. 2015 Jan;35(1):28-38. doi: 10.1111/opo.12185. PMID: 25532544.
2016 Courtin R, Saad A, Grise-Dulac A, Guilbert E, Gatinel D. Changes to Corneal Aberrations and Vision After Monovision in Patients With Hyperopia After Using a Customized Aspheric Ablation Profile to Increase Corneal Asphericity (Q-factor). J Refract Surg. 2016 Nov 1;32(11):734-741. doi: 10.3928/1081597X-20160810-01. PMID: 27824376.
2021 Rahmania N, Salah I, Rampat R, Gatinel D. Clinical Effectiveness of Laser-Induced Increased Depth of Field for the Simultaneous Correction of Hyperopia and Presbyopia. J Refract Surg. 2021 Jan 1;37(1):16-24. doi: 10.3928/1081597X-20201013-03. PMID: 33432991.
2021 Gatinel D, Malet J, Dumas L, Azar DT. Comparison of Low Degree/High Degree and Zernike Expansions for Evaluating Simulation Outcomes After Customized Aspheric Laser Corrections. Transl Vis Sci Technol. 2021 Mar 1;10(3):21. doi: 10.1167/tvst.10.3.21. PMID: 34003958.
2024 Salah-Mabed I, Debellemanière G, Rampat R, Dubois M, Gatinel D. High hyperopic LASIK with reduction of corneal prolateness to control-induced spherical aberration. J Cataract Refract Surg. 2024 Sep 1;50(9):919-925. doi: 10.1097/j.jcrs.0000000000001475. PMID: 38758195.
2025 Stern B, Saad A, Gatinel D. In Vitro Comparison of an Aspherical Monofocal Lens Inducing Positive Spherical Aberrations With a Spherical Lens. J Refract Surg. 2025 May;41(5):e481-e491. doi: 10.3928/1081597X-20250403-02. PMID: 40340676.
Computing...

Corneal Asphericity Variations: Impact on Aberrations, Vergence and Depth of Focus

Explore how corneal asphericity (Q) variations impact optical aberrations, intrapupillary vergence distribution (induced multifocality), and useful depth of focus extension.

Created by Pr. Damien Gatinel to bridge theoretical optics with clinical applications in cataract & refractive surgery, and educate clinicians and researchers on the complex interplay between corneal asphericity, optical aberrations, and induced multifocality.

Surface Parameters

Flat meridian
Principal axis
Asphericity on A1
Steep meridian
Auto: A1+90°
Asphericity on A2

Post-op & Pupil

Target Q1
Target Q2
Optical zone

Computation & Optics

Grid precision
For PSF / TF
Key formulas
OPD (µm) = (ncornea−nair)·Δz(mm)·1000
Vrad (D) = −(1/(π·Rm2))·∂W/∂ρ  (limit ρ→0: −∂²W/∂r²)   |   VΔ (D) = −½·∇²W   (W in meters)
Δzsag(µm) = [zpost − zpre]·1000   (surfaces osculating at vertex)
Fcor = Fspec/(1 − d·Fspec) ;  Fspec = Fcor/(1 + d·Fcor)
Other Simulators Wavefront to Vergence