The Area under the Modulation Transfer Function (MTFa) and its relationship with the Visual Acuity

jose 10 January, 2022 14405 No Comments


The MTFa is an objective in vitro MFT-based metric to assess the optical quality of an intraocular lens: the larger the MTFa value, the better the IOL optical quality.

The MTF is a metric at single spatial frequency.

Figure 1. LuxSmart™ experimental Through-focus MTF at 50 cycles/mm1

And the MTFa is the area under the MTF curve calculated from 0 to 50 cycles/mm.

Figure 2. LuxSmart™ experimental Through-focus MTF for 2 mm pupil size for distance 0.0 D defocus (left) and intermediate +1.50 D defocus (right)1

Mathematically, the MTFa is calculated as the integral of the MTF curve in the spatial frequency (f) range of 0 to 50 cycles/mm.

Figure 3. LuxSmart™ experimental Through-focus MTFa and predicted defocus range1

Studies2,3,4 have shown high correlation between MTFa and clinical visual acuity, so that it can be used to predict the visual performance at different level of focus of pseudophakic patients.

For defocus values where the MTFa value is ≥ 12, the expected visual acuity would be around 0.2 logMAR (required for driving license).

For defocus values where the MTFa value is ≥ 20, the expected visual acuity would be around 0.0 logMAR.

So, in the example of Figure 3 of the LuxSmart™ premium IOL, we may predict around 2.3 D of useful range of vision with a visual acuity around 0.0 logMar for a pupil size of 2 mm. In the case of 3.0 mm pupil size we may predict a useful range of vision around 1.6 D and around 0.7 D for a pupil of 4.5 mm.

All measurements were made in agreement with the International Organization for Standardization (ISO) 11979-2 (2014) recommendations [ISO Standard].


  1. Comparative optical bench analysis of a new extended range of vision intraocular lens. Juan Antonio Azor, Fidel Vega, Jesus Armengol, Maria S. Millan Grupo de Optica Aplicada y Procesado de Imagen (GOAPI). Department of Optics and Optometry Universitat Politecnica de Catalunya BARCELONATECH
  2. Visual acuity of pseudophakic patients predicted from in-vitro measurements of intraocular lenses with different design. F. Vega et al. Biomed. Opt. Express 9, 4893-4906 (2018).
  3. Preclinical metrics to predict through-focus visual acuity for pseudophakic patients. A. Alarcon et al. Biomed. Opt. Express 7, 1877-1888 (2016).
  4. Equivalence of two optical quality metrics to predict the visual acuity of multifocal pseudophakic patients. J. Armengol et al. Biomed. Opt. Express 11, 2818-2829 (2020)

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