Optimizing the subjective depth-of-focus with combinations of fourth- and sixth-order spherical aberration

Abstract

We optimize the subjective depth of focus (DoF) with combinations of spherical aberration (SA4) and secondary spherical aberration (SA6) in various levels. Subjective DoF was defined as the visual interval for which three 20/50 high-contrast letters was perceived acceptable (objectionable blur limits). We used an adaptive optics system to dynamically correct the observer's aberrations and control their accommodation. DoF was measured with a 0.18-D step on three non-presbyopic subjects. The target seen by the subjects was modified to include 25 combinations of SA4 and SA6 (i.e. 0, ± 0.15 and ± 0.30 μm) for 3, 4.5 and 6mm of pupil diameter. We found a mean DoF of 1.97D with a 3mm pupil size, which decreased by 28% with a 4.5mm pupil and by 34% with a 6mm pupil. For 6mm pupil we found an increase of subjective DoF of 45% and 64% with the addition of 0.3 and 0.6 μm of SA4, and of 52% and 117% with the addition of 0.15 and 0.3 μm of SA6. The largest DoF measured (4.78D) increased 3.6 times that of the naked eye and was found for a combination of opposite signs of SA4 and SA6 of 0.6 and 0.3 μm respectively. Reducing the pupil size minimized the effect of aberrations on subjective DoF. Combination of SA4 and SA6 of opposite sign could increase DoF more than three times for pupils larger than 4.5mm. Subjective DoF is well predicted by measuring the induced variation of vergence arising in the pupil size.

Human eyes do not need monochromatic aberrations for dynamic accommodation

“…(compare Figure 5 against Figure 3 in17): that is, no statistical differences were found between conditions. Although there are studies that have shown that SA expands the depth of field,25, 26, 27 this effect did not seem to influence accommodation response gain in our subjects.…”

Subjective through-focus quality of vision with various versions of modified monovision

“…The amounts of SA4 and SA4+SA6 chosen in this study were based on data from a previous study by Benard et al 18 where the authors demonstrated that these amounts of 4th and combinations of 4th and 6th order spherical aberrations were the most effective to increase DoF while maintaining acceptable quality of vision.…”

Focus correction in an apodized system with spherical aberration

“…This relation has been studied recently by means of numerical calculations [10]. After the appropriated defocus correction, SA6 may flatten the wavefront generated by the opposite sign SA4, thus increasing the concentration of light in the image plane [25,26]. This effect may already be anticipated, taking into account the presence of SA4 and SA6 with the opposite sign in the definition of the Zernike's sixth-order SA polynomial (see Chapter 9 in [6]).…”

“…The extension of the through-focus curves may be related to this value. In this regard, some experimental studies have already been performed by inducing SA4 and SA6 in the form of the Zernike polynomials, Z 0 4 and Z 0 6 [25,26]. A recent experimental study has also shown the potential benefits of the apodization in the DoFi [36].…”