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Ocular aberrations as a function of wavelength in the near infrared measured with a femtosecond laser

Enrique J. Fernández, Angelika Unterhuber, Pedro M. Prieto, Boris Hermann, Wolfgang Drexler, and Pablo Artal

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Abstract

A compact mode-locked Ti:sapphire laser, emitting a broad spectrum of 277 nm bandwidth, centered at 790 nm, was used to measure the dependence of the aberrations of the human eye with wavelength in the near infrared region. The aberrations were systematically measured with a Hartmann-Shack wave-front sensor at the following wavelengths: 700, 730, 750, 780, 800, 850, 870 and 900 nm, in four normal subjects. During the measurements, the wavelengths were selected by using 10 nm band-pass filters. We found that monochromatic high order aberrations, beyond defocus, were nearly constant across 700 to 900 nm wavelength in the four subjects. The average chromatic difference in defocus was 0.4 diopters in the considered wavelength band. The predictions of a simple water-eye model were compared with the experimental results in the near infrared. These results have potential applications in those situations where defocus or higher order aberration correction in the near infrared is required. This is the case of many imaging techniques: scanning laser ophthalmoscope, flood illumination fundus camera, or optical coherence tomography.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Scheme of the experimental apparatus. The aberrations are measured by a Hartmann-Shack wave front sensor (HS) specifically designed for the human eye. The femtosecond mode-locked Ti:sapphire laser is coupled to the system through a 100-meters long fiber, preventing the existence of intensity peaks in the illumination beam. The different wavelengths in the NIR band are selected by means of a set of interference filters placed immediately behind the fiber’s collimator. See text for a more detailed description of the experimental system and its operation.

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Fig. 2.
Fig. 2. Color-coded representations of the ocular aberrations (up to 5th order, excluding defocus) over a 7 mm diameter pupil as a function of the illumination wavelength. Wavelengths were selected by means of interference filters of 10 nm band-width. For each subject, bottom-right panel corresponds to broad-band illumination (no interference filter).

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Fig. 3.
Fig. 3. Evolution of selected monochromatic aberrations (7 mm pupil size) as a function of wavelength. Squares: astigmatism; circles: coma aberration; and triangles: fourth order spherical aberration. The aberration estimates obtained for broad-band illumination are showed as larger points. The error bars show the standard deviation. The dashed lines correspond to the linear fit performed in each case.

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Fig. 4.
Fig. 4. RMS of the average ocular aberrations in the near IR band for each subject in a 7 mm pupil size. The defocus aberration was not included in the RMS. The dashed lines represent the linear fits. The obtained RMS when using the broad-band illumination (no interference filter) is showed with larger points for each subject.

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Fig. 5.
Fig. 5. Defocus (Zernike polynomial Z40, 7 mm pupil size) as a function of wavelength. The linear fits are presented as dashed lines in each case. Each curve is labeled with the obtained linear equation together with the r2 parameter. From top to bottom, the curves correspond to the subjects JOS, AUN, BHE and PPR. The error bars represent the standard deviation.

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Fig. 6.
Fig. 6. Average chromatic defocus (D) from all the subjects as a function of wavelength in the near IR range (solid circles). The dashed line shows the linear fit performed to the average values while the blue solid line represents the extended water-eye model (see the text for more details) in the considered band. The obtained equation and the r2 parameter from the calculated linear fit are also included on the figure. The error bars represent the standard deviation.

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Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Δ R = 0.0021 ( λ − 700 ) − 1.4341 ,
Δ R = n 0 − n ( λ ) r · n D ,
n ( λ ) = a + b ( λ − c ) .
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