Derivation of the propagation equations for higher order aberrations of local wavefronts.

From the literature the analytical calculation of local power and astigmatism of a wavefront after refraction and propagation is well known; it is, e.g., performed by the Coddington equation for refraction and the classical vertex correction formula for propagation. Recently the authors succeeded in extending the Coddington equation to higher order aberrations (HOA). However, equivalent analytical propagation equations for HOA do not exist. Since HOA play an increasingly important role in many fields of optics, e.g., ophthalmic optics, it is the purpose of this study to extend the propagation equations of power and astigmatism to the case of HOA (e.g., coma and spherical aberration). This is achieved by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically the aberrations of a propagated wavefront directly from the aberrations of the original wavefront containing both low-order and high-order aberrations.

Single dispersive gradient-index profile for the aging human lens.

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.

Design of an interferometric system for the measurement of phasing errors in segmented mirrors.

One of the new problems that has to be solved for segmented mirrors is related to periodic phasing, because for such mirrors to exhibit diffraction-limited performance the segments have to be positioned with an accuracy of a fraction of a wavelength. We describe the optical design of an instrument that measures the phasing errors (i.e., tip, tilt, and piston) between two segments under daylight conditions. Its design is based on a high-aperture white-light Michelson interferometer. It was developed at the Center for Sensors, Instruments and Systems Development (CD6) of the Technical University of Catalunya, Spain, and its final testing was carried out on the Gran Telescopio Canarias test workbench.