Eva Acosta

Improved phase imaging from intensity measurements in multiple planes

Problems stemming from quantitative phase imaging from intensity measurements play a key role in many fields of physics. Techniques based on the transport of intensity equation require an estimate of the axial derivative of the intensity to invert the problem. Derivation formulas in two adjacent planes are commonly used to experimentally compute the derivative of the irradiance. Here we propose a formula that improves the estimate of the derivative by using a higher number of planes and taking the noisy nature of the measurements into account. We also establish an upper and lower limit for the estimate error and provide the distance between planes that optimizes the estimate of the derivative.

Modified point diffraction interferometer for inspection and evaluation of ophthalmic components

We demonstrate that a modified point diffraction interferometer can be used to measure the power distribution of different kinds of ophthalmic lenses such as spectacles, rigid and soft contact lenses, progressive lenses, etc. The relationship between the shape of the fringes and the power characteristics of the component being tested is simple and makes the design a very convenient and robust tool for inspection or quality control. Some simulations based on the Fresnel approximation are included.

Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens

We present an iterative tomographic algorithm to reconstruct refractive-index profiles for meridional planes of the lens of the spherical fish eye from measurements of deflection angles of refracted rays. Numerical simulations show that the algorithm allows accuracy up to the fourth decimal place, provided that the refractive index can be regarded as an analytical function of the radial coordinate and the experimental errors are neglected. An experimental demonstration is given by applying the algorithm to retrieve the refractive-index profile of a spherical fish lens. The method is conceptually simple and does not require matching of the index of the surrounding medium to that of the surface of the lens, and the related iterative algorithm rapidly converges.

Variable aberration generators using rotated Zernike plates

The rotational properties of Zernike polynomials allow for an easy generation of variable amounts of aberration using two rotated phase plates, each one encoding one or several Zernike modes. This effect may be used to build variable aberration generators useful for calibrating different kinds of aberrometer.

Determination of phase mode components in terms of local wave-front slopes: an analytical approach.

An analytical formulation that relates the modal expansion coefficients of a given wave front to its local transverse phase derivatives is proposed. The modal coefficients are calculated as a weighted integral over the wave-front slopes. The weighting functions for each mode are the components of a two-dimensional vector whose divergence equals the corresponding mode function. This approach is useful for analytical phase reconstruction from the input data provided by shearing interferometers or Hartmann-Shack wave-front sensors. Numerical results for a simulated experiment in terms of a set of Zernike polynomials are given.

Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens

In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.

Performance analysis of curvature sensors: optimum positioning of the measurement planes

Curvature sensors are used to measure wave-front aberrations in a number of different applications ranging from adaptive optics to optical testing. In practice, their performance is limited not only by the quality of the detector used for irradiance measurements but also by the separation between measurement planes used for the calculation of the axial derivative of intensity. This work resolves the problem of determining the separation between intensity measurement planes thus optimizing the variance in experimental measurements. To do this, the variance of the local curvature of the phase will be analyzed as a function of the noise level in the measurements and the separation between planes. Moreover, error bounds will be established for experimental measurements.

Paraxial Propagation of Astigmatic Wavefronts in Optical Systems by an Augmented Stepalong Method for Vergences

Purpose. The propagation of astigmatic wavefronts through astigmatic optical systems is reconsidered in the wavefront perspective. Methods. The stepalong method for vergences, described by 2 × 2 matrices, is applied and augmented to produce off-axis information like the magnification. This so-called augmented stepalong method (ASAM) is derived by applying the paraxial propagation of astigmatic wavefronts to tilted wavefronts as well. Results. The features of the ASAM are discussed for a single surface, a thick lens, and a general system. Conclusions. The ASAM provides all necessary information to describe a centered astigmatic optical system in paraxial approximation.

Analysis of the optical properties of crystalline lenses by point-diffraction interferometry.

Purpose:  To show the feasibility of modified point‐diffraction interferometry for the qualitative analysis and accurate quantification of phase aberrations of eye lenses in vitro.

Minimum-variance phase reconstruction from Hartmann sensors with circular subpupils

Analytical expressions for the minimum-variance phase reconstructor for Hartmann sensors with circular subpupils are presented in this work. The approach assumes a wavefront expansion in terms of orthogonal Zernike polynomials, and takes advantage of the a priori knowlegde of the phase correlation function associated to phase distortions produced by atmospheric turbulence with Kolmogorov statistics.