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.

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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.

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.

In the aberration analysis of a circular wavefront, Zernike circle polynomials are used to obtain its wave aberration coefficients. To obtain these coefficients from the wavefront slope data, we need vector functions that are orthogonal to the gradients of the Zernike polynomials, and are irrotational so as to propagate minimum uncorrelated random noise from the data to the coefficients. In this paper, we derive such vector functions, which happen to be polynomials.