Evaluating rms spot radii by ray tracing

Three-dimensional ray-tracing model for the study of advanced refractive errors in keratoconus

We propose a numerical three-dimensional (3D) ray-tracing model for the analysis of advanced corneal refractive errors. The 3D modeling was based on measured corneal elevation data by means of Scheimpflug photography. A mathematical description of the measured corneal surfaces from a keratoconus (KC) patient was used for the 3D ray tracing, based on Snell's law of refraction. A model of a commercial intraocular lens (IOL) was included in the analysis. By modifying the posterior IOL surface, it was shown that the imaging quality could be significantly improved. The RMS values were reduced by approximately 50% close to the retina, both for on- and off-axis geometries. The 3D ray-tracing model can constitute a basis for simulation of customized IOLs that are able to correct the advanced, irregular refractive errors in KC.

Computational method for deriving the geometric point spread function of an optical system

The distribution of the ray density of the spot diagram formed in the image plane is called the geometric point spread function (PSF). It plays an important role in the image formation theory, since it describes the impulse response of an optical system to a source point. However, the literature contains very few techniques for deriving the PSF of optical systems. Accordingly, this study presents a method based on an irradiance model for computing the geometric PSF of an optical system by considering the energy conservation along a single light ray. It is shown that the proposed method obtains a reliable and accurate estimate of the PSF and enables the computation of the centroid and root-mean-square radius of the focus spot on the image plane. In addition, compared to existing ray-counting methods presented in the literature, in which the quality of the PSF solution depends on the number of rays traced and the grid size used to mesh the image plane, the proposed irradiance-based method requires just one tracing operation. Overall, the results presented in this study confirm that the proposed method provides an ideal solution for calculating the merit function and modulation transfer function of an optical system.

Analysis and design of optical systems by use of sensitivity analysis of skew ray tracing

Optical systems are conventionally evaluated by ray-tracing techniques that extract performance quantities such as aberration and spot size. Current optical analysis software does not provide satisfactory analytical evaluation functions for the sensitivity of an optical system. Furthermore, when functions oscillate strongly, the results are of low accuracy. Thus this work extends our earlier research on an advanced treatment of reflected or refracted rays, referred to as sensitivity analysis, in which differential changes of reflected or refracted rays are expressed in terms of differential changes of incident rays. The proposed sensitivity analysis methodology for skew ray tracing of reflected or refracted rays that cross spherical or flat boundaries is demonstrated and validated by the application of a cat's eye retroreflector to the design and by the image orientation of a system with noncoplanar optical axes. The proposed sensitivity analysis is projected as the nucleus of other geometrical optical computations.

Depth of focus of optical systems with a small amount of spherical aberration

The diffraction focus of optical systems with circular and annular exit pupils affected with primary, secondary and tertiary spherical aberration is calculated for some values of aberration coefficients and obscuration ratios. The depth of focus of these systems is also given.

Automatic design of optical systems using a set of general skew ray tracing formulas

A general equation of high-order surfaces is given. If its second term is equal to zero, this equation will automatically reduce to the conic surfaces. By adding two parameters g and k into the conic equation, we are able to use only one euqation to describe the planar, cylindrical, and conic surfaces. A set of skew ray tracing formulas for these surfaces, including tilted and decentered elements, is derived. The formulas analytical and easy to use. Based on the tracing of skew rays, a merit function of the optical system is defined and an analytical formula for determining the narrowest cross-sectional position of skew rays is given. A program of skew ray tracing is edited for the Sharp-1500 pocket computer. An example for a 2-D infrared scanner is given. Based on the skew ray tracing formulas and by using the damped least-squares method, some examples for automatic design of optical systems are also shown on the IBM PC/XT personal computer.