Comprehensively characterizing ophthalmic freeform lenses with contour plots and astigmatic axis.

An accurate evaluation method is proposed for comprehensively characterizing ophthalmic freeform lenses (OFLs) by computing the curvatures of the freeform surface at an arbitrary direction in the transformed Cartesian coordinates based on space analytic geometry. The proposed method could especially produce the astigmatic axis, which is an indispensable characteristic of OFLs. An OFL designed with an analytical formula is characterized by our comprehensive method, not only with power and astigmatism contour plots that are consistent with the results from the conventional method, but also with the astigmatic axis, which can be analytically confirmed by combining a conventional quadratic equation with directional derivatives. Benefiting from the astigmatic axis, the comprehensive method could produce the combined astigmatism of both surfaces for double OFLs, which is not possible with the conventional method. The evaluation results of a double OFL are also presented and can be experimentally verified by fabrication and measurement. This might provide a new idea and a more comprehensive methodology for evaluatiing OFLs with high precision.

Simulation method for evaluating progressive addition lenses.

Since progressive addition lenses (PALs) are currently state-of-the-art in multifocal correction for presbyopia, it is important to study the methods for evaluating PALs. A nonoptical simulation method used to accurately characterize PALs during the design and optimization process is proposed in this paper. It involves the direct calculation of each surface of the lens according to the lens heights of front and rear surfaces. The validity of this simulation method for the evaluation of PALs is verified by the good agreement with Rotlex method. In particular, the simulation with a "correction action" included into the design process is potentially a useful method with advantages of time-saving, convenience, and accuracy. Based on the eye-plus-lens model, which is established through an accurate ray tracing calculation along the gaze direction, the method can find an excellent application in actually evaluating the wearer performance for optimal design of more comfortable, satisfactory, and personalized PALs.

Design of a freeform varifocal panoramic optical system with specified annular center of field of view.

A new zoom mechanism was proposed for the realization of a freeform varifocal panoramic annular lens (PAL) with a specified annular center of the field of view (FOV). The zooming effect was achieved through a rotation of the varifoal PAL around an optical axis, which is different from a conventional zooming method by moving lenses back and forth. This method solves the problem of FOV deviation from the target scope during the zooming process, since the optical axis was not taken as the zooming center of the FOV. The conical surface corresponding to a certain acceptance angle was specified as the annular center of the FOV, and it was adopted as the reference surface of zooming for the FOV. As an example, the design principle and optimization process of a freeform varifocal PAL was discussed in detail. The annular center of the FOV was specified at the acceptance angle of 90°. The absolute FOV in the direction of acceptance angles is relative to the specified annular center, with cosine deviation from ±20° at 0° rotational angle to ±10° at ±180° rotational angle on both sides around optical axis. An X-Y polynomial (XYP) was used for the representation of freeform surfaces for its simple form and convergence efficiency. The correction for irregular astigmatism and distortion and the position offset of an entrance pupil caused by an irregular aperture spherical aberration are also discussed. The results from the analysis of the modulus of the optical transfer function (MTF) and f-theta distortion show that the zooming method by a rotation of the varifocal freeform PAL is feasible.

Edge effect in fluid jet polishing.

The edge effect is one of the most important subjects in optical manufacturing. The removal function at different positions of the sample in the process of fluid jet polishing (FJP) is investigated in the experiments. Furthermore, by using finite-element analysis (FEA), the distributions for velocity and pressure of slurry jets are simulated. Experimental results demonstrate that the removal function has a ring-shaped profile, except for a little change in the size at the operated area even if the nozzle extends beyond the edge of the sample. FEA simulations reveal a similar distribution of velocity with a cavity resulting in the ring-shaped profile of material removal at different impact positions. To a certain extent, therefore, the removal function at the edge of the surface of the sample appears similar to that inside of it, so that the classical edge effect can be neglected in FJP.

Dwell function algorithm in fluid jet polishing.

Considering the special characteristics of the removal function with the ring-shaped profile in fluid jet polishing (FJP), we present an effective method called the discrete convolution algorithm to compute the dwell function for controlling the figuring process. This method avoids the deconvolution operation, which usually fails to converge. Then an experimental confirmation of FJP figuring was demonstrated by machining a one-dimensional depth profile on a flat sample. The profile was figured from 0.914lambda(lambda=632.8 nm) peak to valley (PV) to 0.260lambda. This experiment demonstrated the successful implementation of the algorithm to solve the dwell function in optical manufacturing.

Surface roughness and material removal in fluid jet polishing.

Based on experiments, the dependence of material removal and surface roughness on the characteristics of abrasive particles, on the workpiece, and on other process parameters such as working pressure and incidence angle in fluid jet polishing (FJP) technology were investigated. Experimental results show a volume removal rate that is approximately proportional to the square root of the Young's modulus (E) and inversely proportional to the square of the Knoop hardness (Hk) of glass. Similarly, surface roughness is also determined in FJP by elastic stiffness E and plastic parameter Hk. The influence of the incidence angle on surface roughness and material removal were studied, and a linear dependence of material removal on the working pressure was obtained. Further, it was found that an optical-quality surface can be achieved by use of Cerox 1650 abrasive particles in FJP and can satisfy the requirements of modern optical manufacturing.