Sponsored by IOT
By Deborah Kotob, ABOM
When it comes to free-form personalized lenses, we hear “Trust the Computer,” which we do, because our proof is in the patient’s response; they love them. Still, we want a rudimentary understanding of how free-form technology works. In this article, we will pull back the curtain and learn about the process behind IOT’s Digital Ray-Path® foundational free-form personalization technology. The upcoming Part 12 will delve into how Digital Ray-Path 2 builds on the classic theory of oblique power error minimization.
The following information is from “Pushing the limits of geometry in lens personalization,” a white paper by Dr. José Alonso, Dr. Daniel Crespo, Carolina Gago, Eduardo Pascual and Dr. Eva Chamorro.
“The optimization of any optical system requires the formulation of a mathematical merit function. This function depends on the parameters describing both the optical system and the way it is used. Some of these parameters are fixed, and some are free. The objective of the optical designer is to find the values of the free parameters that provide the best possible system performance. The value of the merit function is given by a weighted sum of the optical aberrations of the system. To achieve the best lens performance optimization of the optical system means finding the values of the free parameters that make the value of the merit function minimal.” (Dr. Jose Alonso, et al.)
Fixed parameters (includes custom parameters): With the fixed parameters of prescription, the lens design computes target power values for all the considered gaze directions, the refractive index, the base curve, minimum thickness and custom parameters, i.e., frame dimensions, tilts, back vertex distance (BVD), working distance and pupil position.
Free parameters: Free parameters describe the free-form surface. Free parameter starting values are calculated. For example, a free parameter starting value for a single vision lens would describe the toric surface needed to produce paraxial lens power. A lens-eye system’s computer model, including viewing distance per gaze direction, is generated from the free parameter starting values. This model is used next to compute the oblique (wearer-perceived) power through ray tracing or wavefront tracing. The oblique dioptric power error is the difference between oblique powers and the lens eye system model’s target values. The merit function establishes the weighted sum of the oblique dioptric power error for all gaze directions. “An optimization algorithm will look for the set of parameters describing the free-form surface that will make the merit function minimal.” (Dr. Jose Alonso, et al.)
It’s an iterative process, and with each iteration, the optimization algorithm computes new oblique powers closer to the target power. Errors are reduced to minimal but not eliminated. “The sequence of oblique powers will follow a path in dioptric space that will end close to the target power. The paths may differ from one gaze direction to another, and they may follow complex trajectories in dioptric space. The computation method just described is represented in FIG. 1. The merit function involves the four steps bordered by the dashed line. The blue connectors form the loop known as minimization algorithm.” (Dr. Jose Alonso, et al.)
FIG. 2 Illustrates the workings of Digital Ray-Path. Optimization path followed by the oblique power corresponding to a single gaze direction. Each oblique power corresponds to one-step of the optimization algorithm. The optimization of the whole lens requires hundreds of these paths, one of them per gaze direction.
We pulled back the curtain and peeked into Digital Ray-Path’s workings, and we’ll do the same for the exciting breakthrough Digital Ray-Path 2 optimization technology in Part 12. The science, the brainpower behind free-form technology, leaves me in awe, as do the achievements in digital free-form design technology by IOT scientists and optical engineers. The steep rise in ECPs offering customized lenses to their patients is concurrent with increased trust and confidence in free-form customization quality. Thanks to the genius behind Digital Ray-Path and Digital Ray-Path 2 Technology, we can dispense lenses built on these technologies’ foundation with extreme confidence.