Optical: systems and elements – Methods
Reexamination Certificate
1999-03-01
2003-05-20
Chang, Audrey (Department: 2872)
Optical: systems and elements
Methods
C359S565000, C359S566000, C700S036000
Reexamination Certificate
active
06567226
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a method of designing a lens system or an optical system. Further, this invention relates to a design of diffractive optical elements.
2. Introduction
Design of a lens requires setting up equations defining the relations among optical parameters of the lens, solving the equations and obtaining solutions for determining the parameters. In many cases, the set of equations cannot be solved exactly, because some equations are non-linear or too complicated. The set of equations often leads to a plurality of solutions which contain errors. When the equations are solved, the solution must be estimated by some method, whether or not the solution is valid. A “merit function(or cost function)” is sometimes adopted for estimating the validity of the solution. The merit function is defined as a sum of squares of some errors, for example, a sum of position errors or wavefront errors at points in an imaging region. These errors, termed “aberration errors”, appear only in calculation. If aberration errors at individual points are smaller, the merit function is also smaller. Then, a smaller merit function means smaller errors in the solution as a whole. If the merit function is the smallest, the aberration errors should be the smallest. The parameters of lens assemblies or optics are designed by the merit function yielding the minimum value. The function can estimate the validity of the solution as designed parameters. The solutions yielding the merit function of minimum value should realize the most suitable parameters.
In addition to the aberration errors of the solution on the optical equations, production errors appear when the lens assemblies or optical parts are actually manufactured. Production errors hinder the manufacturer from making a lens or optical part having the exact parameters just given by the solution. A production error is defined to be a difference between the designed (calculated) value and the actual value of the product. For simplicity, the word “lens” is used to express both a “lens” and an “optical part” hereafter. A large production error degrades the produced lens and sometimes segregates the produced lens into a classification of inferior goods. Allowable scope of manufacturing errors is beforehand determined for satisfying the requisites for the lens. The maximum of an allowable production error is called “tolerance”. A large tolerance facilitates production; it is easier to manufacture a lens which is defined by parameters with bigger tolerances. A small tolerance imposes a heavy burden on the manufacturer; it is difficult to make a lens having designed parameters with small tolerances. Thus, tolerance is a measure of ease of production.
A solution gives a set of optimum values and tolerances of the parameters. Although a solution gives excellent performance to the lens having the exact parameters which are equal to the solution values, the solution is not necessarily the best solution. If the parameter tolerances of the solution are small, it is difficult to make lens having errors of parameters within tolerance. The performance of the lens which has parameters equal to the designed values is called the “best performance” for the solution. Even if a solution has an excellent and best performance, the solution is not an optimum solution if tolerances are narrow. People believe that the best solution is a solution which gives the highest performance to the product, but this is not necessarily true. If tolerances are small, production is difficult, even though the solution gives the best performance. The best solution is not the solution giving the best performance but should be the solution which gives “wide tolerances” as well as “best performance”. Wide tolerance is more important than best performance. A purpose of the present invention is to provide a method of designing lens assemblies or optical parts which gives parameters large tolerances for facilitating production.
Words are clarified by defining the exact meanings. There are various parameters which define lenses or optical parts. The parameters can be classified by two standpoints. One standpoint is classification into the parameters which are treated as variables in calculation seeking optimum designs for lenses and into the parameters which are treated as constant values in the same calculation. In the case of designing an optical system having a plurality of lenses, variable parameters are, e.g., the thicknesses of lenses, the curvatures of both surfaces of the lenses, and the distances between the lenses for which calculation is done for seeking optimum values which satisfy the required conditions. Other parameters are treated as constants keeping predetermined values in the calculation. For example, constant parameters are the distance between the light source and the lens, the thickness and the curvature (=0) of a window, the shape of some lenses and the distance between selected lenses. The physical constants, for instance, refractive index of lenses or dispersion are treated as constant parameters in the calculation, since they are previously determined by the materials of the lenses. The number of lenses is also a constant parameter, when the number is preliminary determined. The predetermined requirements assign some parameters either to variable parameters or constant parameters. Thus the number of lenses or the material of lenses can be a variable parameter in other case which allows the material and the number to change. Thus, the distinction between variable parameters and constant parameters is the first standpoint of classification.
The other classification of parameters is the parameters to which allocated-errors are given and the parameters to which allocated-errors are not given. The “allocated-error” is not a known concept but is a quite novel concept. The allocated-errors play a central role in the present invention. The classification of parameters by the allocated-error is a key idea of the invention. Above explanation of parameters clarifies the first classification into variable parameters and constant parameters and the second classification into error-allocated parameters and non-error-allocated error parameters. Another important distinction relates to the kinds of errors. There are three errors for a parameter: the first one is an aberration-error, the second is a production error, and the third an allocated-error.
All the parameters have production errors which are the deviations of parameters of the product from the parameters given by the solution. Production errors accompany both variable parameters and constant parameters. A solution gives optimum values for variable parameters, for instance, thicknesses of lenses, curvatures of surfaces and distances between lenses. When a manufacturer produces an optical part, the variable parameters deviate from the designed values. The deviations are the production errors of variable parameters.
Constant parameters which are preliminary determined are also suffering from production errors. Thus, there are extra parameters which exclusively denote production errors themselves. Wedge, decenter, tilt, surface irregularity, and refractive index non-uniformity(inhomogeneity) are the words signifying production errors which should be 0 in an ideal product. Design of lenses premises that the errors are 0. Then, these parameters can be named error parameters. Error parameters are defined as differences between constant parameters and the actual values of a product. Error parameters accompany not variable parameters but constant parameters. Wedge denotes an inclination between a front surface and a rear surface of a lens. Decenter means a vertical difference between central axes of lenses. Tilt is an inclination of a lens to a plane perpendicular to the axis. Surface irregularity is a deviation of a product surface from a designed surface. Non-uniformity of refractive index denotes the spatial fluctuation of refractive index of a lens. This invention in
Chang Audrey
Sumitomo Electric Industries Ltd.
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