When designing a lens, cost and manufacturing concerns are extremely challenging, especially with radical optical designs. The tolerance process is the bridge between design and manufacturing. Three techniques which improve the interaction between lens design and engineers are successfully shown in this thesis along with implementation of these techniques. First, a method to accurately model optomechanical components within lens design is developed and implemented. Yield improvements are shown to increase by approximately 3% by modeling optomechanical components. Second, a method utilizing aberration theory is applied to discover potential tolerance sensitivity of an optical system through the design process. The use of aberration theory gives an engineer ways to compensate for errors. Third, a method using tolerance grade mapping is applied to error values of an optical system. This mapping creates a simplified comparison method between individual tolerances and lens designs.

The lens design is a fundamental but challenging problem, while modern lens design processes still follow the classic aberration optimization theory and need preliminary designs and experienced optical engineers to control the optimization process constantly. In this thesis, we develop a differentiable ray-tracing model and apply it to automatic lens design. Our method can do ray-tracing and render images with high accuracy, with the power to use the back-propagated gradient to optimize optical parameters. Different from traditional optical design, we propose to use the rendered images as the training criteria. The rendering loss shows superior results in optimizing lenses while also making the task easier. To remove the requirements of preliminary design and constant operations in conventional lens design, we propose a curriculum learning method that starts from a small aperture and field-of-view(FoV), gradually increases the design difficulty, and dynamically adjusts attention regions of rendered images. The proposed curriculum strategies empower us to optimize complex lenses from flat surfaces automatically. Given an existing lens design and setting all surfaces flat, our method can entirely recover the original design. Even with only design targets, our method can automatically generate starting points with flat surfaces and optimize to get a design with superior optical performance. The proposed method is applied to both spheric and aspheric lenses, both camera and cellphone lenses, showing a robust ability to optimize different types of lenses. In addition, we overcome the memory problem in differentiable rendering by splitting the differentiable rendering model into two sub-processes, which allows us to work with megapixel sensors and downstream imaging processing algorithms.

Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to the cosine-fourth-power radiometric law, image and pupil aberrations, and light vignetting also count. In this paper, we use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing.

QC 351 A7 no. 37 / This paper derives four one-parameter families of two-surface optical systems having the property that, relative to a well-defined pair of conjugate points, one finite and the other infinite, third-order spherical aberration is zero. The two surfaces can be either refracting or reflecting. Aperture planes are defined for which third-order astigmatism is zero. An expression for coma is also derived. Assuming that the systems will be constructible, a means of defining domains for the free parameter is indicated. Possible applications of these results to optical design are included.

QC 351 A7 no. 39 / Optical systems known as "null correctors" are often required to test certain aspheric optical surfaces. This report classifies these systems on the basis of their first -order geometry and analyzes the merits of each type. The behavior of optical aberrations, especially spherical aberration, in these systems is examined in the context of computer optimization techniques, particular attention being given to some design problems unique to null correcting systems. Orthonormal concepts are applied to the problem of reducing spherical aberration in null correctors. It is shown that exceedingly simple merit functions may be constructed to streamline the optimization process. These merit functions are composed of simple linear sums of the angular spherical aberration coefficients B1, B3, B5, and B7. Thus, minimizing the following sums will improve nearly diffraction - limited systems: ( - 13 B1 + 1 B3 - g' B5 - B7) , ( 4.131 - B3 - B5) , ( - 2B1 - B3) , and ( - B1) /1-5- 3/7 3 or ( 120 B3 + 960 B5 + 840 B7 ) , ( 840 B5 + 2520 B7) , and ( 840 B7) Non -diffraction - limited systems may be optimized by minimizing the sums ( 6 B3 + 5 B5 + 5 B7) , ( p B5 + 3 B7) , and ( 1 0 B7) To demonstrate the effectiveness of the techniques discussed, the process of designing a specific null correcting system is followed in detail.

Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to cosine-fourth-power radiometric law, image and pupil aberrations and light vignetting also count. We use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

Plenoptic cameras and Shack-Hartmann wavefront sensors are lenslet-based optical systems that do not form a conventional image. The addition of a lens array into these systems allows for the aberrations generated by the combination of the object and the optical components located prior to the lens array to be measured or corrected with post-processing. This dissertation provides a ray selection method to determine the rays that pass through each lenslet in a lenslet-based system. This first-order, ray trace method is developed for any lenslet-based system with a well-defined fore optic, where in this dissertation the fore optic is all of the optical components located prior to the lens array. For example, in a plenoptic camera the fore optic is a standard camera lens. Because a lens array at any location after the exit pupil of the fore optic is considered in this analysis, it is applicable to both plenoptic cameras and Shack-Hartmann wavefront sensors. Only a generic, unaberrated fore optic is considered, but this dissertation establishes a framework for considering the effect of an aberrated fore optic in lenslet-based systems. The rays from the fore optic that pass through a lenslet placed at any location after the fore optic are determined. This collection of rays is reduced to three rays that describe the entire lenslet ray set. The lenslet ray set is determined at the object, image, and pupil planes of the fore optic. The consideration of the apertures that define the lenslet ray set for an on-axis lenslet leads to three classes of lenslet-based systems. Vignetting of the lenslet rays is considered for off-axis lenslets. Finally, the lenslet ray set is normalized into terms similar to the field and aperture vector used to describe the aberrated wavefront of the fore optic. The analysis in this dissertation is complementary to other first-order models that have been developed for a specific plenoptic camera layout or Shack-Hartmann wavefront sensor application. This general analysis determines the location where the rays of each lenslet pass through the fore optic establishing a framework to consider the effect of an aberrated fore optic in a future analysis.

In this dissertation fully general conditions are presented to correct linear and quadratic field dependent aberrations that do not use any symmetry. They accurately predict the change in imaging aberrations in the presence of lower order field dependent aberrations. The definitions of the image, object, and coordinate system are completely arbitrary. These conditions are derived using a differential operator on the scalar wavefront function. The relationships are verified using ray trace simulations of a number of systems with varying degrees of complexity. The math is shown to be extendable to provide full expansion of the scalar aberration function about field. These conditions are used to guide the design of imaging systems starting with only paraxial surface patches, then growing freeform surfaces that maintain the analytic conditions satisfied for each point in the pupil. Two methods are proposed for the design of axisymmetric and plane symmetric optical imaging systems. Design examples are presented as a proof of the concept.

Purpose: traditional optical design is a numerical process based on ray tracing theory. The traditional method has the limitation of the application of the spectacle lens because of the necessity of initial configurations and the evaluations of the aberrations of the lens. This study is an initial attempt to investigate an analytic lens design method, Lagrange, which has a potential application in modern spectacle lens for eliminating the limitation of the traditional method. Methods: the Lagrange method can derive the differential equations of an optical system in term of its output and input. The generalized Snell???s law in three-dimensional space and the normal of a refracting surface in fundamental differential geometry are applied to complete the derivation. Based on the Lagrange method, the solution of a refracting surface to perfectly image a point at infinity is obtained. Results: a Plano-convex lens and a Bi-convex lens from this solution were designed. In spherical coordinates, the differential equations of the single surface system and its solution were obtained. The optical design software, ZEMAX, was used to simulate the lenses and evaluate their image qualities. The results illustrated that both of the two lenses were aberration free. Conclusions: the Lagrange solves unknown lens surface based on definable inputs and outputs according to customer requirements. The method has the potential applicants of the modern customized lens design. Moreover, the definable outputs make the simultaneous elimination of several aberrations possible.

We present a miniature camera lens design method that uses a freeform surface based on the pedal curve to the ellipse in polynomial form. Two designs are presented and their benefits of optical performance and tolerance sensitivity are compared to designs with conventional aspheric surfaces. We also reverse a freeform design using even aspherical surfaces to show that the optimization solution of a freeform design cannot be reproduced by even aspherical surfaces.