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We discuss oblique spherical aberration, its balance, and its control. Several ways to mitigate this aberration are listed and some lens design examples are presented. The variation of oblique spherical aberration as a function of index of refraction and the shape factor of a thin lens is also presented. It is argued that controlling the amount and distribution of spherical aberration propagating in a lens system can be an important mechanism for mitigating oblique spherical aberration. The control of oblique spherical aberration is illustrated with a double Gauss lens, with lenses for microlithography, and with a lens for mobile phones. [ABSTRACT FROM AUTHOR]

Two-mirror telescopes possess an agreeable tradeoff between performance and complexity that suits the needs of many scientific tasks, and recent developments in manufacturing technology have enabled unobscured two-mirror designs with freeform surfaces. We illustrate how structural aberration coefficients reveal the fundamental aberration characteristics of such systems and provide a summary table of general solutions that prescribe freeform surface shapes and tilts. Two unobscured design forms with remarkable aberration cancellation, inspired by well-known on-axis anastigmatic solutions, are presented. [ABSTRACT FROM AUTHOR]

Linear astigmatism aberration is undesirable because it rapidly degrades image quality. We discuss some techniques to control and mitigate this aberration, and provide a comparison of lens systems that have been desensitized for linear astigmatism aberration. [ABSTRACT FROM AUTHOR]

We provide an overview of the method of confocal mirror design and report advances with respect to pupil imagery. Two real ray-based conditions, Yþ = -Y- and ΔY = 0, for the absence of linear astigmatism and field tilt are presented. One example illustrates the design of a system confocal of the object and image, and another illustrates the design of a system confocal of the pupils. Stop shifting formulas are provided. Three threemirror anastigmatic systems further illustrate the method. [ABSTRACT FROM AUTHOR]

Freeform imaging systems are a subject of current interest. To aid in the design of such systems, we introduce structural aberration coefficients for plane symmetric imaging with XY-polynomial freeform surfaces that may also be tilted. Further, we extend the coefficients to systems with an arbitrary number of components and specifically provide analytical equations for two-mirror systems. Distinguishing between system configuration and structural parameters enhances clarity, which we highlight by deriving new conditions for minimum root-mean-square (RMS) spot size and minimum RMS wavefront error in aplanatic two-mirror telescopes. [ABSTRACT FROM AUTHOR]

A simple and accurate method for determining the focal length of a lens is presented. There is no need to know the distance between lens principal planes and can be performed with easily available and inexpensive hardware. Depending on the test lens (TL) f-number, the error on determining focal length can be in the order of 0.1% of the focal length. We discuss determining focal length with the Newton equation f2 = zz ′ , with the Bessel equation f = ((L − PP)2 − D2) / 4 (L − PP) , with equation f2 = y ′ (y + y ′ ) , or with equation f = (y2 − PP2) / 4PP. [ABSTRACT FROM AUTHOR]

We present an optical surface in closed form that can be used to design lenses for controlling relative illumination on a target surface. The optical surface is constructed by rotation of the pedal curve to the ellipse about its minor axis. Three renditions of the surface are provided, namely as an expansion of a base surface, and as combinations of several base surfaces. Examples of the performance of the surfaces are presented for the case of a point light source. [ABSTRACT FROM AUTHOR]

A split doublet is more sensitive to aberration because the inner surfaces are typically strong in curvature and can independently misalign. To improve the centering of a lens element, we discuss using a strip of material inserted in the gap between the lens edge and the barrel. This technique has the benefit of relaxing the barrel inner diameter tolerance. Four examples are provided where lens centering was estimated to range between 0.025 and 0.050 mm. [ABSTRACT FROM AUTHOR]

We show that aberration sensitivities are independent of lens scaling when the perturbation amount is kept the same. This behavior is in agreement with the results of actual calculation. Further, we point out that aberration sensitivities scale in the same way as aberration scale as a function of the lens field of view and aperture. [ABSTRACT FROM AUTHOR]

Polarization aberrations by highlighting the concepts of polarization aberration fields and of wavefronts of two sheets are explained. The fields have a vector character and are derived from the aberration function of plane symmetric systems. It is shown that in the presence of retardance, an incoming optical field is split into two fields and therefore one can speak of wavefronts of two sheets. Both concepts, polarization aberration fields and wavefronts of two sheets, ease the understanding of polarization aberrations. [ABSTRACT FROM AUTHOR]

The correction of chromatic aberrations is typically performed using aberration formulas or by using real ray tracing. While the use of aberration formulas might be effective for some simple optical systems, it has limitations for complex and fast systems. For this reason chromatic aberration correction is usually accomplished with real ray tracing. However, existing optimization tools in lens design software typically mix the correction of monochromatic and chromatic aberrations by construction of an error function that minimizes both aberrations at the same time. This mixingmakes the correction of one aberration type dependent on the correction of the other aberration type. We show two methods to separate the chromatic aberrations correction of a lens system. In the first method we use forward and reverse ray tracing and fictitious nondispersive glasses, to cancel themonochromatic aberrationcontent and allow the ray tracing optimization to focus mainly on the color correction. On the second method we provide the algorithm for an error function that separates aberrations. Furthermore, we also demonstrate how these ray tracing methods can be applied to athermalize an optical system. We are unaware that these simple but effective methods have been already discussed in detail by other authors. [ABSTRACT FROM AUTHOR]

Using polarization fields, light interference figures and isogyres of some uniaxial and biaxial birefringent optical elements are modeled. The effects of diattenuation, and linear and circular birefringence are included, and the Airy spiral is displayed for various cases. The two branches of the Airy spiral are shown to separate and surround separately the melatopes in the case of biaxial elements with linear and circular birefringence. A connection and discussion with the aberration field of astigmatism, in particular binodal, is presented. [ABSTRACT FROM AUTHOR]

We propose a high-speed surface profiler using a modified Fourier transform profilometry (FTP) approach. Our system geometry is different from a conventional profiler in that the fringe-projection lens and the imaging lens are at different heights from a reference plane. FTP computer simulation and experimental data are provided that supports our theoretical development. Our profiler provides a 1σ rms error of about 4 μm for an integrated circuit chip sample in an area of 14 mm × 6.5 mm with a 0.13 second data acquisition time. It is shown that our theoretical derivation is suitable for a micrometer scale object measurement. [ABSTRACT FROM AUTHOR]