We made an error of scale in section six of our paper [Opt. Eng., 57(10), 101704 (2018). doi: https://doi.org/10.1117/1.OE.57.10.101704] that resulted in an inappropriate comparison. After properly scaling and optimizing our three mirror telescope design the averaged over the field RMS spot size is 10.4 μm and this represents an improvement of about 26% and not of 40%. We find that the Zf(r) surfaces, the XY polynomial surfaces, and the NURBS surfaces are able to model the mirror system with similar RMS spot size performance.
A systematic method for the design of nonaxially symmetric optical systems is described. Free-form optical surfaces are constructed by superposition of a conic segment and a polynomial, and successfully applied to design relatively fast wide field-of-view optical systems.
Optical systems that do not have axial symmetry can provide useful and unique solutions to certain imaging problems. However, the complexity of the optical design task grows as the degrees of symmetry are reduced and lost: there are more aberration terms to control, and achieving a sharp image over a wide field-of-view at fast optical speeds becomes challenging. Plane-symmetric optical systems represent a large family of practical non-axially symmetric systems that are simple enough to be easily described and thus are well understood. Design methodologies and aberration theory of plane-symmetric optical systems have been discussed in the literature, and various interesting solutions have been reported [1-4]. The little discussed in the literature technique of confocal systems is effective for the design of unsymmetrical optics. A confocal unsymmetrical system is constructed in such a way that there is sharp image along a given ray (called the optical axis ray (OAR)) surface after surface. It is possible to show that such a system can have a reduced number of field aberrations, and that the system will behave closer to an axially symmetric system [5-6]. In this paper, we review a methodology for the design of unsymmetrical optical systems. We utilize an aspherical/freeform surface constructed by superposition of a conic expressed in a coordinate system that is centered on the off-axis surface segment rather than centered on the axis of symmetry, and an XY polynomial. The conic part of the aspherical/freeform surface describes the base shape that is required to achieve stigmatic imaging surface after surface along the OAR. The XY polynomial adds a more refined shape description to the surface sag and provides effective degrees of freedom for higher-order aberration correction. This aspheric/freeform surface profile is able to best model the ideal reflective surface and to allow one to intelligently approach the optical design. Examples of two- and threemirror unobscured wide field-of-view reflective systems are provided to show how the methods and corresponding aspheric/freeform surface are applied. We also demonstrate how the method can be extended to design a monolithic freeform objective.
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.
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.
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.
Optical systems can provide simultaneous imaging in several spectral bands and thus be much more useful. A new and current generation of focal plane arrays is allowing detection in more than one spectral region. The design of a refractive imaging lens for such detectors requires correcting chromatic aberrations over the wider range of wavelengths. However, the fewer available refracting materials, the material properties that change between the spectral bands, and the system transmission requirements make the design of such lenses particularly challenging. We present a dual-field zoom lens designed for a cooled detector sensing across short-wave infrared (SWIR) and midwave infrared (MWIR) spectral bands (continuous imaging for 1-5 μm). This zoom lens has a 75 mm focal length in the wide mode and a 250mm focal length in the narrow mode, and operates at f/4.7 in both discrete zoom positions. The lens is actively compensated to work in thermal environments from -20°C to +60°C. We discuss the optical design methodology, review the selection of materials and coatings for the optical elements, and analyze the transmission of the lens and optical performance. A prototype system has been manufactured and assembled. We validate our design with experimental data.
A compact multi-aperture lens system consists of separate units deployed on a bendable substrate. Each unit includes a fast lens and wobbling sensor which allow high resolution image over a limited field of view.
Ray tracing methods for correcting chromatic aberration of imaging system are described. Monochromatic and chromatic aberration correction is separated into two independent problems. A similar method is applied to athermalize an optical system.
In a lens system a temperature change has the effect of changing the index of refraction and the geometry of the lens
elements. In addition, after a temperature change the lens takes some time to stabilize. As a consequence the optical
properties of the nominal lens system change. We review the concepts of the opto-thermal coefficient and of the thermal
diffusivity, and provide a method for their rapid calculation in lens design software. We also provide tables of these
coefficients that are needed in a lens tolerancing analysis.
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