Stigmatic aspherical refracting surfaces from Cartesian ovoids.

A theory for Descartes ovoids has been developed in terms of four form parameters, (GOTS). This theory allows the design of optical imaging systems that, in addition to a rigorous stigmatism, exhibit the property of aplanatism, necessary for the proper imaging of extended objects. As a decisive step for the production of these systems, in this work, we propose a formulation of Descartes ovoids in the form of standard aspherical surfaces (ISO 10110-12: 2019), by means of explicit formulas for the corresponding aspheric coefficients. Thus, with these results, the designs developed with Descartes ovoids are finally translated into the language of aspherical surfaces for their production, inheriting the aspherical surfaces of all optical properties of Cartesian surfaces. Consequently, these results make this optical design methodology viable for the development of technological solutions using the current optical fabrication capabilities of the industry.

Hyperspectral camera as a compact payload architecture for remote sensing applications.

Monitoring and observation over the surface of the Earth have been a matter of global interest. In this path, recent efforts aim to develop a spatial mission to perform remote sensing applications. Mainly, CubeSat nanosatellites have emerged as a standard for developing low-weight and small-sized instruments. In terms of payloads, state-of-the-art optical systems for CubeSats are expensive and designed to work in general use cases. To overcome these limitations, this paper presents a 1.4 U compact optical system to acquire spectral images from a CubeSat standard satellite at the height of 550 km. To validate the proposed architecture, optical simulations using ray tracing simulation software are presented. Because the performance of computer vision tasks is highly related to data quality, we compared the optical system in terms of the classification performance on a real remote sensing application. The performances of the optical characterization and land cover classification show that the proposed optical system achieves a compact instrument, operating at a spectral range from 450 nm to 900 nm discretized on 35 spectral bands. The optical system has an overall f-number of 3.41 with a ground sampling distance of 52.8 m and a swath of 40 km. Additionally, the design parameters for each optical element are publicly available for validation, repeatability, and reproducibility of the results.

Achromatic stigmatism: achromatic Cartesian ovoid.

Monochromatic and chromatic aberrations are imaging defects mainly studied from a geometrical optics point of view. These defects are treated through optimization and minimization methods to achieve acceptable performance in optical imaging systems, where the correct choice of glass materials is one of the main challenges. The selection of glass materials is a complex issue that requires a large amount of computing power within sophisticated computational algorithms and enough professional experience in the area. However, in this work, we propose a new methodology to treat the chromatic and geometrical aberrations simultaneously by taking advantage of the relationship between form parameters of Cartesian surfaces and wavelength in the material. From this relationship, we obtain an achromatism principle that establishes the conditions for refracting systems to present a strictly achromatic stigmatism.

Rigorously aplanatic Descartes ovoids.

It is known that, besides being stigmatic, spherical refracting surfaces are aplanatic at their Young points since they satisfy the Abbe sine condition rigorously. The Abbe sine condition is commonly applied to different optical systems using numerical methods or optimization processes, obtaining a design of approximately aplanatic systems. Here, we found several families of Cartesian surfaces, whose sets of each of these families constitute exactly aplanatic systems free of spherical aberration and coma. So, studying the different types of systems, it is found that rigorous aplanatism occurs for objects and images on curved surfaces.

Aplanatism in stigmatic optical systems.

The minimization of spherical and coma aberrations in optical imaging systems is currently accomplished through the use of corrective aspheric optical surfaces. In this work, we develop a new, to the best of our knowledge, theory for the design of rigorously aplanatic optical systems, considering as a starting point the rigorous stigmatism theory of optical systems composed of Cartesian surfaces. The main characteristic of these surfaces is their, a priori, zero spherical aberration. In a general parametric formulation for systems made up of a set of these surfaces, the Abbe sine condition is adapted to simultaneously obtain the stigmatism and aplanatism conditions. Thus, we achieved the design of optical systems that in theory are immune to both coma and spherical aberrations.

Superconical aplanatic ovoid singlet lenses.

In this work, we return to Descartes's idea to develop a formalism to construct rigorously stigmatic singlet lenses comprising two Cartesian surfaces. Optical systems are built using a considerable number of spherical surfaces, presenting in most cases spherical aberration. Wasermann and Wolf proposed eliminating spherical aberration and minimizing third-order coma by using two adjacent aspherical surfaces. That is why, using a parametric formulation for Cartesian ovals, we propose the design of singlet lenses where the condition of rigorous stigmatism is guaranteed for each surface, and therefore, strictly speaking, in the pair of stigmatic points, the lens becomes an optical system free of spherical aberration. This formulation is unified to both refractive and reflective optical surfaces. Therefore, within the framework of the theory of rigorously stigmatic optical systems, making use of Cartesian surfaces for the construction of stigmatic ovoid singlet lenses, we achieve the same functionality of optical systems involving a set of spherical lenses. These lenses have the advantage of being formulated according to a generalized shape factor associated with the Coddington shape factor, allowing an easy classification of these stigmatic lenses. The ideal imaging is carried out by applying an exact ray-tracing method through these ovoid singlet lenses.