Experimental investigation in nodal aberration theory (NAT) with a customized Ritchey-Chrétien system: third-order coma

Nodal aberration theory (NAT) describes the aberration properties of optical systems without symmetry. NAT was fully described mathematically and investigated through real-ray tracing software, but an experimental investigation is yet to be realized. In this study, a two-mirror Ritchey-Chrétien telescope was designed and built, including testing of the mirrors in null configurations, for experimental investigation of NAT. A feature of this custom telescope is a high-precision hexapod that controls the secondary mirror of the telescope to purposely introduce system misalignments and quantify the introduced aberrations interferometrically. A method was developed to capture interferograms for multiple points across the field of view without moving the interferometer. A simulation result of Fringe Zernike coma was generated and analyzed to provide a direct comparison with the experimental results. A statistical analysis of the measurements was conducted to assess residual differences between simulations and experimental results. The interferograms were consistent with the simulations, thus experimentally validating NAT for third-order coma.

Theory of aberration fields for general optical systems with freeform surfaces

This paper utilizes the framework of nodal aberration theory to describe the aberration field behavior that emerges in optical systems with freeform optical surfaces, particularly φ-polynomial surfaces, including Zernike polynomial surfaces, that lie anywhere in the optical system. If the freeform surface is located at the stop or pupil, the net aberration contribution of the freeform surface is field constant. As the freeform optical surface is displaced longitudinally away from the stop or pupil of the optical system, the net aberration contribution becomes field dependent. It is demonstrated that there are no new aberration types when describing the aberration fields that arise with the introduction of freeform optical surfaces. Significantly it is shown that the aberration fields that emerge with the inclusion of freeform surfaces in an optical system are exactly those that have been described by nodal aberration theory for tilted and decentered optical systems. The key contribution here lies in establishing the field dependence and nodal behavior of each freeform term that is essential knowledge for effective application to optical system design. With this development, the nodes that are distributed throughout the field of view for each aberration type can be anticipated and targeted during optimization for the correction or control of the aberrations in an optical system with freeform surfaces. This work does not place any symmetry constraints on the optical system, which could be packaged in a fully three dimensional geometry, without fold mirrors.

Assembly of a freeform off-axis optical system employing three φ-polynomial Zernike mirrors

We report on the assembly of an off-axis reflective imaging system employing freeform, φ-polynomial optical surfaces. The sensitivity of the system to manufacturing errors is studied for both a passive and active alignment approach. The as-built system maintains diffraction-limited performance in the long-wave infrared.

Interferometric measurement of a concave, φ-polynomial, Zernike mirror

We report on the surface figure measurement of a freeform, φ-polynomial (Zernike) mirror for use in an off-axis, reflective imaging system. The measurement utilizes an interferometric null configuration that is a combination of subsystems each addressing a specific aberration type, namely, spherical aberration, astigmatism, and coma.

Extending nodal aberration theory to include mount-induced aberrations with application to freeform surfaces

This paper introduces the path forward for the integration of freeform optical surfaces, particularly those related to φ-polynomial surfaces, including Zernike polynomial surfaces, with nodal aberration theory. With this formalism, the performance of an optical system throughout the field of view can be anticipated analytically accounting for figure error, mount-induced errors, and misalignment. Previously, only misalignments had been described by nodal aberration theory, with the exception of one special case for figure error. As an example of these new results, three point mounting error that results in a Zernike trefoil deformation is studied for the secondary mirror of a two mirror and three mirror telescope. It is demonstrated that for the case of trefoil deformation applied to a surface not at the stop, there is the anticipated field constant contribution to elliptical coma (also called trefoil) as well as a newly identified field dependent contribution to astigmatism: field linear, field conjugate astigmatism. The magnitude of this astigmatic contribution varies linearly with the field of view; however, it has a unique variation in orientation with field that is described mathematically by a concept that is unique to nodal aberration theory known as the field conjugate vector.

A new family of optical systems employing φ-polynomial surfaces

Unobscured optical systems have been in production since the 1960s. In each case, the unobscured system is an intrinsically rotationally symmetric optical system with an offset aperture stop, a biased input field, or both. This paper presents a new family of truly nonsymmetric optical systems that exploit a new fabrication degree of freedom enabled by the introduction of slow-servos to diamond machining; surfaces whose departure from a sphere varies both radially and azimuthally in the aperture. The benefit of this surface representation is demonstrated by designing a compact, long wave infrared (LWIR) reflective imager using nodal aberration theory. The resulting optical system operates at F/1.9 with a thirty millimeter pupil and a ten degree diagonal full field of view representing an order of magnitude increase in both speed and field area coverage when compared to the same design form with only conic mirror surfaces.

Airy beams: a geometric optics perspective

Theoretically formulated in the 1970s within the context of nonrelativistic quantum mechanics, Airy beams have been experimentally realized for the first time only recently, paving the way to innovative optical techniques. While their remarkable features, a non-diffracting property and a transverse shift of the intensity maximum during propagation, are currently theoretically described from the wave optics viewpoint, here their exact relation to rays and geometric wavefront aberrations is revealed using a wavefront family that includes two-dimensional Airy beams. Several members of this family are computationally and experimentally implemented here. The lateral shift of Airy beams during propagation is presented in the context of the three-dimensional caustic representation. This new description allows re-emphasizing the use of "Airy-like" beams in computational imaging for depth of focus extension.