Gradient-index Alvarez lenses: publisher's note.

This publisher's note contains a correction to Appl. Opt.62, 3485 (2023)APOPAI0003-693510.1364/AO.487089.

Gradient-index Alvarez lenses.

Gradient-index Alvarez lenses (GALs), a new, to the best of our knowledge, type of freeform optical component, are surveyed in this work for their unique properties in generating variable optical power. GALs display similar behavior to conventional surface Alvarez lenses (SALs) by means of a freeform refractive index distribution that has only recently been achievable in fabrication. A first-order framework is described for GALs including analytical expressions for their refractive index distribution and power variation. A useful feature of Alvarez lenses for introducing bias power is also detailed and is helpful for both GALs and SALs. The performance of GALs is studied, and the value of three-dimensional higher-order refractive index terms is demonstrated in an optimized design. Last, a fabricated GAL is demonstrated along with power measurements agreeing closely with the developed first-order theory.

Multi-material freeform gradient-index spectrometers.

With the advent of 3D printing optical elements, new techniques for manufacturing gradient-index (GRIN) optics have been realized that blend multiple materials in the deposition process. A method to achieve spectral splitting using multi-material GRIN optics is presented. The GRIN is additionally used to generate optical power, allowing for planar entrance and exit surfaces. It is shown that this simultaneous focusing and spectral splitting is not feasible with a two-material GRIN. A comparative design study is then conducted using three and four-material GRIN. A four-material design with optimized materials is also presented to showcase the potential for this new design form.

Achromatization of multi-material gradient-index singlets.

Recent advancements in additive manufacturing have enabled new methods of fabricating gradient-index (GRIN) optics by blending multiple materials in the deposition process. A design study highlighting the advantages of multi-material GRIN optics is presented. It is shown that additional materials in the GRIN allow for higher orders of color correction. A new multi-material refractive index representation, which constrains the GRIN to real materials, is also presented.

Freeform gradient index generalized Coddington's equations.

Coddington's equations and their generalized forms are useful for lens design and analysis of optical performance. Generalized Coddington's equations (GCE) exist in literature for analysis of decentered systems and freeform surfaces, but not for gradient index (GRIN) lenses. In this work, GCE are presented for the analysis of freeform GRIN lenses with freeform surfaces. Examples are shown where the presented theory converges on Coddington's equations and known paraxial GRIN behavior. The method also correctly shows known afocal behavior proximate to azimuthally directed rays in a cylindrical GRIN. The latter case is one of analytically validated local freeform behavior.

Replacing optical surfaces with gradient index functions which preserve ray trajectory.

Laws of reflection and refraction between homogeneous media and gradient index (GRIN) ray behavior are both derived from Fermat's principle. Design methods for GRIN can be difficult to analytically develop. This Letter proposes a foundation for complete replacement of refracting and total internally reflecting optical interfaces in existing designs with GRIN distribution. The proposed method can aid in incorporating GRIN into existing optical designs. Refraction in GRIN is specified to match the ray striking and leaving the optical interface in both position and angle. This result is shown for a collection of similar GRIN functions. One GRIN function is analyzed over a full space of attainable ray bend angles. A local arbitrarily oriented planar interface is replaced with GRIN distribution, and ray behavior is maintained.

Polychromatic annular folded lenses using freeform gradient-index optics.

The annular folded lens (AFL) is a design form offering large aperture, high-resolution imaging in a very axially compact package. The folded optic can be made monolithic for easier fabrication and alignment, yet the introduction of refractive surfaces with a dispersive optical material gives way to chromatic aberrations. AFL designs using homogeneous media are generally limited to the monochromatic regime, with polychromatic performance greatly reduced. By introducing freeform gradient-index (F-GRIN) media, monolithic AFL designs can achieve higher monochromatic performance as well as provide color correction for diffraction-limited polychromatic imaging. Monochromatic and polychromatic design methodologies are surveyed where the F-GRIN is constrained to remain feasible for fabrication.

Freeform gradient index progressive addition lens raytrace performance evaluation.

Raytrace evaluation capable of evaluating progressive addition lens (PAL) designs with freeform surface and gradient index (GRIN) contributions is presented. The method is validated on an analytically generated PAL start design and on optimized surface designs. Surface raytrace evaluations are compared with the surface-geometric evaluation commonly presented for freeform surface PAL designs. The evaluation is also tested on analytically generated freeform GRIN PAL designs with spherical and plano surfaces. The raytrace method agrees with the analytic performance and surface-geometric performance near the center of the lens and deviates at the edge of the lens, due to ray obliquity with the surfaces and aggregate contributions of surfaces and/or GRIN. These deviations are expected, as the raytrace model accounts for more physical contributions to optical performance, including pupil diameter and eye position. This raytrace method enables the evaluation of lens performance contributions other than from polished surfaces on homogeneous materials, enabling further exploration of GRIN in PAL designs.

Freeform gradient-index media: a new frontier in freeform optics.

Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.

Efficient representation of freeform gradient-index profiles for non-rotationally symmetric optical design.

Conventional optical designs with gradient index (GRIN) use rotationally-invariant GRIN profiles described by polynomials with no orthogonality. These GRIN profiles have limited effectiveness at correcting aberrations from tilted/decentered or freeform systems. In this paper, a three-dimensional orthogonal polynomial basis set (the FGRIN basis) is proposed, which enables the design of GRIN profiles with both rotational and axial variations. The FGRIN basis is then demonstrated via the design of a 3D GRIN corrector plate targeted to correct the rotationally-variant aberrations induced from a tilted spherical mirror. A sample corrector is manufactured and tested, showing significant correction of astigmatism. The FGRIN basis opens a new design space of 3D rotational variant GRIN profiles, which has the potential of replacing multiple freeform surfaces and simplifying complex systems.

Simultaneous interferometric measurement of linear coefficient of thermal expansion and temperature-dependent refractive index coefficient of optical materials.

Characterizing the thermal properties of optical materials is necessary for understanding how to design an optical system for changing environmental conditions. A method is presented for simultaneously measuring both the linear coefficient of thermal expansion and the temperature-dependent refractive index coefficient of a sample interferometrically in air. Both the design and fabrication of the interferometer is presented as well as a discussion of the results of measuring both a steel and a CaF2 sample.

Absolute thickness metrology with submicrometer accuracy using a low-coherence distance measuring interferometer.

Absolute physical thickness across the sample aperture is critical in determining the index of a refraction profile from the optical path length profile for gradient index (GRIN) materials, which have a designed inhomogeneous refractive index. Motivated by this application, instrumentation was established to measure the absolute thickness of samples with nominally plane-parallel surfaces up to 50 mm thick. The current system is capable of measuring absolute thickness with 120 nm (1σ) repeatability and submicrometer expanded measurement uncertainty. Beside GRIN materials, this method is also capable of measuring other inhomogeneous and opaque materials.