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.

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 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.

Design of two spherical mirror unobscured relay telescopes using nodal aberration theory.

Nodal aberration theory is used to calculate the third-order aberrations that result in image blur for an unobscured modified 4f relay (2f1 + 2f2) formed by two tilted spherical mirrors for objects at infinity (infinite conjugate) and near the front focal plane of the first mirror (finite conjugate). The field-averaged wavefront variance containing only non-rotationally symmetric aberration coefficients is then proposed as an optimization metric. Analytical and ray tracing optimization are demonstrated through sample designs. The particular cases of in-plane and orthogonal folding of the optical axis ray are discussed, followed by an analysis of a modified 2f1 + 2f2 relay in which the distance of the first mirror to the object or pupil is allowed to vary for aberration correction. The sensitivity of the infinite conjugate 2f1 + 2f2 relay to the input marginal ray angle is also examined. Finally, the optimization of multiple conjugate systems through a weighted combination of wavefront variances is proposed.

Biometry study of foveal isoplanatic patch variation for adaptive optics retinal imaging.

The change in ocular wavefront aberrations with visual angle determines the isoplanatic patch, defined as the largest field of view over which diffraction-limited retinal imaging can be achieved. Here, we study how the isoplanatic patch at the foveal center varies across 32 schematic eyes, each individualized with optical biometry estimates of corneal and crystalline lens surface topography, assuming a homogeneous refractive index for the crystalline lens. The foveal isoplanatic patches were calculated using real ray tracing through 2, 4, 6 and 8 mm pupil diameters for wavelengths of 400-1200 nm, simulating five adaptive optics (AO) strategies. Three of these strategies, used in flood illumination, point-scanning, and line-scanning ophthalmoscopes, apply the same wavefront correction across the entire field of view, resulting in almost identical isoplanatic patches. Two time-division multiplexing (TDM) strategies are proposed to increase the isoplanatic patch of AO scanning ophthalmoscopes through field-varying wavefront correction. Results revealed substantial variation in isoplanatic patch size across eyes (40-500%), indicating that the field of view in AO ophthalmoscopes should be adjusted for each eye. The median isoplanatic patch size decreases with increasing pupil diameter, coarsely following a power law. No statistically significant correlations were found between isoplanatic patch size and axial length. The foveal isoplanatic patch increases linearly with wavelength, primarily due to its wavelength-dependent definition (wavefront root-mean-squared, RMS <λ/14), rather than aberration chromatism. Additionally, ray tracing reveals that in strongly ametropic eyes, induced aberrations can result in wavefront RMS errors as large as λ/3 for an 8-mm pupil, with implications for wavefront sensing, open-loop ophthalmic AO, spectacle prescription and refractive surgery.

Miniature varifocal objective lens for endomicroscopy.

A miniature catadioptric lens for endoscopic imaging based on the principle of wavelength division multiplexing is presented. We demonstrate change of the magnification and the field of view (FOV) of the lens without any mechanical adjustment of the optical elements. The lens provides magnifications of ~-1.5× at 406-750 nm and ~-0.2× at 800 nm. The lens is used to demonstrate large-FOV (1.3 mm) reflectance imaging and high-resolution (0.57 µm) multiphoton fluorescence imaging of unstained mouse tissues.

Long eye relief fundus camera and fixation target with partial correction of ocular longitudinal chromatic aberration.

A combined 32° full field of view refractive fundus camera and fixation target with a -20 to +10 diopter sphere correction range is described and demonstrated. The optical setup partially corrects the average longitudinal chromatic aberration and spherical aberration of the human eye, while providing a long eye relief to allow integration with reflective adaptive optics ophthalmoscopes, as a viewfinder. The fundus camera operates with 940 nm light, using a maximum 2.9 mm diameter imaging pupil at the eye. The fixation target uses a light projector capable of delivering red, green and/or blue spatially and temporally modulated stimuli to the retina. The design and performance of each sub-system are discussed, and retinal imaging at various wavelengths is demonstrated.

Reflectance confocal endomicroscope with optical axial scanning for in vivo imaging of the oral mucosa.

This paper presents the design and evaluation of a reflectance confocal laser endomicroscope using a miniature objective lens within a rigid probe in conjunction with an electrically tunable lens for axial scanning. The miniature lens was characterized alone as well as in the endoscope across a 200 µm axial scan range using the tunable lens. The ability of the confocal endoscope to probe the human oral cavity is demonstrated by imaging of the oral mucosa in vivo. The results indicate that reflectance confocal endomicroscopy has the potential to be used in a clinical setting and guide diagnostic evaluation of biological tissue.

Dual modality endomicroscope with optical zoom capability.

We present a miniature endomicroscope that combines large field-of-view (FOV) (1.15 mm) reflectance imaging with high-resolution (~0.5 µm) multiphoton intrinsic fluorescence imaging. We acquired in vivo and ex vivo images of unstained normal and tumor-laden tissues by using the large-FOV mode to navigate to the site of interest and then switching to the high-resolution modality to resolve cellular details.