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Aug 11, 2011 · the aberrations. A typical GRIN lens has a parabolic re-fractive index distribution decreasing from the central axis to the circumference along the radius [5]. The para-bolic profile inherently possesses spherical and other types of aberration, and their magnitudes increase with the length and NA of the GRIN lens. Some types of the aberration ...
- Axial index profile:
- Generalized GRIN: what is the ray path through arbitrary n(r)?
- Hamiltonian Optics postulates
- Geometrical postulate:
- Dynamical postulate:
- The ray Hamiltonian
- Hamiltonian analogies: optics vs mechanics
fabrication by melding & grinding Stack Meld Grind & polish to a sphere Result: Spherical refractive surface with axial index profile n(z) Correction of spherical aberration by axial GRIN lenses aberrated corrected
material with variable optical “density” P’ light ray P “optical path length” Let’s take a break from optics ...
s: parameterization of the ray trajectory q(s): position vector for the ray trajectory at s; p(s): tangent vector to the ray trajectory at s s p(s) p(s) q(s+Δs) q(s) p(s+Δs) s ∇n(q) = low index n min = high index nmax
Rays are continuous and piecewise differentiable
Momentum changes along trajectory arc length in proportion to the local refractive index gradient These are the “equations of motion,” i.e. they yield the ray trajectories.
s: parameterization of the ray trajectory q(s): position vector for the ray trajectory at s; p(s): tangent vector to the ray trajectory at s s p(s) q(s+Δs) p(s) p(s+Δs) s ∇n(q) = low index n min = high index nmax The choice yields Therefore, the equations of motion become Since the ray trajectory satisfies a set of Hamil...
Hamiltonian of mechanical system physically allowable kinetic energy physically allowable refractive index
the worst aberrations in a GRIN lens arise from off axis aberrations, primarily astigmatism [4]. This astigmatism will decrease both resolution and multiphoton efficiency (brightness). Moving the objective over the region of interest may slightly improve the brightness of the ROI but will not recover the aberrations (see Figure 5).
Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material. Such gradual variation can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional spherical lenses. Gradient-index lenses may have a refraction ...
Jul 1, 2012 · Using ray tracing, Sivak and Kreuzer (1983) measured the degree of spherical aberration present in the lenses of a number of species including fish: goldfish C. auratus, yellow perch Perca flavescens and rock bass Ambloplites rupestris and showed that the GRIN profile minimised aberrations. Out of the three teleost lenses studied, the rock bass showed almost no spherical aberration, while the ...
- Barbara K. Pierscionek, Justyn Wiktor Regini
- 2012
Graded-index (GRIN) lenses serve as a key component for miniature endoscopes because of their small diameters and ease of assembly. However, the nonaplanatic nature of GRIN lenses causes inherent spatial aberrations that lower image resolution and sharpness. Here we present the diagnosis of the aberrations in GRIN probes and the use of adaptive optics to compensate for the wavefront errors in ...
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Sep 11, 2013 · The spherical aberration of the lens was estimated as a function of accommodation using the reconstructed GRIN and a homogeneous refractive index. Results: The lens anterior and posterior radii of curvature decreased with increasing lens power. Both surfaces exhibited negative asphericities in the unaccommodated state.
