Spherical Optics Research Articles

Seidel aberrations in grating pulse stretchers.

We derived a formula for calculation of the spectral phase of ultrashort pulses propagating through aberrated stretchers. Our approach is based on Seidel aberration theory. The dependence of spectral phase dispersion terms and residual angular dispersion on the individual Seidel aberration coefficients is found. As an example, the spectral phase deviation and the residual angular dispersion of an ultrashort pulse for the Martinez/Banks stretcher using spherical optics is calculated.

Research on laser-induced damage resistance of fused silica optics by the fluid jet polishing method.

Laser-induced damage threshold (LIDT) is one important evaluation index for optical glasses applied in large laser instruments which are exposed to high light irradiation flux. As a new kind of precise polishing technology, fluid jet polishing (FJP) has been widely used in generating planar, spherical, and aspherical optics with high-accuracy surfaces. Laser damage resistances of fused silica optics by the FJP process are studied in this paper. Fused silica samples with various FJP parameters are prepared, and laser damage experiments are performed with 351 nm wavelength and a 5.5 ns pulse width laser. Experimental results demonstrate that the LIDT of the samples treated with FJP processes did not increase, compared to their original state. The surface quality of the samples is one factor for the decrease of LIDT. For ceria solution polished samples, the cerium element remaining is another factor of the lower LIDT.

Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres.

Convergent Polishing is a novel polishing system and method for finishing flat and spherical glass optics in which a workpiece, independent of its initial shape (i.e., surface figure), will converge to final surface figure with excellent surface quality under a fixed, unchanging set of polishing parameters in a single polishing iteration. In contrast, conventional full aperture polishing methods require multiple, often long, iterative cycles involving polishing, metrology and process changes to achieve the desired surface figure. The Convergent Polishing process is based on the concept of workpiece-lap height mismatch resulting in pressure differential that decreases with removal and results in the workpiece converging to the shape of the lap. The successful implementation of the Convergent Polishing process is a result of the combination of a number of technologies to remove all sources of non-uniform spatial material removal (except for workpiece-lap mismatch) for surface figure convergence and to reduce the number of rogue particles in the system for low scratch densities and low roughness. The Convergent Polishing process has been demonstrated for the fabrication of both flats and spheres of various shapes, sizes, and aspect ratios on various glass materials. The practical impact is that high quality optical components can be fabricated more rapidly, more repeatedly, with less metrology, and with less labor, resulting in lower unit costs. In this study, the Convergent Polishing protocol is specifically described for fabricating 26.5 cm square fused silica flats from a fine ground surface to a polished ~λ/2 surface figure after polishing 4 hr per surface on a 81 cm diameter polisher.

Spherical lens optics applied to retrodirective reflection

THIS PAPER DESCRIBES SOME EXPEDIENT APPLICATIONS OF ELEMENTARY OPTICAL PRINCIPLES TO THE EVALUATION OF GLASS-BEAD REFLECTORIZING SYSTEMS FOR HIGHWAY SIGNS AND MARKERS. THE OPTICAL FUNCTION OF SPHERICAL LENSES IN ACHIEVING REFLEX REFLECTION IS ILLUSTRATED BOTH PHOTOGRAPHICALLY AND DIAGRAMMATICALLY. VARIOUS OPTICAL DESIGNS ARE DISCUSSED AND ANALYZED. BY SIMPLE GEOMETRIC OPTICS, THE EFFICIENCY OF THESE SYSTEMS IS CORRELATED WITH THE PRACTICAL PERFORMANCE CRITERIA FOR RETRODIRECTIVE REFLECTORIZATION. /AUTHOR/

Effect of an aspheric intraocular lens on the ocular wave‐front adjusted for pupil size and capsulorhexis size

To compare the ocular wave-front of eyes with silicone Intraocular lens (IOLs) with aspheric and spherical optics after cataract surgery, taking into account the patient's pupil size under reading conditions and after pupil dilatation. In this institutional prospective, randomized, controlled, patient and examiner masked, bilateral trial with intra-individual comparison, 60 eyes of 30 patients with bilateral age-related cataract were included. Each patient received a spherical IOL (CeeOn Edge, 911A, AMO, Santa Ana, CA, USA) in one eye and an aspheric IOL (Tecnis, Z9000, AMO) in the contra-lateral eye. Exclusion criteria were other ocular pathologies, capsular changes or zonular weakness. The main outcome variable was spherical aberration of the ocular wave-front under mesopic pupil conditions measured 2 years after surgery. Additional outcome variables were visual acuity and photopic and mesopic contrast sensitivity. There was no significant difference in visual acuity between the two IOL types under physiological pupil conditions and also not after pupil dilation. However, spherical aberrations were significantly lower with the aspheric IOL (SA: spherical 0.38 μm, SD: 0.11 μm; aspheric 0.10 μm, SD: 0.13 μm; p < 0.01), and there was a significant difference in contrast sensitivity at 12 cycles/degree. This is the first randomized and masked trial on visual function and ocular wave-front after implantation with this silicone aspheric IOL, taking the patients' own pupil size into account. The effect on visual function was detectable for mesopic contrast sensitivity, but there was no difference in visual acuity. The SA was found to be significantly lower under physiological pupil conditions as well as when recalculated for the rhexis size and under pharmacological dilatation.

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light. We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light.We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

Wavefront-Guided Scleral Lens Prosthetic Device for Keratoconus

To investigate the feasibility of correcting ocular higher order aberrations (HOAs) in keratoconus (KC) using wavefront-guided optics in a scleral lens prosthetic device (SLPD). Six advanced KC patients (11 eyes) were fitted with an SLPD with conventional spherical optics. A custom-made Shack-Hartmann wavefront sensor was used to measure aberrations through a dilated pupil wearing the SLPD. The position of SLPD, that is, horizontal and vertical decentration relative to the pupil and rotation were measured and incorporated into the design of the wavefront-guided optics for the customized SLPD. A submicron-precision lathe created the designed irregular profile on the front surface of the device. The residual aberrations of the same eyes wearing the SLPD with wavefront-guided optics were subsequently measured. Visual performance with natural mesopic pupil was compared between SLPDs having conventional spherical and wavefront-guided optics by measuring best-corrected high-contrast visual acuity and contrast sensitivity. Root mean square of HOA in the 11 eyes wearing conventional SLPD with spherical optics was 1.17 ± 0.57 μm for a 6-mm pupil. Higher order aberrations were effectively corrected by the customized SLPD with wavefront-guided optics, and root mean square was reduced 3.1 times on average to 0.37 ± 0.19 μm for the same pupil. This correction resulted in significant improvement of 1.9 lines in mean visual acuity (p < 0.05). Contrast sensitivity was also significantly improved by factors of 2.4, 1.8, and 1.4 on average for 4, 8, and 12 cycles/degree, respectively (p < 0.05 for all frequencies). Although the residual aberration was comparable to that of normal eyes, the average visual acuity in logMAR with the customized SLPD was 0.21, substantially worse than normal acuity. The customized SLPD with wavefront-guided optics corrected the HOA of advanced KC patients to normal levels and improved their vision significantly.

Impact of dust particle non‐sphericity on climate simulations

AbstractAlthough mineral aerosol (dust) particles are irregular in shape, they are treated as homogeneous spheres in climate model radiative transfer calculations. Here, we test the effect of dust particle non‐sphericity in the ECHAM5.5‐HAM2 global aerosol–climate model. The short‐wave optical properties of the two insoluble dust modes in HAM2 are modelled using an ensemble of spheroids that has been optimized to reproduce the optical properties of dust‐like aerosols, thereby providing a significant improvement over spheres. First, the direct radiative effects (DRE) of dust non‐sphericity were evaluated diagnostically, by comparing spheroids with both volume‐equivalent and volume‐to‐area (V/A) equivalent spheres. In the volume‐equivalent case, the short‐wave DRE of insoluble dust at the surface and at the top of the atmosphere (TOA) was slightly smaller (typically by 3–4%) for spheroidal than for spherical dust particles. This rather small difference stems from compensating non‐sphericity effects on the dust optical thickness and asymmetry parameter. In the V/A‐equivalent case, the difference in optical thickness was virtually eliminated and the DRE at the TOA (surface) was ∼20% (∼13%) smaller for spheroids than for spheres, due to a larger asymmetry parameter. Even then, however, the global‐mean DRE of non‐sphericity was only 0.055 W m−2at the TOA and 0.070 W m−2at the surface. Subsequently, the effects of dust non‐sphericity were tested interactively in simulations in which ECHAM5.5‐HAM2 was coupled to a mixed‐layer ocean model. Consistent with the rather small radiative effects noted above, the climatic differences from simulations with spherical dust optics were generally negligible.

Objective evaluation of spherical aberration induced by soft contact lenses with spherical and aspherical optics and its effect on visual quality

Purpose: To measure, in mesopic luminance, the effects on ocular spherical aberration (OSA) of soft CLs with spherical optic (SOCL) and aspherical optic (AOCL) and to evaluate the impact on visual quality (VQ).

Engineering a gigapixel monocentric multiscale camera

Multiscale designs greatly simplify the large-scale optics needed to realize the resolution of a large aperture. Unlike most monolithic lens systems, multiscale cameras have interdependencies between the optics at various scales. To realize a successful multiscale design, the relationships between microcamera scale and overall camera scale parameters must be understood. Starting with a specification of the multiscale camera, we present a simplified model that allows paraxial optical quantities to be estimated. Based on these quantities, a monocentric objective and a microcamera can be designed. An example of a practical design using spherical glass optics is presented.

61 Comparison of spherical aberration controland visual acuity with aspheric and spherical contact lens optics

61 Comparison of spherical aberration controland visual acuity with aspheric and spherical contact lens optics

A versatile partial electron yield detector with large acceptance angle and well-defined threshold energy and gain

We describe a partial electron yield detector for X-ray absorption studies with a large angle of acceptance of π sr, a well-defined electron cut-off energy due to a spherical retardation optics, and a linear, well reproducible gain. The detector operates without electron multipliers and is assembled from standard replacement parts of conventional LEED optics.

Thomas Young's Investigations in Gradient-Index Optics

James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some 50 years earlier, Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young's contributions. We attempted to derive Young's equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. We did not confirm Young's equation for the axial gradient to provide aberration-free optics but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index toward the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Young's theoretical work in gradient-index optics received no acknowledgment from either his contemporaries or later authors. Although his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young's work deserves wider recognition.

Optical Image Analysis of the Novel Ultra-Lightweight and High-Resolution MEMS X-Ray Optics

We have been developing novel microelectromechanical systems X-ray optics for future satellites. It can be ultra-lightweight and of high-resolution. For the first time, we fabricated a spherical test optics made of silicon. We used the dry etching and hot plastic deformation method. We conducted imaging tests to examine whether it can focus a parallel beam of light. Visible light was selected instead of X-rays because of the convenience of testing. The focusing was confirmed with a full-width at half-maximum focal size of 2 arcmin. Since the focus is affected by optical diffraction, a smaller focus can be expected in future X-ray imaging tests.

New systematic and time-saving procedure to design cup grinding wheels for the application of ultrasonic-assisted grinding

Since glass and ceramic materials have beneficial properties, they have gained more importance in numerous technical applications during the last 30 years. For example, nowadays, ceramics are used as artificial hip joints or as mechanical seals for highest relative speeds. Glass components are used for multitude of optical applications like cameras and reflectors. But besides a lot of advantages, the processing of these materials is very difficult. In particular, this contains the manufacturing of small components like microreactor plates or glass wafers with hundreds of small holes, too. Using ultrasonic-assisted grinding, the treatment can significantly be optimized and higher removal rates can be realized. For the generation of ultrasonic waves, often piezoactors are used that excite the grinding tools with vibrations of 20 kHz and amplitudes of a few microns (Markov 1966; Kuttruff 1988). Using an ultrasonic wave, the tool geometry is strongly restricted to guarantee the hybrid functionality (Siegert 2002; Dawe Instruments Ltd. 1967; Derks 1984). The paper describes a new way to calculate the design of tools suitable for their use in ultrasonic-assisted grinding. As a machining process, the manufacturing of spherical optics with cup-grinding wheels is selected.

Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors

We describe the elimination of the astigmatism of a Czerny-Turner imaging spectrometer, built using spherical optics and a plane grating, over a broad spectral region. Starting with the principle of divergent illumination of the grating, which removes astigmatism at one chosen wavelength, we obtain design equations for the distance from the grating to the focusing mirror and the detector angle that remove the astigmatism to first order in wavelength. Experimentally, we demonstrate near diffraction-limited performance from 740 to 860 nm and over a 5 mm transverse spatial extent, while ray-tracing calculations show that barring finite-aperture and detector size limitations, this range extends from 640 to 900 nm and over 10 mm transversely. Our technique requires no additional optics and uses standard off-the-shelf components.

Depth of field extension with spherical optics

The introduction of spherical aberration in a lens design can be used to extend the depth of field while preserving resolution up to half the maximum diffraction-limited spatial frequency. Two low-power microscope objectives are shown that achieve an extension of +/- 0.88 lambda in terms of wavefront error, which is shown to be comparable to alternative techniques but without the use of special phase elements. The lens performance is azimuth-independent and achromatic over the visible range.

An alternate approach to free-form surface fabrication

Abstract Surface milling and grinding are widely used for the fabrication of free-form surfaces for molds and dies. The continuous demand for better product quality has led to demand in higher surface accuracy. Limiting factors are the positioning accuracy of the tool and the accuracy of the manufacturing process. Computer controlled optical surfacing (CCOS) has been developed mainly for the fabrication of spherical and aspherical optics. The surface is repeatedly measured and corrected using abrasives until the target accuracy is attained. In principle, sub-micron accuracy is achievable. The accuracy is limited by surface measurement, and not by the processing equipment. The current research investigates the adoption of CCOS for the fabrication of free-form steel surfaces. This paper reports on the development of a test bed and initial experiment results. The test bed is based on a six-axis RX robot as the motion platform with a spindle attached to the wrist of the robot. Surface measurement is carried out using a Talysurf surface profiler. Surface error correction is performed by abrasion of material from the surface. The amount of material to be removed is based on the measured surface error. Following a predetermined tool path, the feed rate along the tool path for surface correction is to be varied according to the required among of material to be removed locally. A free-form surface specimen of mold steel of about 40 mm × 40 mm across is used for the initial experiment. The surface is prepared by CNC surface machining with the initial maximum error over 50 μm. The positioning accuracy of the motion system is estimated to be no better than 0.1 mm. Through surface measurement and correction, the surface accuracy is significantly improved.

Conical optics: the solution to confine light

We compare the performances in terms of confinement and depth of field of spherical and conical optics. It turns out that, if the spherical optics is adapted to the usual parallel imaging, conical optics seems to be the optimized solution for systems based on scanning (sequential imaging). It is shown that the optimized confinement capability of conical optics is due to the ability of conical components to generate a single Bessel beam with high efficiency. The calculations are based on Weyl formulas.