Depth Of Focus Range Research Articles

Design of a long depth of focus Gaussian beam shaping system via aspheric lenses

This paper presents a beam shaping system that uses a Galilean beam shaper. The light mapping function and the aspherical coefficient, which determines the characteristics of the aspheric lens, are derived based on the law of conservation of energy. Furthermore, optical software (i.e., ZEMAX) was utilized to simulate the design of the shaping system. In addition, a spherical collimation system is introduced to achieve the shaping system with long depth of focus. The results show that the output flat-top beam has the uniformity over 90% within the 300mm depth of focus range and the divergence angle no more than 0.6°, which is in line with the theoretical expectation. Compared to the previous works, our beam shaping system is characterized by long depth of focus, simple structure and good beam shaping effect, which makes the present shaping beam more flexible for the application in the field of laser processing.

Generation of needle-shaped beam with super-resolution spot and large depth of focus using diffractive optics

The finite depth of focus (DOF) of a focusing lens gives rise to the degradation of lateral resolution at defocused positions. Consequently, the generation of a needle-shaped beam with sub-diffraction size and extended DOF can break through this limitation, but few studies have effectively balanced these two characteristics. In this paper, we propose a method based on the stochastic parallel gradient descent (SPGD) algorithm for designing multi-ring diffractive optical elements (DOEs) to produce the needle-shaped beam, which maintains a super-resolution and uniform spot within a large extended DOF range. Numerical simulations and experimental results have validated that our method can extend the DOF by 14 times longitudinally and reduce the lateral resolution to 73% of Airy spot, while maintaining up to 92% uniformity of the beam diameter. Furthermore, we demonstrate that the DOF of the needle-shaped beam extends with the increase of the number of rings and phase levels within the DOE. Our work provides an effective strategy for the design of DOF-extended DOE and it is anticipated to find potential applications in microscopy and three-dimensional imaging, photolithography, and optical manipulation.

Quality of vision clinical outcomes for a new fully-refractive extended depth of focus Intraocular Lens

Background/objectiveTo evaluate the visual performance of a purely refractive extended depth of focus (EDF) intraocular lens (IOL).Subjects/methodsA prospective, multi-center, randomized, subject/evaluator-masked study. Subjects were bilaterally implanted with the EDF test (Model ZEN00V, TECNIS PureSee™ IOL, N = 60) or an enhanced monofocal control (Model ICB00, TECNIS Eyhance™ IOL, N = 57) IOL. Monocular corrected distance (CDVA), intermediate (DCIVA), near acuities (DCNVA) and patient reported visual symptoms were evaluated at the 6-month visit. Monocular mesopic contrast sensitivity (CS) and depth of focus (DOF) testing were assessed at 3 months.ResultsCDVA (Mean ± SD) was −0.06 ± 0.08 for test and −0.05 ± 0.08 logMAR for control groups. DCIVA was 0.13 ± 0.08 for test and 0.18 ± 0.14 logMAR for control groups (p = 0.0127). DCNVA was 0.37 ± 0.10 for test and 0.43 ± 0.16 logMAR for control groups (p = 0.0137). Test lens was statistically superior for intermediate and near. Overall, 91.7% (halos), 95.0% (starbursts) and 95.0% (glare) of test lens patients reported that they did not experience, were not bothered, or were slightly bothered by specific visual symptoms, compared to 98.2%, 100% and 96.5% in the control group. The DOF range over which monocular visual acuity was 0.20 logMAR or better was −1.6 D for the test lens. Mesopic CS was comparable between both groups, falling within 0.11 log units for all measured cycles per degree with and without glare.ConclusionThe EDF IOL demonstrated extended range of vision and statistically superior intermediate and near performance compared to the monofocal IOL. Distance visual acuity, contrast sensitivity and dysphotopsia profile were similar to the monofocal IOL.

A Novel Analytical Interpolation Approach for Determining the Locus of a Zoom Lens Optical System

In an optical system with multiple lens groups and increased zoom magnification levels, achieving a smooth zoom locus is increasingly difficult. Traditional methods for calculating zoom loci often involve complex and time-consuming formulas. Consequently, we utilized the Padé approximation in optical design software to compute the zoom locus analytically, irrespective of the number of zoom positions (nodes). The initial data were used to assign orders to rational function polynomials, facilitating Padé approximation. If the image surface extended beyond the depth of focus (DOF), a node was added, with adjustments made until it fell within the DOF range. Furthermore, Padé approximation was performed to prevent singularities. The loci of all lens groups in the optical system can be expressed in a rational function format. Specifically, the numerator and denominator polynomial degrees were 20° and 1°, respectively, with their sum being the total number of nodes. In addition, we calculated the zoom locus by increasing the numerator sequence to minimize the occurrence of the singularity and added the node automatically to enable zoom locus calculation in all optical systems. Accordingly, we could make fast calculations, unlike conventional methods, using complex and time-consuming simultaneous equations. Therefore, we could express the locus of the compensated group in the form of a smooth function, as presently shown.

Depth–Depth of Focus Moiré Fringe Alignment via Broad-Spectrum Modulation

Alignment precision is a crucial factor that directly impacts overlay accuracy, which is one of three fundamental indicators of lithography. The alignment method based on the Moiré fringe has the advantages of a simple measurement optical path and high measurement accuracy. However, it requires strict control of the distance between the mask and wafer to ensure imaging quality. This limitation restricts its application scenarios. A depth–DOF (depth of focus) Moiré fringe alignment by broad–spectrum modulation is presented to enhance the range of the alignment signals. This method establishes a broad–spectrum Moiré fringe model based on the Talbot effect principle, and it effectively covers the width of dark field (WDF) between different wavelength imaging ranges, thereby extending the DOF range of the alignment process, and employs a hybrid of genetic algorithms and the particle-swarm optimization (GA–PSO) algorithm to combine various spectral components in a white spectrum. By calculating the optimal ratio of each wavelength and using white light incoherent illumination in combination with this ratio, it achieves the optimal DOF range of a broad–spectrum Moiré fringe imaging model. The simulation results demonstrate that the available DOF range of the alignment system has been expanded from 400 μm to 800 μm. Additionally, the alignment precision of the system was analyzed, under the same conditions, and the accuracy analysis of the noise resistance, translation amount, and tilt amount was conducted for the Moiré fringe and broad–spectrum Moiré fringe. Compared to a single wavelength, the alignment precision of the broad–spectrum Moiré fringe decreased by an average of 0.0495 nm, equivalent to a 1.5% reduction in the original alignment precision, when using a 4 μm mask and a 4.4 μm wafer. However, the alignment precision can still reach 3.795 nm, effectively enhancing the available depth of focus range and reducing the loss of alignment precision.

M6 formalism – generalization of the laser beam quality factor M2 to the 3D domain

Abstract Here we define a theoretical basis for the generalization of the beam quality factor M2 to three-dimensional (3D) space, which we call M6 formalism. The formalism is established through the use of examples of multifocal and Axicon optical systems to illustrate discrete and continuous axial beam shaping, respectively. For the continuous case, we expand the definition of the Rayleigh range to incorporate a quality factor having both axial and transverse components M add 2 $M_{{\rm{add}}}^2$ and M2. Using geometrical ray tracing simulations, a proportion factor C is found to empirically describe the axial quality factor M z 2 $M_z^2$ of an optical setup including an Axicon and a paraxial focusing lens with a Gaussian single mode input beam. Using our M6 formalism depth of focus (DOF) ranges are calculated for higher M2 beams, and are shown to be in good agreement with the simulated DOF range, demonstrating the usefulness of the M6 formalism for the design of real optical systems.

Depth plane adaptive integral imaging system using a vari-focal liquid lens array for realizing augmented reality.

Augmented reality (AR) is an interactive experience of a real-world environment where the objects that reside in the real world are enhanced by computer-generated perceptual information. Despite its attractive features, AR has not become popular because of the visual fatigue that many people face when they experience it. Many methods have been introduced to solve this visual fatigue problem and one of these methods is an integral imaging system that provides images almost continuous viewpoints and full parallax. However, the integral imaging system, which uses a lens array with a fixed focal length, has limited depth of focus (DOF) range. As a result, images that are outside of the DOF range become distorted. In this paper, a vari-focal liquid lens array was fabricated and the optical characteristics of the lens array were evaluated. Using the vari-focal liquid lens array, the DOF range was extended and high-resolution images are realized without restriction of depth range in an AR system.

A computational analysis of retinal image quality in eyes with keratoconus

Higher-order aberrations (HOA’s) are exaggerated in eyes with keratoconus but little is known about their impact on the retinal image quality (IQ) of these eyes. This computational study determined changes in IQ [peak IQ, best focus and depth of focus (DOF)] of 12 subjects with manifest keratoconus in both eyes (KCE cohort), 9 subjects with very asymmetric ectasia (VAE cohort) with and without their Rigid Gas Permeable contact lenses (RGP CL’s) and 20 age-matched controls, using a HOA-based through-focus analysis performed on the logNS IQ metric over 5 mm pupil diameter following cycloplegia. All IQ parameters were significantly worse in the KCE cohort with their native HOA’s, relative to controls and in the ectatic eye of the VAE cohort, relative to the fellow non-ectatic eye (p ≤ 0.008 for all). Reduction in HOA’s of these eyes with RGP CL’s resulted in a significant improvement in all IQ parameters but they all remained significantly poorer than controls (p ≤ 0.02 for all). The inter-subject variability of best focus and the DOF range were inversely related to peak IQ in these eyes (r = 0.85; p < 0.001). These results provide the optical basis for two clinical observations on keratoconus: (1) optical performance of keratoconic eyes are significantly better with RGP CL’s than with spectacles or unaided conditions and (2) the endpoint of subjective refraction is elusive in keratoconic eyes, relative to healthy controls or to the non-ectatic eye in bilaterally asymmetric ectasia.

Thin film interference effects in an off-axis illumination system

Thin film interference effects on process latitude in an off-axis (quadrupole) illumination system are investigated with a bottom antireflective coating (ARC) or without the bottom ARC over SiO2 substrate using an electrical linewidth measurement technique. Experimental results indicate that an off-axis illumination system can improve an increasing disadvantage in maximum depth-of-focus (DOF) range with increasing resist thickness if using a resist thickness corresponding to a top extreme along the swing curve on a sufficient bottom ARC compared with the standard illumination system. But more serious thin film interference such as the case without the bottom ARC provides less advantage in the maximum DOF range even when reducing resist thickness. It is also found that centered focus positions exhibit a trend to offset in the positive defocus direction with increasing resist thickness, even using a combination of the bottom ARC and the smaller incident angle of illumination light in an off-axis illumination system. The centered focus positions without the bottom ARC are found to show more pronounced swing curve-type behavior with an almost horizontal inclination than that with the bottom ARC.

Effect of thin film interference on process latitude in deep ultraviolet lithography

The effect of thin film interference on process latitude in deep UV lithography is investigated using a precise electrical linewidth measurement technique. The experimental results calculated by exposure–defocus plots show swing curve type dependencies of critical dimension variation, maximum depth-of-focus (DOF) range, and centered focus position. It is demonstrated that the maximum DOF ranges for equivalent incoupling points along the swing curve approximately follow a linear equation introduced in accordance with simulation results of aerial image contrast. It is also verified that a thinner resist with a resist thickness corresponding to an optimum incoupling point along the swing curve can provide a distinct advantage in maximum DOF range, in spite of a remarkably low aerial image contrast, especially in the case of critical patterns. Moreover, it is found that the centered focus positions of the critical patterns exhibit a trend to offset in the positive defocus direction with increasing resist thickness.