Aperture Research Articles

In situ, back-focal-plane-based determination of the numerical apertures in optical microscopes.

In this contribution, we present a technique for in situ determination of the numerical apertures (NAs) of optical microscopes using calibrated diffraction gratings. Many commonly practiced procedures use an external setup to determine the objective and condenser NAs. However, these values may become modified in the used microscope systems, e.g.,by system intrinsic apertures. Therefore, in our improved technique, determination of the imaging NA is conducted in situ within the corresponding microscope at hand. Furthermore, the method has been extended to yield the microscope's illumination NA as well. In total, we tested this procedure for determination of the imaging NA for four different microscope objectives with nominal values of 0.55 and 0.9, together with the illumination NAs for four different circular aperture diaphragms with diameters between 10µm and 500µm using several gratings of different pitches. All determined NA values agree essentially with their nominal values within their experimental uncertainties, but the uncertainties have been reduced by typically an order of magnitude as compared with the manufacturer's specifications.

Active Optics—Progress in Modeling of Tulip-like Variable Curvature Mirrors

We present new results obtained from the modeling of a tulip-like variable curvature mirror (VCM) in the case of a central force that reacts to its contour. From Nastran finite element analysis, we shows that 3-D optimizations, using non-linear static flexural option, with an appropriate solution sequence, provide an accurate tulip-like VCM thickness distribution. This allows us to take into account boundary conditions, including the thin outer collarette and its link to a rigid ring. Modeling with a quenched stainless steel chromium substrate provides diffraction-limited optical surfaces. Rayleigh’s quarter-wave criterion is performed over a zoom range from flat up to f/3.5 convexity over a 13 mm clear aperture and 10 daN central force. The optical testing results of a prototype tulip-like VCM elaborated from the previous analytic theory, show quasi-diffraction-limited figures for a zoom range up to f/5. The present modeling results should significantly help in the future construction of such VCMs with a zoom range extended up to f/3.5.

Adaptive lens for foveal vision, imaging, and projection over large clear apertures.

We report an electrically tunable liquid crystal device that enables the generation of lenses the diameters of which may be dynamically changed from sub-millimeter to multiple millimeter sizes. These lenses can be created in different regions of interest over very large (above 50 mm) optical clear apertures. The approach is based on the activation of periodically spaced contacts on a single serpentine-shaped electrode with phase-shifted electrical signals. It enables a highly reconfigurable operation of locally created lenses with variable position, diameter, optical power (OP) and aberrations. The preliminary demonstration of the capabilities of the proposed device is presented here by creating a local lens, moving its center over an area of 25 mm x 25 mm, gradually changing its diameter from 1.3 mm to 4.55 mm as well as by tuning its OP value from zero up to, respectively, ≈ 40 and ≈3.5 diopters. Typical driving signals are at the order of 3.5 V. We think that such lenses can be used for ophthalmic or augmented reality applications as well as in microscopy, adaptive panoramic cameras with large distorted field of view, dynamic projection, etc.

Double-sided telecentric zoom optical system using adaptive liquid lenses.

In this paper, the adaptive liquid (AL) lenses are introduced into the double-sided telecentric zoom system, which could greatly decrease the mechanical motion group compared with the traditional zoom system, and only one movable aperture stop (STO) is retained. Firstly, this paper derived the Gaussian brackets used in this system, and we found the appropriate screening method to get the suitable initial structure parameters from the solution space. Then we used the lens module design method to create the initial system. Finally, we used CODEV to further optimize the system, and we got an excellent design result, which controlled the telecentricity of both sides within 0.1°, the distortion was controlled within 0.5%, and the MTF of each zoom configuration above 0.3. This optical system has high application potential and value in the field of precision machine vision. The design method proposed in this article can effectively solve the problem that the zoom system using adaptive liquid lenses lacks the initial structure.

3-D Printed All-Dielectric GRIN Lens Antenna With an Integrated Feeder

In this paper we present the design, fabrication, and experimental verification of a new type of Graded-index (GRIN) lens antenna with an integrated feeder. The continuously varying refractive index distribution is chosen appropriately to offer the rays collimation at the lens aperture. It is practically implemented by varying the material density in a host medium, thus realizing a new type of all-dielectric high gain antenna, entirely using 3D printing. This solution can find application to high gain wireless communication and measurement systems. This GRIN lens antenna is printed in one monolithic process and does not require the feeder to be placed at a focal distance, thus complying with more strict space requirements. It accepts interchangeable feeds that can cover a wide frequency range. The directivity and gain are evaluated using near-field measurements in the Ku-band. A 40% measured aperture efficiency is achieved at 14GHz. The challenges and performance limitations that come with 3D printing, as compared to the design of idealized continuous distribution GRIN lenses are discussed.

Design optimization of one-dimensional aberration-free x-ray gradually focusing lenses

In our previous work, we proposed a new design method for an aberration-free x-ray refractive focusing lens based on an ideal Cartesian oval shape to solve the aberration problem in x-ray compound refractive focusing. In this paper, we propose an optimization method for this new lens. By reducing the aperture of each lens, we achieve the objective of increasing the effective aperture and improving the focusing performance of the lens. The simulation of the beam propagation method shows that the focusing performance of the optimized lenses is better in compound refractive lens shape but worse in the kinoform shape. This is different from the results obtained with the conventional kinoform lens. After further comparison, we found that this is because the step height of the kinoform lens is small when the lens aperture is very small, resulting in a strong diffraction effect that weakens the focusing performance of the lens. Further modifications to the structure of the kinoform lens are needed to improve this phenomenon.

Design of Highly Directive GRIN MS Lens Integrated DFHA for Deep Tissue Biomedical Imaging

A novel highly directive gradient refractive index (GRIN) metasurface (MS) lens integrated dielectric-filled horn antenna (DFHA), with an enhanced signal penetration and spatial focusing, is developed for the effective monitoring and detection of tumors deep inside the body. For this purpose, two novel GRIN MS lens topologies are proposed, where an optimized refractive index distribution along with the lens aperture is generated using an improved analytical formulation. In the first lens configuration, the core layer (CL) is sandwiched between two similar impedance matching layers (IMLs) on each side. In the second configuration, the CL is still surrounded by two IMLs on both sides, but one of the IMLs, in this case, is improved to avoid the requirement of an additional dielectric layer between the lens and the biological tissue. All the layers of the MS lens are based on an array of especially designed square ring-shaped unit cells. The proposed MS lens-based DFHA enhances the signal penetration by a maximum of 12 dB at 100 mm penetration inside the torso compared to the case without a lens. It also facilitates better spatial resolution due to the presence of an MS lens, which shrinks threefold the 3 dB beamwidth at 100 mm inside the torso than that of the DFHA without an MS lens. The proposed GRIN MS lens integrated DFHA is fabricated and tested on a realistic torso phantom to evaluate the tumor detection capability deep inside the torso. The simulation and experimental results show that the proposed GRIN MS lens-based DFHA can effectively be employed for tumor detection with high resolution deep inside the body.

Measurement Method for Numerical Aperture of Projection Lens Based on Ronchi Lateral Shearing Interferometry

Measurement Method for Numerical Aperture of Projection Lens Based on Ronchi Lateral Shearing Interferometry

Lateral resolution enhanced interference microscopy using virtual annular apertures

The lateral resolution in microscopic imaging generally depends on both, the wavelength of light and the numerical aperture of the microscope objective lens. To quantify the lateral resolution Ernst Abbe considered an optical grating illuminated by plane waves. In contrast, the Rayleigh criterion holds for two point sources or point scatterers separated by a lateral distance, which are supposed to emit spherical waves. A portion of each spherical wave is collected by the objective lens and results in an Airy disc corresponding to a diffraction limited intensity point spread function (PSF). If incoherent illumination is employed the intensity PSFs related to different scatterers on an object are added resulting in the well-known Rayleigh resolution criterion. In interference microscopy instead of the intensity the electric field scattered or diffracted by an object will be affected by the transfer function of the optical imaging system. For a reflective object the lateral resolution of an interference microscope can be again characterized by the Abbe limit if the object under investigation is a grating. However, if two irregularities on a flat surface are being imaged the resolution no longer obeys the Rayleigh criterion. Instead, it corresponds to an optical system with an annular aperture and thus surpasses the prediction given by the Rayleigh criterion. This holds true for both, amplitude as well as phase objects, as it will be elucidated in this study by theoretical considerations, simulation results and an experimental proof of principle.

Design of large numerical aperture and wide spectrum catadioptric objective lens (invited)

Design of large numerical aperture and wide spectrum catadioptric objective lens (invited)

Calculation of Light Intensity Distribution in Imaging Space of Imaging System with Arbitrary Aperture Diaphragm

Calculation of Light Intensity Distribution in Imaging Space of Imaging System with Arbitrary Aperture Diaphragm

Detection method of large aperture lens based on fringe tracking

Detection method of large aperture lens based on fringe tracking

Analysis and design of a microlens array scanning system based on spherical aberration.

The microlens array (MLA) scanning system is a relatively new solution for beam scanning. The excrescent light generated by overlapping divergent beams from adjacent microlenses increases with the scanning angle, and as a result, the rays do not fill the clear aperture of the MLA. The effect on the detection distance and imaging resolution of the MLA system are analyzed. Based on the principle of minimum spherical aberration, a design method for initial configuration of the MLA system is proposed. The findings of this paper can be beneficial for the design and evaluation of MLA systems.

Three-dimensional density measurements of a heated jet using laser-speckle tomographic background-oriented schlieren

Tomographic background-oriented schlieren (TBOS) is a promising optical technique for 3D density field measurement in turbulent flows. Path-integrated information on refractive index gradients is captured by cameras looking through the flow at textured background patterns in the form of apparent displacements of the patterns. A tomographic reconstruction of the three-dimensional refractive index gradients is performed, from which the instantaneous three-dimensional density field is obtained. Most TBOS measurements to date have been limited by large temporal blurring and/or large defocus blurring. Our 15-camera experimental set-up uses a pulsed laser for both illumination and creation of a laser-speckle background pattern. The high-power laser ensures adequate exposures in nanoseconds, so temporal integration is minimised in each measurement. The beam is spread to illuminate a surface that is observed by fifteen cameras that are evenly spaced circumferentially around the flow. Laser speckle patterns are observed by the cameras due to the diffuse reflection and interference of coherent light from roughness on the surface. We develop a methodology for selecting the optimal focal length, focus distance, and lens aperture by considering the compromise between displacement sensitivity, defocus blurring and speckle size. Low temporal- and spatial-blurring 3D temperature field measurements with excellent resolution of turbulent flow features are obtained and good agreement with thermocouple. Classical behaviours of the potential core instability such as vortex rollup and radial ejections are identified. The behaviour of the potential core is examined further, which reveals that the potential core undergoes considerable deformation and fragmentation during the transition to turbulence.

Active mode single-pixel non-line-of-sight imaging system based on second-order correlation and diffraction

Non-line-of-sight (NLOS) imaging relies on capturing light that has been weakened due to multiple reflections and recovering the occluded scene with high quality is very challenging. To improve the quality of NLOS imaging, an active mode single-pixel NLOS imaging reconstruction framework based on the second-order correlation function and diffraction inverse operation is proposed. Under the collective effect of illumination pattern and single-pixel detector light intensity, the inverse imaging problem is first solved by a statistically weighted average, and then, an additional process is connected to reduce the influence of diffraction on reconstructed image quality based on the Fourier transform and inverse diffraction operation. The simulation and experimental results show that the proposed method with the Hadamard pattern and diffraction inverse operation, which achieved the SSIM value of 0.9286, is superior to the random pattern at a full sampling rate. The lens aperture size, pattern location, and the number of measurements have a significant effect on the system. Therefore, the proposed scheme has potential practical applications.

Optimization of space laser coupling with few-mode fiber in the presence of random angular jitter

In a space laser communication system with a few-mode fiber as the receiving terminal, the influence of random angular jitter on the communication performance cannot be ignored. Therefore, it is necessary to research the coupling characteristics of the space laser–FMF system with random angular jitter. A space laser–FMF coupling model with random angular jitter is proposed based on the Laguerre–Gaussian mode. The coupling efficiency and bit error rate (BER) of the communication system are optimized by the relative aperture of the coupling lens. When the relative aperture is 0.15, the standard deviation of random jitter is 3, the signal-to-noise ratio is 5, the coupling efficiency after optimization is improved by 29%, and the BER is reduced by 46%. In this case, the maximum BER reduction after optimization is 55%. The research shows that in the presence of random angular jitter, adjusting the relative aperture can significantly optimize the coupling efficiency and the BER of the space laser–FMF coupling system. The ability of the relative aperture to optimize the coupling efficiency increases with random jitter standard deviation, which exhibits an upper limit for the optimization of the BER.

Upper bounds on focusing efficiency.

Upper bounds on the focusing efficiency of aperture fields and lens systems are formulated using integral equation representations of Maxwell's equations and Lagrangian duality. Two forms of focusing efficiency are considered based on lens exit plane fields and optimal polarization currents within lens design regions of prescribed shape and available materials. Bounds are compared against the performance of classical prescriptions of ideal lens aperture fields, hyperbolic lens designs, and lenses produced by inverse design. Results demonstrate that, without regularization, focusing efficiency based solely on lens exit plane fields is unbounded, similar to the problem of unbounded antenna directivity. Additionally, results considering extruded two-dimensional dielectric geometries driven by out-of-plane electric fields for the calculation of bounds and inverse design demonstrate that aperture fields based on time-reversal do not necessarily yield optimal lens focusing efficiency, particularly in the case of near-field (high numerical aperture) focusing.

The Influence of the Aperture Stop Fractal Shape of an Optical System on the Illuminance Distribution

In the article the options for the application of aperture shapes with fractal properties in the design of optical systems are considered. Calculations of mathematical models of point spread functions of a diffraction-limited optical system are performed. The diffraction patterns of the light distribution in these systems are presented, and the point spread functions are considered for various shapes of the aperture stop. Analytical expressions are obtained for the light distribution depending on the pupil shape, which can be used to control the process of image formation. The pupil shape, which has the shape of an equilateral triangle, is chosen as the basic one, and the shape of the pupil as a "Koch snowflake" curve is also considered. Using the Fraunhofer integral, the dependences of the distribution of the spectral density of the complex amplitude on the aperture located on an opaque screen are derived in the Fraunhofer approximation and under the condition of illumination by a plane monochromatic wave. Using the relationship with the complex amplitude, the sought-for intensity distribution in the plane of the diffraction pattern is obtained. Taking into account the simplifications adopted in this article, the solution of the Fraunhofer integral is found, by setting the integration limits, depending on: the selected aperture profile, the coordinate system chosen for it, and the position of nodal points in this system

Spectral singularities and threshold gain of a slab laser under illumination of a focused Gaussian beam

Spectral singularities of an infinite planar slab containing homogeneous optically active material at the focal plane of a thin lens are investigated. The field distribution of the beam behind the lens is Gaussian that we approximate by a plane wave concentrated near the optical axis at the focal plane of the lens, such that its phase and amplitude are distance-dependent. The consequences of this configuration are explored by determining the threshold gain of the active medium and tuning the resonance frequencies related to spectral singularities. We find that the spectral singularities and the threshold gain, besides that, vary with distance from the center of the Gaussian beam; also they change with the relative aperture of the focusing lens. Numerical studies show that for the central rays of the beam compared to the side rays, the resonances related to the spectral singularities occur at lower wavelengths (higher frequencies) with the highest threshold gain. Also, for the ray at a fixed distance from the center of the beam, increasing the relative aperture of the illuminating system leads to the same results. Numerical results confirm the theoretical findings.

Correcting the effect of temperature on image quality of thermal imaging objectives by wavefront coding technique

The paper has proposed a method for correcting the effect of temperature on the imaging quality of thermal imaging systems by wavefront coding technology. A cubic phase mask was added to the aperture diaphragm of the thermal imaging objective to obtain a temperature-invariant point spread function (PSF). The received images will be of low quality but almost invariant with the change in temperature. An inverse filter was used to recover high-quality images over a variable temperature range. To demonstrate the effectiveness of the proposed method, a thermal imaging objective was used to experiment. The simulation results demonstrate that the proposed method can effectively eliminate the temperature influence on the image quality of the thermal imaging objective.