Spherical Mirror Research Articles

A sensor based on high-sensitivity multi-pass resonant photoacoustic spectroscopy for detection of hydrogen sulfide

A high-sensitive tunable diode laser sensor based on photoacoustic spectroscopy and multi-pass absorption spectroscopy is developed for hydrogen sulfide (H2S) detection using a target absorption line at 6287.005 cm−1. Two spherical concave mirrors are utilized as the reflectors to make the laser beam pass through the photoacoustic cell for 24 times. The wavelength modulation spectroscopy technique with second harmonic detection (WMS-2f) method is employed to reduce external interference and increase the detection sensitivity. With the enhancement of the effective laser power in the multi-pass PA cell, the photoacoustic 2f signal of the target H2S absorption line has a ∼ 8 times improvement compared to the sensor system without multi-pass cell. Based on the results of Allan variance analysis, the minimum detection concentration of the system could reach 0.68 ppm with a 10-s average time and it can be further lowered down to ∼ 0.1 ppm when a 1-minute averaging time is used. The linear responsivity of the multi-pass PA spectroscopy sensor is estimated to be ∼ 0.00112 mV/ppm by linear fitting for a continuous flow gas measurement results. The excellent performance validates the potential of the sensor for field application.

Method for determining the wavefront aberration of deformed optical components under external forces

Wavefront aberration is an essential factor that significantly affects the image quality of an optical system. We proposed a comprehensive method to determine the wavefront aberration of a deformed optical component caused by clamping forces. First, the displacement of the elements on the optical component, induced by external forces, is calculated using ANSYS software. Then, the deformation surface is fitted with an aspherical surface to obtain Zernike coefficients. Finally, the wavefront aberration is obtained from Zemax using the Zernike coefficients and the parameters of the optical component. An experimental study on a spherical mirror is carried out to verify the accuracy of this method. A Zygo interferometer is used to measure the actual wavefront aberration of the deformed mirror. The result indicates a good agreement between the theoretical calculation and the experimental data, with a variation of <10 % for various applied forces. Our finding provides a meaningful and reliable method for designing and selecting reasonable mounting structures to ensure the image quality of an optical system.

High-precision magnetorheological finishing based on robot by measuring and compensating trajectory error.

The 6-DOF industrial robot has wide application prospects in the field of optical manufacturing because of its high degrees of freedom, low cost, and high space utilisation. However, the low trajectory accuracy of robots will affect the manufacturing accuracy of optical components when the robots and magnetorheological finishing (MRF) are combined. In this study, aiming at the problem of the diversity of trajectory error sources of robot-MRF, a continuous high-precision spatial dynamic trajectory error measurement system was established to measure the trajectory error accurately, and a step-by-step and multistage iterations trajectory error compensation method based on spatial similarity was established to obtain a high-precision trajectory. The experimental results show that compared with the common model calibration method and general non-model calibration method, this trajectory error compensation method can achieve accurate compensation of the trajectory error of the robot-MRF, and the trajectory accuracy of the Z-axis is improved from PV > 0.2 mm to PV < 0.1 mm. Furthermore, the finishing accuracy of the plane mirror from 0.066λ to 0.016λ RMS and the finishing accuracy of the spherical mirror from 0.184λ RMS to 0.013λ RMS using the compensated robot-MRF prove that the robot-MRF has the ability of high-precision polishing. This promotes the application of industrial robots in the field of optical manufacturing and lays the foundation for intelligent optical manufacturing.

Correction of perspective distortion and intensity errors in projected fringe patterns in phase-measuring deflectometry

The relative pose between the projector and screen in a phase-measuring deflectometry (PMD) setup can result in perspective distortion and intensity errors in the projected fringe patterns. These problems degrade the sinusoidal characteristics of the fringe patterns, thus increasing phase, slope, and height errors in the PMD measurement. To overcome these issues, inverse perspective distortion and intensity modification algorithms were developed and applied to computer-generated fringe patterns before projection. The inverse perspective distortion matrices were obtained using a single image of the projected grid distortion target. The pixel intensities in the generated fringe patterns were modified using the relationship between the generated and captured pixel intensity values in grayscale images of uniform intensity. Experiments were conducted to measure the surface topographies of spherical concave and convex mirrors using a monoscopic PMD setup. Based on the experimental results, the root-mean-squared (RMS) intensity and phase errors in the projected sinusoidal fringe patterns were reduced by about 90% after using the modified fringe patterns compared to the original fringe patterns. When comparing the measured and the theoretical heightmaps, the results in PMD measurement showed an 8% and a 14% reduction of the RMS height errors in concave and convex heightmaps, respectively. The effectiveness of the algorithms in improving the accuracy of projector-based PMD measurement was demonstrated successfully.

Demonstration of a spherical plasma mirror for the counter-propagating kilojoule-class petawatt LFEX laser system.

A counter-propagating laser-beam platform using a spherical plasma mirror was developed for the kilojoule-class petawatt LFEX laser. The temporal and spatial overlaps of the incoming and redirected beams were measured with an optical interferometer and an x-ray pinhole camera. The plasma mirror performance was evaluated by measuring fast electrons, ions, and neutrons generated in the counter-propagating laser interaction with a Cu-doped deuterated film on both sides. The reflectivity and peak intensity were estimated as ∼50% and ∼5 × 1018 W/cm2, respectively. The platform could enable studies of counter-streaming charged particles in high-energy-density plasmas for fundamental and inertial confinement fusion research.

Wide-viewing-zone Light-field Capturing Using Turtleback Convex Reflector

Light field cameras have been used for 3-dimensional geometrical measurement or refocusing of captured photo. In this paper, we propose the light field acquiring method using a spherical mirror array. By employing a mirror array and two cameras, a virtual camera array that captures an object from around it can be generated. Since large number of virtual cameras can be constructed from two real cameras, an affordable high-density camera array can be achieved using this method. Furthermore, the spherical mirrors enable the capturing of large objects as compared to the previous methods. We conducted simulations to capture the light field, and synthesized arbitrary viewpoint images of the object with observation from 360 degrees around it. The ability of this system to refocus assuming a large aperture is also confirmed. We have also built a prototype which approximates the proposal to conduct a capturing experiment in order to ensure the system&#x2019;s feasibility.

Commissioning of the upgraded RICH system at the LHCb experiment

The Ring-Imaging Cherenkov (RICH) system is an essential element of the LHCb experiment: it consists of an upstream detector (RICH 1), located close to the interaction point, and a downstream detector (RICH 2), placed after the tracking system and has the task of identifying charged hadrons over the momentum range 2–100 GeV/c. Currently, the LHCb experiment is completing an upgrade phase to allow data collection at a five-fold increase in instantaneous luminosity up to 2 × 1033 cm−2 s−1 and read out data at a rate of 40 MHz. The challenges of the higher luminosity are a significant increase in detector occupancy and a larger radiation dose. To match the new experimental requirements, both RICH detectors have been upgraded with a redesigned opto-electronic chain and new photon detectors. In addition, RICH 1 has a modified layout with new mechanics and spherical mirrors to reduce the maximum occupancy. A summary of the upgrade program and the current status of the commissioning operations will be presented.

Evaluation of Optical Properties of Schmidt Cassegrain Spider Obscuration Telescope by Using Zemax Program

Schmidt Cassegrain spider obscuration telescope (SCT) is one of the types of observations operating with a concave mirror. It combines several lenses and mirrors working together as an optical system. The light rays fall into the tube from the main mirror and gather on another smaller mirror called a secondary mirror. Unlike the formation of Newton's telescope, no light is made from the secondary mirror out the side of the tube but is directed to the middle of the main mirror. There is an opening in the middle of the main mirror so the light beam can go out and direct the vision lens system. The secondary mirror is located in the middle of a glass slice and is installed by thin carriers. The function of this board is to correct the portrait of the significant spherical mirror and reduce this coma aberration in the system to the lowest possible score. In this research, the efficiency of design performance was studied due to image analysis tools provided by the Zemax program. The results showe the image quality when using a variable field of view with a limit (0o- 0.5o) and for a variable focal depth as needed.

Large Piston Error Detection Method Based on the Multiwavelength Phase Shift Interference and Dynamic Adjustment Strategy

As the loading space in rockets and mirror fabrication technology is limited, optical systems in space cannot have large optical apertures. However, the successful launch and excellent performance of the James Webb Telescope indicate that segmented mirrors can help realize large-aperture optical systems in space, owing to the fold–unfold mechanism in the telescope. However, all segments in the segmented mirror should be co-phased so that it is equivalent to a monolithic mirror. The co-phasing problem is significant in optical systems in space because of their low error tolerance. Owing to some accident factors, the piston error can be more than 1 mm after the unfolding process. Here, we introduced a multiwavelength interference method and dynamic adjusting strategy, aiming to solve the two problems of co-phasing: large detection range (~2 mm) and high detection precision (&lt;1/20λ). Numerical simulations were performed, and a 400 mm aperture-segmented spherical mirror system was used to verify this method. The original piston error was set to 1 mm, after the coarse co-phasing, and the residual piston error to less than half the wavelength of the monochromatic light; for fine co-phasing, the achieved detection precision was approximately 1.2 nm.

Design of the VLT-CUBES image slicers:

CUBES is a high efficiency spectrograph designed for a Cassegrain focus of the Very Large Telescope and is expected to be in operation in 2028. It is designed to observe point or compact sources in a spectral range from 300 to 405nm. CUBES will provide two spectral resolving powers: Rge20,000 for high resolution (HR) and Rge5,000 for low resolution (LR). This is achieved by using an image slicer for each resolution mode. The image slicers re-format a rectangular on-sky field of view of either 1.5arcsec by 10arcsec (HR) or 6arcsec by 10arcsec (LR) into six side-by-side slitlets which form the spectrograph slit. The slit dimensions are 0.19mm times 88mm for HR and 0.77mm times 88mm for LR. The on-sky and physical widths of the slicer mirrors are 0.25arcsec/0.5mm (HR) and 1arcsec/2mm (LR). The image slicers reduce the spectrograph entrance slit etendue and hence the size of the spectrograph optics without associated slit losses. Each of the proposed image slicers consists of two arrays of six spherical mirrors (slicer mirror and camera mirror arrays) which provide a straight entrance slit to the spectrograph with almost diffraction-limited optical quality. This paper presents the description of the image slicers at the end of the Phase A conceptual design, including their optical design and expected performance.

Enhancement limit of sensitivity in laser absorption spectroscopy using a multipass cell composed of spherical concave mirrors

The upper limit of sensitivity enhancement in a multipass process was investigated. In the calculation of 3.7 × 1013 ray-trace analysis, the sensitivity enhancement was increased to 13 510 for the mirror diameter of 75 mm with the mirror diameter. In the experiment, the sensitivity was enhanced by a factor of 1790 ± 160 for an effective mirror diameter of 50 mm, which was one-third of the numerical prediction. The lower enhancement could be attributed to the insufficient spatial and angular resolution of alignment optics. Therefore, this multipass cell has the potential to improve the sensitivity by three to four orders of magnitude.

Methane detection system based on a new type of dense optical multi-pass cell

ObjectiveTo increase the optical path of gas absorption in a multi-pass cell (MPC), a dense spot pattern has been obtained on MPC to improve the accuracy of trace gas detection. In this study, an algorithm was proposed to calculate the spot patterns of a new type of dense optical MPC. MethodIn this novel algorithm, the reflected ray equation and spherical equation were combined to obtain the position coordinates of light spots on a mirror surface. The calculation was repeated by changing the reflected optical path parameters until a new dense light spot pattern was obtained. To verify the accuracy of the proposed algorithm, a series of spot numerical simulations and methane (CH4) concentration detection experiments were conducted. ResultsResults showed that in an MPC with a double spherical mirror, a series of dense spot patterns located on the mirror surface was obtained by calculating off-axis incident rays using the new algorithm, effectively increasing optical path length, and obtaining an MPC with a long optical path of 12.92 m. CH4 concentration was detected by combining the long optical path MPC with a tunable diode laser absorption spectroscopy. A good linear relationship was established between the calibrated CH4 concentration and the peak of the second harmonic signal detected by the system. The minimum detection limit of the system for CH4 was 2.33 ppb at an integration time of 20 s obtained via Allan deviation analysis. The long optical path MPC system achieved high detection sensitivity. Hence, a new method for calculating the dense spot pattern of an MPC is provided in this work.

High-aperture low-coherence interferometer with a diffraction reference wave.

A high-aperture low-coherence interferometer with a diffraction reference wave based on a tipped single-mode optical fiber was proposed and investigated. Due to the usage of the central least-aberrated region of the diffracted wavefront, the interferometer comprise record working aperture among known PDIs. The interferometer makes it possible to study samples with a reflectance that varies over a wide range. A demonstration of the use of this interferometer for high-precision measurements of a spherical mirror is presented. Sub-nanometer reproducibility of measurements in terms of the peak to valley (PV) parameter and sub-angstrom reproducibility in terms of the rms are demonstrated.

Dragging three-point method for measurement of telescope optics

We developed the improved three-point method as measuring machine that is applicable for measurements of various telescope optics, including concave, convex, and off-axis mirrors of high aspheric. The method is small and robust against temperature change and vibration and can extend a conventional machining tool to a measurement tool. We measured the cross section of a flat mirror of ϕ300 mm with this method on an old milling machine. The result was consistent with that obtained with an interferometer with a discrepancy of 5.5 nm (RMS). For the next stage, we executed two-dimensional measurements of a concave spherical mirror of ϕ794 mm. The result showed good agreement with that obtained with an interferometer and the method successfully detected an amplitude of 30 nm of small-scale structure in the lateral direction.

Do Leonardo da Vinci’s drawings, room acoustics and radio astronomy have anything in common?

After introducing Leonardo da Vinci’s (LdV) predecessors in the field of light propagation research, his drawings on the topic of reflecting light by a spherical mirror are analysed. The discovery of LdV is presented, according to which, at an infinitely distant source of rays, a small fragment of the canopy is enough to generate a focus, while the rest of the mirror forms a caustic for which LdV did not indicate an application. An analytical description of the energy concentration in the focus and on the caustic is given, together with its reference to the geometric representation of the acoustic field in rooms. Based on the general principles of wave motion, symmetry is shown in the description of energy relations in acoustics and electromagnetism. It is explained why in the sound field in existing halls, instead of a whole caustic only its cusp is observed, which is perceived as a point-like sound focus. The size of the mirror aperture, shown graphically by LdV, is determined. How the development of receiving techniques increased the mirror aperture compared to the LdV estimate is also shown. The implementation of these improvements is presented via the example of the Arecibo and FAST radio telescopes.

Evolutionary algorithm to design high-cooperativity optical cavities

Using an evolutionary algorithm combined with a gradient descent (GD) method we design optical cavities with significantly enhanced strong coupling rates between cavity photons and a single quantum emitter. Our approach allows us to find specially designed non-spherical mirrors which lead to high-finesse cavity eigenmodes with large field enhancement at the center of the cavity. The method is based on adding consecutive perturbations to an initial spherical mirror shape using the GD method for optimization. We present mirror profiles which demonstrate higher cavity cooperativity than any spherical cavity of the same size. Finally, we demonstrate numerically how such a cavity enhances the operation frequency and purity of coupling a Ca+ ion to an optical fiber photon.

Optical system of aplanatic telescope with a 100 m spherical primary mirror

We propose an optical system of an extremely large telescope for ground-based or planetary use. The system comprises a segmented spherical mirror with a diameter of 100 m and f-number of f / 1. There are three annular zones on the primary mirror, which corresponds to three annular telescopes (ATs) with f-numbers f / 2, f / 3.2, and f / 5.2, all using a concave cardioidal secondary mirror with a maximum diameter of 3.18 m. This two-mirror system satisfies Fermat’s principle and the Abbe’s sine condition. The central zone of the primary mirror with a diameter of 23.8 m is used for the central three-mirror telescope, which is based on an afocal two-mirror system with a convex aspheric secondary mirror with a diameter of 3 m. Four possible configurations are presented for the central telescope, which makes it possible to vary the f-number in a wide range with design examples given for f / 1, f / 4.2, f / 14, and f / 33 systems. The ATs form three coherent images of the same astronomical object, which offers possibilities of simultaneous observations at three different wavelengths or image processing of a combined image with enhanced angular resolution. The main goal of the paper is to investigate the properties of new optical systems for ground-based and space telescopes with a fast spherical primary mirror for which aberration correction is achieved with a minimum number of auxiliary aspheric mirrors near the prime focus.

Optical design of Lissajous pattern multipass cells with multiple spherical mirrors based on particle swarm optimization.

We propose a method to intelligently design and optimize a multiple-spherical-mirror-based multipass cell (MPC) with Lissajous patterns. The MPC consists of at least three spherical mirrors, which are placed in a rotationally symmetric arrangement. Particle swarm optimization (PSO) is performed to optimize the parameters of the MPC configurations and accelerate the design process. Two Lissajous patterned MPCs with three and five mirrors are built and tested experimentally. We further develop an open-path gas sensor based on a five-mirror-based MPC to detect methane concentrations in ambient laboratory air, and a detection precision of 1.1 ppb with a 123 s averaging time is realized. The PSO algorithm is efficient for optimizing the proposed MPC, which has superior proprieties of symmetry configuration, cost-effectiveness and high detection sensitivity and is well suited for trace gas sensing applications.

Design and Analysis of Novel Folded Optical Multi-Pass Cell

A novel folded multi-pass cell consisting of three non-coaxial mirrors (spherical mirror or plane mirror) is proposed for laser spectroscopy. Three mirrors of the folded multi-pass cell can arrange in V-shape to form a stable non-coaxial multi-pass cell. Furthermore, in order to research the stability of the multi-pass cell under off-axis mirror’s astigmatism circumstance, an equivalent coaxial multi-pass cell and modified ABCD matrix model for the spot pattern of the folded multi-pass cell is proposed, by which a series of the detailed numerical calculations were implemented to analyze the optical path length of the multi-pass cell. Many spot patterns obtained with a high fill factor improve the utilization efficiency of the surface of the mirror and produce a longer total optical path length. The several typical types of folded multi-pass cells consisting of the different mirrors and base lengths were selected to demonstrate the cell’s self-consistent condition and power for a longer-optical path length. Three effective optical path lengths of 49.6, 97.6 and 173.6 m were obtained, respectively.

Dynamic distribution and correlation analysis of the angle kappa in myopia patients undergoing femtosecond-assisted laser in situ keratomileusis.

Purpose:To explore the offset distribution of pupillary centres, the offset between the pupil centre and the coaxially sighted corneal light reflex (P-Dist) and their correlation in femtosecond laser combined with excimer laser in situ keratomileusis.Methods:Randomly selected 194 patients (398 eyes) who underwent femtosecond-assisted laser in situ keratomileusis with preoperative use of WaveLight Allegro Topolyzer Corneal Topography (WaveLight Laser Technologies AG, Erlangen, Germany) to measure the pupil size and centre position. The P-Dist of the patients was recorded by the X and Y axis eyeball tracking adjustment program of the WaveLight Eagle Vision EX500 excimer laser system.Results:The P-Dist was 0.214 ± 0.092 mm in the right eyes and 0.228 ± 0.105 mm in the left eyes (P = .041). Under scotopic conditions, the pupil centre of left eye X-axis was −0.046 ± 0.091 mm, the right eye was −0.152 ± 0.084 mm, with significant differences (P = .015), and the Y-axis direction showed no significant changes (P = .062). The white to white was positively correlated with changes of pupil diameter (scotopic pupil diameter-photopic pupil diameter) (r = 0.270, P < .001). The equivalent spherical mirror and measured centroid shift were negatively correlated (r = −0.214, P = .002).Conclusion:The angle kappa of the right eye is smaller than that of the left eye and from scotopic to photopic condition, the pupil centroid shift of both eyes to the nasal inferior side. If the cornea is too large, the low illumination environment should be maintained during the operation to improve the efficiency of pupil matching.