Concave Spherical Mirror Research Articles

Single-frame fringe pattern analysis with synchronous phase-shifting based on polarization interferometry phase measuring deflectometry (PIPMD)

In the domain of phase measuring deflectometry (or fringe projection profilometry), utilizing only a single-frame fringe pattern to achieve high-precision three-dimensional reconstruction has emerged as a focal point of ongoing research. To achieve four-step phase-shifting demodulation from a single-frame fringe pattern, this paper proposes a Polarization Interferometry Phase Measuring Deflectometry (PIPMD). This method primarily relies on a Michelson polarization interferometry structure to produce projected polarization interference fringes, which are then captured by a polarization camera as modulated single-frame deformed fringe patterns. These single-frame fringe patterns enable pixelated four-step phase shifting with adjacent 2 × 2 pixel units. To validate the proposed method, a series of experiments has been conducted, including surface shape detection of a concave spherical mirror and an off-axis parabolic mirror, as well as dynamic deformation measurements of a deformable mirror. All experimental results consistently indicate that the polarization interference-based fringe projection technique can achieve synchronized phase-shifting demodulation of single-frame fringe patterns, thereby facilitating high-precision reconstruction of the fringe patterns captured in a single frame. This synchronous phase-shifting technique can overcome the influence of air disturbances in traditional four-step phase-shifting methods, thereby enhancing the accuracy of phase demodulation. Additionally, this polarization interference-based Phase Measuring Deflectometry exhibits promising application prospects in dynamic measurements.

Double light source Ronchi Tester for detection of ruling rotations

Abstract In this work, a modified Ronchi tester with a double light source has been implemented for evaluating and minimizing the rotation angle of the Ronchi ruling. The ruling rotations produced by positioning errors can become very small and could be going unnoticed (0.1°), however we have demonstrated that for these angle sizes the aberrations in the wavefront can not be completely neglicted. Accordingly with a rotatory mechanical device for correctioning the Ronchi ruling has been also added with this proposals. With our aim, in spite of non-straight shape that the ronchigrams can present in the patterns, the process of the ruling rotation degree measuring has hurled some experimental results when three concave mirrors: a concave spherical mirror, a concave parabolic mirror (the primary mirror of a Newtonian telescope) and a spherical concave mirror (the primary mirror of a Maksutov-Cassegrain telescope) have been tested.

FDM-assisted opposite two-way OA-CEAS system employing four lasers for simultaneous multi-species detection.

An FDM-assisted opposite two-way OA-CEAS system is reported in this paper. Compared with the traditional OA-CEAS system with one-way transmission configuration, the new system has two main advantages. One of the advantages is that four lasers can be employed for simultaneous measurements of multiple species in this system. Another advantage is the combination of the silver-coated concave spherical mirror and the narrow bandpass filter employed to realize the opposite two-way transmission in the optical cavity which can also serve as a re-injection mirror and optical enhancement gotten for free in the system. The performance of the system is demonstrated by simultaneous measurements of CO, CO2, C2H4, and CH4. This work highlights a new strategy for simultaneous detection by using four lasers in a single optical integrated cavity, which can improve the utilization rate of the optical cavity and reduce the cost for multiple gas species sensing.

Vision ray model based stereo deflectometry for the measurement of the specular surface

As a slope measuring specular surface measurement technique, deflectometry relies on the characterization of camera vision ray, which is commonly achieved with the distortion compensated pinhole model. However, this model is an approximate and inadequate description of lens layout and distortion, leading to low reproducibility of calibration and uncertainty in vision ray, and hence surface uncertainty. We implement the vision ray model (VRM) to stereo deflectometry, providing a pixelwise characterization of the vision ray that is free of intrinsic lens layout and distortion representation. Based on the VRM, the calibration method and surface reconstruction algorithm are proposed. We demonstrate with experimental study that the VRM can improve both the calibration performance and the surface measurement accuracy. The experimental results of a flat optical element and a concave spherical mirror indicate that the VRM based stereo deflectometry can achieve ten nanometers level RMS error.

Image formation from a concave mirror.

Computing locations and extent of images, except in the most trivial configurations or special cases, is a complex task. Even rays emanating from a point source and passing through an optical system generally fail to converge at a single image point, highlighting the care needed to establish image locations. We use three approaches to study image formation in a simple configuration, that of a point source following reflection from a spherical concave mirror. We calculate the caustic surfaces, compute cross sections of flux densities on image surfaces, and compare the results with experimentally generated light intensity fields. One of the two caustic surfaces is one dimensional while the other forms a surface. The latter undergoes a metamorphosis from a distorted cone to an open surface as the source is moved away from the axis. Cross sections of the caustic surfaces with an image plane are found to coincide with peaks in the flux density. Experimental studies validate these conclusions.

Determining the error in measuring the spherical concave mirror radius of curvature with a laser rangefinder

An instrument and technique for assessing errors of measuring optical surface radius of curvature with a laser rangefinder are presented. Errors of optical instrument alignment with a wave-front sensor are shown to influence the accuracy of measuring the mirror radius. Errors of the rangefinder-aided technique for measuring the surface radius are estimated. A computer analysis shows that the developed scheme of misalignment measurement allows a relative error of 0.02 – 0.3 % to be attained for mirrors ranging in radius from 1 m to 10 m. The choice of the accuracy characteristics of the rangefinders used for measuring the optical surface radius of curvature is justified.

Reflective acoustic jet from a mesoscale concave mirror

An acoustic jet (AJ) is similar to a photonic nanojet (PNJ) in achieving high-intensity and sub-wavelength scale focus. Herein, we numerically investigate a reflective acoustic jet (r-AJ) generated by a mesoscale concave mirror using the finite element method. A sub-λ/2 rotational symmetric r-AJ can be produced by an air-filled polylactic acid (PLA) spherical concave mirror immersed in water under a plane acoustic wave. And the properties of r-AJ affected by the concave angle of the mirror are also presented. By combining a PLA spherical structure with the concave mirror, a sub-λ/3 near-field r-AJ can be achieved. We also present the streamlines of the time-averaged acoustic intensity vectors near the r-AJ and the influence of the structural loss of the designed PLA mirror on the r-AJs. The influences of the incident frequency change and PLA properties change on the r-AJs generation and the slight angle between the incoming field and the mirror are presented. Finally, we numerically discuss the potential application of our designed mirror in direct sound printing.

A Novel Transient Electric Field Measurement for Low Kerr Constant Liquid Dielectrics Based on Concave Spherical Mirror Conjugate Structure

This article proposes a Kerr effect electric field measurement method based on a concave spherical mirror conjugate structure (CSM CS) for a transient electric field in low Kerr constant liquid dielectrics. The accuracy of transient electric field measurement can be greatly improved in a limited space by multiple small-angle reflections. To verify the effect of the proposed structure, the electric field distribution is measured in propylene carbonate (PC) with a high Kerr constant at a switching overvoltage. The measurement results show that the electric field error of a PC under an extremely low electric field is only about 2%. The novel structure improves the electric field measurement accuracy of a liquid with a high Kerr constant. Then, the whole device is applied to the transformer oil, and the accuracy of the measured electric field is also greatly improved. At the same electrode size, the sensitivity of measuring the electric field with the proposed structure is three times that without it. The analysis results show that the introduction of the proposed structure has little effect on the electric field measurement. The proposal and application of the proposed CSM CS further expand the electric field measurement range based on the Kerr effect and improves the electric field measurement accuracy.

Polynomial color compensation model with neural network solver for color-coded fringe patterns in phase-measuring deflectometry

The total image display/projection and image acquisition time in a projector-based phase-measuring deflectometry (PMD) measurement is reduced when color-coded fringe patterns are used since only a single image of the fringe pattern is sufficient to extract phase information using the phase-stepping method. This benefit is, however, offset by the difficulty in resolving various sources of color intensity errors of the fringe patterns in the camera view, such as uneven illumination, color imbalance, color crosstalk, and deviation of color intensity response of the camera and the projector from the calibrated color targets. Thus, a polynomial color compensation model is proposed in this study to compensate for color intensity errors. The model coefficients were estimated using the relationship between the captured and targeted color intensities, which are sequences of monochromatic 8-bit red, green, and blue (RGB) images for projection. The model was applied to modify the color intensities of the generated fringe patterns before projection. The modified color fringe patterns were then used for PMD measurement on spherical concave and convex mirrors. Based on the experimental results, the root-mean-squared (RMS) color intensity errors in R, G, and B channels were reduced by 33.3%, 58.3%, and 36.4%, respectively, after conducting the polynomial color compensation. The RMS phase errors in the fringe patterns were reduced by 71.9%. The RMS height errors and the radius percentage errors of the reconstructed concave and convex heightmaps were 1.87 μm (0.12%) and 1.55 μm (0.17%), respectively. The performance of the proposed polynomial color compensation model in reducing color intensity errors of the captured fringe patterns for accurate PMD measurement was demonstrated successfully.

Analytical design of a cemented-curved-prism based integral field spectrometer (CIFS) with high numerical aperture and high resolution.

Snapshot hyperspectral imaging is superior to scanning spectrometers due to its advantage in dimensionality, allowing longer pixel dwell time and higher data cube acquisition efficiency. Due to the trade-off between spatial and spectral resolution in snapshot spectral imaging technologies, further improvements in the performance of snapshot imaging spectrometers are limited. Therefore, we propose a cemented-curved-prism-based integral field spectrometer (CIFS), which achieves high spatial and high spectral resolution imaging with a high numerical aperture. It consists of a hemispherical lens, a cemented-curved-prism and a concave spherical mirror. The design idea of aplanatic imaging and sharing-optical-path lays the foundation for CIFS to exhibit high-resolution imaging in a compact structure. The numerical model between the parameters of optical elements and the spectral resolution of the system is established, and we analyze the system resolution influenced by the hemispherical lens and the cemented-curved-prism. Thus, the refractive index requirements of the hemispherical lens and the cemented-curved-prism for the optimal spatial and spectral resolution imaging of the system are obtained, providing guidance for the construction of CIFS. The designed CIFS achieves pupil matching with a 1.8 f-number lenslet array, sampling 268 × 76 spatial points with 403 spectral channels in the wavelength band of 400 to 760 nm. The spectral and spatial resolution are further evaluated through a simulation experiment of spectral imaging based on Zemax. It paves the way for developing integral field spectrometers exhibiting high spatial and high spectral resolution imaging with high numerical aperture.

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.

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.

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.

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.

Multi-laser sensor for simultaneous multi-gas measurements using off-axis cavity-enhanced absorption spectroscopy with an opposite two-way configuration.

An opposite two-way off-axis cavity-enhanced absorption spectroscopy-based multi-gas sensor is reported. More than two lasers can be employed in the sensor for simultaneous detection of different gas species. An approximately two times improvement in magnitude of the 2f signal and the signal-to-noise ratio is achieved because the concave spherical mirrors outside each end of the cavity and the narrow bandpass filters before the detectors can act as re-injection mirrors to re-inject the light into the cavity in the scheme. The performance of the sensor is demonstrated by simultaneous measurement of CO2 and CH4 in the atmosphere. This Letter highlights a new, to the best of our knowledge, strategy for simultaneous multi-gas measurement in a single integrated cavity by employing as many as four lasers.

Анализ интерферометра с микрозеркалом на светоделительном кубике

The control of the shape of the optical part surface by the interference method has become an integral part of the process of their shaping. With a precisely focused interferometer interferometry allows obtaining an interference pattern similar to a topographic map of the error profile of the wave surface under investigation. The interferometer must form a map of the optical surface with high accuracy --- the permissible distortion of the interference fringe caused by an interferometer error should not exceed 0.1 of the distortion value caused by an error on the examined surface. The dependence of the interference pattern formation on the errors in the arrangement of the interferometer components, i.e., defocusing, was theoretically analyzed using Fourier transforms. The analysis was performed for an interferometer containing a laser illuminator, a concave spherical mirror with a central hole, coaxial to the illuminator, and a beamsplitting element in the form of a cube-prism with a semitransparent hypotenuse face. On the first flat face of the cube-prism, a microspherical concave mirror is made with the center located on the optical axis of the interferometer. A method for calculating the defocusing of a controlled spherical mirror and the corresponding wave aberration of the working wavefront is presented. An example of calculating the design parameters of the interferometer and the permissible defocusing of the controlled spherical mirror is given

High-sensitivity acetylene detection system using ellipsoid multi-pass cell (EMPC) based on the opposite dual optical source

A multi-pass cell with ellipsoid structure used dual optical source of opposite side was proposed firstly in this paper. The EMPC was composed of double concave spherical mirrors and an ellipsoidal resonator. The radius of curvature of the two symmetric concave spherical mirrors was 200 mm and the length of the cavity was 120 mm. The size of the resonator of the photoacoustic (PA) cell in the experiment is Φ28mm×100mm and the size of the buffer cell at both ends of the PA cell is Φ70mm×10mm. The two laser beams were injected from the two sides of the concave spherical mirrors by the optical fiber. The absorption spectrum line with the acetylene wavelength of 1531.58 nm was selected. The simulation results show that the light beam can be reflected 37 times in EMPC and the optical path length can reach 8.64 m. In the experiment, the 2f signal peak value fitting curve obtained at different concentrations with good linearity. Allan deviation analysis of experimental results shows the detection limit of EMPC was 60 ppb when the average time was 2 s. When the average time was 2 s, the normalized noise equivalent absorption (NNEA) coefficient of the system was9.84×10-8cm-1·W·Hz-1/2. The whole system has high detection sensitivity and stability.

Optical Path Optimal Length for Ultraviolet Ammonia Detection With a Compact and Flexible Gas-Absorption Cell

A flexible and detachable gas-absorption cell with variable optical path length was designed to obtain the optical path optimal length for gas detection based on ultraviolet differential optical absorption spectroscopy. A model of the gas-absorption cell structure was established based on Lambert-Beer law. This model demonstrates the effect of different optical path lengths on ammonia detection, and the optical path optimal length of the proposed system is 1.6 m. A gas detection system was developed with the proposed gas-absorption cell, and the feasibility and stability of the system were evaluated at different ammonia concentrations. Owing to the influence of light loss induced by spherical concave mirror reflection and ammonia absorption, the detection results for ammonia at a concentration of 17 ppm are more accurate when the optical path length is 1.6 m versus 0.8 and 2.4 m. The error is less than 0.6% that is consistent with the simulation results. When the optical path length is 1.6 m, the linearity between the detection and the standard values reaches 0.9993. The standard deviation of the detection results is less than 0.3 ppm, indicating good stability of the system. The minimum detection limit of 0.43 ppm per meter is achieved. Water has a slight influence on the results of ammonia concentration detection. When the relative humidity is 7.5%, the response time of the system is 120 s that becomes longer with the increase of relative humidity. This method can be used to detect other gases with high precision.

Computational program to evaluate local defects type Chalmers Test on a reflective optical surface

A computational tool is developed to measure the local deformations in optical surfaces from the interference patterns obtained by the Chalmers test principle and from the analysis of a reflective optical surface using a commercial Fizeau interferometer of the ZYGO. The tests were made on a concave spherical mirror with a radius of curvature of 60 cm and a diameter of 13 cm. To obtain the measurements of local deformations, a computational tool proposed for the localization of dark fringes is used by evaluating the maximum and minimum of the image obtained in the interference patterns. The results obtained show that the computational tool allows locating fringes within an interference pattern, allowing faster inter-fringe measurements and assigning an error on the surface in terms of wavelength.

Radius of curvature of spherical wave measurement based on vortex beam interference

We proposed a new method for the radius of curvature (ROC) of spherical wave measurement based on vortex beam interference and Fermat's spiral fitting, which can not only provide a large measurement range but also have high precision. Theoretical analysis showed that the maximum distribution of the interference light intensity is in accordance with the Fermat's spiral, and the spiral coefficient is proportional to the ROC of spherical wave. For a concave spherical mirror with a ROC of 899.89mm and a convex spherical lens with a ROC of 59.99mm, the average measurement error of five measurements are 0.080% and 0.083%, respectively. Controlled experiments showed that, our proposed method has a higher measurement accuracy and a larger measurement range than Newton's rings method, it has almost equal measurement accuracy for large and small ROC. This research provides a theoretical basis for the development of a ROC measurement system with large measurement range and high precision.