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Advances in Optical Instrument and Measurement Technology

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Optics and Lasers".

Deadline for manuscript submissions: 20 April 2025 | Viewed by 7782

Special Issue Editors

Prof. Dr. Zhan Gao

E-Mail Website
Guest Editor
Key Laboratory of Luminescence and Optical Information of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China
Interests: optical metrology; image processing; optical sensors
Dr. Jiakun Li

E-Mail Website
Guest Editor
School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China
Interests: photoelectric detection and photoelectric sensing; laser measurement; machine vision measurement; gas imaging detection
Special Issues, Collections and Topics in MDPI journals
Dr. Qixin He

E-Mail Website
Guest Editor
Key Laboratory of Luminescence and Optical Information of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China
Interests: laser measurement; laser sensing; infrared gas detection; TDLAS; CEAS; structured light measurement
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, with the development of laser sources, measurement approaches and new materials, many new technologies or applications of measurement and new optical instruments have appeared. Therefore, this Special Issue is intended for the presentation of new ideas and experimental results in the field of high-performance optical instruments and measurement technology. Potential topics include, but are not limited to: optical design, fabrication and testing; ultrafast optic development; computational optical imaging; analog image processing with optical metasurfaces and metamaterials; novel techniques in microscopy; fiber-optic sensors; laser measurement; digital holographic metrology and sensing; micro- and nanophotoelectric measurement.

Prof. Dr. Zhan Gao
Dr. Jiakun Li
Dr. Qixin He
Guest Editors

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Keywords

  • optical design, fabrication and testing
  • applied industrial optics
  • computational optical imaging
  • novel techniques in microscopy
  • biosensors
  • optical manipulation and its applications
  • advances in meta-optics and metasurfaces
  • hyperspectral and multispectral imaging
  • new ultrafast laser applications
  • digital holographic metrology
  • LIDAR
  • laser measurement
  • micro‐ and nano photoelectric measurement

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Published Papers (7 papers)

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Research

11 pages, 3629 KiB  
Article
Improved Autocollimator for Roll Angle Measurement with an Enlarged Measuring Range
by Yan Guo, Yu Zhang, Jiali Ji, Qing Yan, Huige Di, Li Wang and Dengxin Hua
Appl. Sci. 2025, 15(5), 2256; https://doi.org/10.3390/app15052256 - 20 Feb 2025
Viewed by 224
Abstract
An autocollimator is a goniometer established according to the principle of autocollimation, but it is ineffective for measuring the roll angle. This paper proposes an improved autocollimator available for large-range roll angle measurement, which maintains the optical structure of the classic one while [...] Read more.
An autocollimator is a goniometer established according to the principle of autocollimation, but it is ineffective for measuring the roll angle. This paper proposes an improved autocollimator available for large-range roll angle measurement, which maintains the optical structure of the classic one while incorporating a wedge prism (WP) working in transmissive mode as a roll angle sensing element to dissociate the collimated beam into two beams. According to the moving paths of the two light spots focused on the photodetector, the roll angle of the WP can be solved. The measuring method is expounded, and the calibration results reveal that the improved autocollimator has an accuracy of ±13.55 arcsec over a range of 360°, confirming its feasibility for roll angle measurement where a large measuring range is required. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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Figure 1
<p>Schematic of improved autocollimator for roll angle measurements.</p> Full article ">Figure 2
<p>Roll angle measurement: (<b>a</b>) principle and (<b>b</b>) light spots on CMOS before and after WP’s rolling.</p> Full article ">Figure 3
<p>Photograph of improved autocollimator for large-range roll angle measurement.</p> Full article ">Figure 4
<p>Results of stability test.</p> Full article ">Figure 5
<p>Calibration experiment: (<b>a</b>) setup and (<b>b</b>) results.</p> Full article ">Figure 6
<p>Results of resolution test.</p> Full article ">Figure 7
<p>Actual test of linear stage: (<b>a</b>) experimental setup and (<b>b</b>) results.</p> Full article ">
13 pages, 2250 KiB  
Article
Absorption Measurement in Ultrapure Crystalline Quartz with the Eliminated Influence of Ambient Air Absorption in the Time-Resolved Photothermal Common-Path Interferometry Scheme
by Ksenia Vlasova, Alexandre Makarov and Nikolai Andreev
Appl. Sci. 2024, 14(20), 9474; https://doi.org/10.3390/app14209474 - 17 Oct 2024
Viewed by 1000
Abstract
We demonstrate measurements of the absorption coefficient α ≈ 2.5 × 10−7 cm−1 in synthetic crystalline quartz at a wavelength of 1071 nm with a signal-to-noise ratio of 10/1 using the Time-resolved photothermal common-path interferometry (TPCI) scheme. It utilized cells filled [...] Read more.
We demonstrate measurements of the absorption coefficient α ≈ 2.5 × 10−7 cm−1 in synthetic crystalline quartz at a wavelength of 1071 nm with a signal-to-noise ratio of 10/1 using the Time-resolved photothermal common-path interferometry (TPCI) scheme. It utilized cells filled with flowing argon and eliminated the influence of ambient air absorption. The scheme elements limiting the sensitivity of measurements at the level of ≈7.8 × 10−8 cm−1 were revealed. When these elements are replaced by better ones in terms of their thermal influence, the sensitivity of absorption coefficient measurements in crystalline quartz is ~10−8 cm−1. The calculation of the correction due to these optical elements of the values of the measured absorption coefficients is also described, which makes it possible to achieve the same sensitivity without replacing the elements. The improved scheme confirms the presence of the spatial inhomogeneity of absorption with a minimum coefficient of 2.5 × 10−7 cm−1 in synthetic crystalline quartz. The discrepancy of the absorption coefficient values in different regions of the crystal in the presented series of experiments was 2.5 × 10−7 cm−1 to 4 × 10−6 cm−1. Taking into account the ratio of thermo-optical parameters and the heat diffusion effect, the calculation shows that for quartz glasses the corresponding sensitivity of the absorption coefficient measurements equals ≈1.5 × 10−9 cm−1. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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Figure 1
<p>Time-resolved photothermal common-path interferometry (TPCI) electro-optical scheme (argon cells not shown).</p> Full article ">Figure 2
<p>The part of the optical scheme modified in this paper consisting of cells with open ends into which argon of 99.99% purity was supplied. The dashed lines show the argon flows.</p> Full article ">Figure 3
<p>Example of single (i.e., without averaging) waveforms of the time-varying component of the probe radiation power U(t), at a time interval of 0.1 s, obtained when argon was used as a sample at gas flow velocity below the threshold of turbulence (red) and above the threshold (blue).</p> Full article ">Figure 4
<p>Scheme of arrangement of beam propagation direction (k<sub>h</sub>), heating beam polarization (E<sub>h</sub>) and crystallographic axes (C and a<sub>i</sub>) in the sample.</p> Full article ">Figure 5
<p>The waveforms of the time-varying component of the probe radiation power U(t) in the experiments with argon and ambient air averaged over 10<sup>4</sup> realizations: (<b>a</b>) Waveforms obtained during the co-propagation of the heating and probe beams in argon (color) and the waveform due to the absorption of ambient air filling the entire space between the elements M<sub>2</sub> and M<sub>3</sub> (black). Different color curves correspond to five independent experiments; (<b>b</b>) The same waveforms with a 40-times scale increase along the ordinate axis (color) and the waveform due to the absorption of air with the amplitude reduced 40 times (black).</p> Full article ">Figure 6
<p>Averaged over 10<sup>4</sup> realizations and over time (≈100 μs) waveforms of the time-varying component of the probe radiation power U(t) in experiments with argon and ambient air: (<b>a</b>) Waveforms obtained when the heating and probe beams were co-propagated in argon (color), and an waveform (amplitude reduced 40 times) due to ambient air absorption (black). Different color curves correspond to five independent experiments; (<b>b</b>) Arithmetic averages from five waveforms similar to (<b>a</b>), which were obtained in two independent experiments conducted on different days (color) and a waveform due to ambient air absorption (black). The amplitudes of the black curves are reduced 40 times.</p> Full article ">Figure 7
<p>Averaged over 10<sup>4</sup> realizations waveforms of the time-varying component of the probe radiation power U(t) in experiments with synthetic crystalline quartz (different color curves correspond to different positions of the crystal under test and, accordingly, to its different spatial regions): (<b>a</b>) Waveforms obtained when the cells were filled with ambient air (black negative) and argon (black positive) and the crystal was in the same position, and waveforms obtained when the cells were filled with argon and the crystal position was varied perpendicular to the beam axis (color); rectangular function reflects the influence of electronic nonlinearity of the refractive index (black rectangular); (<b>b</b>) Waveforms shown in (<b>a</b>), obtained after subtracting the rectangular function from them; (<b>c</b>) Waveforms shown in (<b>b</b>), normalized to their maximum amplitude.</p> Full article ">Figure 8
<p>Differences of waveforms of the time-varying component of the probe radiation power U(t) in experiments with synthetic crystalline quartz (different color curves in figures (<b>a</b>,<b>b</b>) correspond to different positions of the crystal under test and, accordingly, to its different spatial regions): (<b>a</b>) Differences of waveforms obtained at different positions of the sample with the waveform obtained at the position with minimal absorption (<a href="#applsci-14-09474-f007" class="html-fig">Figure 7</a>a, black positive curve); (<b>b</b>) The same waveforms normalized to their maximum amplitude; the light blue curve is used as a universal curve describing the time dependence of the absorption contribution of the crystal in U(t); (<b>c</b>) Characteristic curves, which are the difference between the curves of the corresponding color shown in <a href="#applsci-14-09474-f007" class="html-fig">Figure 7</a>b and the universal curve with the matched amplitude. The black curve is a piecewise linear approximation of the corresponding curves shown in <a href="#applsci-14-09474-f006" class="html-fig">Figure 6</a>b.</p> Full article ">
15 pages, 975 KiB  
Article
Analysis of Beam Walk in Inter-Satellite Laser Link: Implications for Differential Wavefront Sensing in Gravitational Wave Detection
by Xing-Guang Qian, Zhao Cui, Hao-Qi Shi, Xue Wang, Wei-Lai Yao, Rui-Hong Gao and Yi-Kun Wang
Appl. Sci. 2024, 14(13), 5526; https://doi.org/10.3390/app14135526 - 25 Jun 2024
Viewed by 1184
Abstract
Achieving space-based gravitational wave detection requires the establishment of an interferometer constellation. It is necessary to establish and maintain stable laser interferometric links using the differential wavefront sensing (DWS) technnique. When the distant measurement beam experiences pointing jitter, it causes beam walk on [...] Read more.
Achieving space-based gravitational wave detection requires the establishment of an interferometer constellation. It is necessary to establish and maintain stable laser interferometric links using the differential wavefront sensing (DWS) technnique. When the distant measurement beam experiences pointing jitter, it causes beam walk on the surface of the local detector. The reduced overlap between the local reference spot and the distant spot increases the nonlinear errors in the DWS technique, which need to be suppressed. Numerical analysis was conducted on the spatial beam interference signals of the DWS technique when the distant measurement beam experienced pointing jitter. An experimental measurement system was designed, and the beam walk was suppressed using a conjugate imaging system. The results show that within a range of 300 μrad, the optical path with the imaging system can reduce measurement errors by at least 83%. This way also helps to reduce pointing jitter noise in inter-satellite links, thereby improving laser pointing control accuracy.This method would provide a valuable reference for future DWS measurement systems. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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Figure 1
<p>(<b>a</b>) Coincidingwiththe local beam, the distal incident beam is incident vertically to the center of QPD without beam walk. When beam walk exists in the pitch direction, the spot will shift in the y-axis direction. (<b>b</b>) The measurement results of the DWS technique when beam walk occurs in the incident beam. The left side indicates the interference conditions, while the right side shows the phases of each quadrant.</p> Full article ">Figure 2
<p>Representation of interference dynamics amidst x-axis beam walk. (<b>a</b>) Depicts the QPD surface within the black circle. The centrally injected local Gaussian beam is denoted by the red circle, while the blue circle with the dotted line demonstrates the beam walk of the distant Gaussian flat-top spot, establishing an angle <math display="inline"><semantics> <mi>φ</mi> </semantics></math> between the two beams. (<b>b</b>) Exhibits Gaussian flat-top beam post-square-aperture truncation, encapsulated in the blue box. Here, the y-axis integration ranges for both left and right quadrants extend from <math display="inline"><semantics> <mrow> <mo>−</mo> <msub> <mi>ω</mi> <mi>f</mi> </msub> </mrow> </semantics></math> to <math display="inline"><semantics> <msub> <mi>ω</mi> <mi>f</mi> </msub> </semantics></math>, whereas the x-axis spans from <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>−</mo> <mfrac> <msub> <mi>ω</mi> <mi>f</mi> </msub> <mrow> <mo form="prefix">cos</mo> <mo>(</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mfrac> <mo>,</mo> <mo>−</mo> <mi>h</mi> <mo>)</mo> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>h</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <msub> <mi>ω</mi> <mi>f</mi> </msub> <mrow> <mo form="prefix">cos</mo> <mo>(</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mfrac> <mo>)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>Variation of angle measurement error <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>φ</mi> <mo>(</mo> <mi>φ</mi> <mo>)</mo> </mrow> </semantics></math> in the absence of beam walk (0 μm Scenario).</p> Full article ">Figure 4
<p>DWS signals for various degrees of beam walk during light propagation over a 2 m axial distance.</p> Full article ">Figure 5
<p>DWS error signals for various degrees of beam walk during light propagation over a 2 m axial distance.</p> Full article ">Figure 6
<p>Correlation between propagation distance and angle measurement precision. Note: Blue dots represent the magnitude of angle measurement errors that fall within the Taiji program’s acceptable linearity range across various propagation distances, while the orange line depicts the trend through linear fitting.</p> Full article ">Figure 7
<p>Design of imaging system.</p> Full article ">Figure 8
<p>Schematic diagram of the inter-satellite laser link simulation system.</p> Full article ">Figure 9
<p>Comparative analysis of the DWS angle measurement error with and without imaging system correction for beam walk.</p> Full article ">Figure 10
<p>Comparative analysis of angular measurement errors: assessing performance with (red line) and without (blue line) the imaging system.</p> Full article ">Figure 11
<p>Comparative analysis of angular measurement errors in 20 μrad: assessing performance with (red line) and without (blue line) the imaging system.</p> Full article ">Figure 12
<p>Comparative analysis of jitter RMS: assessing performance with (red line) and without (blue line) the imaging system.</p> Full article ">
16 pages, 8909 KiB  
Article
Establishment and Accuracy Analysis of Measurement Control Network Based on Length–Angle Mixed Intersection Adjustment Model
by Zhi Xiong, Chunsen Li, Hao Zhang, Chenxiaopeng Zhong, Zhongsheng Zhai and Ziyue Zhao
Appl. Sci. 2024, 14(11), 4948; https://doi.org/10.3390/app14114948 - 6 Jun 2024
Viewed by 1247
Abstract
To achieve high-precision measurements of target points on long straight tracks, a multi-level measurement method based on length–angle mixed intersection techniques was explored. Firstly, a control network with graded measurement levels was proposed, based on the spatial error characteristics of different measuring devices [...] Read more.
To achieve high-precision measurements of target points on long straight tracks, a multi-level measurement method based on length–angle mixed intersection techniques was explored. Firstly, a control network with graded measurement levels was proposed, based on the spatial error characteristics of different measuring devices and the principle of nonlinear least squares, and a method for adjustment calculation based on length–angle mixed intersection was studied. Secondly, numerical simulation was conducted to assess the impact of instrument placement on measurement accuracy, and the results indicated that central positioning within the measurement range can effectively minimize the overall point location errors. Finally, the methodology was validated in a practical setting at a rocket sled test site. Experimental results demonstrated that, within a measurement range of approximately 669 m, when target points were located on one side of the track and distance measurements were used as benchmark values, the measurement control network achieved a distance standard deviation of 0.20 mm. The range of distance deviations was between −0.85 mm and 0.98 mm. This approach offers substantial reference value for high-precision coordinate measurements over extended distances. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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<p>Grading of measurement control network.</p> Full article ">Figure 2
<p>Schematic of the coordinate system of the measuring instrument.</p> Full article ">Figure 3
<p>Angular measurement error of the laser tracker.</p> Full article ">Figure 4
<p>Repeatability cloud for single−point coordinate measurement by laser tracker: (<b>a</b>) projection on the xoy plane; (<b>b</b>) projection on the xoz plane; and (<b>c</b>) projection on the yoz plane.</p> Full article ">Figure 5
<p>Repeatability cloud for single−point coordinate measurement by total station.</p> Full article ">Figure 6
<p>Repeatability cloud of single−point measurement error in the x, y, and z directions by total station: (<b>a</b>) projection on the xoy plane; (<b>b</b>) projection on the xoz plane; and (<b>c</b>) projection on the yoz plane.</p> Full article ">Figure 7
<p>Distribution of target points, reference points, and stations on a long track.</p> Full article ">Figure 8
<p>The schematic diagram for calculating the horizontal angle <span class="html-italic">α</span> in the global coordinate system.</p> Full article ">Figure 9
<p>The schematic diagram of measuring station distribution.</p> Full article ">Figure 10
<p>Contour plot of measurement error of target point coordinates under different instrument positions.</p> Full article ">Figure 11
<p>Standard deviation of target points after adjustment.</p> Full article ">Figure 12
<p>Standard deviation of target points after adjustment compared to networking with laser trackers.</p> Full article ">Figure 13
<p>Flow chart of the experimental process.</p> Full article ">Figure 14
<p>Distribution of measuring stations and points at the experimental site.</p> Full article ">Figure 15
<p>Comparative analysis of distance measurement: (<b>a</b>) distance benchmark value and adjusted distance value and (<b>b</b>) deviation.</p> Full article ">
15 pages, 7816 KiB  
Article
The Microchip Laser and Its Drive Control System for Planetary Mass Spectrometry Measurements
by Wenbo Liu, Peng Sang, Yang Cao, Yaning Liu, Huan Wang and Baoquan Li
Appl. Sci. 2024, 14(8), 3251; https://doi.org/10.3390/app14083251 - 12 Apr 2024
Viewed by 953
Abstract
To fulfill the requisites of planetary mass spectrometry applications, this paper introduces the creation of a miniaturized, low-power passive Q-switched microchip laser system. The entire system, inclusive of the laser and all electronic components, weighs 106 g, with power consumption below 3 W. [...] Read more.
To fulfill the requisites of planetary mass spectrometry applications, this paper introduces the creation of a miniaturized, low-power passive Q-switched microchip laser system. The entire system, inclusive of the laser and all electronic components, weighs 106 g, with power consumption below 3 W. The laser output exhibits a pulse duration of 410 ps, accompanied by a single pulse energy of 16.8 μJ. Augmented by the optical focusing system, the system attains a focal spot size of approximately 15 μm and laser irradiance of up to 22 GW/cm2. The driving control system facilitates versatile regulation of parameters such as output current amplitude, pulse duration, and frequency, thereby modulating the laser output frequency and duty cycle. The microchip laser fully meets the power requirements for exciting plasma from planetary rocks and soil. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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<p>Illustration of a passively Q-switched microchip laser.</p> Full article ">Figure 2
<p>Schematic of imaging optical system of LD pumped laser.</p> Full article ">Figure 3
<p>Structural diagram of microchip laser.</p> Full article ">Figure 4
<p>Design diagram of the optical focusing system.</p> Full article ">Figure 5
<p>Overall Structure Diagram of Laser Driver System.</p> Full article ">Figure 6
<p>Control Circuit Structure Diagram.</p> Full article ">Figure 7
<p>Schematic Diagram of Control Circuit.</p> Full article ">Figure 8
<p>Structure diagram of temperature control system.</p> Full article ">Figure 9
<p>Photograph of microchip laser.</p> Full article ">Figure 10
<p>Experimentally measured current waveform plot.</p> Full article ">Figure 11
<p>Laser output waveform plot.</p> Full article ">Figure 12
<p>Power stability testing under single pulse output conditions.</p> Full article ">Figure 13
<p>Initial laser pulse energy stability test.</p> Full article ">Figure 14
<p>The image depicting the laser spot output tested with a CCD detector.</p> Full article ">Figure 15
<p>Laser excitation of microchip laser for the generation of plasma in stone.</p> Full article ">Figure 16
<p>The impact craters on the aluminum foil generated by laser irradiation observed under a microscope.</p> Full article ">
8 pages, 2156 KiB  
Communication
Efficient Method for Identifying Key Errors Based on 21-Geometric-Error Measurement of Three Linear Axes of Machine Tools
by Fajia Zheng, Bin Zhang, Yuqiong Zhao, Jiakun Li, Fei Long and Qibo Feng
Appl. Sci. 2024, 14(7), 2982; https://doi.org/10.3390/app14072982 - 2 Apr 2024
Cited by 2 | Viewed by 1323
Abstract
Key errors of machine tools have a significant impact on their accuracy, however accurately and quickly measuring the geometric errors of machine tools is essential for key error identification. Fortunately, a quick and direct laser measurement method and system for 21 geometric errors [...] Read more.
Key errors of machine tools have a significant impact on their accuracy, however accurately and quickly measuring the geometric errors of machine tools is essential for key error identification. Fortunately, a quick and direct laser measurement method and system for 21 geometric errors of three linear axes of machine tools were proposed previously, which enables the measurement of all 21 geometric errors via a one-step installation and a three-step automated measurement process. Based on this, to efficiently identify the key error factors, this paper first utilizes the 21 geometric errors obtained from the proposed measurement system to evaluate the contribution of each error to the volumetric errors of machine tools, leading to the building of a 21-geometric-error sensitivity analysis model. Then, experiments are carried out on the vertical machining tool TH5656, and all 21 geometric errors are obtained in 5 min. After this, the volumetric error distribution in the machining workspace is mapped according to the relationship between the geometric errors and the machining errors, and the key error factors affecting the manufacturing and machining accuracy of the TH5656 are ultimately determined. Thus, this new method provides a way to quickly identify key errors of the three linear axes of machine tools, and offers guidance for the machine tool configuration design, machining technology determination, and geometric error compensation. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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<p>Measurement of 21 geometric errors for the vertical machine tool: (<b>a</b>) developed measurement system; (<b>b</b>) vertical machine tool TH5656; and (<b>c</b>–<b>e</b>) measurement of six errors of the <span class="html-italic">X</span>-, <span class="html-italic">Y</span>-, and <span class="html-italic">Z</span>-axes, respectively.</p> Full article ">Figure 2
<p>Comparison results: (<b>a</b>) yaw of <span class="html-italic">X</span>-axis; (<b>b</b>) position error of <span class="html-italic">Y</span>-axis; and (<b>c</b>) straightness of <span class="html-italic">Z</span>-axis.</p> Full article ">Figure 3
<p>Volumetric error distribution of TH5656: (<b>a</b>) volumetric error Δ<span class="html-italic">x</span> in <span class="html-italic">X</span>-direction; (<b>b</b>) volumetric error Δ<span class="html-italic">y</span> in <span class="html-italic">Y</span>-direction; (<b>c</b>) volumetric error Δ<span class="html-italic">z</span> in <span class="html-italic">Z</span>-direction.</p> Full article ">Figure 4
<p>Influence factor distribution of TH5656: (<b>a</b>) influence factor <span class="html-italic">E<sub>x</sub></span> in X-direction; (<b>b</b>) influence factor <span class="html-italic">E<sub>y</sub></span> in Y-direction; (<b>c</b>) influence factor <span class="html-italic">E<sub>z</sub></span> in Z-direction.</p> Full article ">
14 pages, 5672 KiB  
Article
An Iterative High-Precision Algorithm for Multi-Beam Array Stitching Method Based on Scanning Hartmann
by Xiangyu Yan, Dahai Li, Kewei E, Fang Feng, Tao Wang, Xun Xue, Zekun Zhang and Kai Lu
Appl. Sci. 2024, 14(2), 794; https://doi.org/10.3390/app14020794 - 17 Jan 2024
Viewed by 893
Abstract
The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane [...] Read more.
The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane of the optical system. The centroid position of the spot contains the information about the wavefront slope of the sub-aperture at that specific location in the optical system. Scanning the optical system with this small-aperture beam across the entire aperture of the optical system, we can yield the aberration information to be tested. To mitigate pointing errors induced by scanning motion and accurately obtain the aberration signals of the optical system, nine beams are integrated into a 3 × 3 multi-beam array system, and their directions are aligned to be identical. However, achieving complete alignment in the same direction for all nine beams is a challenging task, resulting in errors due to their pointing differences within the array. This paper introduces an iterative algorithm designed to obtain high-precision multi-beam pointing errors and to reconstruct the wavefront of the optical system under test. This enables a more accurate measurement of wavefront aberrations in the optical system to be tested. Firstly, simulation models were implemented to validate the algorithm’s feasibility. Additionally, a scanning optical measurement system with a multi-beam array was developed in our lab, and the iterative algorithm was applied to process our experimental data. The results were then compared with interferometer data, demonstrating that our algorithm is feasible for MASTS to measure aberrations in large-aperture optical systems with high accuracy. Full article
(This article belongs to the Special Issue Advances in Optical Instrument and Measurement Technology)
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<p>Schematic diagrams of (<b>a</b>) multi-beam array measuring optical system and (<b>b</b>) the path covering the entire aperture in a multi-beam array scanning optical system.</p> Full article ">Figure 2
<p>Iterative process flowchart.</p> Full article ">Figure 3
<p>Schematic diagrams of (<b>a</b>) the simulation model of the optical system and (<b>b</b>) the aberrations in the simulation model of the optical system.</p> Full article ">Figure 4
<p>Schematic diagrams of array scanning way with (<b>a</b>) non-overlapping, (<b>b</b>) partially overlapping (one column), (<b>c</b>) extensively overlapping (two columns), and (<b>d</b>) schematic diagrams of sampled points distribution. (The dashed line in figure represents the position of a multi-beam array system before the scanning movement, while the solid line represents the position after the movement. The red circles indicate beams undergoing repeated sampling. In (<b>d</b>), the green circle represents the optical system aperture (1 m), and the blue circle with red dots indicates the effective sampled points).</p> Full article ">Figure 5
<p>In the first row, the reconstructed wavefront through the iterative method when the scanning step (<b>a</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>b</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>c</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively. In the second row, the residuals after subtracting the reconstructed wavefront distribution from the preset aberrations when the scanning step (<b>d</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>e</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>f</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively. In the third row, the curves depicting the convergence of aberration PV values and RMS values of the difference between the preset and the reconstructed when the scanning step (<b>g</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>h</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>i</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively.</p> Full article ">Figure 5 Cont.
<p>In the first row, the reconstructed wavefront through the iterative method when the scanning step (<b>a</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>b</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>c</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively. In the second row, the residuals after subtracting the reconstructed wavefront distribution from the preset aberrations when the scanning step (<b>d</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>e</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>f</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively. In the third row, the curves depicting the convergence of aberration PV values and RMS values of the difference between the preset and the reconstructed when the scanning step (<b>g</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>h</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>i</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively.</p> Full article ">Figure 6
<p>Distribution plots obtained by subtracting the preset aberrations from the reconstructed wavefront using the averaging method when the scanning step (<b>a</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>b</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>c</b>) refers to <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c, respectively.</p> Full article ">Figure 7
<p>Comparison of the Zernike coefficients of aberrations with the iterative method and the averaging method, which are presented for different scanning steps, (<b>a</b>) referencing <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>b</b>) referencing <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>c</b>) referencing <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c.</p> Full article ">Figure 7 Cont.
<p>Comparison of the Zernike coefficients of aberrations with the iterative method and the averaging method, which are presented for different scanning steps, (<b>a</b>) referencing <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>a, (<b>b</b>) referencing <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>b, and (<b>c</b>) referencing <a href="#applsci-14-00794-f004" class="html-fig">Figure 4</a>c.</p> Full article ">Figure 8
<p>The setup for the wavefront calibration of the beams in the multi-beam array system.</p> Full article ">Figure 9
<p>The setup for the alignment of multiple beams.</p> Full article ">Figure 10
<p>Experimental setup of (<b>a</b>) multi-beam array and (<b>b</b>) MASTS.</p> Full article ">Figure 11
<p>The reconstructed wavefront distributions of optical system (<b>a</b>) using interferometer data, (<b>b</b>) using iterative method with step size of 20 mm, (<b>c</b>) using iterative method with step size of 40 mm, (<b>d</b>) using averaging method with step size of 20 mm, (<b>e</b>) using averaging method with step size of 40 mm, (<b>f</b>) without correcting for multi-beam pointing error E and with step size of 20 mm, and (<b>g</b>) without correcting for multi-beam error E and with step size of 40 mm.</p> Full article ">
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