rus
Issue #7/2021
M. A. Zavyalova, P. S. Zavyalov, M. V. Savchenko
Experimental Studies of Fiber Confocal Sensor Based on Chromatic Coding Method
Experimental Studies of Fiber Confocal Sensor Based on Chromatic Coding Method
DOI: 10.22184/1993-7296.FRos.2021.15.7.598.609
The paper presents the results of experimental studies of a fiber confocal sensor based on the chromatic coding method with the developed hybrid refractive-diffractive and hyperchromatic lenses. This sensor allows you to determine the position of the controlled surfaces with a high resolution (the error does not exceed 0.1–1 µm) on working segments from 20 to 220 µm.
The paper presents the results of experimental studies of a fiber confocal sensor based on the chromatic coding method with the developed hybrid refractive-diffractive and hyperchromatic lenses. This sensor allows you to determine the position of the controlled surfaces with a high resolution (the error does not exceed 0.1–1 µm) on working segments from 20 to 220 µm.
Теги: chromatic coding method confocal sensor diffractive optical element laser micromachining of materials дифракционный оптический элемент конфокальный датчик лазерная микрообработка материалов метод хроматического кодирования
Experimental Studies of Fiber Confocal Sensor Based on Chromatic Coding Method
M. A. Zavyalova, P. S. Zavyalov, M. V. Savchenko
Tecnological Design Institute of Scientific Instrument Engineering, SB RAS, Novosibirsk, Russia
The paper presents the results of experimental studies of a fiber confocal sensor based on the chromatic coding method with the developed hybrid refractive-diffractive and hyperchromatic lenses. This sensor allows you to determine the position of the controlled surfaces with a high resolution (the error does not exceed 0.1–1 µm) on working segments from 20 to 220 µm.
Keywords: confocal sensor, chromatic coding method, diffractive optical element, laser micromachining of materials
Received on: 11.10.2021
Accepted on: 25.11.2021
Introduction
Laser synthesis of microstructures on the surface of various materials requires the development of methods for precision positioning of microlens that focus the radiation. For these purposes, as a rule, optical non-contact sensors are used, which make it possible to determine the position of the surface of the objects being processed with a high resolution. Such sensors are used in laser technological installations for the synthesis of high-precision photonic elements with sizes from a few millimeters to tens of nanometers [1–3].
The most important requirements for optical proximity sensors are high speed (up to 1 MHz) and resolution. In addition, the task of designing such sensors becomes more complicated for the cases of recording microstructures on three-dimensional surfaces, which is important at this stage in the development of a high-tech element base [4, 5]. Since the synthesized elements of photonics are optically transparent media with a low reflection coefficient, such sensors must have the necessary power reserve of the probing radiation.
The possibility of synthesizing micro- and nanostructures on flat and curved surfaces makes it possible to produce unique optical elements and devices based on them, which are in high demand in modern technology [6–9]. Over the past 15–20 years, impressive progress has been observed in the field of creating laser technological complexes for processing and structuring various types of materials. Among them, unique are systems that allow micro- and nanostructuring of three-dimensional surfaces with a resolution of less than 0.1 μm [10].
To implement many of these methods, it is necessary to accurately control the position of the focal plane of the working microlens, which must be aligned either with the plane of the photosensitive layer applied to the substrate surface, or with the substrate surface. The position sensor, which is part of the automatic focusing system (AFS), is required to constantly hold the focused recording spot on the surface of the synthesized element during recording at speeds up to 10 m / s. It is important to note that a focusing error exceeding ±0.2 μm (for a lens with a numerical aperture of 0.65) leads to a significant change in the size and shape of the recording spot and, consequently, in the recording parameters, and the tilt of the lens axis leads to an error in the recording coordinate [11]. If the recording surface is three-dimensional, then the task becomes more complicated and requires the development and implementation of previously unused precision autofocusing methods. AFSs developed on these principles allow controlling technological processes with great accuracy. As a rule, such systems contain a large number of original sensors, which largely determine the efficiency of the technological process.
Basic technical requirements for sensors for monitoring the position of objects
The following requirements are imposed on sensors for monitoring the position of objects used in laser technological installations for the formation of high-quality micro- and nanostructures:
1. Compactness and integration into the technological laser channel.
Typically, such sensors must be embedded in the existing optical channels of processing units. This is due to the fact that for focusing laser radiation into a spot with a diameter of 1 μm or less, micro lenses with a large numerical aperture – from 0.65 and higher, and, therefore, with a small focal distance are used, which makes it difficult to integrate the finished sensor directly in front of the focusing element. Thus, the probe radiation of the sensor should be focused by the same element as the radiation of the working laser.
2. High performance
Since laser technological installations have a high recording speed (up to 10 m / s), the position sensors must perform precise positioning of the actuators at a signal frequency from several kilohertz to 1 MHz.
3. High resolution
For the formation of high quality microstructures with a depth of up to several tens of micrometers, the resolution of the sensors should be an order of magnitude better – 1 μm or less.
4. Working range
This characteristic of the sensor related to the depth of the synthesized structures, and determines the possibility of structuring the curved surfaces (the angle of inclination of the tangent to the surface should not exceed 8° to microscope lenses having a numerical aperture of 0.65).
5. Recordable on curved surfaces
Since, in this case, the probing radiation of the sensors for monitoring the position of objects can additionally change its parameters due to the curvature of the surface, a preliminary assessment of the influence of the curvature on the signal from the sensor must be carried out.
6. Advanced functionality
Along with the main task of such sensors in tracking the linear movement of the controlled object and converting the change in its position into the corresponding output signal, they must automatically search for the surface to be treated, determine the size of the focused spot, measure the profile of the resulting structures, etc. All this improves the technical capabilities of laser technological installations and makes it possible to improve the quality of synthesized structures.
The optical methods of surface control used in laser technological complexes are very diverse. Non-contact optical sensors for measuring distances with high resolution (less than 1 μm) include interferometric [12], triangulation [13] and confocal sensors [14, 15], which are mass-produced and in large volumes and, in general, provide the growth of the measuring equipment industry. However, they satisfy only part of the requirements described above. Thus, laser interferometric sensors have the necessary sensitivity and speed, but at the same time they cannot be combined with a working microlens that focuses laser radiation. Triangulation sensors can only measure distance to flat surfaces. Available commercial sensors (interferometric and confocal types) are mainly produced abroad and are expensive. They have closed-type optical circuits and cannot be incorporated into laser systems that use micro-lenses with a short focal distance (less than 1 mm). Therefore, the areas and scales of their application in laser technological installations are still very limited, and it is quite natural that the efforts of developers are aimed at creating such sensors and reducing their cost.
Therefore, an urgent task in the design of laser technological complexes is the development and study of high-speed precision sensors for automatic focusing of laser radiation on optical surfaces, monitoring the result of interaction and measuring the profile of synthesized structures.
The paper will consider a fiber confocal sensor based on the chromatic coding method developed in Novosibirsk at the Tecnological Design Institute of Scientific Instrument Engineering, SB RAS (hereinafter referred to as TDISIE, SB RAS).
The principle of operation of this sensor is described in detail in [16, 17]. It evaluates the spectral distribution of the intensity of optical signals reflected from the measured surfaces. For these purposes, a polychromatic sounding signal is used in combination with hyperchromatic lenses (HCL), which focus the spectral components at different distances along the direction of light propagation. The use of a special point (or confocal) diaphragm limiting the flow of background scattered light from points outside the focal plane of the lens makes it possible to select radiation with a narrow spectrum, in which the central wavelength is the chromatic code of the distance to the surface, and its change is proportional to the surface displacement.
This sensor is necessary for precise control of the position of the focusing plane of the working microlens. With its help, a constant retention of the focused recording spot on the surface of the synthesized element should be carried out during high-speed processing of optically transparent media.
At this stage, an optical scheme was developed to study the accuracy characteristics of the sensor (Fig. 1). It uses an illuminator based on a halogen lamp (1) DL150 (Dedolight, Germany), a fiber confocal sensor (TDISIE, SB RAS, Novosibirsk) (2). The object is displaced using a three-coordinate stage (3) ZSS 33.200.1.2 (Phytron, Germany). The change in the reflected signal is controlled using an analyzer (4), which includes a GT13–06V diffraction grating (Thorlabs, Germany) and a KTs‑1310 video camera (TDISIE, SB RAS, Novosibirsk). The scheme also includes an XL‑80 interferometer (5) (RENISHAW, Great Britain), which makes it possible to control the displacement of an object with an error of less than 0.1 μm.
The developed LineIntensity software allows processing the signal from the analyzer of the confocal sensor. A video camera displays an image of the reflected signal spectrum shown Fig. 2. It can be colored Fig. 2 a, or black and white Fig. 2b depending on the mode of use of the camera.
Further signal processing consists of three stages. At the first stage, the result of the subtraction is processed with a Gaussian blur. Blur is applied to reduce the effect of noise on the original result. At the second stage, the specified constant (in fact, the background component) is subtracted to select significant pixels. At the third stage, the peak detection algorithms are implemented. In total, three algorithms were investigated: the search for the brightest point, the center of mass, and a linear approximation of the differential signal. The obtained peak coordinates are used to estimate the measurement error.
The brightest point search algorithm takes the brightest pixel available as the peak. Due to the absence of any further processing, it is the fastest algorithm available, but it increases the measurement error.
The algorithm for finding the center of mass takes as the peak the center of mass of the brightness of pixels, calculated by the formula , where rc are the coordinates of the center of mass, ri are the coordinates of the pixel, and mi is the brightness of the pixel. This algorithm is slightly slower than the brightest point search algorithm, but at the same time its accuracy is higher.
The linear approximation of the differential signal (LFDS) algorithm is performed in three stages. At the first stage, the difference approximation of the first derivative is calculated by the formula, where is the value of the derivative at the point x, f(x) is the value of the function at the point x, d is the approximation step. Then the resulting array of values of derivatives at points is used for linear approximation by the least squares method. And finally, at the third stage, the coordinate of the point of intersection of the obtained straight line with zero is calculated, which is the desired peak. This algorithm is the most time consuming of all the presented ones, but its accuracy is the best.
Investigation of the precision characteristics of a fiber confocal sensor based on the chromatic coding method
The purpose of the experimental studies was to determine the error of the fiber confocal sensor. The object was displaced using a three-coordinate stage (3) with a step of 0.1 μm, and the displacement value was determined by an interferometer (5). A typical graph of dependence is shown Fig. 3.
The resulting curve of the dependence of the coordinate of the center of mass of the spectral distribution of the signal power on the surface displacement was approximated by the power function y(х) = λ(х) = a0 + a1х + a2х2 + a3x3.
The measure of the deviation of y(x) from the given function at the root-mean-square approximation was the value of the root-mean-square deviation, equal to the sum of the squares of the differences between the values of y(x) and the experimental function at each point. To construct the approximating curve, the built-in functions of the Excel program were used, with the help of which the coefficients a0, a1, a2 and a3 were selected so that the value of the root-mean-square deviation was the smallest.
Further, the root-mean-square deviation was analyzed when determining the surface displacements.
During experimental studies, two types of hyperchromatic lenses were used: refractive-diffractive (RD-lense, decomposition into a chromatic segment is carried out using diffraction of rays) and refractive (decomposition is due to the phenomenon of glass dispersion, hereinafter referred to as hyperchromate). So in [18] an RD lens is described (Fig. 5), which consists of a standard microlens (3.7, 10 and 20×) and a diffractive optical element (DOE). DOE is a phase plate with an axisymmetric diffraction structure. Taken together, this approach makes it possible to obtain a chromatic segment Δz, in which light of a certain wavelength is focused into diffraction-quality spots without aberration distortion.
The table summarizes the sensor parameters established in the course of experimental studies. The following results were obtained: for the 3,7× lense, the error in determining the displacement of the object was 1 μm in the linear section of 200 μm, for the microlens 10× – 0.6 μm in the linear section of 50 μm, and for the microlens 20× – 0.1 in the linear section 20 microns.
The main advantages of these lenses are: ease of implementation, compactness and linear dependence of the focus shift on the wavelength. However, such lenses have a number of disadvantages. First of all, this is the presence of parasitic diffraction orders, as well as low efficiency at the edges of the wavelength range (400–700 nm). The calculation and design of hyperchromatic lenses based on a combination of glasses with different dispersion is preferable when using a wide range of wavelengths Δλ (within the visible range of the spectrum 400–700 nm).
In [16, 17], approaches to the design of hyperchromates are described. In the course of experimental studies, a developed three-lens lense was used (Fig. 6) with the following characteristics: a focal length of 30 mm, a chromatic segment length of 300 µm; focal length – 24 mm; magnification 5 times; aperture ratio: 1 / 3.3; distortion – 0.03%.
As a result of experimental studies, it was found that the use of a hyperchromate in conjunction with an apodizing mask (which filters radiation with a wide spectrum) makes it possible to reduce the error in measuring the distance to the surface by a factor of three or more. In the absence of an apodizing mask in the central part of the hyperchromat, the root-mean-square deviation is 0.9 μm in the linear measuring range of 225 μm. The introduction of an apodizing mask with a diameter of 0.2D (D is the diameter of the hyperchromate), the root-mean-square deviation is reduced to 0.29 µm while reducing the linear range to 120 µm.
Development of a fiber confocal sensor with increased energy characteristics
To determine the position of optical transparent media, it is necessary to provide increased energy characteristics of the probe radiation. The performed calculation showed that the use of a superluminescent diode SLD‑790-14BF (Nolatech, Russia) instead of a halogen lamp will make it possible to increase the signal level from the confocal sensor by a factor of 100. On its basis, a fiber-coupled illuminator was developed. It has an output power of 5 mW and a spectral width of 40 nm (760–800 nm). To decompose such a narrow spectrum into a chromatic section, a diffractive optical element was calculated using the software for calculating optical systems Zemax Optical Studio. Fig. 6–7 show the data of the result of calculation and modeling of such an element. It can be seen that the dependence of the focus shift on the wavelength (Fig. 6) is rather linear (nonlinearity does not exceed 1%), and the spot sizes for radiation with wavelengths of 760, 770, 780, 790, and 800 nm are less than the diffraction limit (Fig. 7).
At the next stage of research, experiments will be carried out to determine the level of the signal reflected from the optically transparent medium in the confocal sensor.
Conclusion
As a result of an analysis of the market for commercially available proximity sensors for monitoring the position of the surface of objects, it was found that, despite their variety, they are difficult to integrate into laser technological installations. The requirements for sensors in such installations are formulated, namely: high speed (up to 1 MHz) and resolution (the error should not exceed 0.1 μm), the ability to control the position of spherical (convex or concave) surfaces, as well as acceptable weight and size characteristics. The most important requirement is the compatibility of the optical circuits of the sensors with the optical circuits of the laser channels.
Research has been carried out on a fiber confocal sensor developed at the TDISIE, SB RAS, which can be part of laser technological complexes and will allow monitoring the position and profile of the surface to be treated. It has been shown that the use of a color video camera as a spectrum analyzer, as well as a refractive-diffractive lens in confocal sensors, makes it possible to determine the position of the controlled surface with an error of up to 0.1 μm.
In the course of experimental studies of a three-lens hyperchromate with an introduced apodizing mask, it was found that the error in determining the position of the controlled surface is 0.2 μm.
The results of calculating a diffractive optical element for monitoring the position of optically transparent media, which allows focusing light from a source with increased energy characteristics and a narrow spectrum, are presented.
Acknowledgments
The work was carried out on the basis of the laboratory of laser industrial technologies of the TDISIE, SB RAS. Financial support was provided by the Ministry of Science and Higher Education of the Russian Federation.
AUTHORS
Marina Andreevna Zavyalova, Candidate of Technical Sciences; e-mail: mzav@tdisie.nsc.ru; Ph.D., Researcher, Tecnological Design Institute of Scientific Instrument Engineering SB RAS (hereinafter – TDI SIE, SB RAS), info@tdisie.nsc.ru; www.tdisie.nsc.ru; Novosibirsk, Russia. Area of interest: optoelectronic devices and systems, laser technologies.
ORCID: 0000-0003-2000-6226
Zavyalov Petr Sergeevich, Candidate of Technical Sciences; e-mail: zavyalov@tdisie.nsc.ru; Ph.D., Director of TDI SIE, SB RAS, www.tdisie.nsc.ru; Novosibirsk, Russia. Area of interest: optoelectronic devices and systems, vision systems, diffractive optics.
ORCID: 0000-0001-6222-5000
Savchenko Mark Vladimirovich, e-mail: savchenko_mark@bk.ru; software engineer, TDI SIE, SB RAS, www.tdisie.nsc.ru; Novosibirsk, Russia. Area of interest: programming.
CONTRIBUTION OF AUTHORS
Zavyalova M. A.: calculation of a diffractive optical element, concept of experiment and measurement, analysis of results; Zavyalov P. S.: organization of the experiment, analysis of results and discussion; Savchenko M. V.: measurements, processing of results
CONFLICT OF INTERESTS
All members of the writing team took part in writing the manuscript according to the contribution of each to the general experiment and the analysis of its results. The authors guarantee the originality of the results and declare no conflicts of interest.
M. A. Zavyalova, P. S. Zavyalov, M. V. Savchenko
Tecnological Design Institute of Scientific Instrument Engineering, SB RAS, Novosibirsk, Russia
The paper presents the results of experimental studies of a fiber confocal sensor based on the chromatic coding method with the developed hybrid refractive-diffractive and hyperchromatic lenses. This sensor allows you to determine the position of the controlled surfaces with a high resolution (the error does not exceed 0.1–1 µm) on working segments from 20 to 220 µm.
Keywords: confocal sensor, chromatic coding method, diffractive optical element, laser micromachining of materials
Received on: 11.10.2021
Accepted on: 25.11.2021
Introduction
Laser synthesis of microstructures on the surface of various materials requires the development of methods for precision positioning of microlens that focus the radiation. For these purposes, as a rule, optical non-contact sensors are used, which make it possible to determine the position of the surface of the objects being processed with a high resolution. Such sensors are used in laser technological installations for the synthesis of high-precision photonic elements with sizes from a few millimeters to tens of nanometers [1–3].
The most important requirements for optical proximity sensors are high speed (up to 1 MHz) and resolution. In addition, the task of designing such sensors becomes more complicated for the cases of recording microstructures on three-dimensional surfaces, which is important at this stage in the development of a high-tech element base [4, 5]. Since the synthesized elements of photonics are optically transparent media with a low reflection coefficient, such sensors must have the necessary power reserve of the probing radiation.
The possibility of synthesizing micro- and nanostructures on flat and curved surfaces makes it possible to produce unique optical elements and devices based on them, which are in high demand in modern technology [6–9]. Over the past 15–20 years, impressive progress has been observed in the field of creating laser technological complexes for processing and structuring various types of materials. Among them, unique are systems that allow micro- and nanostructuring of three-dimensional surfaces with a resolution of less than 0.1 μm [10].
To implement many of these methods, it is necessary to accurately control the position of the focal plane of the working microlens, which must be aligned either with the plane of the photosensitive layer applied to the substrate surface, or with the substrate surface. The position sensor, which is part of the automatic focusing system (AFS), is required to constantly hold the focused recording spot on the surface of the synthesized element during recording at speeds up to 10 m / s. It is important to note that a focusing error exceeding ±0.2 μm (for a lens with a numerical aperture of 0.65) leads to a significant change in the size and shape of the recording spot and, consequently, in the recording parameters, and the tilt of the lens axis leads to an error in the recording coordinate [11]. If the recording surface is three-dimensional, then the task becomes more complicated and requires the development and implementation of previously unused precision autofocusing methods. AFSs developed on these principles allow controlling technological processes with great accuracy. As a rule, such systems contain a large number of original sensors, which largely determine the efficiency of the technological process.
Basic technical requirements for sensors for monitoring the position of objects
The following requirements are imposed on sensors for monitoring the position of objects used in laser technological installations for the formation of high-quality micro- and nanostructures:
1. Compactness and integration into the technological laser channel.
Typically, such sensors must be embedded in the existing optical channels of processing units. This is due to the fact that for focusing laser radiation into a spot with a diameter of 1 μm or less, micro lenses with a large numerical aperture – from 0.65 and higher, and, therefore, with a small focal distance are used, which makes it difficult to integrate the finished sensor directly in front of the focusing element. Thus, the probe radiation of the sensor should be focused by the same element as the radiation of the working laser.
2. High performance
Since laser technological installations have a high recording speed (up to 10 m / s), the position sensors must perform precise positioning of the actuators at a signal frequency from several kilohertz to 1 MHz.
3. High resolution
For the formation of high quality microstructures with a depth of up to several tens of micrometers, the resolution of the sensors should be an order of magnitude better – 1 μm or less.
4. Working range
This characteristic of the sensor related to the depth of the synthesized structures, and determines the possibility of structuring the curved surfaces (the angle of inclination of the tangent to the surface should not exceed 8° to microscope lenses having a numerical aperture of 0.65).
5. Recordable on curved surfaces
Since, in this case, the probing radiation of the sensors for monitoring the position of objects can additionally change its parameters due to the curvature of the surface, a preliminary assessment of the influence of the curvature on the signal from the sensor must be carried out.
6. Advanced functionality
Along with the main task of such sensors in tracking the linear movement of the controlled object and converting the change in its position into the corresponding output signal, they must automatically search for the surface to be treated, determine the size of the focused spot, measure the profile of the resulting structures, etc. All this improves the technical capabilities of laser technological installations and makes it possible to improve the quality of synthesized structures.
The optical methods of surface control used in laser technological complexes are very diverse. Non-contact optical sensors for measuring distances with high resolution (less than 1 μm) include interferometric [12], triangulation [13] and confocal sensors [14, 15], which are mass-produced and in large volumes and, in general, provide the growth of the measuring equipment industry. However, they satisfy only part of the requirements described above. Thus, laser interferometric sensors have the necessary sensitivity and speed, but at the same time they cannot be combined with a working microlens that focuses laser radiation. Triangulation sensors can only measure distance to flat surfaces. Available commercial sensors (interferometric and confocal types) are mainly produced abroad and are expensive. They have closed-type optical circuits and cannot be incorporated into laser systems that use micro-lenses with a short focal distance (less than 1 mm). Therefore, the areas and scales of their application in laser technological installations are still very limited, and it is quite natural that the efforts of developers are aimed at creating such sensors and reducing their cost.
Therefore, an urgent task in the design of laser technological complexes is the development and study of high-speed precision sensors for automatic focusing of laser radiation on optical surfaces, monitoring the result of interaction and measuring the profile of synthesized structures.
The paper will consider a fiber confocal sensor based on the chromatic coding method developed in Novosibirsk at the Tecnological Design Institute of Scientific Instrument Engineering, SB RAS (hereinafter referred to as TDISIE, SB RAS).
The principle of operation of this sensor is described in detail in [16, 17]. It evaluates the spectral distribution of the intensity of optical signals reflected from the measured surfaces. For these purposes, a polychromatic sounding signal is used in combination with hyperchromatic lenses (HCL), which focus the spectral components at different distances along the direction of light propagation. The use of a special point (or confocal) diaphragm limiting the flow of background scattered light from points outside the focal plane of the lens makes it possible to select radiation with a narrow spectrum, in which the central wavelength is the chromatic code of the distance to the surface, and its change is proportional to the surface displacement.
This sensor is necessary for precise control of the position of the focusing plane of the working microlens. With its help, a constant retention of the focused recording spot on the surface of the synthesized element should be carried out during high-speed processing of optically transparent media.
At this stage, an optical scheme was developed to study the accuracy characteristics of the sensor (Fig. 1). It uses an illuminator based on a halogen lamp (1) DL150 (Dedolight, Germany), a fiber confocal sensor (TDISIE, SB RAS, Novosibirsk) (2). The object is displaced using a three-coordinate stage (3) ZSS 33.200.1.2 (Phytron, Germany). The change in the reflected signal is controlled using an analyzer (4), which includes a GT13–06V diffraction grating (Thorlabs, Germany) and a KTs‑1310 video camera (TDISIE, SB RAS, Novosibirsk). The scheme also includes an XL‑80 interferometer (5) (RENISHAW, Great Britain), which makes it possible to control the displacement of an object with an error of less than 0.1 μm.
The developed LineIntensity software allows processing the signal from the analyzer of the confocal sensor. A video camera displays an image of the reflected signal spectrum shown Fig. 2. It can be colored Fig. 2 a, or black and white Fig. 2b depending on the mode of use of the camera.
Further signal processing consists of three stages. At the first stage, the result of the subtraction is processed with a Gaussian blur. Blur is applied to reduce the effect of noise on the original result. At the second stage, the specified constant (in fact, the background component) is subtracted to select significant pixels. At the third stage, the peak detection algorithms are implemented. In total, three algorithms were investigated: the search for the brightest point, the center of mass, and a linear approximation of the differential signal. The obtained peak coordinates are used to estimate the measurement error.
The brightest point search algorithm takes the brightest pixel available as the peak. Due to the absence of any further processing, it is the fastest algorithm available, but it increases the measurement error.
The algorithm for finding the center of mass takes as the peak the center of mass of the brightness of pixels, calculated by the formula , where rc are the coordinates of the center of mass, ri are the coordinates of the pixel, and mi is the brightness of the pixel. This algorithm is slightly slower than the brightest point search algorithm, but at the same time its accuracy is higher.
The linear approximation of the differential signal (LFDS) algorithm is performed in three stages. At the first stage, the difference approximation of the first derivative is calculated by the formula, where is the value of the derivative at the point x, f(x) is the value of the function at the point x, d is the approximation step. Then the resulting array of values of derivatives at points is used for linear approximation by the least squares method. And finally, at the third stage, the coordinate of the point of intersection of the obtained straight line with zero is calculated, which is the desired peak. This algorithm is the most time consuming of all the presented ones, but its accuracy is the best.
Investigation of the precision characteristics of a fiber confocal sensor based on the chromatic coding method
The purpose of the experimental studies was to determine the error of the fiber confocal sensor. The object was displaced using a three-coordinate stage (3) with a step of 0.1 μm, and the displacement value was determined by an interferometer (5). A typical graph of dependence is shown Fig. 3.
The resulting curve of the dependence of the coordinate of the center of mass of the spectral distribution of the signal power on the surface displacement was approximated by the power function y(х) = λ(х) = a0 + a1х + a2х2 + a3x3.
The measure of the deviation of y(x) from the given function at the root-mean-square approximation was the value of the root-mean-square deviation, equal to the sum of the squares of the differences between the values of y(x) and the experimental function at each point. To construct the approximating curve, the built-in functions of the Excel program were used, with the help of which the coefficients a0, a1, a2 and a3 were selected so that the value of the root-mean-square deviation was the smallest.
Further, the root-mean-square deviation was analyzed when determining the surface displacements.
During experimental studies, two types of hyperchromatic lenses were used: refractive-diffractive (RD-lense, decomposition into a chromatic segment is carried out using diffraction of rays) and refractive (decomposition is due to the phenomenon of glass dispersion, hereinafter referred to as hyperchromate). So in [18] an RD lens is described (Fig. 5), which consists of a standard microlens (3.7, 10 and 20×) and a diffractive optical element (DOE). DOE is a phase plate with an axisymmetric diffraction structure. Taken together, this approach makes it possible to obtain a chromatic segment Δz, in which light of a certain wavelength is focused into diffraction-quality spots without aberration distortion.
The table summarizes the sensor parameters established in the course of experimental studies. The following results were obtained: for the 3,7× lense, the error in determining the displacement of the object was 1 μm in the linear section of 200 μm, for the microlens 10× – 0.6 μm in the linear section of 50 μm, and for the microlens 20× – 0.1 in the linear section 20 microns.
The main advantages of these lenses are: ease of implementation, compactness and linear dependence of the focus shift on the wavelength. However, such lenses have a number of disadvantages. First of all, this is the presence of parasitic diffraction orders, as well as low efficiency at the edges of the wavelength range (400–700 nm). The calculation and design of hyperchromatic lenses based on a combination of glasses with different dispersion is preferable when using a wide range of wavelengths Δλ (within the visible range of the spectrum 400–700 nm).
In [16, 17], approaches to the design of hyperchromates are described. In the course of experimental studies, a developed three-lens lense was used (Fig. 6) with the following characteristics: a focal length of 30 mm, a chromatic segment length of 300 µm; focal length – 24 mm; magnification 5 times; aperture ratio: 1 / 3.3; distortion – 0.03%.
As a result of experimental studies, it was found that the use of a hyperchromate in conjunction with an apodizing mask (which filters radiation with a wide spectrum) makes it possible to reduce the error in measuring the distance to the surface by a factor of three or more. In the absence of an apodizing mask in the central part of the hyperchromat, the root-mean-square deviation is 0.9 μm in the linear measuring range of 225 μm. The introduction of an apodizing mask with a diameter of 0.2D (D is the diameter of the hyperchromate), the root-mean-square deviation is reduced to 0.29 µm while reducing the linear range to 120 µm.
Development of a fiber confocal sensor with increased energy characteristics
To determine the position of optical transparent media, it is necessary to provide increased energy characteristics of the probe radiation. The performed calculation showed that the use of a superluminescent diode SLD‑790-14BF (Nolatech, Russia) instead of a halogen lamp will make it possible to increase the signal level from the confocal sensor by a factor of 100. On its basis, a fiber-coupled illuminator was developed. It has an output power of 5 mW and a spectral width of 40 nm (760–800 nm). To decompose such a narrow spectrum into a chromatic section, a diffractive optical element was calculated using the software for calculating optical systems Zemax Optical Studio. Fig. 6–7 show the data of the result of calculation and modeling of such an element. It can be seen that the dependence of the focus shift on the wavelength (Fig. 6) is rather linear (nonlinearity does not exceed 1%), and the spot sizes for radiation with wavelengths of 760, 770, 780, 790, and 800 nm are less than the diffraction limit (Fig. 7).
At the next stage of research, experiments will be carried out to determine the level of the signal reflected from the optically transparent medium in the confocal sensor.
Conclusion
As a result of an analysis of the market for commercially available proximity sensors for monitoring the position of the surface of objects, it was found that, despite their variety, they are difficult to integrate into laser technological installations. The requirements for sensors in such installations are formulated, namely: high speed (up to 1 MHz) and resolution (the error should not exceed 0.1 μm), the ability to control the position of spherical (convex or concave) surfaces, as well as acceptable weight and size characteristics. The most important requirement is the compatibility of the optical circuits of the sensors with the optical circuits of the laser channels.
Research has been carried out on a fiber confocal sensor developed at the TDISIE, SB RAS, which can be part of laser technological complexes and will allow monitoring the position and profile of the surface to be treated. It has been shown that the use of a color video camera as a spectrum analyzer, as well as a refractive-diffractive lens in confocal sensors, makes it possible to determine the position of the controlled surface with an error of up to 0.1 μm.
In the course of experimental studies of a three-lens hyperchromate with an introduced apodizing mask, it was found that the error in determining the position of the controlled surface is 0.2 μm.
The results of calculating a diffractive optical element for monitoring the position of optically transparent media, which allows focusing light from a source with increased energy characteristics and a narrow spectrum, are presented.
Acknowledgments
The work was carried out on the basis of the laboratory of laser industrial technologies of the TDISIE, SB RAS. Financial support was provided by the Ministry of Science and Higher Education of the Russian Federation.
AUTHORS
Marina Andreevna Zavyalova, Candidate of Technical Sciences; e-mail: mzav@tdisie.nsc.ru; Ph.D., Researcher, Tecnological Design Institute of Scientific Instrument Engineering SB RAS (hereinafter – TDI SIE, SB RAS), info@tdisie.nsc.ru; www.tdisie.nsc.ru; Novosibirsk, Russia. Area of interest: optoelectronic devices and systems, laser technologies.
ORCID: 0000-0003-2000-6226
Zavyalov Petr Sergeevich, Candidate of Technical Sciences; e-mail: zavyalov@tdisie.nsc.ru; Ph.D., Director of TDI SIE, SB RAS, www.tdisie.nsc.ru; Novosibirsk, Russia. Area of interest: optoelectronic devices and systems, vision systems, diffractive optics.
ORCID: 0000-0001-6222-5000
Savchenko Mark Vladimirovich, e-mail: savchenko_mark@bk.ru; software engineer, TDI SIE, SB RAS, www.tdisie.nsc.ru; Novosibirsk, Russia. Area of interest: programming.
CONTRIBUTION OF AUTHORS
Zavyalova M. A.: calculation of a diffractive optical element, concept of experiment and measurement, analysis of results; Zavyalov P. S.: organization of the experiment, analysis of results and discussion; Savchenko M. V.: measurements, processing of results
CONFLICT OF INTERESTS
All members of the writing team took part in writing the manuscript according to the contribution of each to the general experiment and the analysis of its results. The authors guarantee the originality of the results and declare no conflicts of interest.
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