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Issue #6/2022
V. Yu. Venediktov, B. Nyamweru, R. A. Larichev, Yu. V. Filatov, E. V. Shishalova
Optical null-indicators for goniometric systems: a review
Optical null-indicators for goniometric systems: a review
DOI: 10.22184/1993-7296.FRos.2022.16.6.464.474
Nowadays, high-precision angle measurement is necessary in many fields of science and industry. Precision angle measurements are especially important when checking and controlling various optical parts and angular measures. One of the most accurate devices at the moment is a goniometer, which allows you to measure angles by non-contact methods. This article discusses various types of null-indicators used in goniometric systems, their advantages and disadvantages are indicated. The review is intended to provide a basic understanding of goniometric systems and null-indicators used in angular measurements.
Nowadays, high-precision angle measurement is necessary in many fields of science and industry. Precision angle measurements are especially important when checking and controlling various optical parts and angular measures. One of the most accurate devices at the moment is a goniometer, which allows you to measure angles by non-contact methods. This article discusses various types of null-indicators used in goniometric systems, their advantages and disadvantages are indicated. The review is intended to provide a basic understanding of goniometric systems and null-indicators used in angular measurements.
Теги: autocollimator goniometric systems null-indicator optical polygon автоколлиматор гониометрические системы многогранная призма нуль-индикатор
Optical Null-Indicators for Goniometric Systems: a Review
V. Yu. Venediktov, B. Nyamweru, R. A. Larichev, Yu. V. Filatov, E. V. Shishalova
Saint Petersburg Electrotechnical University “LETI”,
St. Petersburg, Russia
Nowadays, high-precision angle measurement is necessary in many fields of science and industry. Precision angle measurements are especially important when checking and controlling various optical parts and angular measures. One of the most accurate devices at the moment is a goniometer, which allows you to measure angles by non-contact methods. This article discusses various types of null-indicators used in goniometric systems, their advantages and disadvantages are indicated. The review is intended to provide a basic understanding of goniometric systems and null-indicators used in angular measurements.
Keywords: goniometric systems, optical polygon, autocollimator, null-indicator
Received on: 03.08.2022
Accepted on: 29.08.2022
1. Introduction
The development of goniometers is inextricably linked with the development of research in the field of crystallography. In 1783, Arnold Carangeau invented the first device for measuring the angle between two faces of a crystal. The scientist called this device a contact goniometer. It consisted of two metal rods that were connected by hinges in the center of a graduated semicircle. The accuracy of this device was about 15 arc minutes [1].
In 1809, the English physicist William Hyde Wollaston developed an optical goniometer that measured the angles between the faces of a crystal using light reflected from them. The crystal was attached to a rotating graduated table, and the light source was directed to various facets of the crystal. The angle between the crystal faces was determined as the difference in the readings of the graduated table on which the light reflected from the faces fell. This goniometer had an accuracy of 5 arc minutes [2].
The development of science in the field of goniometry led to the creation of new devices and progressive methods and means of measuring angles, allowing the object under study to rotate automatically, use various auxiliary elements, optimize designs and improve the accuracy of goniometers.
The idea of measuring the angles of a optical polygon using a goniometer appeared a long time ago. When it became necessary to measure angles in astronomy with very high accuracy, it also became necessary to calibrate measuring instruments to improve the accuracy of their measurements. In 1954, in his publication entitled “The calibration of circular scale and precision polygon”, A. H. Cook described the calibration of a optical polygon by accurately solving a set of equations for the difference of angles between its faces [3]. With the development of metrology in the field of angular measurements, the optical polygon began to play an important role as an angular measure. International comparisons, ensuring the unity of measurements, are carried out using a multi-faceted prism, which is consistently calibrated on the reference goniometric systems of national metrological institutes of different countries [4,5].
2. Classification of contactless goniometers
Based on the history of the invention of goniometers and their measurement methods, we can conclude that there are two types of goniometers: contact and reflective (contactless). The contactless goniometer is the most accurate and is currently widely used in metrology, instrumentation and other scientific and industrial fields.
A complete goniometric system consists of such elements as an angular scale; a turntable; a drive that sets the rotation; an optical device that sets the reference direction; an electronic unit that controls the engine and pre-processing data; a personal computer for receiving and processing data. The object under study is fixed on the turntable as shown in Fig. 1 [6].
According to the principle of operation, contactless goniometers are divided into static and dynamic. The static measurement method differs in that the moving parts of the goniometric system (the object under study and the turntable) remain stationary at the moment of measurement. In this mode, the optical device is an autocollimator, which measures the deviation of the normal to the reflecting face of the prism from the sighting axis of the autocollimator. The measurement result in such a system is determined by the readings of the angular scale and the autocollimator. The main problem associated with a static goniometer is the long duration of measurements.
A dynamic goniometer is a device in which, during the measurement process, the object under study rotates at a quasi-constant speed. In this type of goniometers, the optical device that sets the reference direction is a null-indicator.
The block diagram shown in Fig. 1 is suitable for both static and dynamic types of goniometers [7]. The two modes of operation have several differences, which we will consider. In modern static goniometers, the angular scale is always represented by angle sensors (usually optical) or a limb, while in dynamic goniometers, either a ring laser or an optical angle sensor can be used as an angular scale. The second feature is the type of optical device used in the system. As part of static goniometers, an autocollimator is used, and as part of dynamic goniometers, a null-indicator is used.
In addition to the principle of operation, goniometers are also divided according to their purpose. The tasks performed using goniometers can be as follows: calibration of optical polygons, measurement of refractive index, measurement of external angles, measurement of angles between two reflecting surfaces [8].
An optical polygon is one of the most common objects used in measurements with goniometers. An optical polygon is a product with a fixed number of sides, which is considered one of the most accurate and reliable reference standards in the field of angular metrology. Examples are shown in Fig. 2.
As noted above, they are mainly used for calibration of measuring instruments, in particular, for transmitting the angle value from the primary standard to the working equipment. In addition to these applications, optical polygons are also used as elements of various laser and optical systems [9]. There are many parameters describing optical polygons. The main parameters are the following: the number of faces, model, dimensions, coating of the reflecting surface and the material from which the prism is made [10].
3. Types of optical null-indicators
A null-indicator is an optical device that sets a reference direction in space and fixes the moment when its optical axis is perpendicular to the reflecting surface of the object under study. There are various configurations of null-indicators, but two main types can be distinguished: interference and autocollimation [11].
3.1. Autocollimation null-indicator
One of the first null-indicators that began to be used as part of dynamic goniometers is a device built on the basis of an autocollimator. The optical scheme of such a device is shown in Fig. 3. A reference slit 6 of a certain width is placed in front of the light source 7. Of the same width, an analyzing slit 2 is placed in front of the photodetector 1. The width of the slits must be the same in order for the output signal to have a quasi-triangular shape. The light passing through the beam-splitting cube 3 falls on the lens 4 and then on the reflecting surface 5. When it becomes perpendicular to the axis of the null-indicator, the image of the reference slit falls on the analyzing slit and an analog signal is formed at the output of the photodetector.
The moment when the normal to the surface coincides with the optical axis of the AK corresponds to the maximum of the analog signal. The output pulse used for further processing is formed using a threshold circuit for a certain signal level, and this level is selected so that the steepness of the signal is at its maximum in order to reduce the random measurement error.
In general, the contribution of a null-indicator with a threshold analog signal processing circuit to the random error of a single measurement of a goniometric system is determined by two parameters: the angular steepness of the signal itself and the signal-to-noise ratio, which is set by optoelectronic components and the circuit itself involved in the formation and preprocessing of the signal. Instead of the steepness of the analog signal, with various kinds of estimates, you can also operate with the parameter of its angular width, because the required signal amplitude is determined by the input parameters of the processing circuit and is usually about 3 V. A typical sample of the considered autocollimation null-indicator (the focal length of the lens is 250 mm and the width of the setting and analyzing slit is 40 microns) is characterized by the width of the analog signal of the order of 60 arc-sec and the signal–to-noise ratio is 50. In this case, the value of the random error of a single measurement is about 0.6 arc-sec, which is an unacceptable value in modern high-precision measurements [12].
3.2. Interference null-indicator
The interference null-indicator is a two-beam interferometer based on beam splitting by a Kesters prism (or a Dove biprism) (Fig.4). The analog output signal of such a null-indicator is a combination of a narrow pulse and a constant component that is much wider than the pulse (about 1600 times) [13].
This type of null-indicator is characterized by an extremely small pulse width (the pulse width in an interference null indicator is determined by the width of the light beams and the distance between them, see Fig.4). With the width of the light beams and the distance between them equal to 10 mm, the angular width of the pulse is only 0.6 arc-sec. With a signal-to-noise ratio on the order of 100, the random error (RMS) is 0.03 arc-sec. [14]. Based on such accuracy characteristics, interference null-indicators were considered one of the most accurate in dynamic goniometric measurements.
The disadvantage of this type of null-indicators is the strong dependence of the possibilities of its functioning on the quality of the reflecting surface and the uniformity of the medium in which light propagates. Distortion of the recorded wavefront corresponding to even one interference fringe can lead to malfunction of the goniometric system.
In addition, there is another disadvantage of the interference null-indicator. Goniometers-refractometers measure the refractive indices of materials that are used to make special test prisms. To determine the refractive indices, the angles between the rays reflected from the inner and outer surfaces of the prism under study are measured. The beam reflected from the inner surface of the face passes through the prism twice, being refracted by the medium of this prism, while the beam is significantly influenced by dispersion. The phenomenon of dispersion is manifested in the fact that the rays passing through the medium are decomposed in space into components that have different frequencies. In this case, when using a light source with a wide spectrum, a narrow interference pulse turns into a blurry picture, which significantly reduces the accuracy of the device.
3.3. Autocollimation null-indicator with differential registration scheme
In connection with the above problems, an autocollimation null-indicator scheme with a differential registration scheme was proposed. The diagram of such a device is shown in Fig. 5.
The photodetector in this scheme is a quadrant photodiode, which is a silicon photodetector with four photosensitive regions (quadrants). The photodetector is positioned so that the optical axis of the null-indicator passes through the crosshair formed by the gaps between the quadrants. In this case, the vertical gap must be parallel to the axis of rotation of the reflecting surface.
After the light reflected from the surface of the object under study hits the quadrants, signals from the left and right areas of the photodiode begin to form at the output of the null-indicator. At the moment when the reflecting surface is perpendicular to the optical axis of this device, these signals intersect and a logical pulse is formed at the intersection point, which is fed to the goniometer for further processing. The signal generation process is shown in Fig. 6.
The image of the gap is larger than the gap between the pads, so there is a moment when the signals from the right and left pads are equal. In this case, the desired moment corresponds to the one when the center of mass of the image of the target slit is in the center of the vertical gap.
This type of null-indicators has shown good results in the course of research, its random error turned out to be at the same level as that of the interference type – about five hundredths of an arc second [12]. Its advantage is that the instability of the rotation speed of the object under study and the instability of the analog signal have virtually no effect on the accuracy of the device. But a significant drawback was also identified.
When installing this null-indicator relative to a rotating angular measure, it is necessary to fairly accurately set the parallelism of the vertical gap of the quadrant photodiode relative to the axis of rotation – with an accuracy of the order of several arc minutes [12]. With a deviation from parallelism by 20 arc-min the systematic measurement error of the goniometric system reached 0.4 arc-sec.
3.4. Autocollimation null-indicator with digital processing of an analog signal
At the moment, one of the most accurate autocollimation null-indicators is a null-indicator with digital signal processing, which is based on an estimate of its center of mass. The optical circuits of such a device have several variations, one of which is similar to the scheme shown in Fig. 3.
The photodetector generates an analog signal, the maximum of which corresponds to the moment of exact coincidence of the normal to the reflecting surface and the axis of the null-indicator. Digital signal processing, based on the evaluation of its center of mass, allows you to achieve measurement accuracy determined by the random error of a single measurement of 0.02 arc-sec [15]. The scheme of the digital autocollimation null-indicator is shown in Fig. 7.
The signal entering the photodetector is amplified and fed into the signal recording device, where it is digitized for further determination of the center of mass. The logic device outputs a data packet that contains the number of periods of the optical encoder from the moment the signal exceeds the threshold level to the moment when the signal is below the threshold; the values of the signal within this interval; the duration of the signal and time bindings in microseconds. Then all the data is processed and the center of mass is calculated using the software package, based on which the moment of perpendicular of the controlled surface to the optical axis of the null-indicator is determined.
The disadvantage of such a null-indicator is the presence of post-processing, which can make a certain contribution to the error of the device. However, according to experimental data, this null-indicator still outperforms other types in accuracy. In [15], model experiments were carried out, the task of which was to determine the random error of the null indication and its dependence on the signal-to-noise ratio. The table shows the results obtained.
The results obtained show that with a signal-to-noise ratio of 50, the random error turns out to be less than 0.02 arc-sec., which is characterized by a null-indicator with digital signal processing in the best way.
3.5. Other schemes of null-indicators
In addition to the presented configurations of null-indicators, there are others, but now they are practically not used due to their shortcomings (operating features and low accuracy).
The first type that we will consider is an autocollimation null-indicator, the defining and analyzing slits of which are masks whose transparency areas alternate according to a pseudo–noise law (randomly distributed slits). The transparent and opaque parts of the mask correspond to the elements of the code sequence – 1 and 0. In this case, the output signal is determined by the autocorrelation function. When the controlled surface is perpendicular to the axis of the null-indicator, the autocorrelation function has a sharp spike, the maximum of which determines the desired moment. The disadvantage of such a null-indicator is the diffraction distortion of the light beam, which as it turned out, as a result of an experimental study of the prototype, it negates all the advantages of using a pseudo-noise mask [16].
The second type is an autocollimation null-indicator with a rocking direction of the optical beam. In this null-indicator, after passing through the slit, the beam is reflected from a “rocking mirror” mounted on a piezoelectric base, which moves the mirror relative to the central axis. The output signal of the photodetector goes to the built-in amplifier, which allows filtering the signal by the swing frequency, and to the synchronous detector [3]. The disadvantage of this option is the requirement of a sufficiently low rotation speed of the object under study, which slows down the measurement process.
4. Conclusion
Depending on the technical capabilities, requirements and tasks, you should choose a suitable null-indicator, taking into account its parameters and factors affecting the accuracy of a specific configuration of the null-indicator. Summing up, we will make a brief comparison of the null-indicators considered in this article.
The autocollimation null-indicator with a threshold processing scheme has a relatively simple design, however, due to the large width of the analog signal, the accuracy of the device drops significantly.
The interference null-indicator is one of the most accurate due to the small width of the interference pulse. This type of null-indicator is extremely demanding on the quality of the controlled surface, since due to various irregularities and inhomogeneities, the light beam experiences dispersion, the interference pattern is blurred and the accuracy of the device decreases, or the device fails.
An autocollimation null-indicator with a differential registration scheme has a significant advantage from the point of view of the formation of a logical signal, since the formation of a logical pulse occurs strictly at the intersection point of signals symmetrical with respect to the moment of formation of this pulse. The systematic error of this null-indicator depends mainly on the accuracy of the alignment of its components and the uniformity of illumination of the photodiode.
An autocollimation null-indicator with digital signal processing is one of the most accurate types of null-indicators, but its disadvantage is the presence of post-processing.
Null-indicators with pseudo-noise masks and with a rocking direction of the light beam are practically not used at the moment. The disadvantage of the first is the diffraction distortion of the light beam. The disadvantage of the second null-indicator is that the rotation speed of the object under study should be low, which affects the duration of measurements.
CREDITS
Yu. V. Filatov and R. A. Larichev are grateful for the financial support provided by the RSF Grant No. 20-19-00412
AUTHORS
V. Yu. Venediktov, B. Nyamweru, R. A. Larichev, Yu. V. Filatov, E. V. Shishalova, Laser Measurement and Navigation Systems department, Saint Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
V. Yu. Venediktov, B. Nyamweru, R. A. Larichev, Yu. V. Filatov, E. V. Shishalova
Saint Petersburg Electrotechnical University “LETI”,
St. Petersburg, Russia
Nowadays, high-precision angle measurement is necessary in many fields of science and industry. Precision angle measurements are especially important when checking and controlling various optical parts and angular measures. One of the most accurate devices at the moment is a goniometer, which allows you to measure angles by non-contact methods. This article discusses various types of null-indicators used in goniometric systems, their advantages and disadvantages are indicated. The review is intended to provide a basic understanding of goniometric systems and null-indicators used in angular measurements.
Keywords: goniometric systems, optical polygon, autocollimator, null-indicator
Received on: 03.08.2022
Accepted on: 29.08.2022
1. Introduction
The development of goniometers is inextricably linked with the development of research in the field of crystallography. In 1783, Arnold Carangeau invented the first device for measuring the angle between two faces of a crystal. The scientist called this device a contact goniometer. It consisted of two metal rods that were connected by hinges in the center of a graduated semicircle. The accuracy of this device was about 15 arc minutes [1].
In 1809, the English physicist William Hyde Wollaston developed an optical goniometer that measured the angles between the faces of a crystal using light reflected from them. The crystal was attached to a rotating graduated table, and the light source was directed to various facets of the crystal. The angle between the crystal faces was determined as the difference in the readings of the graduated table on which the light reflected from the faces fell. This goniometer had an accuracy of 5 arc minutes [2].
The development of science in the field of goniometry led to the creation of new devices and progressive methods and means of measuring angles, allowing the object under study to rotate automatically, use various auxiliary elements, optimize designs and improve the accuracy of goniometers.
The idea of measuring the angles of a optical polygon using a goniometer appeared a long time ago. When it became necessary to measure angles in astronomy with very high accuracy, it also became necessary to calibrate measuring instruments to improve the accuracy of their measurements. In 1954, in his publication entitled “The calibration of circular scale and precision polygon”, A. H. Cook described the calibration of a optical polygon by accurately solving a set of equations for the difference of angles between its faces [3]. With the development of metrology in the field of angular measurements, the optical polygon began to play an important role as an angular measure. International comparisons, ensuring the unity of measurements, are carried out using a multi-faceted prism, which is consistently calibrated on the reference goniometric systems of national metrological institutes of different countries [4,5].
2. Classification of contactless goniometers
Based on the history of the invention of goniometers and their measurement methods, we can conclude that there are two types of goniometers: contact and reflective (contactless). The contactless goniometer is the most accurate and is currently widely used in metrology, instrumentation and other scientific and industrial fields.
A complete goniometric system consists of such elements as an angular scale; a turntable; a drive that sets the rotation; an optical device that sets the reference direction; an electronic unit that controls the engine and pre-processing data; a personal computer for receiving and processing data. The object under study is fixed on the turntable as shown in Fig. 1 [6].
According to the principle of operation, contactless goniometers are divided into static and dynamic. The static measurement method differs in that the moving parts of the goniometric system (the object under study and the turntable) remain stationary at the moment of measurement. In this mode, the optical device is an autocollimator, which measures the deviation of the normal to the reflecting face of the prism from the sighting axis of the autocollimator. The measurement result in such a system is determined by the readings of the angular scale and the autocollimator. The main problem associated with a static goniometer is the long duration of measurements.
A dynamic goniometer is a device in which, during the measurement process, the object under study rotates at a quasi-constant speed. In this type of goniometers, the optical device that sets the reference direction is a null-indicator.
The block diagram shown in Fig. 1 is suitable for both static and dynamic types of goniometers [7]. The two modes of operation have several differences, which we will consider. In modern static goniometers, the angular scale is always represented by angle sensors (usually optical) or a limb, while in dynamic goniometers, either a ring laser or an optical angle sensor can be used as an angular scale. The second feature is the type of optical device used in the system. As part of static goniometers, an autocollimator is used, and as part of dynamic goniometers, a null-indicator is used.
In addition to the principle of operation, goniometers are also divided according to their purpose. The tasks performed using goniometers can be as follows: calibration of optical polygons, measurement of refractive index, measurement of external angles, measurement of angles between two reflecting surfaces [8].
An optical polygon is one of the most common objects used in measurements with goniometers. An optical polygon is a product with a fixed number of sides, which is considered one of the most accurate and reliable reference standards in the field of angular metrology. Examples are shown in Fig. 2.
As noted above, they are mainly used for calibration of measuring instruments, in particular, for transmitting the angle value from the primary standard to the working equipment. In addition to these applications, optical polygons are also used as elements of various laser and optical systems [9]. There are many parameters describing optical polygons. The main parameters are the following: the number of faces, model, dimensions, coating of the reflecting surface and the material from which the prism is made [10].
3. Types of optical null-indicators
A null-indicator is an optical device that sets a reference direction in space and fixes the moment when its optical axis is perpendicular to the reflecting surface of the object under study. There are various configurations of null-indicators, but two main types can be distinguished: interference and autocollimation [11].
3.1. Autocollimation null-indicator
One of the first null-indicators that began to be used as part of dynamic goniometers is a device built on the basis of an autocollimator. The optical scheme of such a device is shown in Fig. 3. A reference slit 6 of a certain width is placed in front of the light source 7. Of the same width, an analyzing slit 2 is placed in front of the photodetector 1. The width of the slits must be the same in order for the output signal to have a quasi-triangular shape. The light passing through the beam-splitting cube 3 falls on the lens 4 and then on the reflecting surface 5. When it becomes perpendicular to the axis of the null-indicator, the image of the reference slit falls on the analyzing slit and an analog signal is formed at the output of the photodetector.
The moment when the normal to the surface coincides with the optical axis of the AK corresponds to the maximum of the analog signal. The output pulse used for further processing is formed using a threshold circuit for a certain signal level, and this level is selected so that the steepness of the signal is at its maximum in order to reduce the random measurement error.
In general, the contribution of a null-indicator with a threshold analog signal processing circuit to the random error of a single measurement of a goniometric system is determined by two parameters: the angular steepness of the signal itself and the signal-to-noise ratio, which is set by optoelectronic components and the circuit itself involved in the formation and preprocessing of the signal. Instead of the steepness of the analog signal, with various kinds of estimates, you can also operate with the parameter of its angular width, because the required signal amplitude is determined by the input parameters of the processing circuit and is usually about 3 V. A typical sample of the considered autocollimation null-indicator (the focal length of the lens is 250 mm and the width of the setting and analyzing slit is 40 microns) is characterized by the width of the analog signal of the order of 60 arc-sec and the signal–to-noise ratio is 50. In this case, the value of the random error of a single measurement is about 0.6 arc-sec, which is an unacceptable value in modern high-precision measurements [12].
3.2. Interference null-indicator
The interference null-indicator is a two-beam interferometer based on beam splitting by a Kesters prism (or a Dove biprism) (Fig.4). The analog output signal of such a null-indicator is a combination of a narrow pulse and a constant component that is much wider than the pulse (about 1600 times) [13].
This type of null-indicator is characterized by an extremely small pulse width (the pulse width in an interference null indicator is determined by the width of the light beams and the distance between them, see Fig.4). With the width of the light beams and the distance between them equal to 10 mm, the angular width of the pulse is only 0.6 arc-sec. With a signal-to-noise ratio on the order of 100, the random error (RMS) is 0.03 arc-sec. [14]. Based on such accuracy characteristics, interference null-indicators were considered one of the most accurate in dynamic goniometric measurements.
The disadvantage of this type of null-indicators is the strong dependence of the possibilities of its functioning on the quality of the reflecting surface and the uniformity of the medium in which light propagates. Distortion of the recorded wavefront corresponding to even one interference fringe can lead to malfunction of the goniometric system.
In addition, there is another disadvantage of the interference null-indicator. Goniometers-refractometers measure the refractive indices of materials that are used to make special test prisms. To determine the refractive indices, the angles between the rays reflected from the inner and outer surfaces of the prism under study are measured. The beam reflected from the inner surface of the face passes through the prism twice, being refracted by the medium of this prism, while the beam is significantly influenced by dispersion. The phenomenon of dispersion is manifested in the fact that the rays passing through the medium are decomposed in space into components that have different frequencies. In this case, when using a light source with a wide spectrum, a narrow interference pulse turns into a blurry picture, which significantly reduces the accuracy of the device.
3.3. Autocollimation null-indicator with differential registration scheme
In connection with the above problems, an autocollimation null-indicator scheme with a differential registration scheme was proposed. The diagram of such a device is shown in Fig. 5.
The photodetector in this scheme is a quadrant photodiode, which is a silicon photodetector with four photosensitive regions (quadrants). The photodetector is positioned so that the optical axis of the null-indicator passes through the crosshair formed by the gaps between the quadrants. In this case, the vertical gap must be parallel to the axis of rotation of the reflecting surface.
After the light reflected from the surface of the object under study hits the quadrants, signals from the left and right areas of the photodiode begin to form at the output of the null-indicator. At the moment when the reflecting surface is perpendicular to the optical axis of this device, these signals intersect and a logical pulse is formed at the intersection point, which is fed to the goniometer for further processing. The signal generation process is shown in Fig. 6.
The image of the gap is larger than the gap between the pads, so there is a moment when the signals from the right and left pads are equal. In this case, the desired moment corresponds to the one when the center of mass of the image of the target slit is in the center of the vertical gap.
This type of null-indicators has shown good results in the course of research, its random error turned out to be at the same level as that of the interference type – about five hundredths of an arc second [12]. Its advantage is that the instability of the rotation speed of the object under study and the instability of the analog signal have virtually no effect on the accuracy of the device. But a significant drawback was also identified.
When installing this null-indicator relative to a rotating angular measure, it is necessary to fairly accurately set the parallelism of the vertical gap of the quadrant photodiode relative to the axis of rotation – with an accuracy of the order of several arc minutes [12]. With a deviation from parallelism by 20 arc-min the systematic measurement error of the goniometric system reached 0.4 arc-sec.
3.4. Autocollimation null-indicator with digital processing of an analog signal
At the moment, one of the most accurate autocollimation null-indicators is a null-indicator with digital signal processing, which is based on an estimate of its center of mass. The optical circuits of such a device have several variations, one of which is similar to the scheme shown in Fig. 3.
The photodetector generates an analog signal, the maximum of which corresponds to the moment of exact coincidence of the normal to the reflecting surface and the axis of the null-indicator. Digital signal processing, based on the evaluation of its center of mass, allows you to achieve measurement accuracy determined by the random error of a single measurement of 0.02 arc-sec [15]. The scheme of the digital autocollimation null-indicator is shown in Fig. 7.
The signal entering the photodetector is amplified and fed into the signal recording device, where it is digitized for further determination of the center of mass. The logic device outputs a data packet that contains the number of periods of the optical encoder from the moment the signal exceeds the threshold level to the moment when the signal is below the threshold; the values of the signal within this interval; the duration of the signal and time bindings in microseconds. Then all the data is processed and the center of mass is calculated using the software package, based on which the moment of perpendicular of the controlled surface to the optical axis of the null-indicator is determined.
The disadvantage of such a null-indicator is the presence of post-processing, which can make a certain contribution to the error of the device. However, according to experimental data, this null-indicator still outperforms other types in accuracy. In [15], model experiments were carried out, the task of which was to determine the random error of the null indication and its dependence on the signal-to-noise ratio. The table shows the results obtained.
The results obtained show that with a signal-to-noise ratio of 50, the random error turns out to be less than 0.02 arc-sec., which is characterized by a null-indicator with digital signal processing in the best way.
3.5. Other schemes of null-indicators
In addition to the presented configurations of null-indicators, there are others, but now they are practically not used due to their shortcomings (operating features and low accuracy).
The first type that we will consider is an autocollimation null-indicator, the defining and analyzing slits of which are masks whose transparency areas alternate according to a pseudo–noise law (randomly distributed slits). The transparent and opaque parts of the mask correspond to the elements of the code sequence – 1 and 0. In this case, the output signal is determined by the autocorrelation function. When the controlled surface is perpendicular to the axis of the null-indicator, the autocorrelation function has a sharp spike, the maximum of which determines the desired moment. The disadvantage of such a null-indicator is the diffraction distortion of the light beam, which as it turned out, as a result of an experimental study of the prototype, it negates all the advantages of using a pseudo-noise mask [16].
The second type is an autocollimation null-indicator with a rocking direction of the optical beam. In this null-indicator, after passing through the slit, the beam is reflected from a “rocking mirror” mounted on a piezoelectric base, which moves the mirror relative to the central axis. The output signal of the photodetector goes to the built-in amplifier, which allows filtering the signal by the swing frequency, and to the synchronous detector [3]. The disadvantage of this option is the requirement of a sufficiently low rotation speed of the object under study, which slows down the measurement process.
4. Conclusion
Depending on the technical capabilities, requirements and tasks, you should choose a suitable null-indicator, taking into account its parameters and factors affecting the accuracy of a specific configuration of the null-indicator. Summing up, we will make a brief comparison of the null-indicators considered in this article.
The autocollimation null-indicator with a threshold processing scheme has a relatively simple design, however, due to the large width of the analog signal, the accuracy of the device drops significantly.
The interference null-indicator is one of the most accurate due to the small width of the interference pulse. This type of null-indicator is extremely demanding on the quality of the controlled surface, since due to various irregularities and inhomogeneities, the light beam experiences dispersion, the interference pattern is blurred and the accuracy of the device decreases, or the device fails.
An autocollimation null-indicator with a differential registration scheme has a significant advantage from the point of view of the formation of a logical signal, since the formation of a logical pulse occurs strictly at the intersection point of signals symmetrical with respect to the moment of formation of this pulse. The systematic error of this null-indicator depends mainly on the accuracy of the alignment of its components and the uniformity of illumination of the photodiode.
An autocollimation null-indicator with digital signal processing is one of the most accurate types of null-indicators, but its disadvantage is the presence of post-processing.
Null-indicators with pseudo-noise masks and with a rocking direction of the light beam are practically not used at the moment. The disadvantage of the first is the diffraction distortion of the light beam. The disadvantage of the second null-indicator is that the rotation speed of the object under study should be low, which affects the duration of measurements.
CREDITS
Yu. V. Filatov and R. A. Larichev are grateful for the financial support provided by the RSF Grant No. 20-19-00412
AUTHORS
V. Yu. Venediktov, B. Nyamweru, R. A. Larichev, Yu. V. Filatov, E. V. Shishalova, Laser Measurement and Navigation Systems department, Saint Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
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