rus
Issue #5/2025
M. V. Ostanin, D. G. Otkupman, M. V. Shakhmatov
Parameter Selection Methods for the Basic Range Sensors and Determination of Its Range Characteristic
Parameter Selection Methods for the Basic Range Sensors and Determination of Its Range Characteristic
DOI: 10.22184/1993-7296.FRos.2025.19.5.390.399
FSBEI HE “Moscow State University of Geodesy and Cartography” (MIIGAiK), Moscow, Russia
The parameter selection methods for the onboard basic automatic active optical range sensors and determination of its range characteristic are considered. The paper provides for the dependences and influence of the base value, focal distance and the circle of confusion value on the relative response error of range sensors, as well as selection of these parameters at a given relative error and response distance. The models and optical circuits of the sensors based on a photo- and laser diode developed according to the established method are shown.
FSBEI HE “Moscow State University of Geodesy and Cartography” (MIIGAiK), Moscow, Russia
The parameter selection methods for the onboard basic automatic active optical range sensors and determination of its range characteristic are considered. The paper provides for the dependences and influence of the base value, focal distance and the circle of confusion value on the relative response error of range sensors, as well as selection of these parameters at a given relative error and response distance. The models and optical circuits of the sensors based on a photo- and laser diode developed according to the established method are shown.
Теги: energy efficiency function laser range sensors range characteristic reference distance базовое расстояние дистанционная характеристика лазерные датчики дальности функция энергетической эффективности
Parameter Selection Methods for the Basic Range Sensors and Determination of Its Range Characteristic
M. V. Ostanin 1, D. G. Otkupman 2, M. V. Shakhmatov 1
RPC “Impulse”, Moscow, Russia
FSBEI HE “Moscow State University of Geodesy and Cartography” (MIIGAiK), Moscow, Russia
The parameter selection methods for the onboard basic automatic active optical range sensors and determination of its range characteristic are considered. The paper provides for the dependences and influence of the base value, focal distance and the circle of confusion value on the relative response error of range sensors, as well as selection of these parameters at a given relative error and response distance. The models and optical circuits of the sensors based on a photo- and laser diode developed according to the established method are shown.
Keywords: laser range sensors, reference distance, range characteristic, energy efficiency function
Article received: 01.12.2024
Article accepted: 02.02.2025
INTRODUCTION
At present, in the field of short-range measurement, the basic active optical range sensors are used [1].
During many years of service, the basic range sensors have approved themselves to be the reliable devices. Due to the design and signal processing algorithm simplicity, the absence of any moving parts, high reliability and noise immunity, they remain in high demand up to this day.
The following specifications of the basic automatic range sensors are given in the references:
height measurement range from 1 to 30 m; base size of 1 m; pulse duration of 200 ns, repetition rate of about 1 kHz; height measurement accuracy of not worse than 0.5 m [2];
height measurement limit from 2 to 4 m; base size of 50 mm; relative measurement error of 10% [3, 4].
The main specification of onboard automatic range sensors is the range characteristic that is the dependence of the electrical signal the magnitude at the radiation receiver output on the distance to the object being studied.
The development of basic range sensors has been underway since the 1960s. However, there was no generalized method for selecting the parameters of such systems. The parameters were selected experimentally, based on the specified dimensions of the device and the limited circuit technology.
OPERATING PRINCIPLE
OF THE BASIC RANGE SENSORS
The basic range sensors are the active optical and electronic systems. They are similar to the geometric distance gauges and have become widespread in the field of short-range measurement due to the design simplicity and relatively high accuracy, allowing to solve the remote-control problems.
Figure 1 shows a generalized operation diagram of a basic range sensor. Such systems contain two channels: a transit channel and a receipt channel. The channels are spaced at a fixed (reference) distance and are located at a fixed (reference) angle to each other. The reference angle value at a known reference distance determines the response range (controlled distance).
The value of the reference distance (base) B affects the device accuracy and its dimensions. In the case of a small distance between the emitter and receiver, the range resolution may be insufficient [5]. Therefore, when developing a range sensor, the minimum possible value of the base B is selected that will ensure the specified response error.
The occurrence of a reflective object near the controlled range leads to the generation of an image of the radiation source (RS) spot in the plane of the sensitive elements of the radiation receiver (RR). The image position depends on the object movement along the range. The image movement in the plane of the sensitive elements relevant to the object movement leads to a change in the overlapping degree of the receiving areas and an image and, accordingly, to a change in the signal at the RR output. That is, the RR output signal carries information about compliance of the current range to the object to the controlled range [6, 7].
DETERMINATION
OF A RANGE CHARACTERISTIC
To assess the possible development of the basic automatic range sensors, a construction method for the main output range characteristic for an ideal optical system (OS) with a point and area RS is used at the first stages of design process. It is considered that the OS is an ideal system, and the RR sensitive element is a rectangular area.
In the first case, with due regard to the fact that the RS is point-like and its spot image on the object is also point-like, the range characteristic for the ideal OS is a rectangular function. In this case, the rectangle width corresponds to the dimensions of the sensitivity area (the extent of the area by range), depends on the dimensions of the RR sensitive element and is determined by the following inequality set:
K =
where K is the use factor of the emitting region image of a point source on the RR; l(y) is the current range corresponding to the y coordinate of the radiation source image on the RR sensitive element; l is the near boundary of the sensitivity area; l′ is the far boundary of the sensitivity area; l – l′ is the width of the sensitivity area.
Construction of the range characteristic of the range sensor is more complicated when the RS is a rectangular area, like a semiconductor laser diode (SLD). Accordingly, the RS spot image in the RR plane with an ideal OS is a rectangle. The issue is that it is necessary to ensure high response accuracy with an a priori uncertain relationship between the energy received by the RR and the object position relative to the controlled range. The ideal situation is when the response signal is generated when the image edge and the radiation receiver touch. However, the amount of energy received is very small and can be lower than the level of internal noise and extraneous flare. Therefore, a certain threshold value of the received energy is set based on the radiation source details, the controlled range and reflection coefficients of the typical surfaces. The threshold value corresponds to the situation when the RS spot image and the sensitive area of the receiver overlap to some extent (see Figure 2). This figure also shows how a coordinate system is selected on the radiation receiver plane to obtain the range characteristic; the coordinate system origin coincides with the center of the RS spot image when the threshold energy level is reached.
It is evident on the basis of Figure 2 that the use factor of the SLD emitting region image on the RR is determined by the following inequality set:
K =
where yи is the dimensions of the SLD emitting region image in the RR plane; y0 is the distance from the coordinate system origin to the boundary of the sensitive element (it corresponds to the threshold energy level); yПИ is the dimensions of the RR sensitive area along the y coordinate; y(l) is the coordinate of the center of the SLD radiation spot image in the RR plane relative to the coordinate origin; Δy(l) is the overlapping region length of the RR spot image and the sensitive area along the y coordinate.
The type of range characteristic for an ideal OS with the area RS is shown in Figure 3.
DETERMINATION OF THE RESPONSE RANGE AND PARAMETER SELECTION OF THE BASIC RANGE SENSORS
In general, the range characteristic for basic automatic range sensors on an energy basis is described by the following equation:
Фh, B, f ' = ρ · gh − l, B, f ' · sl, B, f ' dl,
where sl, B, f ' is the pulse response,
gl, B, f ' is the dimensions of the radiation source image on the RR,
l is the range,
B is the base,
h is the distance to the range sensor,
f ' is the focal length of the receiving lens,
ρ is the reflection coefficient of the object.
Having solved the equation (3) for the value h and given the threshold value Фh, B, f ', it is possible to determine the value of the sensor response range. In this case, on the basis of (3) one can obtain a formula for the response range when working with an object with a minimum reflection coefficient:
lcp =,
where B is the reference distance; l' is the response distance for the maximum reflection coefficient of the object under study; Kср is the use factor of the radiation source at the moment of response; Kρ is the ratio of the minimum reflection coefficient to the maximum reflection coefficient for the objects under study.
As for the error Δl in determining the response distance, it can be noted that this error is due to the range sensor operation with the objects with various reflection coefficients:
Δl = lρmax − lρmin ,
where lρmax is the response range at the maximum reflection coefficient; lρmin is the response range at the minimum reflection coefficient.
In this case, the relative error σ of the range sensor is determined by the following formula:
σ =,
where lср.зад is the specified response range.
Having set the value of the relative error σ, it is possible to construct a spatial graph demonstrating the nature of dependence of yи, В, f ' [7]. The set of points corresponding to the values of yи, В, f ' of the obtained surface allows one to determine the product parameters for a given relative error.
APPLICATION OF THE ENERGY EFFICIENCY FUNCTION TO CALCULATE THE RESPONSE RANGE
The considered methods of constructing the range characteristic for the basic range sensors allow selecting the OS parameters such as the base, focal length, angular field and diameter of the entrance pupil of the receiving lens, as well as setting the requirements for the size of the circle of confusion for the receiving lens and determining the potential capabilities of the resulting system. However, it should be noted that the provided methods are based on the simplest geometric relations and do not consider various specific features of the actual OS.
As it has been mentioned above, the range characteristic is the dependence of the reflected signal magnitude perceived by the RR on the distance to it, i. e. the calculation of range characteristic is an energy calculation. In this case, the range characteristic is most simply and efficiently described by the energy efficiency function:
Ф(l) =·,
where Ф0 is the radiation flux capacity incident on the object (item) under study; ρ is the reflection coefficient of the object (item) under study; D is the diameter of the entrance pupil of the receiving lens; l is the distance to the object (item) under study; Sгеом(l) is the effective area of the entrance pupil at a distance l; Sгеом.max is the maximum value of the effective area of the entrance pupil.
EVALUATION OF THE RESULTS OBTAINED
To verify the basic automatic range sensors, a special stand was developed by Research and Production Company “Impulse” PJSC, and the results obtained confirm the operability and adequacy of this method.
The developed method has been successfully evaluated during the development of basic automatic range sensors. An example of a 3-D model of the receiving and transmitting unit and the appearance of the sensor model are shown in Figures 5 and 6. A simplified schematic diagram is given in Figure 7.
CONCLUSIONS
As a result of the project implementation, a generalized method for selecting the parameters of basic automatic range sensors has been developed. The relations between the system parameters have been obtained, allowing the range characteristic to be calculated for various sensor models. A function has been proposed that determines the response distance as a function of the device operating parameters (focal length, reference distance, and dimensions of the source emitting area (SLD). Based on this function, the relationship between the relative error of range measurement and the device operating parameters has been investigated. This has made it possible to develop a procedure for selecting the parameters of basic range sensors. The method for calculating the range characteristic of range sensors is based on the energy efficiency function. Further implementation of the method under the bench testing conditions has demonstrated its successful application.
FUNDING
The studies have been financed by Research and Production Company “Impulse” PJSC.
CONTRIBUTION OF THE AUTHORS
The article was prepared on the basis of the work of all members of the team of contributors.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest and they supplemented the manuscript in part of their work.
M. V. Ostanin 1, D. G. Otkupman 2, M. V. Shakhmatov 1
RPC “Impulse”, Moscow, Russia
FSBEI HE “Moscow State University of Geodesy and Cartography” (MIIGAiK), Moscow, Russia
The parameter selection methods for the onboard basic automatic active optical range sensors and determination of its range characteristic are considered. The paper provides for the dependences and influence of the base value, focal distance and the circle of confusion value on the relative response error of range sensors, as well as selection of these parameters at a given relative error and response distance. The models and optical circuits of the sensors based on a photo- and laser diode developed according to the established method are shown.
Keywords: laser range sensors, reference distance, range characteristic, energy efficiency function
Article received: 01.12.2024
Article accepted: 02.02.2025
INTRODUCTION
At present, in the field of short-range measurement, the basic active optical range sensors are used [1].
During many years of service, the basic range sensors have approved themselves to be the reliable devices. Due to the design and signal processing algorithm simplicity, the absence of any moving parts, high reliability and noise immunity, they remain in high demand up to this day.
The following specifications of the basic automatic range sensors are given in the references:
height measurement range from 1 to 30 m; base size of 1 m; pulse duration of 200 ns, repetition rate of about 1 kHz; height measurement accuracy of not worse than 0.5 m [2];
height measurement limit from 2 to 4 m; base size of 50 mm; relative measurement error of 10% [3, 4].
The main specification of onboard automatic range sensors is the range characteristic that is the dependence of the electrical signal the magnitude at the radiation receiver output on the distance to the object being studied.
The development of basic range sensors has been underway since the 1960s. However, there was no generalized method for selecting the parameters of such systems. The parameters were selected experimentally, based on the specified dimensions of the device and the limited circuit technology.
OPERATING PRINCIPLE
OF THE BASIC RANGE SENSORS
The basic range sensors are the active optical and electronic systems. They are similar to the geometric distance gauges and have become widespread in the field of short-range measurement due to the design simplicity and relatively high accuracy, allowing to solve the remote-control problems.
Figure 1 shows a generalized operation diagram of a basic range sensor. Such systems contain two channels: a transit channel and a receipt channel. The channels are spaced at a fixed (reference) distance and are located at a fixed (reference) angle to each other. The reference angle value at a known reference distance determines the response range (controlled distance).
The value of the reference distance (base) B affects the device accuracy and its dimensions. In the case of a small distance between the emitter and receiver, the range resolution may be insufficient [5]. Therefore, when developing a range sensor, the minimum possible value of the base B is selected that will ensure the specified response error.
The occurrence of a reflective object near the controlled range leads to the generation of an image of the radiation source (RS) spot in the plane of the sensitive elements of the radiation receiver (RR). The image position depends on the object movement along the range. The image movement in the plane of the sensitive elements relevant to the object movement leads to a change in the overlapping degree of the receiving areas and an image and, accordingly, to a change in the signal at the RR output. That is, the RR output signal carries information about compliance of the current range to the object to the controlled range [6, 7].
DETERMINATION
OF A RANGE CHARACTERISTIC
To assess the possible development of the basic automatic range sensors, a construction method for the main output range characteristic for an ideal optical system (OS) with a point and area RS is used at the first stages of design process. It is considered that the OS is an ideal system, and the RR sensitive element is a rectangular area.
In the first case, with due regard to the fact that the RS is point-like and its spot image on the object is also point-like, the range characteristic for the ideal OS is a rectangular function. In this case, the rectangle width corresponds to the dimensions of the sensitivity area (the extent of the area by range), depends on the dimensions of the RR sensitive element and is determined by the following inequality set:
K =
where K is the use factor of the emitting region image of a point source on the RR; l(y) is the current range corresponding to the y coordinate of the radiation source image on the RR sensitive element; l is the near boundary of the sensitivity area; l′ is the far boundary of the sensitivity area; l – l′ is the width of the sensitivity area.
Construction of the range characteristic of the range sensor is more complicated when the RS is a rectangular area, like a semiconductor laser diode (SLD). Accordingly, the RS spot image in the RR plane with an ideal OS is a rectangle. The issue is that it is necessary to ensure high response accuracy with an a priori uncertain relationship between the energy received by the RR and the object position relative to the controlled range. The ideal situation is when the response signal is generated when the image edge and the radiation receiver touch. However, the amount of energy received is very small and can be lower than the level of internal noise and extraneous flare. Therefore, a certain threshold value of the received energy is set based on the radiation source details, the controlled range and reflection coefficients of the typical surfaces. The threshold value corresponds to the situation when the RS spot image and the sensitive area of the receiver overlap to some extent (see Figure 2). This figure also shows how a coordinate system is selected on the radiation receiver plane to obtain the range characteristic; the coordinate system origin coincides with the center of the RS spot image when the threshold energy level is reached.
It is evident on the basis of Figure 2 that the use factor of the SLD emitting region image on the RR is determined by the following inequality set:
K =
where yи is the dimensions of the SLD emitting region image in the RR plane; y0 is the distance from the coordinate system origin to the boundary of the sensitive element (it corresponds to the threshold energy level); yПИ is the dimensions of the RR sensitive area along the y coordinate; y(l) is the coordinate of the center of the SLD radiation spot image in the RR plane relative to the coordinate origin; Δy(l) is the overlapping region length of the RR spot image and the sensitive area along the y coordinate.
The type of range characteristic for an ideal OS with the area RS is shown in Figure 3.
DETERMINATION OF THE RESPONSE RANGE AND PARAMETER SELECTION OF THE BASIC RANGE SENSORS
In general, the range characteristic for basic automatic range sensors on an energy basis is described by the following equation:
Фh, B, f ' = ρ · gh − l, B, f ' · sl, B, f ' dl,
where sl, B, f ' is the pulse response,
gl, B, f ' is the dimensions of the radiation source image on the RR,
l is the range,
B is the base,
h is the distance to the range sensor,
f ' is the focal length of the receiving lens,
ρ is the reflection coefficient of the object.
Having solved the equation (3) for the value h and given the threshold value Фh, B, f ', it is possible to determine the value of the sensor response range. In this case, on the basis of (3) one can obtain a formula for the response range when working with an object with a minimum reflection coefficient:
lcp =,
where B is the reference distance; l' is the response distance for the maximum reflection coefficient of the object under study; Kср is the use factor of the radiation source at the moment of response; Kρ is the ratio of the minimum reflection coefficient to the maximum reflection coefficient for the objects under study.
As for the error Δl in determining the response distance, it can be noted that this error is due to the range sensor operation with the objects with various reflection coefficients:
Δl = lρmax − lρmin ,
where lρmax is the response range at the maximum reflection coefficient; lρmin is the response range at the minimum reflection coefficient.
In this case, the relative error σ of the range sensor is determined by the following formula:
σ =,
where lср.зад is the specified response range.
Having set the value of the relative error σ, it is possible to construct a spatial graph demonstrating the nature of dependence of yи, В, f ' [7]. The set of points corresponding to the values of yи, В, f ' of the obtained surface allows one to determine the product parameters for a given relative error.
APPLICATION OF THE ENERGY EFFICIENCY FUNCTION TO CALCULATE THE RESPONSE RANGE
The considered methods of constructing the range characteristic for the basic range sensors allow selecting the OS parameters such as the base, focal length, angular field and diameter of the entrance pupil of the receiving lens, as well as setting the requirements for the size of the circle of confusion for the receiving lens and determining the potential capabilities of the resulting system. However, it should be noted that the provided methods are based on the simplest geometric relations and do not consider various specific features of the actual OS.
As it has been mentioned above, the range characteristic is the dependence of the reflected signal magnitude perceived by the RR on the distance to it, i. e. the calculation of range characteristic is an energy calculation. In this case, the range characteristic is most simply and efficiently described by the energy efficiency function:
Ф(l) =·,
where Ф0 is the radiation flux capacity incident on the object (item) under study; ρ is the reflection coefficient of the object (item) under study; D is the diameter of the entrance pupil of the receiving lens; l is the distance to the object (item) under study; Sгеом(l) is the effective area of the entrance pupil at a distance l; Sгеом.max is the maximum value of the effective area of the entrance pupil.
EVALUATION OF THE RESULTS OBTAINED
To verify the basic automatic range sensors, a special stand was developed by Research and Production Company “Impulse” PJSC, and the results obtained confirm the operability and adequacy of this method.
The developed method has been successfully evaluated during the development of basic automatic range sensors. An example of a 3-D model of the receiving and transmitting unit and the appearance of the sensor model are shown in Figures 5 and 6. A simplified schematic diagram is given in Figure 7.
CONCLUSIONS
As a result of the project implementation, a generalized method for selecting the parameters of basic automatic range sensors has been developed. The relations between the system parameters have been obtained, allowing the range characteristic to be calculated for various sensor models. A function has been proposed that determines the response distance as a function of the device operating parameters (focal length, reference distance, and dimensions of the source emitting area (SLD). Based on this function, the relationship between the relative error of range measurement and the device operating parameters has been investigated. This has made it possible to develop a procedure for selecting the parameters of basic range sensors. The method for calculating the range characteristic of range sensors is based on the energy efficiency function. Further implementation of the method under the bench testing conditions has demonstrated its successful application.
FUNDING
The studies have been financed by Research and Production Company “Impulse” PJSC.
CONTRIBUTION OF THE AUTHORS
The article was prepared on the basis of the work of all members of the team of contributors.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest and they supplemented the manuscript in part of their work.
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