Issue #4/2020

Passive Rangefinders: from Optical Systems to Optoelectronic Ones

**A. V. Medvedev, A. V. Grinkevich, S. N. Knyazeva**Passive Rangefinders: from Optical Systems to Optoelectronic Ones

DOI: 10.22184/1993-7296.FRos.2020.14.4.344.358

Passive optical rangefinders provide stealth, but do not provide high accuracy range measurements in comparison with laser ones. New optical solutions based on a combination of digital methods and original optical solutions are proposed. The combination provides a variety of options for small-sized passive sights-rangefinders with high accuracy of measuring the distance to the target with secretive measurements.

Passive optical rangefinders provide stealth, but do not provide high accuracy range measurements in comparison with laser ones. New optical solutions based on a combination of digital methods and original optical solutions are proposed. The combination provides a variety of options for small-sized passive sights-rangefinders with high accuracy of measuring the distance to the target with secretive measurements.

Теги: defocusing image splitting normalized correlation function axisymmetric apertures passive optoelectronic rangefinder subpixel interpolation нормированная корреляционная функция осесимметричные апертуры пассивный оптико-электронный дальномер раздвоение изображения расфокусировка субпикселная интерполяция

Passive Rangefinders: from Optical Systems to Optoelectronic Ones

A. V. Medvedev1, A. V. Grinkevich2, S. N. Knyazeva3

Rostov Optical and Mechanical Plant OJSC (ROMZ OJSC), Rostov Veliky, Yaroslavl Reg., Russia

ZAO “EVS”, Moscow, Russia

Design Bureau of Rostov Optical and Mechanical Plant OJSC, Rostov the Great, Yaroslavl Reg., Russia

Passive optical rangefinders provide stealth, but do not provide high accuracy range measurements in comparison with laser ones. New optical solutions based on a combination of digital methods and original optical solutions are proposed. The combination provides a variety of options for small-sized passive sights-rangefinders with high accuracy of measuring the distance to the target with secretive measurements.

Keywords: passive optoelectronic rangefinder, normalized correlation function, axisymmetric apertures, image splitting, defocusing, subpixel interpolation

Received: 06.03.2020

Accepted for publication: 27.03.2020

Most modern sights with high-precision rangefinders are based on an active method of measuring range. It consists in sending a laser pulse to a distance, but does not ensure the secrecy of measurements. The reason is that optical sensors mounted on the target make it easy to identify the fact of measurement and determine the direction and coordinates of the point from where this measurement was made [1].

For example, in a modern US army, an infantryman is equipped with sensors located on a helmet developed as a result of combat use in Afghanistan, when cases of “friendly fire” in their units have become more frequent (Fig. 1).

The system can “detect” exposure to lasers with wavelengths of 1.064 and 1.55 microns, which are used in laser rangefinders on various platforms, as well as PRF coded laser markers for guided bombs. The signal to the infantryman when irradiated with a laser beam is supplied by the system in the form of “tactile signals” (vibration), after which you need to quickly change position, in extreme cases, by running to the nearest shelter. In addition, such a device on the helmet can detect reflected laser radiation.

In military technology today, at almost every object, a laser radiation warning system is installed, when triggered, a target suppression system comes into play. In other words, modern optoelectronic devices easily detect any action using the active laser mode. As a result of declassification of an object, it is destroyed by appropriate means.

Passive optical rangefinders differ from active rangefinders and possess stealth. At the same time, they do not provide high accuracy of range measurement in comparison with laser rangefinders.

In [2], two methods of passive range measurement were considered. The first of them is based on measuring the magnitude of the lens movement when focusing on the target (focusing method). The second is based on measuring the parallactic angle when combining two images formed by two channels spaced by the size of the internal base (intrabase method).

Passive methods make it possible to solve the problem of measuring the distance to a target located at a distance of up to 500 m with an error of an acceptable value (approximately 2–4 m). But these conditions are preserved when using telephoto lenses with a focus (Flens) of at least 600 mm or with an internal base size of at least 300 mm. The small size and practicality of the device when implementing such solutions is a fairly relative concept.

Low absolute and relative accuracy of measuring the distance to the target in passive optical rangefinders is associated with a low angular sensitivity of the human eye and the influence of the subjective factor of the human-rangefinder system. This factor manifests itself in the implementation of a complex algorithm for focusing or combining two images. They are supplemented by additional subjective errors by the operator and a low measurement rate.

At the current level of development of digital technology, passive methods of measuring range can be solved at a new technical level. It is based on a computer analysis of images of objects obtained as a result of video recording. For example, the passive method of determining the range to the target can be implemented on digital video cameras [3, 4], spaced a known distance from each other (Fig. 2).

Here, two digital images of the measured object 1 are formed by lenses 2 on cameras 3 and 4. Then, processor 5 calculates the estimated function between the two images “x1” and “x2” of object 1. The shift between the images of object 1 is determined from the minimum value of the two-dimensional normalized correlation function. the maximum of the correlation function is refined in the subpixel range, after which the maximum with the highest value of the correlation function is localized.

Thus, the shift between the images on the photodetector arrays 3 and 4 can be determined to within tenths of the size of one pixel of the photodetector 3 or 4. The distance “D” to object 1 is estimated from the shift “Δx” between the images “x1” and “x2”. It is necessary to know the distance “B” between the cameras 3 and 4, as well as the focal length “f” of the lenses of 2 cameras.

, (1)

where: f is the focal length of the lenses 2 of the cameras 3 and 4;

B – the distance between the lenses 2 of the cameras 3 and 4;

∆x is the measured shift between the images “x1” and “x2”.

The technique of subpixel interpolation is aimed at increasing the accuracy of determining the shift between images. The procedure includes the calculation of a two-dimensional correlation function and its normalization. This eliminates the effect of differences in the brightness and contrast of both images on the measurement accuracy.

However, such a design of the range finder requires the use of two identical television channels with two lenses and two photodetectors, as well as the use of a system for automatically focusing lenses on a selected target. This makes it difficult to create a simple and compact design rangefinder with low weight.

Using digital methods in combination with new original optical solutions allows you to create a variety of small-sized passive sights, rangefinders with high accuracy of measuring the distance to the target with secretive measurements.

Suggestions of new optical solutions are based on a combination of both methods: the target focusing method and the intra-base method [2]. One of the solution options implements the principle of using one lens with the separation of two small apertures from its large aperture, spaced by a certain amount. This value is an internal base. This principle is used in the so-called optical “dual image rangefinders” [5].

With its implementation, it becomes possible to sharply increase the angle of the aperture (along the extreme rays from the spaced apertures), determined by the internal base of the device and the focal length of the selected apertures – the focal length of the actual rangefinder lens. The photodetector is placed in the focal plane of the rangefinder lens. Such a circuit design of a passive optoelectronic rangefinder will be called the focusing method with selected apertures (Fig. 3).

In the design, the central part of the rangefinder lens (which is not involved in image building) can be excluded, and in this zone to place a guidance channel on the target – an aimed television channel.

A constructive solution to the scheme is that in the focal plane of the rangefinder lens, a photodetector is fixedly mounted on which the image of a target located at a distance of “infinity” will be sharp. When aiming the sight at a target located at a distance D from the front lens, the target image will shift relative to the focal plane of the rangefinder lens (relative to the plane of the stationary photodetector) by a certain amount of “x′”, which can be determined by Newton’s formula [6]:

, (2)

where x is the distance measured from the front focus of the lens to the observed object and taken as D, provided that D is much larger than the removal of the front focus from the first lens of the lens; Fd is the focal length of a rangefinder lens.

The main goal of such a combined method is to reduce the depth of field many times by creating an “equivalent” aperture of the rangefinder lens equal to “B / Fd” by the internal base “B” and to achieve a split image of the object closer to “infinity”.

Moreover, the bifurcation of the image will be the greater, the closer the object and the larger the “equivalent” aperture, which is important for increasing the accuracy of measuring the magnitude of the bifurcation when calculating the two-dimensional correlation function.

If we take the “equivalent” aperture of the rangefinder lens to unity (when B = Fd), then in this case the value “x′” becomes equal to the amount of image bifurcation to be measured.

Then the final formula for calculating the distance to the target will be:

, (3)

Using the minimum value of the two-dimensional normalized correlation function, it is possible to determine the distance between the images of the object with an accuracy of tenths of the size of one pixel of the photodetector of the rangefinder channel “dpxl”.

Obviously, the error in measuring the range in this case will be determined by the error in measuring the magnitude of the split image “Δx′”. Assuming the measurement accuracy equal to Δx′ = 0,2 · dpxl, we obtain:

, (4)

In the scheme of the rangefinder: a lens with a focal length Fd = 200 mm with a value of B = 200 mm; VAA‑136-USB television camera with a minimum working illumination of 0.005 lux and a frequency of 25 Hz (developed by EVS LLC, Moscow) based on a CMOS photodetector (MT9M034, format 1 280 × 960 elements, pixel size 3.75 × 3.75 μm, the Nyquist frequency ~130 lines / mm), the size of the sensitive area 4.8 × 3.6 mm (diagonal DTV = 6.0 mm). When using such a set of parts in the rangefinder circuit, the error Δx′ = 0,2 · dpxl will be 0.75 μm.

The results of calculations of the magnitude of the theoretical errors of range measurement are presented in Table 1.

A television sighting channel can be built on a VAA‑136-USB television camera and a small-sized lens with a focal length Flens = 18.2 mm, and use an eyepiece with a focal length foc = 15.67 mm and a SXGA060 1 280 × format microdisplay as an eyepiece channel 1024 with a pixel size of 9.3 × 9.3 μm and an active region size of 11.941 × 9.56 mm (Dmd diagonal = 15.296 mm).

The angular field of view of such a sighting channel will be ~15.0° × 11.2° (diagonal 18.7°), and the increase in the television channel will be calculated by the formula:

. (5)

After substituting the corresponding numerical values, the obtained value of the increase in the television channel will be Г ≈ 3 times.

The television sighting channel will be quite small and its objective part can be easily placed inside the device in the central free zone, and the ocular channel in the back free position of the device.

It is advisable to construct a rangefinder lens using a mirror-lens scheme, since it provides a fairly simple solution with a minimum number of optical parts, and also allows to achieve sufficiently large values of the relative aperture at high image quality, determined by the pixel size of the photodetector for a Nyquist frequency of ~ 130 lines / mm

Then, the embodiment of the passive optoelectronic sight-rangefinder with a mirror-lens lens consisting of an input lens, a main mirror and a three-lens aberration compensator, which includes one negative lens and two positive lenses, can be performed according to the scheme shown in Fig. 4.

The working areas of the rangefinder lens are the areas of the rangefinding channels No. 1 and No. 2.

The proposed implementation of the principle of measuring range by the magnitude of the image split from spaced axisymmetric apertures provides for the fixed installation of all elements in all channels of the sight. In this case, the range measurement process is similar to the measurement with a laser range finder – the central mark of the target channel is aimed at the object and, by pressing the measurement button, the range calculation is started in accordance with the calculation formula (4). The value of the measured range is displayed on the microdisplay of the ocular channel. In this case, the main processing load is borne by the processor of the device.

The complexity of analyzing the image taken from the photodetector of the rangefinder channel and the process of further calculations for such a scheme lies in the fact that the target at finite distances (for example, 500 m and 50 m) is not only bifurcated, but also defocused.

The bifurcation of the image from a point object in the plane of a fixedly mounted photodetector and the corresponding increase in the defocusing of this image are shown by the ray path in Fig. 5.

According to the data given in Table 1, the theoretical error of range measurement is relatively small: less than 1% per 500 m, and the measurement speed (fraction of a second) allows you to confidently use such a device as a universal one.

However, the practical use will still have some limitations due to the significant transverse size determined by the chosen base.

The length of the sight, implemented according to the scheme of Fig. 4, is ~258 mm, height ~50 mm. Such dimensions of the device are comparable with the corresponding sizes of standard sights of the PSO‑1 type. The width of the device is determined by the selected base (B = 200 mm) and is about 205 mm.

For comparison of sizes, Fig. 6 shows an example of setting the layout of elements with a base equal to B = 200 mm on a Dragunov sniper rifle. The total weight of the optical part of the rangefinder sight is ~ 614 g, which allows the device to be made with a total weight of less than 2 kg.

Obviously, it is necessary to look for ways to reduce weight, for which it is advisable to reduce the transverse size of the device.

Furthermore, for a defocused image, the accuracy of determining the distance by calculating a two-dimensional correlation function between two images on the same photodetector of the rangefinder channel will decrease as the focus is defocused – as the distance to the target decreases. In this case, the magnitude of the decrease in accuracy will need to be determined in a practical way and compensated by the introduction of an appropriate amendment.

In order to reduce the overall dimensions and weight, the second variant of the passive optoelectronic sight-range finder was developed. To this end, the possibility of drastically reducing the transverse size of the device, as well as the possibility of maintaining a sharp area of the target image, was considered. A drastic decrease in the transverse size was obtained due to the original layout solution (Fig. 7).

Given that the proportion of the rangefinder part with the VAI‑136-USB television camera is ~369 g out of 614 g, it was decided to exclude one of the rangefinder channels shown in Fig. 4. In this case, the rangefinder channel itself will be a combination of “halves” of axisymmetric optical elements constructed according to a similar mirror-lens scheme, i. e. image formation will be carried out by only one optical channel, which builds the image of the object on a fixed photodetector. The center of the image of the object located at “infinity” is “built” by the optical system in the center of the photodetector of the range-finding channel, and the center of the targeting channel is also aligned with this center.

The ability to maintain a sharp area of the target image is provided by tilting the plane of the photodetector relative to the optical axis of the rangefinder lens.

Then, when the distance to the target changes, the center of the target image on the photodetector will shift relative to the pointing point (center of the photodetector) according to the change in the distance to the object, remaining sharp.

With this scheme, the center of the target will be seen sharp and mixed relative to the center of the photodetector for the corresponding range. But to the right and left of the center of the target there will be a defocus due to the inclination of the plane of the photodetector, i. e. the area of the sharp image of the target will be narrow and shifted along the inclined plane of the photodetector inversely with the decrease in the distance to the target.

The corresponding ray path in the plane of the photodetector of the rangefinder channel is shown in Fig. 8.

Auxiliary values necessary to derive the final formula by which the distance to the target is calculated are indicated in the figure by the letters “h”, “x′1” and “x′2”.

The distance to the target is determined by the measured shift “x′f” of the center of the area of the sharp image of the target relative to the reference pixel of the photodetector of the rangefinder channel, corresponding to the distance to the target at “infinity”, as well as the pixel of the aiming mark for aiming at the target in the target channel.

Analyzing the geometric relationships illustrated in Fig. 8 and using Newton’s formula (2), we can obtain the final ratio for use in the computer calculator:

, (6)

where: α is the angle between the optical axis of the lens of the rangefinder channel and the plane of the photodetector of the rangefinder channel;

x′f is the measured value of the displacement of the center of the region of the sharp image of the observed target in the plane of the photodetector of the rangefinder channel relative to the pixel of the photodetector corresponding to the image of the target at “infinity”.

It is characteristic that the width of the area with a sharp target image will be determined by the angle α of the tilt of the photodetector relative to the optical axis of the rangefinder lens.

With a decrease in the angle of inclination of the plane of the photodetector “α”, the width of the section with a sharp image of the target will decrease, since the plane of the sharp image of the target built by the rangefinder lens is perpendicular to the optical axis of the lens. Optical calculations unambiguously show the presence of the effect of changing the sharpness of the image and can be clearly demonstrated by the path of the rays in the plane of the photodetector of the rangefinder channel.

For the mirror-lens optical scheme shown in Fig. 7, the ray path when the plane of the photodetector of the rangefinder channel is tilted at α ≈ 5° from the optical axis of the rangefinder lens is shown in Fig. 9.

In fig. Figure 9 also shows the size of the target image along the extreme beams of rays for each range by the course of rays of the same color: blue – the target at “infinity”, green – the target at a distance of 500 m, red – the target at a distance of 50 m.

To optimize the scattering circles of the rangefinder lens and maintain the image quality of the center of the field of view for different ranges, it is advisable to tilt the plane of the photodetector relative to the optical axis of the lens in the range of angles:

0° ≤ α ≤ 15°, (7)

The field of view of the rangefinder channel itself is also determined by the inclination of the plane of the photodetector and is 1.0° vertically and 0.6° horizontally.

If the size of the target is large and it covers the entire field of view of the rangefinder channel, then the entire field of view of the rangefinder channel corresponds to the same range to the target.

Then the narrow area of the sharp image of the target will be located vertically on the plane of the photodetector (Fig. 10).

In this case, it is possible to calculate the position of the maximum value of the two-dimensional normalized correlation function in the subpixel range using the entire area of the photodetector.

The situation is complicated when the target occupies a section smaller than the field of view of the rangefinder channel. At the same time, besides the target, in the field of view of the rangefinder channel, areas of terrain will also fall at ranges differing from the range to the target.

Then the narrow area of the sharp image of the target will have a complex profile different from the vertical, in which the target itself will occupy a section of the sharp image, offset from the point of pointing at the target along a horizontal line passing through the point of pointing at the target (Fig. 11). The remaining objects can be farther than the target (upper section in the figure), or closer than the target (lower section in the figure).

In this case, it would be most appropriate to calculate the position of the maximum value of the two-dimensional normalized correlation function in the subpixel range using a smaller portion of the photodetector area, but close to the central horizontal line passing through the targeting point (the figure shows the dotted line for calculations in the figure).

The theoretical error in determining the range is determined by the formula:

, (8)

If we use the calculation of the position of the maximum value of the two-dimensional normalized correlation function in the subpixel range to determine the shift of the center of the region of the sharp image of the target, then it is possible to measure “x′f” with an accuracy of no worse than 0.2 of the pixel size of the photodetector of the ranging channel.

With a photodetector pixel size of 0.00375 mm, the bias measurement error will be Δx′f = 0.00075 mm, and the theoretical measurement errors of the range to the target will take values for different range values (Table 2).

The calculations were performed for Fd = 200 mm, B = 200 mm, α = 5°, a pixel size of 3.75 μm, the error in measuring the displacement is 0.2 of the pixel size.

As can be seen from the calculations, the opto-electronic passive rangefinder option provides an acceptable error of passive range measurement at the main distances of accurate firing of weapons of the SVD type (~500 m) with a theoretical error of ~1.1%, and also allows firing at a range of ~1 km s theoretical error of range measurement ~2.25%.

Here, without limitations, the capabilities of the method for calculating a two-dimensional correlation function for determining the image shift can be used, since the region of sharp image of the target on the photodetector of the rangefinder channel is used for analysis.

Such a design in terms of overall and mass characteristics is quite acceptable for practical use, since the transverse size of the device is about 110 mm instead of the 205 mm obtained in the first embodiment (Fig. 12) due to the use of a fragment of the lens of the rangefinder channel and the inclination of the plane of the photodetector rangefinder channel relative to the optical axis of the rangefinder lens.

The total weight of the optical parts of the rangefinder scope option is ~428 g. This makes it possible to realize a passive optical-electronic rangefinder scope in a weight of not more than 1 kg in a small version. Table 2 shows the calculated values of the theoretical errors of the measurement method.

AUTHORS

Medvedev Alexander Vladimirovich, design@romz.ru, General Designer, Rostov Optical and Mechanical Plant OJSC (ROMZ OJSC), Rostov Veliky, Yaroslavl Region, Russia.

Grinkevich Alexander Vasilievich, lyu1455@yandex.ru, ZAO EVS, Moscow, Russia.

Knyazeva Svetlana Nikolaevna, ksn 61@yandex.ru, Design Engineer, Design Bureau of OJSC Rostov Optical and Mechanical Plant (OJSC ROMZ), Rostov the Great, Yaroslavl Region, Russia.

A. V. Medvedev1, A. V. Grinkevich2, S. N. Knyazeva3

Rostov Optical and Mechanical Plant OJSC (ROMZ OJSC), Rostov Veliky, Yaroslavl Reg., Russia

ZAO “EVS”, Moscow, Russia

Design Bureau of Rostov Optical and Mechanical Plant OJSC, Rostov the Great, Yaroslavl Reg., Russia

Passive optical rangefinders provide stealth, but do not provide high accuracy range measurements in comparison with laser ones. New optical solutions based on a combination of digital methods and original optical solutions are proposed. The combination provides a variety of options for small-sized passive sights-rangefinders with high accuracy of measuring the distance to the target with secretive measurements.

Keywords: passive optoelectronic rangefinder, normalized correlation function, axisymmetric apertures, image splitting, defocusing, subpixel interpolation

Received: 06.03.2020

Accepted for publication: 27.03.2020

Most modern sights with high-precision rangefinders are based on an active method of measuring range. It consists in sending a laser pulse to a distance, but does not ensure the secrecy of measurements. The reason is that optical sensors mounted on the target make it easy to identify the fact of measurement and determine the direction and coordinates of the point from where this measurement was made [1].

For example, in a modern US army, an infantryman is equipped with sensors located on a helmet developed as a result of combat use in Afghanistan, when cases of “friendly fire” in their units have become more frequent (Fig. 1).

The system can “detect” exposure to lasers with wavelengths of 1.064 and 1.55 microns, which are used in laser rangefinders on various platforms, as well as PRF coded laser markers for guided bombs. The signal to the infantryman when irradiated with a laser beam is supplied by the system in the form of “tactile signals” (vibration), after which you need to quickly change position, in extreme cases, by running to the nearest shelter. In addition, such a device on the helmet can detect reflected laser radiation.

In military technology today, at almost every object, a laser radiation warning system is installed, when triggered, a target suppression system comes into play. In other words, modern optoelectronic devices easily detect any action using the active laser mode. As a result of declassification of an object, it is destroyed by appropriate means.

Passive optical rangefinders differ from active rangefinders and possess stealth. At the same time, they do not provide high accuracy of range measurement in comparison with laser rangefinders.

In [2], two methods of passive range measurement were considered. The first of them is based on measuring the magnitude of the lens movement when focusing on the target (focusing method). The second is based on measuring the parallactic angle when combining two images formed by two channels spaced by the size of the internal base (intrabase method).

Passive methods make it possible to solve the problem of measuring the distance to a target located at a distance of up to 500 m with an error of an acceptable value (approximately 2–4 m). But these conditions are preserved when using telephoto lenses with a focus (Flens) of at least 600 mm or with an internal base size of at least 300 mm. The small size and practicality of the device when implementing such solutions is a fairly relative concept.

Low absolute and relative accuracy of measuring the distance to the target in passive optical rangefinders is associated with a low angular sensitivity of the human eye and the influence of the subjective factor of the human-rangefinder system. This factor manifests itself in the implementation of a complex algorithm for focusing or combining two images. They are supplemented by additional subjective errors by the operator and a low measurement rate.

At the current level of development of digital technology, passive methods of measuring range can be solved at a new technical level. It is based on a computer analysis of images of objects obtained as a result of video recording. For example, the passive method of determining the range to the target can be implemented on digital video cameras [3, 4], spaced a known distance from each other (Fig. 2).

Here, two digital images of the measured object 1 are formed by lenses 2 on cameras 3 and 4. Then, processor 5 calculates the estimated function between the two images “x1” and “x2” of object 1. The shift between the images of object 1 is determined from the minimum value of the two-dimensional normalized correlation function. the maximum of the correlation function is refined in the subpixel range, after which the maximum with the highest value of the correlation function is localized.

Thus, the shift between the images on the photodetector arrays 3 and 4 can be determined to within tenths of the size of one pixel of the photodetector 3 or 4. The distance “D” to object 1 is estimated from the shift “Δx” between the images “x1” and “x2”. It is necessary to know the distance “B” between the cameras 3 and 4, as well as the focal length “f” of the lenses of 2 cameras.

, (1)

where: f is the focal length of the lenses 2 of the cameras 3 and 4;

B – the distance between the lenses 2 of the cameras 3 and 4;

∆x is the measured shift between the images “x1” and “x2”.

The technique of subpixel interpolation is aimed at increasing the accuracy of determining the shift between images. The procedure includes the calculation of a two-dimensional correlation function and its normalization. This eliminates the effect of differences in the brightness and contrast of both images on the measurement accuracy.

However, such a design of the range finder requires the use of two identical television channels with two lenses and two photodetectors, as well as the use of a system for automatically focusing lenses on a selected target. This makes it difficult to create a simple and compact design rangefinder with low weight.

Using digital methods in combination with new original optical solutions allows you to create a variety of small-sized passive sights, rangefinders with high accuracy of measuring the distance to the target with secretive measurements.

Suggestions of new optical solutions are based on a combination of both methods: the target focusing method and the intra-base method [2]. One of the solution options implements the principle of using one lens with the separation of two small apertures from its large aperture, spaced by a certain amount. This value is an internal base. This principle is used in the so-called optical “dual image rangefinders” [5].

With its implementation, it becomes possible to sharply increase the angle of the aperture (along the extreme rays from the spaced apertures), determined by the internal base of the device and the focal length of the selected apertures – the focal length of the actual rangefinder lens. The photodetector is placed in the focal plane of the rangefinder lens. Such a circuit design of a passive optoelectronic rangefinder will be called the focusing method with selected apertures (Fig. 3).

In the design, the central part of the rangefinder lens (which is not involved in image building) can be excluded, and in this zone to place a guidance channel on the target – an aimed television channel.

A constructive solution to the scheme is that in the focal plane of the rangefinder lens, a photodetector is fixedly mounted on which the image of a target located at a distance of “infinity” will be sharp. When aiming the sight at a target located at a distance D from the front lens, the target image will shift relative to the focal plane of the rangefinder lens (relative to the plane of the stationary photodetector) by a certain amount of “x′”, which can be determined by Newton’s formula [6]:

, (2)

where x is the distance measured from the front focus of the lens to the observed object and taken as D, provided that D is much larger than the removal of the front focus from the first lens of the lens; Fd is the focal length of a rangefinder lens.

The main goal of such a combined method is to reduce the depth of field many times by creating an “equivalent” aperture of the rangefinder lens equal to “B / Fd” by the internal base “B” and to achieve a split image of the object closer to “infinity”.

Moreover, the bifurcation of the image will be the greater, the closer the object and the larger the “equivalent” aperture, which is important for increasing the accuracy of measuring the magnitude of the bifurcation when calculating the two-dimensional correlation function.

If we take the “equivalent” aperture of the rangefinder lens to unity (when B = Fd), then in this case the value “x′” becomes equal to the amount of image bifurcation to be measured.

Then the final formula for calculating the distance to the target will be:

, (3)

Using the minimum value of the two-dimensional normalized correlation function, it is possible to determine the distance between the images of the object with an accuracy of tenths of the size of one pixel of the photodetector of the rangefinder channel “dpxl”.

Obviously, the error in measuring the range in this case will be determined by the error in measuring the magnitude of the split image “Δx′”. Assuming the measurement accuracy equal to Δx′ = 0,2 · dpxl, we obtain:

, (4)

In the scheme of the rangefinder: a lens with a focal length Fd = 200 mm with a value of B = 200 mm; VAA‑136-USB television camera with a minimum working illumination of 0.005 lux and a frequency of 25 Hz (developed by EVS LLC, Moscow) based on a CMOS photodetector (MT9M034, format 1 280 × 960 elements, pixel size 3.75 × 3.75 μm, the Nyquist frequency ~130 lines / mm), the size of the sensitive area 4.8 × 3.6 mm (diagonal DTV = 6.0 mm). When using such a set of parts in the rangefinder circuit, the error Δx′ = 0,2 · dpxl will be 0.75 μm.

The results of calculations of the magnitude of the theoretical errors of range measurement are presented in Table 1.

A television sighting channel can be built on a VAA‑136-USB television camera and a small-sized lens with a focal length Flens = 18.2 mm, and use an eyepiece with a focal length foc = 15.67 mm and a SXGA060 1 280 × format microdisplay as an eyepiece channel 1024 with a pixel size of 9.3 × 9.3 μm and an active region size of 11.941 × 9.56 mm (Dmd diagonal = 15.296 mm).

The angular field of view of such a sighting channel will be ~15.0° × 11.2° (diagonal 18.7°), and the increase in the television channel will be calculated by the formula:

. (5)

After substituting the corresponding numerical values, the obtained value of the increase in the television channel will be Г ≈ 3 times.

The television sighting channel will be quite small and its objective part can be easily placed inside the device in the central free zone, and the ocular channel in the back free position of the device.

It is advisable to construct a rangefinder lens using a mirror-lens scheme, since it provides a fairly simple solution with a minimum number of optical parts, and also allows to achieve sufficiently large values of the relative aperture at high image quality, determined by the pixel size of the photodetector for a Nyquist frequency of ~ 130 lines / mm

Then, the embodiment of the passive optoelectronic sight-rangefinder with a mirror-lens lens consisting of an input lens, a main mirror and a three-lens aberration compensator, which includes one negative lens and two positive lenses, can be performed according to the scheme shown in Fig. 4.

The working areas of the rangefinder lens are the areas of the rangefinding channels No. 1 and No. 2.

The proposed implementation of the principle of measuring range by the magnitude of the image split from spaced axisymmetric apertures provides for the fixed installation of all elements in all channels of the sight. In this case, the range measurement process is similar to the measurement with a laser range finder – the central mark of the target channel is aimed at the object and, by pressing the measurement button, the range calculation is started in accordance with the calculation formula (4). The value of the measured range is displayed on the microdisplay of the ocular channel. In this case, the main processing load is borne by the processor of the device.

The complexity of analyzing the image taken from the photodetector of the rangefinder channel and the process of further calculations for such a scheme lies in the fact that the target at finite distances (for example, 500 m and 50 m) is not only bifurcated, but also defocused.

The bifurcation of the image from a point object in the plane of a fixedly mounted photodetector and the corresponding increase in the defocusing of this image are shown by the ray path in Fig. 5.

According to the data given in Table 1, the theoretical error of range measurement is relatively small: less than 1% per 500 m, and the measurement speed (fraction of a second) allows you to confidently use such a device as a universal one.

However, the practical use will still have some limitations due to the significant transverse size determined by the chosen base.

The length of the sight, implemented according to the scheme of Fig. 4, is ~258 mm, height ~50 mm. Such dimensions of the device are comparable with the corresponding sizes of standard sights of the PSO‑1 type. The width of the device is determined by the selected base (B = 200 mm) and is about 205 mm.

For comparison of sizes, Fig. 6 shows an example of setting the layout of elements with a base equal to B = 200 mm on a Dragunov sniper rifle. The total weight of the optical part of the rangefinder sight is ~ 614 g, which allows the device to be made with a total weight of less than 2 kg.

Obviously, it is necessary to look for ways to reduce weight, for which it is advisable to reduce the transverse size of the device.

Furthermore, for a defocused image, the accuracy of determining the distance by calculating a two-dimensional correlation function between two images on the same photodetector of the rangefinder channel will decrease as the focus is defocused – as the distance to the target decreases. In this case, the magnitude of the decrease in accuracy will need to be determined in a practical way and compensated by the introduction of an appropriate amendment.

In order to reduce the overall dimensions and weight, the second variant of the passive optoelectronic sight-range finder was developed. To this end, the possibility of drastically reducing the transverse size of the device, as well as the possibility of maintaining a sharp area of the target image, was considered. A drastic decrease in the transverse size was obtained due to the original layout solution (Fig. 7).

Given that the proportion of the rangefinder part with the VAI‑136-USB television camera is ~369 g out of 614 g, it was decided to exclude one of the rangefinder channels shown in Fig. 4. In this case, the rangefinder channel itself will be a combination of “halves” of axisymmetric optical elements constructed according to a similar mirror-lens scheme, i. e. image formation will be carried out by only one optical channel, which builds the image of the object on a fixed photodetector. The center of the image of the object located at “infinity” is “built” by the optical system in the center of the photodetector of the range-finding channel, and the center of the targeting channel is also aligned with this center.

The ability to maintain a sharp area of the target image is provided by tilting the plane of the photodetector relative to the optical axis of the rangefinder lens.

Then, when the distance to the target changes, the center of the target image on the photodetector will shift relative to the pointing point (center of the photodetector) according to the change in the distance to the object, remaining sharp.

With this scheme, the center of the target will be seen sharp and mixed relative to the center of the photodetector for the corresponding range. But to the right and left of the center of the target there will be a defocus due to the inclination of the plane of the photodetector, i. e. the area of the sharp image of the target will be narrow and shifted along the inclined plane of the photodetector inversely with the decrease in the distance to the target.

The corresponding ray path in the plane of the photodetector of the rangefinder channel is shown in Fig. 8.

Auxiliary values necessary to derive the final formula by which the distance to the target is calculated are indicated in the figure by the letters “h”, “x′1” and “x′2”.

The distance to the target is determined by the measured shift “x′f” of the center of the area of the sharp image of the target relative to the reference pixel of the photodetector of the rangefinder channel, corresponding to the distance to the target at “infinity”, as well as the pixel of the aiming mark for aiming at the target in the target channel.

Analyzing the geometric relationships illustrated in Fig. 8 and using Newton’s formula (2), we can obtain the final ratio for use in the computer calculator:

, (6)

where: α is the angle between the optical axis of the lens of the rangefinder channel and the plane of the photodetector of the rangefinder channel;

x′f is the measured value of the displacement of the center of the region of the sharp image of the observed target in the plane of the photodetector of the rangefinder channel relative to the pixel of the photodetector corresponding to the image of the target at “infinity”.

It is characteristic that the width of the area with a sharp target image will be determined by the angle α of the tilt of the photodetector relative to the optical axis of the rangefinder lens.

With a decrease in the angle of inclination of the plane of the photodetector “α”, the width of the section with a sharp image of the target will decrease, since the plane of the sharp image of the target built by the rangefinder lens is perpendicular to the optical axis of the lens. Optical calculations unambiguously show the presence of the effect of changing the sharpness of the image and can be clearly demonstrated by the path of the rays in the plane of the photodetector of the rangefinder channel.

For the mirror-lens optical scheme shown in Fig. 7, the ray path when the plane of the photodetector of the rangefinder channel is tilted at α ≈ 5° from the optical axis of the rangefinder lens is shown in Fig. 9.

In fig. Figure 9 also shows the size of the target image along the extreme beams of rays for each range by the course of rays of the same color: blue – the target at “infinity”, green – the target at a distance of 500 m, red – the target at a distance of 50 m.

To optimize the scattering circles of the rangefinder lens and maintain the image quality of the center of the field of view for different ranges, it is advisable to tilt the plane of the photodetector relative to the optical axis of the lens in the range of angles:

0° ≤ α ≤ 15°, (7)

The field of view of the rangefinder channel itself is also determined by the inclination of the plane of the photodetector and is 1.0° vertically and 0.6° horizontally.

If the size of the target is large and it covers the entire field of view of the rangefinder channel, then the entire field of view of the rangefinder channel corresponds to the same range to the target.

Then the narrow area of the sharp image of the target will be located vertically on the plane of the photodetector (Fig. 10).

In this case, it is possible to calculate the position of the maximum value of the two-dimensional normalized correlation function in the subpixel range using the entire area of the photodetector.

The situation is complicated when the target occupies a section smaller than the field of view of the rangefinder channel. At the same time, besides the target, in the field of view of the rangefinder channel, areas of terrain will also fall at ranges differing from the range to the target.

Then the narrow area of the sharp image of the target will have a complex profile different from the vertical, in which the target itself will occupy a section of the sharp image, offset from the point of pointing at the target along a horizontal line passing through the point of pointing at the target (Fig. 11). The remaining objects can be farther than the target (upper section in the figure), or closer than the target (lower section in the figure).

In this case, it would be most appropriate to calculate the position of the maximum value of the two-dimensional normalized correlation function in the subpixel range using a smaller portion of the photodetector area, but close to the central horizontal line passing through the targeting point (the figure shows the dotted line for calculations in the figure).

The theoretical error in determining the range is determined by the formula:

, (8)

If we use the calculation of the position of the maximum value of the two-dimensional normalized correlation function in the subpixel range to determine the shift of the center of the region of the sharp image of the target, then it is possible to measure “x′f” with an accuracy of no worse than 0.2 of the pixel size of the photodetector of the ranging channel.

With a photodetector pixel size of 0.00375 mm, the bias measurement error will be Δx′f = 0.00075 mm, and the theoretical measurement errors of the range to the target will take values for different range values (Table 2).

The calculations were performed for Fd = 200 mm, B = 200 mm, α = 5°, a pixel size of 3.75 μm, the error in measuring the displacement is 0.2 of the pixel size.

As can be seen from the calculations, the opto-electronic passive rangefinder option provides an acceptable error of passive range measurement at the main distances of accurate firing of weapons of the SVD type (~500 m) with a theoretical error of ~1.1%, and also allows firing at a range of ~1 km s theoretical error of range measurement ~2.25%.

Here, without limitations, the capabilities of the method for calculating a two-dimensional correlation function for determining the image shift can be used, since the region of sharp image of the target on the photodetector of the rangefinder channel is used for analysis.

Such a design in terms of overall and mass characteristics is quite acceptable for practical use, since the transverse size of the device is about 110 mm instead of the 205 mm obtained in the first embodiment (Fig. 12) due to the use of a fragment of the lens of the rangefinder channel and the inclination of the plane of the photodetector rangefinder channel relative to the optical axis of the rangefinder lens.

The total weight of the optical parts of the rangefinder scope option is ~428 g. This makes it possible to realize a passive optical-electronic rangefinder scope in a weight of not more than 1 kg in a small version. Table 2 shows the calculated values of the theoretical errors of the measurement method.

AUTHORS

Medvedev Alexander Vladimirovich, design@romz.ru, General Designer, Rostov Optical and Mechanical Plant OJSC (ROMZ OJSC), Rostov Veliky, Yaroslavl Region, Russia.

Grinkevich Alexander Vasilievich, lyu1455@yandex.ru, ZAO EVS, Moscow, Russia.

Knyazeva Svetlana Nikolaevna, ksn 61@yandex.ru, Design Engineer, Design Bureau of OJSC Rostov Optical and Mechanical Plant (OJSC ROMZ), Rostov the Great, Yaroslavl Region, Russia.

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