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DOI: 10.22184/1993-7296.FRos.2021.15.3.238.245
There are considered an optical performances of three classical lenses: Gelios, Industar and Tair, which are applicable for modern digital cameras.
There are considered an optical performances of three classical lenses: Gelios, Industar and Tair, which are applicable for modern digital cameras.
Diffraction-Limited Resolution Lenses
I. P. Shishkin, A. P. Shkadarevich
STC “LEMT” Belomo, Minsk, Belarus
There are considered an optical performances of three classical lenses: Gelios, Industar and Tair, which are applicable for modern digital cameras.
Keywords: camera lens, sensor format
Received on: 09.03.2021
Accepted on: 27.04.2021
INTRODUCTION
The diffraction limiting criterion is the most convenient way to compare different optical designs of objectives. For further calculations, we will use the well-known formulas [1].
The limiting lens resolution is limited by the Rayleigh diffraction criterion
,
where x is the minimum pixel size in microns, is the aperture, λ is the operating wavelength in microns.
On the other hand, the required lens resolution for a given pixel size can be calculated using the formula
,
where N is the spatial frequency in lines / mm, x is the pixel size in microns.
To calculate the camera resolution in pixels, use the expression
,
where R is the camera resolution in pixels, S is the sensor area in mm2, x is the pixel size in μm.
CLASSIC LENSES: GELIOS, INDUSTAR, TAIR
Before embarking on the development of any lens, it is necessary to determine which of the existing schemes could provide the given technical characteristics. Often, to solve the problem, it is enough to use a simple and well-known lens scheme, and not to develop an original one.
The view of the lenses and the graphs of the optical transfer function are shown in Fig. 1, and we will estimate their main parameters under the same conditions:
diffraction-limited resolution;
no vignetting.
The parameters of the lenses are presented in Table 1. The lenses are designed for the 1 / 3" sensor format, which has recently been widely used in many technical devices.
Despite the fact that the results obtained during the calculation are quite obvious and expected (for example, the Gelios lens [2], consisting of six lenses, has a better resolution in comparison with the Industar [3] and Tair [4]), based on this basic data, you can make a preliminary assessment and select the optimal lens design for a camera for any purpose. Using the method of scaling the design parameters of the lens, it is possible to obtain the required combination of angular field, relative aperture and resolution for any sensor format.
When a compromise is observed between certain lens parameters, priority improvement is achieved. For example, by decreasing the angular field or allowing vignetting across the field, you can increase the resolution by proportionally increasing the lens aperture and vice versa, by reducing the requirements for resolution and distortion, you can expand the angular field of the lens.
GELIOS LENS
The optical design of the Gelios lens remains one of the most widespread, despite more than a century of history since its creation by the German engineer Gauss. It should be noted that most modern lenses are, to one degree or another, a modification of this lens. And it would be advisable to consider the characteristics of the lens from the point of view of application with digital sensors for mobile devices.
Let us first consider the Gelios family of 21 mm fixed focal length lenses for sensor formats from 1 / 3" to APS-C, subject to diffraction-limited resolution and in the absence of vignetting.
Variants of Gelios objectives with various combinations of sensor format, angular field, aperture and resolution are shown in Table 2. Figure 2 shows the graphs of the dependence of the angular field of the lens on the aperture, the graph of the dependence of the resolution on the sensor format.
Let us consider the Gelios lens family for a fixed sensor format 1 / 3". The Gelios lens options with different combinations of focal lengths, angular field, aperture and resolution are shown in Table 3.
The graphs in Fig. 3 show the dependence of the resolution on the focal length and the angular field on the Gelios lens aperture.
INDUSTAR LENS
Industar lens options with various combinations of focal lengths, angular field, aperture and resolution are shown in Table 4.
The graphs in Fig. 4 show the dependence of the resolution on the focal length and the angular field on the Industar lens aperture.
TAIR LENS
Tair lens options with various combinations of focal lengths, angular field, aperture and resolution are shown in Table 5.
The graphs in Fig. 5 show the dependence of the resolution on the focal length and the angular field on the Tair lens aperture for a 1 / 3" sensor.
The results of the study are summarized in Table 6. Using the table, you can select the version of the sensor and lens with the required parameters: focal length, aperture, field of view, format and resolution.
CONCLUSION
With the right choice of sensor, classic lenses provide diffraction-limited resolution and can be successfully used in modern digital devices for various purposes. The optimal lens layout for any camera application can be selected by making a compromise between the specific lens parameters. Using the method of scaling the design parameters of the lens, it is possible to obtain the required combination of angular field, relative aperture and resolution for any sensor format.
About authors
Shishkin Igor Petrovich, Candidate of Technical Sciences, shipoflens@mail.ru, RTC “LEMT” BelOMO, Minsk, Republic of Belarus.
ORCID ID: 0000-0002-4592-1060
Shkadarevich Alexey Petrovich, Doctor of Technical Sciences, RTC «LEMT» BelOMO, Minsk, Republic of Belarus.
Contribution by the members of the team of authors
The article was prepared on the basis of many years of work by all members of the team of authors. Development and research are carried out at the expense of RTC “LEMT” BELOMO.
Conflict of interest
The authors claim that they have no conflict of interest.
I. P. Shishkin, A. P. Shkadarevich
STC “LEMT” Belomo, Minsk, Belarus
There are considered an optical performances of three classical lenses: Gelios, Industar and Tair, which are applicable for modern digital cameras.
Keywords: camera lens, sensor format
Received on: 09.03.2021
Accepted on: 27.04.2021
INTRODUCTION
The diffraction limiting criterion is the most convenient way to compare different optical designs of objectives. For further calculations, we will use the well-known formulas [1].
The limiting lens resolution is limited by the Rayleigh diffraction criterion
,
where x is the minimum pixel size in microns, is the aperture, λ is the operating wavelength in microns.
On the other hand, the required lens resolution for a given pixel size can be calculated using the formula
,
where N is the spatial frequency in lines / mm, x is the pixel size in microns.
To calculate the camera resolution in pixels, use the expression
,
where R is the camera resolution in pixels, S is the sensor area in mm2, x is the pixel size in μm.
CLASSIC LENSES: GELIOS, INDUSTAR, TAIR
Before embarking on the development of any lens, it is necessary to determine which of the existing schemes could provide the given technical characteristics. Often, to solve the problem, it is enough to use a simple and well-known lens scheme, and not to develop an original one.
The view of the lenses and the graphs of the optical transfer function are shown in Fig. 1, and we will estimate their main parameters under the same conditions:
diffraction-limited resolution;
no vignetting.
The parameters of the lenses are presented in Table 1. The lenses are designed for the 1 / 3" sensor format, which has recently been widely used in many technical devices.
Despite the fact that the results obtained during the calculation are quite obvious and expected (for example, the Gelios lens [2], consisting of six lenses, has a better resolution in comparison with the Industar [3] and Tair [4]), based on this basic data, you can make a preliminary assessment and select the optimal lens design for a camera for any purpose. Using the method of scaling the design parameters of the lens, it is possible to obtain the required combination of angular field, relative aperture and resolution for any sensor format.
When a compromise is observed between certain lens parameters, priority improvement is achieved. For example, by decreasing the angular field or allowing vignetting across the field, you can increase the resolution by proportionally increasing the lens aperture and vice versa, by reducing the requirements for resolution and distortion, you can expand the angular field of the lens.
GELIOS LENS
The optical design of the Gelios lens remains one of the most widespread, despite more than a century of history since its creation by the German engineer Gauss. It should be noted that most modern lenses are, to one degree or another, a modification of this lens. And it would be advisable to consider the characteristics of the lens from the point of view of application with digital sensors for mobile devices.
Let us first consider the Gelios family of 21 mm fixed focal length lenses for sensor formats from 1 / 3" to APS-C, subject to diffraction-limited resolution and in the absence of vignetting.
Variants of Gelios objectives with various combinations of sensor format, angular field, aperture and resolution are shown in Table 2. Figure 2 shows the graphs of the dependence of the angular field of the lens on the aperture, the graph of the dependence of the resolution on the sensor format.
Let us consider the Gelios lens family for a fixed sensor format 1 / 3". The Gelios lens options with different combinations of focal lengths, angular field, aperture and resolution are shown in Table 3.
The graphs in Fig. 3 show the dependence of the resolution on the focal length and the angular field on the Gelios lens aperture.
INDUSTAR LENS
Industar lens options with various combinations of focal lengths, angular field, aperture and resolution are shown in Table 4.
The graphs in Fig. 4 show the dependence of the resolution on the focal length and the angular field on the Industar lens aperture.
TAIR LENS
Tair lens options with various combinations of focal lengths, angular field, aperture and resolution are shown in Table 5.
The graphs in Fig. 5 show the dependence of the resolution on the focal length and the angular field on the Tair lens aperture for a 1 / 3" sensor.
The results of the study are summarized in Table 6. Using the table, you can select the version of the sensor and lens with the required parameters: focal length, aperture, field of view, format and resolution.
CONCLUSION
With the right choice of sensor, classic lenses provide diffraction-limited resolution and can be successfully used in modern digital devices for various purposes. The optimal lens layout for any camera application can be selected by making a compromise between the specific lens parameters. Using the method of scaling the design parameters of the lens, it is possible to obtain the required combination of angular field, relative aperture and resolution for any sensor format.
About authors
Shishkin Igor Petrovich, Candidate of Technical Sciences, shipoflens@mail.ru, RTC “LEMT” BelOMO, Minsk, Republic of Belarus.
ORCID ID: 0000-0002-4592-1060
Shkadarevich Alexey Petrovich, Doctor of Technical Sciences, RTC «LEMT» BelOMO, Minsk, Republic of Belarus.
Contribution by the members of the team of authors
The article was prepared on the basis of many years of work by all members of the team of authors. Development and research are carried out at the expense of RTC “LEMT” BELOMO.
Conflict of interest
The authors claim that they have no conflict of interest.
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