Television Lenses for Surveillance Systems
The features of constructing television lenses for surveillance systems are considered. When
designing television lenses, it is necessary to take into account a set of factors that affect the
magnitude of the detection range: the pixel size of the selected matrix and its resolution, focal length, relative aperture and field of view of the lens. The optimal combination of these factors along with the design of the lens allows you to achieve high resolution and get the maximum detection range.
for Surveillance Systems
I. P. Shishkin, A. P. Shkadarevich
RTC «LEMT» BelOMO, Minsk, Republic of Belarus
The features of constructing television lenses for surveillance systems are considered. When designing television lenses, it is necessary to take into account a set of factors that affect the magnitude of the detection range: the pixel size of the selected matrix and its resolution, focal length, relative aperture and field of view of the lens. The optimal combination of these factors along with the design of the lens allows you to achieve high resolution and get the maximum detection range.
Keywords: lenses, surveillance systems
The magnitude of the range of observation (detection) directly depends on the focal length of the lens. Currently, the market offers a wide selection of television lenses with a range of focal lengths (10 ~ 700 mm), relative apertures (F / 2.5 ~ F / 8) and angular fields (1 ~ 30°). But, as practice shows, lenses with variable focal lengths cannot provide the required resolution, especially at large focal lengths, which means that they do not allow to obtain a clear image of an object remote at long distances. In this case, it is more advisable to use telephoto lenses with a fixed focal length.
With the development of digital technology, the pixel size in cameras is constantly decreasing, however, to obtain a theoretical resolution of the lens, you must use a sensor with a large pixel. We clarify this statement using well-known formulas.
The lens resolution for a given pixel size is calculated by the formula
where N is the spatial frequency in lines / mm, x is the pixel size in microns.
For example, for a 6.25 μm pixel, you need to calculate a lens with a resolution of 80 lines / mm, and for a 4.16 μm pixel, a resolution of at least 120 lines / mm is already required.
The magnitude of the relative aperture of the lens at a large focal length is to a large extent determined by the ability to manufacture lenses of maximum diameter with the required accuracy. Table 1 shows the dependence of the diameter of the lenses, their number, length, and weight of the lens on the type, focal length, and relative aperture.
To determine the minimum relative aperture of the lens, we use the Rayleigh criterion:
where x is the pixel size in microns, f ‘ / D is the relative aperture, and λ is the working wavelength in microns.
For λ = 0.55 μm and a pixel of 3.75 μm, we get F / 5.6, and for a pixel of 5.36 μm, we get F / 8.
LENS ANGLE FIELD AND SENSOR DIAGONAL
The diagonal of the sensor is determined by the focal length and the angular field of the lens. In turn, the larger the angular field, the smaller the achievable limit of the resolution of the lens in the calculation.
To calculate the camera resolution, we use the expression
where R is the camera resolution in pixels, S is the sensor area in mm2, x is the pixel size in microns.
A camera created on the basis of a 1" matrix (16 mm diagonal, sensor area S = 123 mm2, pixel x = 5.5 μm) will have a resolution of R = 4 MP, and with a 4 / 3" matrix (21.6 mm diagonal, S = 225 mm2, x = 5.5 μm) – 7.4 MP.
For lenses with large focal length, the telephoto lens circuitry is usually chosen, which is the most compact of all known lenses.
When developing telephoto lenses, special attention is paid to dimensions, the number of lenses, weight, cost, and also the maximum tolerances on the shape and alignment of large-diameter lenses during manufacture. For example, a lens with a focus of 300 mm and a relative aperture of F / 4 will have a front lens diameter of about 75 mm. The manufacture and monitoring of large-diameter lenses greatly complicates the production of lenses. The requirements for mechanics are also quite stringent, given the length and diameters of the frames in the lens housing.
The large size and weight of the lenses in telephoto lenses (1–3 kg) force us to look for a solution with internal focusing – by moving the inner group of lenses.
Figure 1 shows a 7-lens and a 3-lens telephoto lens with a focal length of 300 mm and a relative aperture of F / 5.6. The lenses are designed for a 4 / 3" sensor and have an estimated resolution of 80 lines / mm. The light diameter of the front lens is 52 mm.
7-lens telephoto lens – apochromat is more compact (length 240 mm) and generally has better characteristics. Internal focusing is carried out by moving the last lens. The 3-lens design is somewhat longer (285 mm), but has several advantages: the lens has a minimum number of lenses, there is a focusing function (by moving the front group of lenses) and relatively low manufacturing requirements.
Table 2 shows the result of the influence of tolerances on the image contrast of a 7-lens (left) and a 3-lens (right) lens. A change in contrast is shown for 5 points of the angular field at a spatial frequency of 80 lines / mm.
Table 3 shows the tolerances for decentration and tilt, in Table 4 for the shape and thickness of the lenses, air gaps and glass.
Comparison shows that the 7-lens lens has a larger number of lenses with extreme tolerances, and from this point of view, the 3-lens design is more preferable.
INCREASE IN THE RELATIVE APERTURE
An increase in the relative aperture in a telephoto lens (Table 1) will inevitably lead to an increase in the number of lenses and their sizes [1,2], which, accordingly, will increase the laboriousness of manufacturing. In addition, to maintain high image quality over the entire range of the observation distance, the design of the focusing mechanism becomes more complex.
Figure 2 shows an example of a 12-lens lens  with a focal length of 300 mm and a relative aperture of F / 4. The lens is designed for a 4 / 3" sensor and has a resolution of 80 lines / mm within the entire angular field. The light diameter of the front lens is ~72 mm. Focusing in the lens is carried out by a group of lenses (9–11). The high image quality of the lens is confirmed by the optical transfer function graph (Fig.2b) The results of calculating the tolerances of a 12-lens lens by the Monte Carlo method are presented in Tables 5–7.
The calculation shows that the tolerances on the lenses of the lens, taking into account large diameters, are rather strict: surface shape 2 / 0.5, thickness 0.02–0.04 mm, glass 0.0002 / 0.2, decentration 0.005–0.01 mm, tilt 0.5'-1'.
For comparison, Fig. 3 shows the construction of the more sophisticated Olympus 17-lens lens with a focal length of 300mm and a relative aperture of F / 4. Overall dimensions ø92 × 227 mm, weight 1.3 kg, resolution 80 lines / mm.
Ultimately, the design of a television lens will depend not only on the optimal combination of all factors determining the image quality, but also on the level of technology that can be used in the actual manufacture of lenses.
Shishkin Igor Petrovich, Candidate of Technical Sciences, firstname.lastname@example.org, 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.