A device and method for correcting the thermal aberration of a catadioptric telescope based on structural compensation

Abstract

The present application belongs to the technical field of telescope, and particularly relates to a device and method for eliminating thermal aberration of a camera telescope based on structural compensation. The device comprises a support structure, two ends of the support structure are coaxially arranged with a primary mirror and a secondary mirror, and the support structure is made of a thermal expansion and contraction material, so that the change of the focal plane of the primary mirror and the secondary mirror is kept within the focal depth range under the condition of temperature difference in a set range. In the present application, the support structure is made of a thermal expansion and contraction material, and the principle of eliminating thermal aberration is used, that is, the ratio of the effective support length is reasonably designed to offset the defocus amount generated by the mirror surface, so that the defocus problem of the camera telescope in a certain temperature range is solved, and the device can realize high-precision measurement work at a certain temperature.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of telescopes, and particularly relates to a device and method for eliminating thermal aberration of a Cassegrain telescope based on structural compensation. BACKGROUND

[0002] The Cassegrain telescope is a reflective telescope composed of two mirrors, which was invented by Cassegrain in 1672 and named after him. Based on the classic Cassegrain structure, various improved reflective and catadioptric structure telescopes have been derived, such as R-C telescope, Schmidt-Cassegrain telescope, Makstov-Cassegrain telescope, and Schmidt-Crooked Moon-Cassegrain telescope, which are mainly used in space exploration and ground observation. However, for telescopes that work in all-weather and long-time outdoor environments, the support structure and mirrors of the telescope will deform due to seasonal and daily temperature changes, which will change the imaging focal plane and reduce the signal-to-noise ratio, even seriously affecting the results of precision measurement.

[0003] Therefore, in order to ensure the observation results of the telescope, the defocus problem must be solved. Automatic focusing is a common method, which adjusts the best imaging position through image analysis. This image feedback type focusing method needs to analyze and process the image, which is difficult to adjust in real time. At the same time, the judgment condition of image processing has a great influence on the final adjustment result, and sometimes the focusing will fail due to the ambiguity of the judgment condition. Another way is to design a non-thermal aberration for the entire telescope system. This method is commonly used for non-thermal aberration design of infrared optical systems. The optical expansion coefficient of a diffractive lens is negative, while the optical expansion coefficient of a refractive lens is positive. Therefore, according to this characteristic, the use of refractive and diffractive lenses can effectively design a non-thermal aberration optical system to ensure that the lens has a high imaging weight within a certain temperature range. The cost of the diffractive element and aspherical lens is relatively high. Therefore, a new way is needed to solve the defocus problem of the Cassegrain telescope within a certain temperature range. SUMMARY

[0004] In order to solve the above technical problems, the present application proposes a device and method for eliminating thermal aberration of a Cassegrain telescope based on structural compensation, and the specific technical solutions are as follows:

[0005] A device for eliminating thermal aberration of a Cassegrain telescope based on structural compensation, comprising a support structure, the support structure is coaxially installed with a primary mirror and a secondary mirror at both ends, and the support structure uses a thermal expansion and contraction material, so that the change amount of the focal plane of the primary mirror and the secondary mirror is kept within the depth of focus range under the condition of a certain temperature difference.

[0006] Further, the support structure comprises a first support structure and a second support structure arranged along the line connecting the primary mirror and the secondary mirror, the total length of the first support structure and the second support structure before temperature change is l, which is equal to the distance d between the primary mirror and the secondary mirror in value, the length of the second support structure made of thermal expansion material is βl, and β≤1.

[0007] Further, the material of the second support structure is aluminum alloy.

[0008] Further, the material of the first support structure is carbon fiber.

[0009] Further, the variation ε of the focal plane of the device with temperature is:

[0010]

[0011] wherein f1 and f2 are the focal lengths of the primary mirror and the secondary mirror before temperature change, f'1 and f'2 are the focal lengths of the primary mirror and the secondary mirror after temperature change, d ′ is the distance between the primary mirror and the secondary mirror after temperature change, α A is the thermal expansion coefficient of the second support structure, and dT is the temperature change value.

[0012] Optionally, the first support structure and the second support structure form a barrel structure, the primary mirror is installed on the end of the second support structure away from the first support structure, and the secondary mirror is installed on the end of the first support structure away from the second support structure.

[0013] A structural compensation-based heat compensation method for a catadioptric telescope, comprising

[0014] Before temperature change, the distance d between the primary mirror and the secondary mirror is determined according to the focal length f1 of the primary mirror and the focal length f2 of the secondary mirror.

[0015] According to the variation ε of the focal plane not being greater than the maximum focal depth, the thermal expansion material used by the support structure and the length of the support structure in the line direction of the primary mirror and the secondary mirror are determined.

[0016] Further, in the step of obtaining the variation ε of the focal plane in the step of determining the variation ε of the focal plane not being greater than the maximum focal depth, the step of obtaining the variation ε of the focal plane is:

[0017] The variation of the focal length caused by temperature change is obtained, and the formula is:

[0018]

[0019] wherein α G is the thermal expansion coefficient of the mirror material, the materials of the primary mirror and the secondary mirror are the same, f'1 and f'2 represent the focal lengths of the primary mirror and the secondary mirror after change, and the formula is:

[0020]

[0021] The thermal deformation of the support structure affects the distance between the primary mirror and the secondary mirror. Other parts have a thermal expansion coefficient that is small relative to the thermal expansion coefficient of the thermal expansion and contraction material part, so the change in distance is only caused by the thermal expansion and contraction of the thermal expansion and contraction material part. Therefore, the changed distance is:

[0022] d' = d + a A βl·dT

[0023] In the formula, a A is the thermal expansion coefficient of the aluminum alloy;

[0024] In the initial state, the relative position of the imaging focal plane of the system is:

[0025] Δ = q + d

[0026] In the formula, q is the distance from the secondary mirror to the secondary mirror focal point;

[0027] According to the imaging principle of the mirror and the known conditions, we have:

[0028]

[0029] In the formula, the sum of p and the distance d between the primary mirror and the secondary mirror is the distance from the primary mirror to the secondary mirror focal point;

[0030] The value of the focal plane before the temperature change and the relative position of the primary mirror before the temperature change are obtained

[0031]

[0032] The value of the focal plane after being affected by the temperature change can be expressed as:

[0033]

[0034] Therefore, the change ε of the imaging focal plane of the system affected by the temperature change is:

[0035]

[0036] Further, in the step of obtaining the maximum focal depth, the maximum focal depth is obtained when the change ε of the focal plane is not greater than the maximum focal depth.

[0037] Let δ represent the deviation between the ideal imaging plane and the actual observation plane. The optical path difference OPD between the two wavefronts emitted by the center and edge of the exit pupil of the projection objective is:

[0038]

[0039] In the formula, θ is the included angle between the reflected light of the secondary mirror and the central axis of the support structure;

[0040] When the maximum optical path does not exceed one quarter of the wavelength,

[0041]

[0042] That is, the depth of focus is:

[0043]

[0044] The advantages of the present application are:

[0045] (1) The support structure in the present application uses a material that expands when heated and contracts when cooled. By utilizing the principle of anastigmatism, that is, by reasonably designing the proportion of the effective support length, the defocus amount generated by the mirror surface can be offset, thereby solving the defocus problem of the Cassegrain telescope within a certain temperature range, and enabling the device to achieve high-precision measurement work at a certain temperature.

[0046] (2) The first support structure and the second support structure are spliced to form the support structure in the present application. The deformation amount of the first support structure is very small with respect to temperature changes, and the deformation amount of the second support structure is related to temperature changes. In this way, the first support structure and the second support structure can be determined among relatively common materials, and the defocus problem can be solved by only adjusting the length proportion of the second support structure to the entire support structure.

[0047] (3) The material of the second support structure in the present application is aluminum alloy, which is highly affected by environmental temperature, light in weight, and low in cost.

[0048] (4) The material of the first support structure in the present application is carbon fiber, which is also low in environmental temperature effect when the stiffness meets the requirements, and light in weight.

[0049] (5) The variation amount ε of the focal plane of the device disclosed in the present application with respect to temperature can be more conveniently determined according to the maximum temperature difference. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 It is a structural diagram of a Cassegrain telescope anastigmatism compensation device based on structural compensation.

[0051] Figure 2 It is a relationship diagram of the length of aluminum alloy and the defocus amount in a Cassegrain telescope anastigmatism compensation device based on structural compensation.

[0052] Figure 3 It is a relationship diagram of the length of aluminum alloy within the depth of focus in a Cassegrain telescope anastigmatism compensation device based on structural compensation.

[0053] In the figure:

[0054] 1. First support structure; 2. Second support structure; 3. Primary mirror; 4. Secondary mirror. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work are within the scope of protection of the present application. In the description of the embodiments of the present application, it should be understood that the terms "first", "second" are used only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first", "second" can explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the meaning of "multiple" is two or more, unless otherwise explicitly and specifically limited.

[0056] When the telescope is affected by external heat, the temperature of the mirror and the support structure for fixing the mirror will change, thermal expansion and contraction can cause the shape and position of the mirror to change, which in turn affects the propagation and focusing of light, resulting in a decrease in imaging weight, defocusing, and a decrease in precision when observing the target, making the observed target unclear and difficult to distinguish details, thereby affecting the observation effect. In this case, the focus needs to be adjusted again, and when the primary mirror and the secondary mirror are fixed, the maintenance needs to be performed again. This method requires a large amount of manual intervention, and with temperature changes, adjustment and maintenance are required, which greatly increases the labor cost. Another way is to stabilize the temperature, which has a high cost and also increases the overall weight of the telescope. In order to solve this problem, it is found through research that the change of the support structure of the telescope affected by temperature and the change of the imaging focal point position of the reflecting mirror itself are opposite.

[0057] Based on the above principle, an embodiment of the present application discloses a device for eliminating thermal aberration of a cassette telescope based on structural compensation, which comprises a support structure. The primary mirror and the secondary mirror are coaxially installed at both ends of the support structure. The support structure uses thermal expansion and contraction materials, so that the change amount of the focal plane of the primary mirror and the secondary mirror is kept within the depth of focus range under the condition of a certain range of temperature difference. In the present application, the support structure uses thermal expansion and contraction materials. By using the principle of eliminating thermal aberration, that is, reasonably designing the proportion of the effective support length, the defocusing amount generated by the reflecting mirror can be offset, thereby solving the defocusing problem of the cassette telescope within a certain temperature range, and enabling the device to realize high-precision measurement work at a certain temperature.

[0058] In one of the embodiments, the support structure comprises a first support structure and a second support structure arranged along the line connecting the primary mirror and the secondary mirror, the total effective support structure length of the first support structure and the second support structure before temperature change is l, which is equal to the distance d between the primary mirror and the secondary mirror in value, the length of the second support structure made of thermal expansion material is βl, and β≤1. In this scheme, the support structure is formed by splicing the first support structure and the second support structure, the deformation of the first support structure is small under temperature change, and the deformation of the second support structure is large under temperature change. In this way, the first support structure and the second support structure can be determined in a relatively common material, and the defocus problem can be solved by adjusting the length of the second support structure to the proportion of the total support structure length.

[0059] In one of the embodiments, the material of the second support structure is aluminum alloy. The material of the second support structure is aluminum alloy, which is highly affected by the ambient temperature, light in weight, and low in cost, and is convenient for fixing the lens.

[0060] In one of the embodiments, the material of the first support structure is carbon fiber. The material of the first support structure is carbon fiber, which is low in temperature influence under the condition that the rigidity meets the requirements, and is light in weight.

[0061] In one of the embodiments, the change amount ε of the focal plane of the device with temperature is:

[0062]

[0063] Where f1 and f2 are the focal lengths of the primary mirror and the secondary mirror before temperature change, f'1 and f'2 are the focal lengths of the primary mirror and the secondary mirror after temperature change, d' is the distance between the primary mirror and the secondary mirror after temperature change, and α A is the thermal expansion coefficient of the second support structure, and dT is the temperature change value. The change amount ε of the focal plane of the device with temperature disclosed in the application can be determined more conveniently according to the maximum temperature difference to determine the length of the second support structure.

[0064] In one of the embodiments, the first support structure and the second support structure form a barrel structure, the primary mirror is installed on the end of the second support structure away from the first support structure, and the secondary mirror is installed on the end of the first support structure away from the second support structure.

[0065] In one of the embodiments, a structural compensation-based heat compensation method for a C mount telescope is disclosed, which comprises

[0066] Before temperature change, the distance d between the primary mirror and the secondary mirror is determined according to the focal length f1 of the primary mirror and the focal length f2 of the secondary mirror;

[0067] According to the variation of the focal plane ε is not greater than the maximum focal depth, the thermal expansion and contraction material used by the support structure and the length of the length in the primary and secondary mirror along the line direction are determined.

[0068] In the variation of the focal plane ε is not greater than the maximum focal depth, the variation of the focal plane ε is obtained by the following steps:

[0069] When the ambient temperature changes, the primary and secondary mirrors change due to thermal expansion, and the optical element structure parameters in the optical system under uniform temperature change also change, and the change of the radius of curvature of the primary and secondary mirrors caused by the temperature difference is:

[0070] r' = r + dr = r (1 + X g × dT) (1)

[0071] In the formula, X g is the linear thermal expansion coefficient of the material. From the change of the radius of curvature r', it can be seen that when the temperature difference occurs, the curvature only increases or decreases, so the surface of the spherical mirror is still spherical after the temperature change, and the same parabolic surface is still parabolic after the temperature change. The relationship between the focal length and the radius of curvature of the primary and secondary mirrors is:

[0072]

[0073] The change of the focal length caused by the change of the temperature is obtained, and the formula is:

[0074]

[0075] In the formula, α G is the thermal expansion coefficient of the mirror material, and the materials of the primary and secondary mirrors are the same.

[0076] The changed focal length of the primary and secondary mirrors is represented by f'1 and f'2, and is represented as:

[0077]

[0078] The defocus amount caused by the deformation of the mirror surface under different temperature differences is shown in Table 1.

[0079] The thermal deformation of the support structure affects the distance between the primary and secondary mirrors, and other parts relative to the thermal expansion coefficient of the thermal expansion and contraction material part are small and can be ignored, so the change of the distance is only caused by the thermal expansion and contraction of the thermal expansion and contraction material part, and the changed distance is:

[0080] d' = d + α A · β1 · dT (5)

[0081] In the formula, α A is the thermal expansion coefficient of the aluminum alloy;

[0082] In the initial state, the relative position of the imaging focal plane of the system is:

[0083] Δ = q + d (6)

[0084] where q is the distance from the secondary mirror to the secondary mirror focal point;

[0085] According to the principle of mirror imaging and known conditions:

[0086]

[0087] where the sum of p and the distance d between the primary and secondary mirrors is the distance from the primary mirror to the secondary mirror focal point;

[0088] The value of the relative position of the focal plane before temperature change and the primary mirror is obtained

[0089]

[0090] The value of the focal plane after being affected by temperature change can be expressed as:

[0091]

[0092] Therefore, the change amount ε of the imaging focal plane of the system affected by temperature change is:

[0093]

[0094] The step of obtaining the maximum focal depth according to the change amount ε of the focal plane not being greater than the maximum focal depth is:

[0095] The deviation between the ideal imaging plane and the actual observation plane is represented by δ, and the optical path difference OPD between the two wavefronts emitted by the center and edge of the exit pupil of the projection objective is:

[0096]

[0097] where θ is the angle between the reflected light of the secondary mirror and the central axis of the support structure;

[0098] When the maximum optical path does not exceed one quarter of the wavelength,

[0099]

[0100] That is, the focal depth is:

[0101]

[0102] Therefore, when we perform athermalization design, we do not need to strictly set the change amount ε of the imaging focal plane to zero, but only need to keep it within the focal depth range:

[0103] |ε|≤δ max #(14)

[0104] Take one of the distance cases as an example, the basic parameters of the telescope provided by MEADE company are used for design, in which the aperture is 200mm, the primary mirror focal length |f1| is 600mm, the secondary mirror focal length |f2| is 300mm, the materials of the primary and secondary mirrors are borosilicate, the thermal expansion coefficient is 4.27*10-6 / K, the distance between the two mirrors |d| is 400mm, and the combined focal length is 1800mm. The thermal expansion coefficient of aluminum alloy is 2.38*10-6 / K. -6 K -1 . -5 K -1 .

[0105] Taking the center wavelength of 635nm as an example, the focal depth of the optical system can be obtained as 0.1032mm through the above basic parameters. And the change amount ε of the focal plane with the temperature difference and the length of the aluminum alloy support structure as independent variables is obtained:

[0106]

[0107] When the change of the imaging focal plane caused by the temperature influence on the support structure is not considered, or it can also be considered that the support structure is entirely composed of carbon fiber material, which has a very small thermal expansion coefficient, the influence on the distance between the primary and secondary mirrors can be ignored, and the change of the focal plane is only caused by the change of the reflective surface. Therefore, formula (15) can be expressed as:

[0108]

[0109] The defocus amount caused by the mirror surface deformation under different temperature differences is shown in Table 1

[0110]

[0111] Table 1

[0112] Taking the maximum temperature difference of ±50K(℃) as a design index, it can meet the vast majority of field experimental environment. It can be seen from Table 1 that the change of the focal plane caused by the mirror surface deformation is far greater than the focal depth of the system, and if it is not processed, it will affect the measurement result. In addition, we first ignore the influence of the surface deformation, and only consider the change of the imaging focal plane caused by the thermal expansion and contraction of the support structure affected by the temperature, when the support material is aluminum alloy, formula (15) can be expressed as:

[0113]

[0114] 9.52*10 -3 -6 / K, the product of the thermal expansion coefficient of aluminum alloy 2.38*10-6 / K and β1=400. -5 .

[0115] The defocus amount caused by the deformation of the support structure at different temperature differences is shown in Table 2

[0116]

[0117] Table 2

[0118] Comparing Table 1 and Table 2, it can be found that the movement of the imaging plane caused by the deformation of the mirror and the deformation of the support structure is opposite at the same temperature difference. Therefore, the combination of carbon fiber and aluminum alloy material can be used as the support structure of the telescope, and the length ratio thereof is reasonably selected, so that the influence of thermal difference on the imaging focal plane can be effectively eliminated. The influence of the combination of aluminum alloy support material and carbon fiber with different lengths on the imaging focal plane position is shown in Figure 2 and Figure 3 .

[0119] Comparing Table 1 and Table 2, it can be found that the movement of the imaging plane caused by the deformation of the mirror and the deformation of the support structure is opposite at the same temperature difference. Therefore, the combination of carbon fiber and aluminum alloy material can be used as the support structure of the telescope, and the length ratio thereof is reasonably selected, so that the influence of thermal difference on the imaging focal plane can be effectively eliminated. The influence of the combination of aluminum alloy support material and carbon fiber with different lengths on the imaging focal plane position is shown in Figure 2 and Figure 3 .

[0120] It can be seen from Figure 3 that if the movement of the imaging plane in the environment with the maximum temperature difference of ±50K is within the focal depth range of the system, the length of the support material of the aluminum alloy part is in the range of 67-83mm. If the installation fixing interface is considered, the length of the material in this part is as long as possible, and the length thereof can be set to 83mm, and if the installation fixing requirement is met, the length thereof can be set to 75.5mm, and the imaging quality can be ensured to be higher.

[0121] In the description of the present specification, the description referring to the terms "some embodiments" or "example" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiments or examples are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present specification.

[0122] The above merely describes the preferred embodiments of the present application and does not limit the present application in any way. Any person skilled in the art can make any form of equivalent replacement or modification to the technical solutions and technical contents disclosed by the present application without departing from the scope of the technical solutions of the present application, and such changes still belong to the protection scope of the present application.

Claims

1. A device for athermalization of a catadioptric telescope based on structural compensation, characterized in that, The support structure includes two ends of the support structure corresponding coaxially installed primary mirror and secondary mirror, the support structure uses thermal expansion and contraction material, so that the focal plane of the primary mirror and the secondary mirror changes within the depth of focus range under the temperature difference in the set range; The support structure includes first support structure and second support structure arranged along the line direction of the primary mirror and the secondary mirror, the total effective length of the first support structure and the second support structure before temperature change is l, which is equal to the distance d between the primary mirror and the secondary mirror in value, the length of the second support structure using thermal expansion and contraction material is βl, and β≤1; The material of the second support structure is aluminum alloy; The material of the first support structure is carbon fiber.

2. The device for eliminating chromatic aberration of a card telescope based on structural compensation according to claim 1, characterized in that, The focal plane change amount ε of the device with temperature is: where f1 and f2 are the focal lengths of the primary and secondary mirrors, respectively, before the temperature change, f'1 and f'2 are the focal lengths of the primary and secondary mirrors, respectively, after the temperature change, d' is the distance between the primary and secondary mirrors after the temperature change, and a A is the coefficient of thermal expansion of the second support structure, and dT is the temperature change.

3. The device for eliminating chromatic aberration of a catadioptric telescope based on structural compensation according to claim 1, characterized in that, The first support structure and the second support structure form a barrel structure, the primary mirror is installed on the end of the second support structure away from the first support structure, and the secondary mirror is installed on the end of the first support structure away from the second support structure.

4. A method for athermalization of a catadioptric telescope based on structural compensation, characterized in that, The support structure includes first support structure and second support structure arranged along the line direction of the primary mirror and the secondary mirror, the total effective length of the first support structure and the second support structure before temperature change is l, which is equal to the distance d between the primary mirror and the secondary mirror in value, the length of the second support structure using thermal expansion and contraction material is βl, and β≤1; The method includes Before temperature change, the distance d between the primary mirror and the secondary mirror is determined according to the focal length f1 of the primary mirror and the focal length f2 of the secondary mirror; According to the focal plane change amount ε not greater than the maximum focal depth, the thermal expansion and contraction material used by the support structure and the length in the line direction of the primary mirror and the secondary mirror are determined; The material of the second support structure is aluminum alloy; The material of the first support structure is carbon fiber.

5. A method for athermalization of a catadioptric telescope based on structural compensation according to claim 4, characterized in that, In the step of obtaining the focal plane change amount ε not greater than the maximum focal depth, the focal plane change amount ε is obtained by: The focal length change amount caused by temperature change is obtained by: wherein α G is the coefficient of thermal expansion of the mirror material, the primary and secondary mirrors being of the same material; f'1 and f'2 represent the changed focal lengths of the primary and secondary mirrors, respectively, and are given by The thermal deformation of the support structure affects the distance between the primary mirror and the secondary mirror, and other parts relative to the thermal expansion coefficient of the thermal expansion and contraction material part are small and can be ignored, so the distance change is only caused by the thermal expansion and contraction of the thermal expansion and contraction material part, and the changed distance is: d' = d + a A • βl • dT wherein α A is the coefficient of thermal expansion of the aluminum alloy; In the initial state, the relative position of the imaging focal plane of the system is: Δ=q+d In the formula, q is the distance from the secondary mirror to the secondary mirror focal point; According to the imaging principle of the reflecting mirror and the known conditions, it is known that: In the formula, the sum of p and the distance d between the primary mirror and the secondary mirror is the distance from the primary mirror to the secondary mirror focal point; The value of the relative position of the focal plane and the primary mirror before temperature change before temperature change is obtained The value of the focal plane after being affected by temperature change can be expressed as: Therefore, the focal plane change amount ε of the system imaging is:

6. A method for athermalization of a catadioptric telescope based on structural compensation according to claim 4 or 5, characterized in that, In the step of obtaining the maximum focal depth in the step of obtaining the focal plane change amount ε not greater than the maximum focal depth, the maximum focal depth is obtained by: The deviation δ between the ideal imaging plane and the actual observation plane is represented by the optical path difference OPD between the two wavefronts emitted by the center and the edge of the exit pupil of the projection objective: In the formula, θ is the included angle between the reflected light of the secondary mirror and the central axis of the support structure; When the maximum optical path does not exceed one fourth of the wavelength, That is, the depth of focus is:

Images