Design method of broadband transmission-type relay optical system

Abstract

The invention provides a design method of a broadband transmission-type relay optical system. The design method is used for solving the technical problems that an existing method for selecting and building an initial structure of the relay optical system is low in efficiency, and the imaging quality of the finally generated relay optical system is unstable. The invention provides a design method of a broadband transmission-type relay optical system, and the method comprises the steps: constructing an object space telecentric initial structure with a central diaphragm, selecting a lens material pair meeting an achromatic condition according to a working waveband, taking an equal-curvature biconvex lens as an optimization starting point, and calculating the initial curvature radius of each lens; after the initial center thickness and the air space of each lens are given, modeling of the initial structure of the relay optical system is achieved, and the optimization efficiency is greatly improved; finally, the view field is gradually increased from the zero view field, the final broadband transmission-type relay optical system is obtained after iterative optimization, any relay amplification factor can be achieved through the method, and high-quality imaging in the wide waveband range is achieved.

Description

Technical Field

[0001] The invention relates to the field of optical imaging, and in particular to a design method for a wide-band transmission-type relay optical system. Background Art

[0002] The relay optical system is a post-optical system that has the function of transmitting the image plane over a long distance, such as transmitting the image plane of the front optical system to the detector or to the object plane of the next optical system to meet the needs of structural or optical design. The relay optical system is widely used in various front optical systems, such as sights, high-temperature endoscopes, copy optical systems, etc. It can not only be used to extend the length of the optical system, but also play the role of image transfer. With the development of industrial technology, the working band of optical instruments is required to be wider and wider, and the imaging quality of the system is also required to be higher and higher. For example, in the objective lens system of ultra-wide spectrum imaging, it is necessary to increase the relay optical system to achieve higher magnification and more target monitoring needs. In the monitoring system of extreme environments (such as ultra-high temperature, ultra-low temperature, ultra-high pressure, ultra-low pressure, strong electromagnetic radiation, etc.), the electronic system of the camera needs to be isolated from the environment to be tested by the relay optical system to ensure that it can work stably. Therefore, it is of great significance to design a wide-band transmission relay optical system.

[0003] At present, the selection and construction of the initial structure of the relay optical system is difficult due to the large number of design freedoms. If the initial structure is not properly constructed, it will be difficult to map the various input parameters of the relay optical system, such as numerical aperture, field of view, working band, object distance, vertical axis magnification, etc., to the initial structure. In addition, due to the limitations of requirements such as external dimensions and relay distance, wide-band transmission relay optical systems can usually only be designed as systems with small F numbers, but such systems usually require complex lens groups to correct their off-axis aberrations and chromatic aberrations, further increasing the difficulty of selecting and building the initial structure. Therefore, it is necessary to find an efficient initial structure to provide support for the efficient optimization of the relay optical system. Therefore, when selecting and building the initial structure of the relay optical system in the industry, it is usually based on the design requirements of the system to find a roughly matching system from the historical design results as the initial structure of the relay optical system, or to estimate a system as the initial structure of the relay optical system based on design experience, but this method is usually inefficient and the imaging quality of the resulting relay optical system is unstable. Summary of the invention

[0004] The purpose of the present invention is to solve the technical problems that the existing methods for selecting and building the initial structure of a relay optical system are relatively low in efficiency and the imaging quality of the ultimately generated relay optical system is unstable, and to provide a design method for a wide-band transmission relay optical system.

[0005] The technical concept of the present invention is:

[0006] From the aberration theory, we know that for an optical system whose structural parameters are completely symmetrical with the aperture, its axial aberrations (spherical aberration, axial chromatic aberration) are twice the value on either side, and its vertical aberrations (coma, distortion, vertical chromatic aberration) can offset each other. Therefore, it is necessary to select a reasonable number of lenses and a reasonable combination of materials on this basis to achieve the purpose of correcting spherical aberration and axial chromatic aberration.

[0007] In order to achieve the above purpose, the technical solution of the present invention is as follows:

[0008] A design method for a wide-band transmission relay optical system is characterized in that it comprises the following steps:

[0009] Step 1, preliminarily determining the maximum outer diameter and numerical aperture of the relay optical system according to the system parameters of the front optical system, and then calculating the object distance of the relay optical system; and then calculating the focal length of the relay optical system according to the object distance of the relay optical system and the required magnification;

[0010] Step 2, according to the numerical aperture of the relay optical system, the number of lenses of the relay optical system is calculated; based on the number of lenses, an object-side telecentric initial structure with the aperture centered is constructed; and then the optical power of each lens in the object-side telecentric initial structure is allocated according to the focal length of the relay optical system;

[0011] Step 3, selecting a lens material pair that meets the achromatic condition according to the working band;

[0012] Step 4, according to the selected lens material pair, taking the equal curvature biconvex lens as the optimization starting point, calculate the initial radius of curvature of each lens; given the initial center thickness and air spacing of each lens, complete the modeling of the initial structure of the relay optical system;

[0013] Step 5, by controlling the magnification, total length, back intercept, image telecentricity, air spacing between the center and edge of the lens, thickness between the center and edge of the lens, and diameter-thickness ratio of the initial structure of the relay optical system, the field of view is gradually increased starting from zero field of view, and the final wide-band transmission relay optical system is obtained after iterative optimization.

[0014] Furthermore, step 3 is specifically as follows:

[0015] According to the requirements of the working band, multiple groups of lens material pairs with large differences in Abbe numbers are determined in the Abbe diagram, and multiple groups of lens material pairs with small differences in partial dispersion are determined in the partial dispersion diagram;

[0016] Based on the transmittance of different materials in the working band and the usage scenarios, the lens material pair with the smallest ratio of partial dispersion difference to Abbe number difference among multiple groups of lens material pairs is selected as the lens material pair that meets the achromatic condition.

[0017] Furthermore, in step 3, the operating band is a far-infrared band, and the lens material pair is Ge and ZnSe.

[0018] Furthermore, in step 1, the object distance l of the relay optical system is calculated by the following formula:

[0019]

[0020] Wherein, D0 is the maximum outer diameter of the relay optical system, and NA is the numerical aperture of the relay optical system;

[0021] In step 1, the focal length f' of the optical system is calculated by the following formula:

[0022]

[0023] Where β is the vertical axis magnification, l' is the image distance of the relay optical system.

[0024] Furthermore, in step 2, the number of lenses N is calculated by the following formula:

[0025]

[0026] Furthermore, in step 2, the optical power of each lens in the object-side telecentric initial structure is distributed in an average distribution manner according to the focal length of the relay optical system.

[0027] Furthermore, in step 4, the initial radius of curvature of each lens is calculated by the following formula:

[0028]

[0029] Among them, R k-1 is the initial radius of curvature of the front surface of the lens, R k-2 is the initial radius of curvature of the rear surface of the lens, k represents the type of material, and n k Indicates the refractive index of the material k corresponding to the central wavelength of the working band, φ i is the optical power of the lens, i=1,2,…,N.

[0030] Furthermore, in step 4, according to the selected lens material, the equal curvature biconvex lens is used as the optimization starting point, and the initial curvature radius of each lens is calculated as follows:

[0031] Divide N lenses into two groups with the aperture as the center, so that the N / 2 lenses located in front of the aperture alternately use two materials in the lens material pair selected in step 3, take the equal curvature biconvex lens as the optimization starting point, and calculate the initial curvature radius of the N / 2 lenses in front of the aperture;

[0032] The N / 2 lenses located behind the aperture and the N / 2 lenses located in front of the aperture are arranged in a mirror-symmetrical manner about the aperture, and the materials and initial curvature radii at the symmetrical positions are the same.

[0033] Furthermore, in step 4, the initial center thickness of each lens is determined according to the diameter-to-thickness ratio, and the air gap is 1 / 3 to 2 times the initial center thickness of the previous lens.

[0034] Furthermore, in step 4, the initial center thickness of each lens is

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] 1. The present invention provides a design method for a wide-band transmission relay optical system. According to the basic formula and empirical formula of paraxial optics, an object-side telecentric initial structure with an aperture in the center can be efficiently constructed, and then a lens material pair that meets the achromatic condition is selected according to the working band, and an equal-curvature biconvex lens is used as the optimization starting point to calculate the initial curvature radius of each lens; after the initial center thickness and air spacing of each lens are given, the initial structure of the relay optical system is modeled, and it is used as the starting point for the optimization design, which greatly improves the optimization efficiency and facilitates subsequent optimization and processing, and has the application potential of wide band, light weight and long relay distance; the relay optical system constructed by this method can achieve any relay magnification and high-quality imaging in a wider band range, and can be suitable for various scenarios and different application requirements.

[0037] 2. The relay optical system constructed by the design method of the present invention has the characteristics of double telecentricity in the object and image space, and the front and rear parts are mirror-symmetric about the aperture, which has important application value in optical measurement systems.

[0038] 3. The present invention provides a design method for a wide-band transmission relay optical system, which takes the minimum value of the ratio of the partial dispersion difference to the Abbe number difference of the lens material pair as a criterion to construct an achromatic relay optical system, further realizing high-quality imaging within a wider band. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of ΔP / Δν of multiple groups of lens material pairs obtained in the far-infrared band in step 3 of an embodiment of a design method for a wide-band transmission relay optical system of the present invention;

[0040] Figure 2 A schematic diagram of modeling the initial structure of the relay optical system completed in step 4 of the embodiment of the present invention;

[0041] Figure 3Schematic diagram of a wide-band transmission-type relay optical system finally obtained after iterative optimization in step 5 of an embodiment of the present invention;

[0042] Figure 4 is a design point diagram of an embodiment of the present invention;

[0043] Figure 5 is a modulation transfer function curve diagram of an embodiment of the present invention;

[0044] Figure 6 This is a design grid distortion diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the advantages and features of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] A design method for a wide-band transmission relay optical system specifically comprises the following steps:

[0047] Step 1, calculate the focal length of the relay optical system.

[0048] Step 1.1, when designing the initial structure of the relay optical system, the parameters that need to be determined in advance include the numerical aperture, field of view at object height, working band, maximum outer diameter and magnification of the relay optical system. The above parameters are used as input parameters to realize the design of the initial structure of the relay optical system. The numerical aperture, field of view and working band of the relay optical system need to be determined according to the front optical system, among which the numerical aperture of the relay optical system needs to be greater than or equal to the numerical aperture of the front optical system, the field of view at object height of the relay optical system needs to be greater than or equal to the field of view at object height of the front optical system (i.e., the image height of the front optical system), and the working band of the relay optical system needs to completely cover the working band of the front optical system. In addition, the maximum outer diameter of the relay optical system is determined according to the actual working space, and the magnification is determined according to the design requirements, usually -1.

[0049] This embodiment is described by taking the design of a far-infrared transmission relay optical system as an example.

[0050] The F number of the far-infrared transmission relay optical system is the most commonly used F number in the far-infrared band of the front optical system, and its object height field of view is The working band is 8μm-12μm (far infrared band), the maximum outer diameter is 40mm, the magnification is -1 (ie 1:1 imaging), and the total length of the relay optical system does not exceed 150mm.

[0051] Step 1.2, after determining the F number of the front optical system, calculate the numerical aperture NA of the relay optical system by the following formula:

[0052]

[0053] Wherein, F / # is the F number of the front optical system, and F / #=1.

[0054] Considering leaving a certain margin, select NA=0.45.

[0055] Step 1.3, since the object distance of the relay optical system is limited by its radial optical size, the object distance l of the relay optical system is calculated according to the numerical aperture NA of the relay optical system and the maximum outer diameter D0 of the relay optical system. The specific calculation formula is as follows:

[0056]

[0057] Step 1.4, since the object-image relationship of the paraxial optical system is: The ratio relationship is: Among them, l' is the image distance of the relay optical system, f' is the focal length of the relay optical system, and β is the vertical axis magnification, then the following formula can be obtained:

[0058]

[0059] The focal length f'=10 mm of the relay optical system in this embodiment can be calculated by the above formula.

[0060] Step 2, calculate the number of lenses in the relay optical system and construct the object-side telecentric initial structure with the aperture centered.

[0061] Step 2.1, according to the numerical aperture NA of the relay optical system and the corresponding empirical formula, calculate the number of lenses N of the relay optical system. The specific calculation formula is:

[0062]

[0063] in, Indicates rounding up.

[0064] Step 2.2, after obtaining the number of lenses N of the relay optical system, construct an object-side telecentric initial structure with the aperture centered in the ZEMAX software based on the number of lenses N. In this embodiment, the calculated number of lenses N=10, so it is necessary to construct an object-side telecentric initial structure with the aperture centered based on 10 lenses.

[0065] Step 2.3, allocate the optical power of each of the 10 lenses in the object telecentric initial structure according to the focal length of the optical system. Specifically, the optical power of each lens is determined by the following formula:

[0066]

[0067] Among them, φ iis the optical power of each lens, i=1,2,…,10.

[0068] Preferably, in this embodiment, the optical power is distributed in an average distribution manner. Since the focal length f' of the relay optical system in this embodiment is 10 mm, the optical power of each lens is obtained to be 0.01 / mm.

[0069] Step 3: Select a lens material pair that meets the achromatic condition according to the working band.

[0070] In order to meet the application requirements of ultra-wide band, it is usually necessary to design the optical system for apochromatic aberration, that is, to eliminate axial chromatic aberration and secondary spectrum by selecting lens material pairs. For transmissive optical systems, the chromatic aberration comes from the difference in refractive index of lens materials for light of different wavelengths. In order to realize the apochromatic aberration design of relay optical systems, the selection method of lens materials is as follows:

[0071] According to the requirements of the working band, select multiple groups of Abbe numbers (ν λ ) is used to eliminate the axial chromatic aberration of the relay optical system; then, according to the requirements of the working band, multiple groups of partial dispersion (P λ1,λ2 ) are used to eliminate the secondary spectrum of the relay optical system. Specifically, each group of lens material pairs includes two lens materials, a lens material pair with a large difference in Abbe number, i.e., a lens material pair with a large difference in Abbe number of the two lens materials, and a lens material pair with a small difference in partial dispersion, i.e., a lens material pair with a small difference in partial dispersion of the two lens materials.

[0072] Then, taking into account the transmittance of different materials within the working band and the requirements of the lens materials in the usage scenarios (such as high temperature resistance, high humidity resistance, high transmittance, etc.), a suitable lens material pair is selected from the multiple groups of lens material pairs determined above as the lens material pair that meets the achromatic condition. The selection criterion is the lens material pair with the smallest ratio of the partial dispersion difference ΔP to the Abbe number difference Δν in the lens material pair, that is, the lens material pair with the smallest ΔP / Δν value is selected.

[0073] like Figure 1 As shown, it is a schematic diagram of ΔP / Δν of multiple lens material pairs obtained in the far-infrared band in this embodiment. It can be seen that, taking germanium (Ge) with the widest application range as a benchmark, the ΔP / Δν value of germanium (Ge) and silicon (Si) is the lowest. However, since the maximum transmittance of Si is 10μm, and the transmittance of materials in the far-infrared band is 8μm-12μm, germanium (Ge) and zinc selenide (ZnSe) are selected as the lens material pair in this embodiment.

[0074] Step 4: Divide the 10 lenses into two groups with the aperture as the center, each group has 5 lenses, and first optimize the 5 lenses located in front of the aperture. During the optimization, the 5 lenses use Ge and ZnSe alternately as lens materials, that is, the first lens is Ge, the second lens is ZnSe, the third lens is Ge, the fourth lens is ZnSe, and the fifth lens is Ge. Then, take the equal curvature biconvex lens as the optimization starting point, calculate the 5 lenses respectively by the following formula to obtain the initial curvature radius of the 5 lenses:

[0075]

[0076] Among them, R Ge-1 Represents the initial radius of curvature of the front surface of the lens made of Ge, R Ge-2 Represents the initial radius of curvature of the rear surface of the lens made of Ge, n Ge is the material refractive index of Ge corresponding to the central wavelength of the working band; R ZnSe-1 The initial radius of curvature of the front surface of the lens made of ZnSe is shown in Figure 1. ZnSe-2 The initial radius of curvature of the rear surface of the lens made of ZnSe, n ZnSe is the material refractive index of ZnSe corresponding to the central wavelength of the working band.

[0077] The five lenses behind the aperture are mirror-symmetrically arranged with the five lenses in front of the aperture. The materials and initial curvature radii at the symmetrical positions are the same. After obtaining the initial curvature radii of the ten lenses, the center thickness and air spacing of each lens are given. Considering the processability, the center thickness range of the lens needs to be determined based on a reasonable diameter-to-thickness ratio, which is usually selected as The air gap can be set to be 1 / 3 to 2 times the center thickness of the previous lens. Therefore, considering the limitation of the total length of the optimized system, in this embodiment, the center thickness of the given 10 lenses is 4 mm, and the air gaps between lenses and between lenses and apertures are 1.5 mm.

[0078] According to the above calculation results, the initial structure of the relay optical system is modeled in ZEMAX software. Figure 2 The initial structure of the relay optical system has an aperture type of object space NA, an aperture value of 0.45, and a telecentric object space; the field of view type is object height, and the size is The working band is 8μm-12μm; the distance from the object to the front surface of the first lens (front intercept) is 20mm, and the distance from the rear surface of the last lens to the image plane (rear intercept) is 20mm.

[0079] Step 5, after the initial structure of the relay optical system is modeled, the field of view is gradually increased from zero field of view by controlling the magnification, total length (relay distance), back intercept, image telecentricity, air spacing between the center and edge of the lens, thickness between the center and edge of the lens, and diameter-thickness ratio of the initial structure of the relay optical system. The wide-band transmission relay optical system is finally obtained after iterative optimization, as shown in FIG. Figure 3 As shown. The far-infrared transmission relay optical system is a coaxial optical system with a total of 10 lenses. The materials of the 1st to 3rd and 8th to 10th lenses are Ge, and the materials of the 4th to 7th lenses are ZnSe. All lenses are spherical. The physical aperture is located between the 5th and 6th lenses, and the lenses 1-5 and 6-10 are completely symmetrical about the aperture. The parameters of the relay optical system in this embodiment are shown in the following table:

[0080]

[0081]

[0082] The first thickness corresponding to each lens in Table 1 is the center thickness of the current lens, and the second thickness is the air space between the current lens and the next lens, and between the current lens and the aperture. It can be seen that the vertical axis magnification β of the far-infrared transmission relay optical system is -1, the aperture size is Φ24.577, the back intercept is 20mm, the maximum image telecentricity does not exceed 0.07°, and the overall spatial size of the optical part is less than Φ40mm (XY) × 150mm (Z).

[0083] Figure 4 This is the design spot diagram of this embodiment. It can be seen that the GEO radius of the designed full-field spot diagram does not exceed the Airy disk radius of 13.56 μm. Figure 5 This is a design modulation transfer function curve diagram of this embodiment. It can be seen that the design modulation transfer function is higher than 0.5 at 33.3 line pairs per millimeter, and the imaging quality is excellent. Figure 6 This is a grid distortion diagram of this embodiment. It can be seen that the designed grid distortion of its transmission light path does not exceed 0.008%.

[0084] The above description is only used to illustrate the technical solution of the present invention rather than to limit it. For ordinary professional and technical personnel in the field, the specific technical solution recorded in the above embodiment can be modified, or some of the technical features therein can be replaced by equivalents, and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the scope of the technical solution protected by the present invention.

Claims

1. A design method for a wide-band transmission relay optical system, characterized in that: The following steps are involved: Step 1, preliminarily determining the maximum outer diameter and numerical aperture of the relay optical system according to the system parameters of the front optical system, and then calculating the object distance of the relay optical system; Then the focal length of the relay optical system is calculated according to the object distance of the relay optical system and the required magnification; Step 2, according to the numerical aperture of the relay optical system, the number of lenses of the relay optical system is calculated; based on the number of lenses, an object-side telecentric initial structure with the aperture centered is constructed; Then, the optical power of each lens in the object-side telecentric initial structure is allocated according to the focal length of the relay optical system; Step 3, selecting a lens material pair that meets the achromatic condition according to the working band; Step 4, according to the selected lens material pair, taking the equal curvature biconvex lens as the optimization starting point, calculating the initial curvature radius of each lens; Given the initial center thickness and air spacing of each lens, the initial structure of the relay optical system is modeled; Step 5, by controlling the magnification, total length, back intercept, image telecentricity, air spacing between the center and edge of the lens, thickness between the center and edge of the lens, and diameter-thickness ratio of the initial structure of the relay optical system, the field of view is gradually increased starting from zero field of view, and the final wide-band transmission relay optical system is obtained after iterative optimization.

2. The design method of a wide-band transmission relay optical system according to claim 1, characterized in that: Step 3 is as follows: According to the requirements of the working band, multiple groups of lens material pairs with large differences in Abbe numbers are determined in the Abbe diagram, and multiple groups of lens material pairs with small differences in partial dispersion are determined in the partial dispersion diagram; Based on the transmittance of different materials in the working band and the usage scenarios, the lens material pair with the smallest ratio of partial dispersion difference to Abbe number difference among multiple groups of lens material pairs is selected as the lens material pair that meets the achromatic condition.

3. The design method of a wide-band transmission relay optical system according to claim 2, characterized in that: In step 3, the operating band is the far infrared band, and the lens material pair is Ge and ZnSe.

4. A method for designing a wide-band transmission relay optical system according to any one of claims 1 to 3, characterized in that: In step 1, the object distance l of the relay optical system is calculated by the following formula: Wherein, D0 is the maximum outer diameter of the relay optical system, and NA is the numerical aperture of the relay optical system; In step 1, the focal length f' of the optical system is calculated by the following formula: Where β is the vertical axis magnification, l' is the image distance of the relay optical system.

5. The design method of a wide-band transmission relay optical system according to claim 4, characterized in that: In step 2, the number of lenses N is calculated by the following formula:

6. The method for designing a wide-band transmission relay optical system according to claim 5, characterized in that: In step 2, an average distribution method is adopted when distributing the optical power of each lens in the object-side telecentric initial structure according to the focal length of the relay optical system.

7. The design method of a wide-band transmission relay optical system according to claim 6, characterized in that: In step 4, the initial radius of curvature of each lens is calculated by the following formula: Among them, R k-1 is the initial radius of curvature of the front surface of the lens, R k-2 is the initial radius of curvature of the rear surface of the lens, k represents the type of material, and n k Indicates the refractive index of the material k corresponding to the central wavelength of the working band, φ i is the optical power of the lens, i=1,2,…,N.

8. The method for designing a wide-band transmission relay optical system according to claim 7, characterized in that: In step 4, based on the selected lens material, the equal curvature biconvex lens is used as the optimization starting point, and the initial curvature radius of each lens is calculated as follows: Divide N lenses into two groups with the aperture as the center, so that the N / 2 lenses located in front of the aperture alternately use two materials in the lens material pair selected in step 3, take the equal curvature biconvex lens as the optimization starting point, and calculate the initial curvature radius of the N / 2 lenses in front of the aperture; The N / 2 lenses located behind the aperture and the N / 2 lenses located in front of the aperture are arranged in a mirror-symmetrical manner about the aperture, and the materials and initial curvature radii at the symmetrical positions are the same.

9. The method for designing a wide-band transmission relay optical system according to claim 8, characterized in that: In step 4, the initial center thickness of each lens is determined according to the diameter-to-thickness ratio, and the air gap is 1 / 3 to 2 times the initial center thickness of the previous lens.

10. The method for designing a wide-band transmission relay optical system according to claim 9, characterized in that: In step 4, the initial center thickness of each lens is

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