rus
Issue #4/2022
A. P. Semenov, M. A. Abdulkadyrov, V. E. Patrikeev, A. B. Morozov, R. K. Nasyrov
Testing Methods for the Shape of Axial and Extra-Axial Aspherical Surfaces with a Computer-Generated Holograms, Decentering Determination and Distortion Consideration During its Formation. Part I
Testing Methods for the Shape of Axial and Extra-Axial Aspherical Surfaces with a Computer-Generated Holograms, Decentering Determination and Distortion Consideration During its Formation. Part I
DOI: 10.22184/1993-7296.FRos.2022.16.4.318.327
LZOS JSC has been using the diffractive optical elements (DOE) or computer-generated holograms (CGH) for many years to test the surfaces of large-sized optical mirrors for astronomical and space purposes. They are used for aspherical surface shape testing, control of the shape of extra-axial aspherical surfaces with registration of extra-axial mirror parameters and orientation, testing of the aspherical surface vertex position relative to the mirror geometric center, distortion consideration in the interferogram images, mutual adjustment of mirrors in the testing schemes, etc. Thus, the CGHs have become an integral part of the up-to-date testing of aspherical surfaces of the large-sized optical mirrors and optical systems.
LZOS JSC has been using the diffractive optical elements (DOE) or computer-generated holograms (CGH) for many years to test the surfaces of large-sized optical mirrors for astronomical and space purposes. They are used for aspherical surface shape testing, control of the shape of extra-axial aspherical surfaces with registration of extra-axial mirror parameters and orientation, testing of the aspherical surface vertex position relative to the mirror geometric center, distortion consideration in the interferogram images, mutual adjustment of mirrors in the testing schemes, etc. Thus, the CGHs have become an integral part of the up-to-date testing of aspherical surfaces of the large-sized optical mirrors and optical systems.
Теги: distortion during formation large-sized optical systems synthesized diffraction gratings testing of aspherical surfaces дисторсия при формообразовании контроль асферических поверхностей крупногабаритные оптические системы синтезированные дифракционные решетки
Testing Methods for the Shape of Axial and Extra-Axial Aspherical Surfaces with a Computer-Generated Holograms, Decentering Determination and Distortion Consideration During its Formation. Part I
A. P. Semenov1, M. A. Abdulkadyrov1, V. E. Patrikeev1, A. B. Morozov1, R. K. Nasyrov2
Lytkarinsky Optical Glass Plant, Lytkarino, Moscow region.
Institute of Automation and Electrometry, Siberian branch of the Russian Academy of Sciences, Novosibirsk, Russia
LZOS JSC has been using the diffractive optical elements (DOE) or computer-generated holograms (CGH) for many years to test the surfaces of large-sized optical mirrors for astronomical and space purposes. They are used for aspherical surface shape testing, control of the shape of extra-axial aspherical surfaces with registration of extra-axial mirror parameters and orientation, testing of the aspherical surface vertex position relative to the mirror geometric center, distortion consideration in the interferogram images, mutual adjustment of mirrors in the testing schemes, etc. Thus, the CGHs have become an integral part of the up-to-date testing of aspherical surfaces of the large-sized optical mirrors and optical systems.
Keywords: testing of aspherical surfaces, large-sized optical systems, synthesized diffraction gratings, distortion during formation
Received on: 05.04.2022
Accepted on: 04.05.2022
The advanced optoelectronic systems allow to solve problems that have seemed unresolvable even 10–15 years ago. This is largely due to the development of computer technologies for data receipt and transfer, improvement of the CCD sensor-based devices, introduction of the laser measuring systems and occurrence of the unique surface shape control technologies using the wavefront correctors, such as the diffractive optical elements (DOE, or CGH – computer-generated holograms) [1–6], as well as the complication of optical elements, including the high-aperture extra-axial mirrors, the testing and formation of which have not been previously possible.
TESTING AND FORMATION OF THE OPTICAL COMPONENT ASPHERICAL SURFACE WITH DEVIATION OF AXIAL SYMMETRY
In order to describe the testing and formation processes for the surfaces of large-sized astronomical mirrors, we will use the formation results of the 4‑meter main mirror of the Turkish DAG telescope (Doğu Anadolu Gözlemevi). DAG is a Ritchey-Chrétien telescope with the active and adaptive optics to be installed in a new observatory located on a 3170 m mountain near Erzurum in Turkey [7–8]. The telescope has a focal distance of 56 m and a field of 30 arc minutes, as well as two Nasmyth foci. The telescope includes a concave hyperbolic mirror M1 and a convex hyperbolic mirror M2, a flat mirror M3 that rotates the optical axis towards two Nasmyth foci using a rotation system.
The telescope design and production are performed by the Belgian company AMOS. Under the contract with AMOS, LZOS JSC manufactured the optics for this telescope. The main concave hyperbolic mirror has a diameter of 4 m, a vertex radius Rс = 14 420 mm ± 12 mm (F / 1.80), a conical constant K = –1.006574 ± 0.0004, an asphericity of 153 µm at full diameter and 139 µm in the light area, the mirror is made of Zerodur® by SCHOTT.
The mirror formation procedure includes grinding and polishing the optical aspherical surface. During the mirror processing and testing, a membrane and pneumatic frame was used that held the mirror on 66 supporting interface elements [9–11]. The mirror was tested on a vertical stand, the upper platform of which had the control equipment with a CGH corrector.
Stress relief on the membrane and pneumatic frame supports differs from stress relief using a standard telescope frame, where the additional end interface elements are used. Moreover, various forces are applied to each support. Stress relief on the membrane and pneumatic supports is designed to relieve the mirror evenly with the same forces, or with the same weight on each membrane. Therefore, it was necessary to make model calculations of the mirror face deformations on a membrane and pneumatic frame in comparison with stress relief using a standard frame and consider this difference in the formation process [12].
The membrane and pneumatic frame leads to the errors in the mirror surface shape deformations during the process and certification monitoring within the limits smaller in amplitude than the required error range of the processed mirror surface. Each membrane support is calibrated to provide the same force on the mirror, with an accuracy of less than 10 g. At a given point on the back mirror surface, each support has a load of 65 kg. The frame is equipped with a mirror automatic stabilization system in the case of changes of environmental conditions (atmospheric pressure, humidity) during testing that ensures the unchanged surface shape with the required accuracy during the repeated testing. The frame is shown in Fig.1–2.
In accordance with the simulation results, it is calculated that if the membranes are located at the loading points of the standard frame, then deformations occur on the surface. Such deformations mainly include defocusing, astigmatism, triangular coma, and spherical aberration.
The remaining deformations, such as the “traces” of the stress relief elements (high-frequency deformations that are equal on the standard frame and on the process one), are rather insignificant and are eliminated in the formation process. Defocusing is 1.5 µm and leads to the radius error of only 0.12 mm. However, it can also be considered during formation.
By subtracting the simulated wavefront from the wavefront obtained during the mirror surface inspection, we thereby eliminate the difference between stress relief on a standard frame and on a process one when processing is performed according to the specification requirements. Possible errors in simulation of differences in the mirror stress relief during processing and during operation shall be compensated by the mirror action system.
The wavefront shape and the relevant interferogram to be obtained on a membrane and pneumatic frame, are shown in Fig. 3–4. The subtracted wavefront chart was confirmed by mutual independent calculations of AMOS and LZOS. The required values of wavefront errors were also given. Thus, it is necessary to form a “free form” surface with deviations of the axisymmetric aspherical surface. Such a surface can only be obtained using an automated surface formation system with the small tools.
The mirror testing was performed using a CGH corrector designed and manufactured at the Institute of Automation and Electrometry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk [13–17]. The corrector is designed for the nominal mirror parameters. The testing circuit is shown in Fig. 5 [20]. The distance from the corrector to the focal point is 1170 mm.
The CGH converts a spherical wavefront into an aspherical one and operates in the autocollimation state. The corrector is made on a quartz plate with a diameter of 102 mm (Fig. 6, 7). It has a working area with a diameter of 80 mm and an auxiliary adjusting annular surface with the diameters from 82 to 92 mm. The distance from the hologram to the focal point is 1 170 mm. For the test verification of the CGH corrector, a CGH simulator was made on an Astrositall substrate with a diameter of 102 mm and a working area of 92 mm in diameter.
The Zernike polynomials or power polynomials are currently used to describe and analyze the the reflected wavefront shape. Additionally, the degree of surface “smoothness” is determined by calculating the root-mean-square slope of the normals to the wavefront (RMS Slope) that is measured in arc seconds. The requirements can also be set to the aberrations of the reflected wavefront, described by individual terms of a series of Zernike polynomials. In particular, the following restrictions given in Table 1 were imposed on the wavefront deviations for the M1 mirror. The calculated values of the polynomial coefficients in nanometers are also given in Table 1.
DETERMINATION OF OPTICAL AXIS DECENTERING
The mirror testing at the final stage of polishing is performed using the CGH. The CGH makes it possible to determine not only the reflected wavefront shape of the controlled aspherical surface, but also the aspherical surface vertex position. It also helps to calculate its displacement relative to the geometric center of the part. Previously, the control method with a linear three-point spherometer was used for these purposes [18–19]. At present, the displacement can be determined using the CGH. As an example, we will consider the main mirror DAG M1 with a diameter of 4 000 mm and an appropriate corrector.
An unequal-arm interferometer with a reference spherical mirror and a beam-splitting cube (1 in Fig. 5) contains a DOE 2, 3 is the controlled surface. The main diffractive structure 5 is made on the CGH optical round substrate 4, an additional focusing ring-type structure 6 is placed around it, and a second additional ring-type centering structure 7 is designed for the CGH centering in relation to the interferometer. The focusing structure 6 is located in a ring with the radii from 80.4 to 84.4 mm and the centering structure 7 is located in a ring with the radii from 86 to 96 mm. The distance from the focus F of the lens 1 to the CGH 2 is 1170 mm, the distance from the CGH 2 to the mirror 3 is L=14274 mm.
The positioning accuracy of a point simulating the aspherical surface vertex depends on the DOE installation accuracy relative to the interferometer. If the CGH is based on a divergent beam, it is adjusted using an auxiliary reflective centering structure of the CGH surface. Such a reflective structure is designed so that an endless band appears on it when the CGH is precisely aligned with the interferometer.
In real practice, the vertex point is shown as a spot. The spot size was determined by the Rayleigh criterion 2.44 λL / D, where D is the focusing structure diameter, and λ = 0.6328 µm is the interferometer wavelength. It is obvious that the vertex displacement (48 µm) is less than the inherent size of the spot (260 µm). However, in practice, even one band is difficult to be available consistently, usually there can be three or four such bands. Therefore, the vertex displacement shall be multiplied by the number of bands. This is true for a small number of bands on the interferogram. Thus, the error of this method makes it possible to determine the mirror vertex position with an accuracy of about 300 μm.
During the testing procedure, the mirrors are adjusted, and the CGH 2 is centered relative to the interferometer according to the wavefront interferogram from the centering structure 7. The luminous point (spot) 8 from the focusing structure 6 shall coincide with the geometric mirror center. To materialize the geometric center of the part, a vertex simulator was used in the form of an insert with a cross (Fig. 8, 9).
Availability of an optical axis decentering on the part working surface is represented by an asymmetrical aberration, namely a third-order coma (Fig. 12–13) in the wavefront reflected from the surface. The video camera was installed in order to synchronize the alignment process for the control equipment and the controlled surface and the interferometric inspection process in the vertex simulator area to observe the vertex marker laser point (Fig. 8). It provided data transmission via Wi-Fi that made it possible to simultaneously observe the vertex marker position and the interference pattern.
Using the main structure of the CGH 5, the interferometric inspection of the aspherical surface shape was performed. The displacement of the luminous point 8 (Fig. 5) from the square center (Fig. 9, 10, 11) was used to determine decentering.
When the decentering coma is prevented during the interferometric inspection, we measure the decentering value based on displacement of the luminous spot imitating the physical mirror vertex (Fig. 10). To the contrary, by aligning the luminous spot with the geometric center position, we are able to establish the decentering coma value and, therefore, determine the decentering value (Fig. 9–11). As a result, the optical axis decentering value and direction are determined based on the decentering coma. The optical axis displacement by 1 mm leads to a coma coefficient C3 = 4.05. The decentering coma coefficient value according to the mirror certification results was С3 = 0.689l that corresponds to an optical axis displacement of 0.2 mm.
It should be noted that in this case decentering was eliminated in the formation process that was required by the specifications. This method theoretically allows to determine the mirror vertex position with an accuracy of about 300 μm. Moreover, the proposed method for decentering measurement and elimination is much more efficient than the applied mechanical measurement method with a spherometer [18–19].
One more important advantage of this method in comparison with the above analogue is that it can be used to measure decentering of extra-axial aspherical parts, when there are several focusing structures on the CGH that are used for the CGH adjustment relative to the extra-axial part and determination of position of the optical vertex located outside the part, with the required accuracy.
Thus, using special focusing structures on the CGH, it is possible not only to determine the optical axis displacement relative to the geometric center of the part, but also to eliminate decentering in the formation process in accordance with the specification requirements.
In the continuation of the article, the features of the control of off-axis aspherical surfaces with CGH and the control and shaping of an off-axis aspherical mirror will be considered.
ABOUT AUTHORS
Semenov Aleksander Pavlovich, Cand.of Sc.(Eng.), a leading engineer of Lytkarinsky Optical Glass Plant , LZOS JSC, www.lzos.ru.
ORSID ID 0000-0001-8769-8111
Participation: software and mathematical implementation of the testing results, formation of aspherical optics, technical materials analysis and preparation.
Abdulkadyrov Magomed Abdurazakovich, Cand.of Sc.(Eng.), assistant chief engineer of Lytkarinsky Optical Glass Plant, LZOS JSC, www.lzos.ru.
Participation: overall supervision, administrative support.
Patrikeev Vladimir Evgenievich – deputy head of Lytkarinsky Optical Glass Plant, LZOS JSC. Participation: mathematical modeling of the optical inspection results.
Morozov Aleksey Borisovich, head of the bureau, LZOS JSC.
Participation: development and installation of a control equipment stand, aspheric control, development of control methods and its analysis.
Nasyrov Ruslan Kamilevich, Cand.of Sc.(Eng.), llaboratory head, IAE SB RAS. Novosibirsk. Participation: design and production of wavefront correctors.
A. P. Semenov1, M. A. Abdulkadyrov1, V. E. Patrikeev1, A. B. Morozov1, R. K. Nasyrov2
Lytkarinsky Optical Glass Plant, Lytkarino, Moscow region.
Institute of Automation and Electrometry, Siberian branch of the Russian Academy of Sciences, Novosibirsk, Russia
LZOS JSC has been using the diffractive optical elements (DOE) or computer-generated holograms (CGH) for many years to test the surfaces of large-sized optical mirrors for astronomical and space purposes. They are used for aspherical surface shape testing, control of the shape of extra-axial aspherical surfaces with registration of extra-axial mirror parameters and orientation, testing of the aspherical surface vertex position relative to the mirror geometric center, distortion consideration in the interferogram images, mutual adjustment of mirrors in the testing schemes, etc. Thus, the CGHs have become an integral part of the up-to-date testing of aspherical surfaces of the large-sized optical mirrors and optical systems.
Keywords: testing of aspherical surfaces, large-sized optical systems, synthesized diffraction gratings, distortion during formation
Received on: 05.04.2022
Accepted on: 04.05.2022
The advanced optoelectronic systems allow to solve problems that have seemed unresolvable even 10–15 years ago. This is largely due to the development of computer technologies for data receipt and transfer, improvement of the CCD sensor-based devices, introduction of the laser measuring systems and occurrence of the unique surface shape control technologies using the wavefront correctors, such as the diffractive optical elements (DOE, or CGH – computer-generated holograms) [1–6], as well as the complication of optical elements, including the high-aperture extra-axial mirrors, the testing and formation of which have not been previously possible.
TESTING AND FORMATION OF THE OPTICAL COMPONENT ASPHERICAL SURFACE WITH DEVIATION OF AXIAL SYMMETRY
In order to describe the testing and formation processes for the surfaces of large-sized astronomical mirrors, we will use the formation results of the 4‑meter main mirror of the Turkish DAG telescope (Doğu Anadolu Gözlemevi). DAG is a Ritchey-Chrétien telescope with the active and adaptive optics to be installed in a new observatory located on a 3170 m mountain near Erzurum in Turkey [7–8]. The telescope has a focal distance of 56 m and a field of 30 arc minutes, as well as two Nasmyth foci. The telescope includes a concave hyperbolic mirror M1 and a convex hyperbolic mirror M2, a flat mirror M3 that rotates the optical axis towards two Nasmyth foci using a rotation system.
The telescope design and production are performed by the Belgian company AMOS. Under the contract with AMOS, LZOS JSC manufactured the optics for this telescope. The main concave hyperbolic mirror has a diameter of 4 m, a vertex radius Rс = 14 420 mm ± 12 mm (F / 1.80), a conical constant K = –1.006574 ± 0.0004, an asphericity of 153 µm at full diameter and 139 µm in the light area, the mirror is made of Zerodur® by SCHOTT.
The mirror formation procedure includes grinding and polishing the optical aspherical surface. During the mirror processing and testing, a membrane and pneumatic frame was used that held the mirror on 66 supporting interface elements [9–11]. The mirror was tested on a vertical stand, the upper platform of which had the control equipment with a CGH corrector.
Stress relief on the membrane and pneumatic frame supports differs from stress relief using a standard telescope frame, where the additional end interface elements are used. Moreover, various forces are applied to each support. Stress relief on the membrane and pneumatic supports is designed to relieve the mirror evenly with the same forces, or with the same weight on each membrane. Therefore, it was necessary to make model calculations of the mirror face deformations on a membrane and pneumatic frame in comparison with stress relief using a standard frame and consider this difference in the formation process [12].
The membrane and pneumatic frame leads to the errors in the mirror surface shape deformations during the process and certification monitoring within the limits smaller in amplitude than the required error range of the processed mirror surface. Each membrane support is calibrated to provide the same force on the mirror, with an accuracy of less than 10 g. At a given point on the back mirror surface, each support has a load of 65 kg. The frame is equipped with a mirror automatic stabilization system in the case of changes of environmental conditions (atmospheric pressure, humidity) during testing that ensures the unchanged surface shape with the required accuracy during the repeated testing. The frame is shown in Fig.1–2.
In accordance with the simulation results, it is calculated that if the membranes are located at the loading points of the standard frame, then deformations occur on the surface. Such deformations mainly include defocusing, astigmatism, triangular coma, and spherical aberration.
The remaining deformations, such as the “traces” of the stress relief elements (high-frequency deformations that are equal on the standard frame and on the process one), are rather insignificant and are eliminated in the formation process. Defocusing is 1.5 µm and leads to the radius error of only 0.12 mm. However, it can also be considered during formation.
By subtracting the simulated wavefront from the wavefront obtained during the mirror surface inspection, we thereby eliminate the difference between stress relief on a standard frame and on a process one when processing is performed according to the specification requirements. Possible errors in simulation of differences in the mirror stress relief during processing and during operation shall be compensated by the mirror action system.
The wavefront shape and the relevant interferogram to be obtained on a membrane and pneumatic frame, are shown in Fig. 3–4. The subtracted wavefront chart was confirmed by mutual independent calculations of AMOS and LZOS. The required values of wavefront errors were also given. Thus, it is necessary to form a “free form” surface with deviations of the axisymmetric aspherical surface. Such a surface can only be obtained using an automated surface formation system with the small tools.
The mirror testing was performed using a CGH corrector designed and manufactured at the Institute of Automation and Electrometry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk [13–17]. The corrector is designed for the nominal mirror parameters. The testing circuit is shown in Fig. 5 [20]. The distance from the corrector to the focal point is 1170 mm.
The CGH converts a spherical wavefront into an aspherical one and operates in the autocollimation state. The corrector is made on a quartz plate with a diameter of 102 mm (Fig. 6, 7). It has a working area with a diameter of 80 mm and an auxiliary adjusting annular surface with the diameters from 82 to 92 mm. The distance from the hologram to the focal point is 1 170 mm. For the test verification of the CGH corrector, a CGH simulator was made on an Astrositall substrate with a diameter of 102 mm and a working area of 92 mm in diameter.
The Zernike polynomials or power polynomials are currently used to describe and analyze the the reflected wavefront shape. Additionally, the degree of surface “smoothness” is determined by calculating the root-mean-square slope of the normals to the wavefront (RMS Slope) that is measured in arc seconds. The requirements can also be set to the aberrations of the reflected wavefront, described by individual terms of a series of Zernike polynomials. In particular, the following restrictions given in Table 1 were imposed on the wavefront deviations for the M1 mirror. The calculated values of the polynomial coefficients in nanometers are also given in Table 1.
DETERMINATION OF OPTICAL AXIS DECENTERING
The mirror testing at the final stage of polishing is performed using the CGH. The CGH makes it possible to determine not only the reflected wavefront shape of the controlled aspherical surface, but also the aspherical surface vertex position. It also helps to calculate its displacement relative to the geometric center of the part. Previously, the control method with a linear three-point spherometer was used for these purposes [18–19]. At present, the displacement can be determined using the CGH. As an example, we will consider the main mirror DAG M1 with a diameter of 4 000 mm and an appropriate corrector.
An unequal-arm interferometer with a reference spherical mirror and a beam-splitting cube (1 in Fig. 5) contains a DOE 2, 3 is the controlled surface. The main diffractive structure 5 is made on the CGH optical round substrate 4, an additional focusing ring-type structure 6 is placed around it, and a second additional ring-type centering structure 7 is designed for the CGH centering in relation to the interferometer. The focusing structure 6 is located in a ring with the radii from 80.4 to 84.4 mm and the centering structure 7 is located in a ring with the radii from 86 to 96 mm. The distance from the focus F of the lens 1 to the CGH 2 is 1170 mm, the distance from the CGH 2 to the mirror 3 is L=14274 mm.
The positioning accuracy of a point simulating the aspherical surface vertex depends on the DOE installation accuracy relative to the interferometer. If the CGH is based on a divergent beam, it is adjusted using an auxiliary reflective centering structure of the CGH surface. Such a reflective structure is designed so that an endless band appears on it when the CGH is precisely aligned with the interferometer.
In real practice, the vertex point is shown as a spot. The spot size was determined by the Rayleigh criterion 2.44 λL / D, where D is the focusing structure diameter, and λ = 0.6328 µm is the interferometer wavelength. It is obvious that the vertex displacement (48 µm) is less than the inherent size of the spot (260 µm). However, in practice, even one band is difficult to be available consistently, usually there can be three or four such bands. Therefore, the vertex displacement shall be multiplied by the number of bands. This is true for a small number of bands on the interferogram. Thus, the error of this method makes it possible to determine the mirror vertex position with an accuracy of about 300 μm.
During the testing procedure, the mirrors are adjusted, and the CGH 2 is centered relative to the interferometer according to the wavefront interferogram from the centering structure 7. The luminous point (spot) 8 from the focusing structure 6 shall coincide with the geometric mirror center. To materialize the geometric center of the part, a vertex simulator was used in the form of an insert with a cross (Fig. 8, 9).
Availability of an optical axis decentering on the part working surface is represented by an asymmetrical aberration, namely a third-order coma (Fig. 12–13) in the wavefront reflected from the surface. The video camera was installed in order to synchronize the alignment process for the control equipment and the controlled surface and the interferometric inspection process in the vertex simulator area to observe the vertex marker laser point (Fig. 8). It provided data transmission via Wi-Fi that made it possible to simultaneously observe the vertex marker position and the interference pattern.
Using the main structure of the CGH 5, the interferometric inspection of the aspherical surface shape was performed. The displacement of the luminous point 8 (Fig. 5) from the square center (Fig. 9, 10, 11) was used to determine decentering.
When the decentering coma is prevented during the interferometric inspection, we measure the decentering value based on displacement of the luminous spot imitating the physical mirror vertex (Fig. 10). To the contrary, by aligning the luminous spot with the geometric center position, we are able to establish the decentering coma value and, therefore, determine the decentering value (Fig. 9–11). As a result, the optical axis decentering value and direction are determined based on the decentering coma. The optical axis displacement by 1 mm leads to a coma coefficient C3 = 4.05. The decentering coma coefficient value according to the mirror certification results was С3 = 0.689l that corresponds to an optical axis displacement of 0.2 mm.
It should be noted that in this case decentering was eliminated in the formation process that was required by the specifications. This method theoretically allows to determine the mirror vertex position with an accuracy of about 300 μm. Moreover, the proposed method for decentering measurement and elimination is much more efficient than the applied mechanical measurement method with a spherometer [18–19].
One more important advantage of this method in comparison with the above analogue is that it can be used to measure decentering of extra-axial aspherical parts, when there are several focusing structures on the CGH that are used for the CGH adjustment relative to the extra-axial part and determination of position of the optical vertex located outside the part, with the required accuracy.
Thus, using special focusing structures on the CGH, it is possible not only to determine the optical axis displacement relative to the geometric center of the part, but also to eliminate decentering in the formation process in accordance with the specification requirements.
In the continuation of the article, the features of the control of off-axis aspherical surfaces with CGH and the control and shaping of an off-axis aspherical mirror will be considered.
ABOUT AUTHORS
Semenov Aleksander Pavlovich, Cand.of Sc.(Eng.), a leading engineer of Lytkarinsky Optical Glass Plant , LZOS JSC, www.lzos.ru.
ORSID ID 0000-0001-8769-8111
Participation: software and mathematical implementation of the testing results, formation of aspherical optics, technical materials analysis and preparation.
Abdulkadyrov Magomed Abdurazakovich, Cand.of Sc.(Eng.), assistant chief engineer of Lytkarinsky Optical Glass Plant, LZOS JSC, www.lzos.ru.
Participation: overall supervision, administrative support.
Patrikeev Vladimir Evgenievich – deputy head of Lytkarinsky Optical Glass Plant, LZOS JSC. Participation: mathematical modeling of the optical inspection results.
Morozov Aleksey Borisovich, head of the bureau, LZOS JSC.
Participation: development and installation of a control equipment stand, aspheric control, development of control methods and its analysis.
Nasyrov Ruslan Kamilevich, Cand.of Sc.(Eng.), llaboratory head, IAE SB RAS. Novosibirsk. Participation: design and production of wavefront correctors.
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