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Abstract
Large aperture off-axis Fresnel lens will play an important role in the future 10 m scale aperture transmission space telescope system. Improving diffraction efficiency and wavefront image quality is always the goal of engineering applications. A 4-level off-axis fresnel lens with Ф350 mm effective aperture was fabricated through overlay etching technique by laser direct writing system. The wavefront aberration characteristics of the off-axis Fresnel lens at 632.8 nm wavelength are analyzed and discussed in detail, and the large aperture off-axis Fresnel lenses wavefront aberration measurement scheme, including a high-precision plane reflector, measured LAOFL, CGH, interferometer and laser tracker to compensate for certain low-order aberrations caused by LAOFL imperfect imaging, is proposed. Wavefront aberration of 0.020 λ(1/50 λ) RMS was achieved. This work presented the best results to our knowledge among the same field with similar aperture in open publications and provided a strong foundation for the future 10 m scale aperture transmission space telescope system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Transmissive diffractive Fresnel lens and segmented-mirror technology provide alternative solutions for next-generation 10 m scale aperture transmission space telescope systems due to relaxed surface figure tolerance, higher foldable ratio and light weight, compared to traditional refraction-reflective optics [1–3]. Transmissive diffractive Fresnel lens can tolerate centimeter-level etching perpendicular to the substrate without significant focal spot distortion, which is equivalent to a relaxation of more than two orders of magnitude compared with the reflective component [2]. At the same time, the optical segmented-mirror technology can solve the considerable problems of large aperture fabrication and measurement encountered in the manufacture of large monolithic primary mirror [4–7]. To construct a 10 m scale aperture primary lens, over 100 pieces of large aperture off-axis Fresnel lenses (LAOFL) should be stitched precisely and co-phased [8]. Diffraction efficiency and wavefront image quality are two important technical specifications for fabricating LAOFL. It was found that nearly 60% of the average diffraction efficiency of coaxial 4-level Fresnel lens was reported in recent years [9–11]. The primary mirror of the Giant Magellan Telescope consists of seven 8.4 m off-axis segments whose reflective surface is 2um RMS [12]. A 4-level Fresnel coaxial diffractive polyimide membrane optic in 200 mm diameter and 20 um thickness was manufactured, the thickness variation of which has an RMS of 30 nm [13]. Improving diffraction efficiency and wavefront image quality is always the goal of engineering applications.
The LAOFL measurement of diffraction efficiency and wavefront image quality was carried out in our laboratory. Previous papers describe the fabrication of LAOFL and present measured DE distribution. We have achieved over 75% average DE experimentally [14]. In this paper, the wavefront aberration characteristics of the off-axis Fresnel lens at 632.8 nm wavelength are analyzed and discussed in detail, and the large aperture off-axis Fresnel lenses wavefront aberration measurement scheme is proposed. We analyzed and discussed the wavefront aberration characteristics of the off-axis Fresnel lens at 632.8 nm wavelength, and proposed a wavefront aberration measurement scheme.
2. Fabrication of large aperture off-axis Fresnel lens
The segmented large-scaled lightweight diffractive telescope (SLLDT), consisting of one 710-mm-diameter coaxial Fresnel lens in the center surrounded by eight 352-mm-diameter LAOFLs and an eyepiece of achromatic lenses, can realize wide-band high-resolution imaging from 550 nm to 650 nm, with F number at 7 and field of view at 0.12 degrees [15]. Fabrication and measurement of the LAOFL are challenging and have led to several innovations in astronomical observation. The key technical specification of LAOFL is shown in Table 1. This paper focuses on the measurement of LAOFL wavefront aberration.
Table 1. Technical specification of LAOFL
4-level LAOFL is made from Φ390 mm aperture fused silica substrate, and the effective aperture of the diffraction pattern is Φ352 mm. the minimum line width is 2.1µm. In the whole diffraction pattern, the etching depth of each level is the same at 330 nm. The transmission wavefront of the substrate is required to be better than λ/30 RMS. At present, our processing level can reach better than λ/50 RMS.
The fabrication process of LAOFL is based on LDW system (VPG800, Heidelberg, Germany) and Reactive Ion Etching machine (RIE600, developed by Institute of Optics and Electronics, China). The fabrication process of LAOFL was described in our previous work [14]. A schematic diagram of the LAOFL pattern fabrication process is shown in Fig. 1 below. Firstly, a fused silica substrate was coated with a layer of AZ1500 photoresist with a thickness of ∼1µm by spin coating and hot plate. Then, the substrate coated with the photoresist was placed in the LDW system to produce a photoresist diffraction pattern after the first exposure followed by development. A RIE600 transfer machine was used for the first pattern transfer, and the residual photoresist was washed off with acetone solution. In this way, a 2-order diffraction pattern layer was formed on fused silica substrate. Repeat the above steps again for the second exposure, development and pattern transfer to generate a 4-level diffractive pattern layer.
3. Measurement of large aperture off-axis Fresnel lens
3.1 Theoretical simulation and measurement
To propose the wavefront aberration measurement scheme of LAOFL, supposing that the 1.5 m primary mirror of the diffractive telescope is a non-segmented and monolithic full aperture Fresnel lens, we optimized the SLLDT system by optical simulation software, and obtained the distribution of wavefront aberration of the 1.5 m primary mirror when λ=600 nm and λ=632.8 nm, as shown in Fig. 3(a) and Fig. 3(b). It can be seen that the theoretical wavefront RMS = 0.000λ (λ=600 nm) and RMS = 0.4749λ (λ=632.8 nm). Since the designed working wavelength of the 1.5 m primary mirror is 600 nm and the theoretical focal length is 10500 mm, while the laser wavelength used by interferometer during measurement is 632.8 nm (wavelength in air), spherical aberration was introduced when the interferometer is directly used for focus positioning. The Zernike coefficient output in the simulation software when λ=632.8 nm was generated into the wavefront as shown in Fig. 4(a). Based on the parameter decomposition of the optical system, the PV value of the wavefront of the 1.5 m primary mirror at 632.8 nm (wavelength in air) is 1.593λ, with RMS value at 0.475λ as shown in Fig. 4(a). Then, according to the structure positioning diagram of the primary mirror of SLLDT in Fig. 2, a 350 mm LAOFL wavefront is extracted from the simulation wavefront of the 1.5 m primary mirror at the corresponding spatial position, with PV value at 1.593 λ and RMS value at 0.45λ as shown in Fig. 4(b).
Fig. 3. The simulated 1.5 m primary mirror wavefront aberration (a) wavefront aberration of λ=600 nm; (b) wavefront aberration of λ=632.8 nm.
For the simulated 1.5 m primary mirror (Ф1500 mm), the focus value of the wavefront aberration of the 1.5 m primary mirror is the minimum at 9954.330 mm from the primary mirror to the interferometer focus. The focus of its diffraction wavefront moves forward 545.670 mm at 632.8 nm, compared with 600 nm according to the simulation results. The wavefront is mainly spherical aberration with amplitude of 3.186λ (PV). The defocus component (power and spherical) is mainly introduced when the primary mirror moves along the optical axis.
For the simulated LAOFL (Ф352 mm), the wavefront aberration is complicated because of the lack of symmetry. At 9954.330 mm from the LAOFL to the interferometer focus, the low-order wave aberration is introduced, and the Zernike coefficients of the wavefront aberration are X tilt (0.742λ), focus (0.294λ), astigmatism (0.479λ), coma (0.102λ) and spherical (0.004λ) as shown in Fig. 5.
The LAOFL wavefront aberration measurement was carried out on a conventional interferometric autocollimation. The measurement results of fabricated LAOFL sample are shown in Fig. 6. The PV value is 1.854λ, with RMS value of 0.594 λ. The results show that low-order wave aberrations are also introduced into the measurement wavefront by a non-axisymmetric set of optics, and the Zernike coefficients of the wavefront aberration are X tilt (0.72450λ), focus (0.29214λ), astigmatism (0.39266λ), coma (0.0456λ) and spherical (0.0313λ), indicating a similar distribution pattern with simulated results.
It is noticeable that the theoretical simulation results are consistent with the measured results. The aberration type of LAOFL is different from that of traditional coaxial transmission or reflection optical elements, including the inherent focus, astigmatism, coma and spherical aberration. Therefore, its measurement method is also different from the traditional interferometric autocollimation. LAOFL is imperfect imaging, so the directly measured results by interferometer contain certain low-order aberrations in the lab because of the lack of symmetry and difference between measuring wavelength and design wavelength. For the evaluation of LAOFL imaging wavefront, it is necessary to deduct a certain amount of tilt, astigmatism and coma, which is the wavefront image quality of LAOFL at 600 nm design wavelength. To solve this problem, wavefront measurement can be realized by designing a computer-generated hologram to compensate for the aberration.
3.2 CGH design
Optical elements with large aspheric departures are often tested with the help of a computer-generated hologram (CGH). The primary role of CGH is to generate reference wavefronts of any desired shape [16]. The pattern on a CGH determines whether the wavefront is split into several beams, compensates for some aberrations in an optical assembly, or performs other useful optical functions. As a null corrector, CGH is widely used in aspheric surface testing. In this paper, a CGH is designed to compensate for the inherent aberration of LAOFL to realize wavefront measurement.
The above optical path diagram is obtained through optical simulation. As shown in Fig. 7, an 8.04 mm thick CGH is inserted at 9730 mm from the 1.5 m primary mirror. The light is focused at 149.96 mm behind the CGH and enters the interferometer. The CGH consists of two segments: main CGH and alignment CGH. Main CGH, fabricated on the inner part of a fused silica substrate, is used for deducting the aberration of a specific value. The outer segment is alignment CGH, which was used to accurately align the main CGH and interferometer by eliminating defocus, decentration and tilt errors. The design technical specification of twin-CGH was shown in Table 2, and the theoretical residual wave aberration designed by this method is better than λ /1000.
Table 2. Technical specification of twin-CGH
3.3 Final measurement scheme and results
Combining the interferometric autocollimation with spatial positioning by laser tracker, we propose the final measurement scheme in this paper to measure the wavefront aberration of LAOFL by using CGH to compensate for aberration. The measurement system includes a high-precision plane reflector, measured LAOFL, CGH, interferometer and laser tracker as shown in Fig. 8. Firstly, the measured LAOFL was placed into the specially designed mechanical fixture, and a high-precision plane reflector with a slightly larger aperture than the LAOFL is placed behind LAOFL. Taking the relative position calibrated by laser tracker of the high-precision plane reflector and the measured LAOFL as feedback, the five-dimensional adjustment frame of the measured LAOFL was adjusted to make the measured LAOFL and the high-precision plane reflector parallel. Then, the spatial coordinate system of the laser tracker was established with the center of the measured LAOFL pattern as the origin and the normal and off-axis directions as the X and Y directions. Adjust the existing focus of the interferometer to the theoretical position of the spatial coordinate system. In the optical path, insert CGH at 149.96 mm from the focal point of the interferometer, adjust the alignment CGH ring to align the interferometer, and then take the interferometer and CGH as a whole. The aberration term in the interferometer wavefront measurement result is the minimum by coarse-tuning and fine-tuning adjustment of the pitch and tilt of the measured LAOFL, that is, the wavefront image quality result of LAOFL.
In the whole measurement system, the alignment of the high precision plane reflector and measured LAOFL was guaranteed by the accuracy of the laser tracker. The alignment of CGH and interferometer adopts the reflective FZM band calibration method. By observing the interference fringes of alignment CGH, we can judge whether the CGH has defocus, eccentricity and tilt errors. The accuracy is guaranteed by the manufacturing error of the alignment CGH. The overall alignment of the four components is mainly realized by the fringes of the interferometer.
The LAOFL wavefront aberration measurement was carried out in our laboratory. Figure 9 shows the photograph of LAOFL on-site measurement. The wavefront measurement result of two fabricated LAOFL samples is shown in Fig. 10(a) and (b) below. For Sample 1 the PV value is 0.126 λ with RMS value of 0.020 λ(1/50 λ), and Sample 2 presents PV value of 0.193λ and RMS value of 0.020 λ(1/50 λ). The measurements guide all stages of fabrication and guarantee that the LAOFLs meet all requirements.
Fig. 10. Measured wavefront aberration of two fabricated LAOFL samples. (a) wavefront aberration of Sample 1; (b) wavefront aberration of Sample 2.
The transmission wavefront of the substrate is required to be better than λ/30 RMS in Section 2. At present, we selected two substrates whose wavefront aberration can reach better than λ/50 RMS. In the pattern fabrication process, the substrate has undergone two rounds of exposure, development and pattern transfer. Wavefront aberration of 0.020 λ (1/50 λ) RMS of LAOFLs was achieved finally. Therefore, the main error sources of wavefront image quality are substrate wavefront and pattern fabrication process. Which pattern fabrication errors affect wavefront image quality will be discussed later.
3. Conclusions
In conclusion, we have presented a LAOFL with Ф350 mm effective aperture through overlay etching technique by LDW system. The wavefront aberration characteristics of the off-axis Fresnel lens at 632.8 nm wavelength are analyzed and discussed in detail, and the large aperture off-axis Fresnel lenses wavefront aberration measurement scheme is proposed. We have experimentally achieved wavefront aberration of 0.020 λ (1/50 λ) RMS in accordance with theoretical simulation. This work presented the best results to our knowledge in the same field with similar aperture and critical dimensions in open publications and provided a strong foundation for future large aperture diffractive telescope development. In the following work, further improvement of wavefront aberration relies on higher fabrication processes and better measurement strategies.
Funding
National Key Research and Development Program of China (2016YFB0500200); National Natural Science Foundation of China (62075220); National Natural Science Foundation of China (61905254).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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