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Abstract
Bright daylight photon noise and the saturation of wavefront sensors pose challenges to high-resolution daytime imaging. In this paper, a daytime hybrid wavefront sensor (HyWFS) approach for real-time wavefront sensing in daylight adaptive optics (AO) is described. The Shack-Hartmann wavefront sensor (SHWFS) algorithm is used to efficiently compensate large-scale wavefronts, while the pyramid wavefront sensor (PyWFS) algorithm offers highly sensitive correction of small wavefronts. Daylight closed-loop AO experiments were performed using the daytime HyWFS approach with both algorithms, respectively. The experiment results indicate that the proposed approach provides accurate daylight AO correction and allows for a simple switch between the two algorithms without increasing system complexity. The daytime HyWFS approach can serve as an alternative for daylight natural guide star AO, enabling high-resolution observation of resident space objects no longer limited to dawn and dusk.
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1. Introduction
During the day, shot noise induced by a bright daytime sky background may fluctuate as a function of time and look angle. A high level of daylight noise easily obscures the weak signal from the resident space object (RSO) of interest [1], leading to saturation and a low signal-to-noise ratio (SNR) of the wavefront sensor (WFS), severely. Consequently, daytime high-resolution observations of RSOs are severely hindered, and adaptive optics (AO) systems for space situational awareness (SSA) are currently limited to nighttime [2–6]. Developing daylight AO and eventually expanding the capabilities of the ground-based telescopes for SSA to the daytime merit further investigation.
As the near-blackbody emission of the sun’s radiant energy peaks at visible wavelengths, the radiance of the sky background is much brighter in the visible band than in the IR band for a given sun angle. According to Rayleigh scattering [7], the daytime sky background decreases rapidly as the wavelength of the detected light increases. Hence, the advent of IR astronomy has allowed optical telescopes to operate during both day and night [8,9]. Beckers and Cacciani [10] proposed a daytime detection method utilizing a sufficiently narrow spectral filter in the thermal IR band for laser-guided AO correction. Hart et al. [11] experimentally demonstrated that sodium laser guide star (LGS) systems can use magneto-optical filters (MOFs) to enable daylight AO operation, as suggested in [10]. An IR pyramid wavefront sensor (PyWFS) installed on the Keck II AO bench was used to obtain K-band images during the daytime [12,13]. Esposito et al. [14] presented the daytime application of an IR PyWFS mounted on the Large Binocular Telescope (LBT) to correct the non-common path aberration (NCPA). In summary, most astronomical AO systems are designed for daylight observation in bands at 3.5 µm and longer [10,11].
Visible observation is generally the preferred scheme for daylight AO systems considering various practical inconveniences. Nevertheless, real-time visible wavefront sensing in the daytime is challenging not merely because daylight noise is always much brighter than object signal, but also due to the fluctuation of daylight background noise, which invalidates the constant-threshold algorithm by continuously altering the light intensity distribution at the wavefront sensor (WFS). Consequently, both the amount of sky and the timing accessible for RSO imaging are constrained for visible WFS [15]. The hybrid wavefront sensor (HyWFS) proposed by Guthery and Hart [16] is a highly advantageous and promising option for AO systems. Given its attractive properties in daylight AO applications, we have proposed an approach for applying a visible PyWFS to daylight natural guide star AO systems [17]. However, it is limited to small aberrations within the linearity range of PyWFS.
This paper introduces a novel daytime HyWFS approach that is flexible to handle various conditions for daylight AO observations. In addition to the PyWFS algorithm, the Shack-Hartmann wavefront sensor (SHWFS) algorithm is introduced to obtain daytime HyWFS output signals for large-scale wavefronts. The remainder of this paper is organized as follows. Section 2 provides a detailed description and experimental setup of the daytime HyWFS approach. Subsequently, the linearity ranges of the daytime HyWFS with both algorithms are explained experimentally, and the closed-loop experimental results are described to verify the feasibility of the daytime HyWFS for AO systems. Section 3 presents an analysis of the appropriate size of the field stop (FS) in the daylight AO system. Moreover, the daylight correction results obtained using the daytime HyWFS approach with both algorithms are presented and contrasted. Section 4 summarizes the conclusion of this research, affirming that the daytime HyWFS approach is practical for daylight adaptive optics wavefront sensing, allowing an easy switch between two separate signal calculation algorithms to satisfy different practical requirements.
2. Daytime HyWFS approach
2.1 Principle
A sufficient SNR provided by WFS is an essential precondition for daylight AO when the daylight background noise is strong and exhibits rapid fluctuations. The daytime HyWFS approach proposed here integrates the daytime HyWFS with the background elimination algorithm. The daytime HyWFS, comprising a field stop (FS), pyramid prism, relay lens, and lenslet array, is employed to effectively distinguish object signal from daylight noise. Figure 1 shows the principle of the daytime HyWFS for daylight AO. In Fig. 1(a), the red line represents the object light, and the blue area represents the daylight background.
Fig. 1. (a) Optical layout of daytime HyWFS in daylight AO system. The green and blue dashed boxes indicate the optical layouts of PyWFS and SHWFS, respectively. (b) PyWFS and (c) daytime HyWFS images during the day.
An FS is installed before the pyramid prism to block the extended strong daylight. The daylight illuminates the vertex of the pyramid, forming a circular disk, and the object light is focused at the center of the disk. Four subbeams are split by the pyramid prism. Figure 1(b) illustrates the PyWFS subpupil images in the daytime. The weak object photons are easily obscured and cannot be extracted from the daylight noise. After passing through a relay lens, the object light is focused by a lenslet array and reimaged as four spot arrays onto the WFS camera. In contrast, the daylight photon noise is evenly distributed in four quarter-circle arrays, as shown in Fig. 1(c). It can be observed that the FS partially obstructs the unwanted light, and the lenslet array separates the useful object photons from the daylight noise. The SNR detected by the daytime HyWFS is the same as the usual SHWFS due to the identical detection image when adding the four daytime HyWFS subpupil images. In contrast, it provides an improved SNR with a highly concentrated object signal compared to the usual PyWFS [17]. Subsequently, the background elimination algorithm is applied to extract the useful object signal from the daylight signal, as demonstrated in [17].
As a main component of an AO system, an ideal WFS is required to possess several characteristics, such as sufficient spatial resolution, a wide dynamic range, and good linearity. However, these characteristics present a trade-off between them. As a common WFS, the SHWFS provides a wide dynamic range and excellent linearity but has constrained sensitivity. In contrast, the PyWFS offers high sensitivity and adjustable sampling for real-time operations but is limited by its small dynamic range [18–24]. The plenoptic WFS behaves well in large aberration detection but suffers from low sensitivity [25,26]. Another WFS, the curvature wavefront sensor, features a simple structure but has poor accuracy in wavefront measurements at low spatial frequencies [27,28].
In our proposal, the daytime HyWFS approach integrates the desired properties of the SHWFS and PyWFS by respectively using both WFSs’ signal calculation algorithms to calculate the WFS responses. For the SHWFS algorithm, the four subpupil images are added, and the daytime HyWFS signal is measured using the following expressions:
In this way, the daytime HyWFS performs as an SHWFS with the SHWFS algorithm and behaves as a traditional PyWFS with the PyWFS algorithm. In particular, the two algorithms can be easily switched with no need for any element movement to handle certain conditions, which makes it superior to other WFSs.
2.2 Optical structure analysis
The relationship between the diameters of the daytime HyWFS subpupil image and the incident pupil image was analyzed in two ways. Figure 2 presents the optical path of the daytime HyWFS.
Fig. 2. (a) Optical path of daytime HyWFS. (b) Enlarged version of the green dashed box. ${d_1}$ and ${d_2}$ are the diameters of the incident pupil and the pyramid subpupil, respectively. ${f_1}$, ${f_2}$, and ${f_{\textrm{lenslet}}}$ are the focal lengths of L1, L2, and the lenslet. ${F^\# }$ represents the F-number of the optical system. $\alpha $ and $\delta $ are the base angle and the deflection angle of the pyramid prism, respectively.
The first way is to calculate the demagnification factor. The focal focus of the converging lens L1 coincides with that of the collimating lens L2 on the tip of the pyramid prism, forming a 4$F$ optical system, as shown in Fig. 2(a). The pupil image with a diameter of ${d_1}$ is conjugated to the pyramid subpupil image with a diameter of ${d_2}$, and the diameters are related as Eq. (5). The output parallel subbeam behind L2 is demagnified by a factor $M = {f_1}/{f_2}$.
The second way is to analyze from the perspective of geometrical optics. The following equations can be obtained by analyzing the enlarged optical path within the green dashed line, as shown in Fig. 2(b):
where $2x$ represents the distance between the edges of adjacent subpupil images, and n is the refraction index of the pyramid prism. After simplification, the diameter of the subpupil image ${d_2}\textrm{}$ is given byA lenslet array whose size is chosen according to the diameter of the pyramid subpupil image ${d_2}$ is positioned in front of the detector plane at a distance of ${f_{\textrm{lenslet}}}$.
Here, the daytime HyWFS images were simulated in an SNR of 7.18, as presented in Fig. 3. The SNR calculation method has been mentioned in [17]. Figures 3(a)–3(c) respectively present the simulated daytime HyWFS images with only the object signal, only the fluctuated daylight noise, and the mixed signal. An 8 ${\times} $ 8 lenslet array was used to sample each subpupil. The simulated results verified the hypothesis of the daytime HyWFS images. The daytime HyWFS images are the same as the traditional SHWFS images during the day when the four subpupil images are added up. In contrast to the typical PyWFS, the object signal can be distinguished rather than being masked by the daylight when the daytime HyWFS image is used in the daytime.
Fig. 3. Simulated daytime HyWFS images of the (a) object, (b) daylight, and (c) mixed signal in an SNR of 7.18.
2.3 Experimental setup
A laboratory experimental bench was constructed to verify the principle of the daytime HyWFS approach for daylight AO, as presented in Fig. 4. An LED surface light source with a power of 10 W was employed to simulate a strong daylight background during on-sky daytime observations, while a fiber-coupled laser source operating at 660 nm was used as the object light.
Fig. 4. Schematic of the daylight AO system experimental setup based on daytime HyWFS. The focal lengths are unscaled.
The daytime HyWFS was employed as the WFS in the AO system. Instead of a traditional single pyramid, a custom double pyramid prism composed of two four-sided pyramids aligned back-to-back was used in the WFS. Unlike the single pyramid whose base angle is always in the range of 1∼2°, the double pyramid entails no extremely high processing requirement due to its much larger base angles. Additionally, the use of the double pyramid effectively reduces the chromatic effect by using two types of glass with various refractive indexes [29]. The detailed parameters of the double pyramid are presented in Fig. 5. A lenslet array with a 7.0 mm focal length and a 0.2 mm pitch was placed before the WFS camera. A deformable mirror (DM) with 192 actuators and a 21 mm aperture was positioned at the pupil plane, serving as the wavefront-correcting component to precisely introduce and correct wavefront aberrations. This continuous reflective surface DM operated with the Zernike order of Noll ordering, excluding the piston mode [30]. The WFS camera is a Teledyne Photometrics 16-bit scientific CMOS camera with a pixel area of 6.5 µm ${\times} $ 6.5 µm. Its peak quantum efficiency (QE) achieves over 95% at 600 nm. The focal plane camera is an Imaging Source 8-bit CCD camera with a pixel area of 3.75 µm ${\times} $ 3.75 µm. Its QE peaks at 520 nm. The focal lengths of L1, L2, and L3 are 500 mm, 2000 mm, and 150 mm, respectively. The daylight AO experiments using the daytime HyWFS approach can also be carried out in other bands with the proper optical elements, such as an appropriately designed pyramid prism and chosen detectors.
Fig. 5. (a) Left view and (b) front view of the double pyramid prism. The blue and yellow glass represent BAK6 and ZK9, respectively.
With the values of the focal lengths associated with the 4$F$ system (${f_{\textrm{L}2}}$ = 2000 mm and ${f_{\textrm{L}3}}$ = 150 mm) and the diameter of the DM (${d_{\textrm{DM}}}$ = 21 mm), the diameter of each pyramid subpupil image ${d_{\textrm{PySub}}}$ was calculated as 1.575 mm using Eq. (5). As the pixel area of the WFS camera is 6.5 µm × 6.5 µm, each subpupil image occupied approximately 242 × 242 pixels. Furthermore, the experimental bench of the daytime HyWFS was analyzed from the perspective of geometrical optics. Given that the refractive indexes of the glass (${n_1}$ and ${n_2}$) are 1.5609 and 1.6171 at 660 nm, the deflection angle of the double pyramid used in our experimental bench can be calculated as 1.09$^\circ $ by
where ${\alpha _1}$ and ${\alpha _2}$ are the base angles of the two pyramids. With the aperture angle of the incident beam is $1/{F^\# } \approx $0.60$^\circ $, ${d_2}$ was calculated to be 1.575 mm by Eq. (10), which coincides with the previous analysis.The daytime HyWFS response to a flat wavefront was obtained with only the object light to verify the analyses, as shown in Fig. 6. Alignment and manufacturing errors can cause the image to slightly differ from the simulation. Each subpupil image had a diameter of approximately 240 pixels on the detector plane and was sampled by an 8 ${\times} $ 8 lenslet array, which is consistent with the previous analyses. Given that each subpupil image was sampled by 8 subapertures in diameter, 240 × 240 pixels were regarded as a subpupil for simplification of the calculation.
2.4 Performance for AO
Before closing the loop, the daylight AO system was calibrated using only object light by recording daytime HyWFS responses to a series of Zernike modes. Corresponding SHWFS centroid displacements were recorded for the SHWFS reconstruction matrix, and the PyWFS phase slopes were obtained for the PyWFS reconstruction matrix. A data-binning operation was performed to ensure accuracy and simultaneously simplify the computation when using the PyWFS algorithm. During the calibration and closed-loop processes, 30$\times \textrm{}$30 pixels in each subaperture were binned to a single pixel. Calibration matrices for the SHWFS and PyWFS algorithms were created using a standard single-value decomposition algorithm with an amplitude of 0.1λ, preventing the WFS from exhibiting saturated responses due to an excessively large calibrated input. With the calibration matrices and the daytime HyWFS responses obtained by the two algorithms separately, the reconstructed amplitudes of various Zernike modes were obtained and plotted as a function of the applied amplitude from -0.5λ to +0.5λ, as illustrated in Fig. 7. The relationship between the reconstructed wavefront and the applied wavefront is nearly linear for small wavefronts. The mild deviation observed may be attributed to several factors, such as DM hysteresis, manufacturing tolerance of the pyramid prism, and optical effects of the bench. The daytime HyWFS with the SHWFS algorithm exhibits a wider linearity range than that with the PyWFS algorithm.
Fig. 7. Reconstructed wavefront using (a) SHWFS and (b) PyWFS algorithms with calibration amplitude of 0.1λ. The red and green dashed boxes indicate the linearity ranges with the SHWFS and PyWFS algorithms, respectively.
For a large-scale aberration beyond the linearity range, closed-loop operations were carried out for wavefront compensation in a few iterations. The feasibility of the daytime HyWFS approach for AO systems was verified by the closed-loop wavefront corrections. The DM first introduced a static wavefront distortion, and the corresponding daytime HyWFS responses were recorded. With the reconstruction matrix, the reconstructed Zernike aberration was obtained and generated by the DM at each iteration until the system converged and stabilized. Notably, the SHWFS (Eq. (1) and Eq. (2)) and PyWFS algorithms (Eq. (3) and Eq. (4)) were respectively applied to calculate the daytime HyWFS signals during the calibration and correction processes.
The closed-loop performances with an initial RMS of 0.837 λ are presented in Fig. 8 and Fig. 9. Figures 8(a) and 8(b) depict the initial wavefront and focal plane image before correction. After correction using either algorithm, the wavefront distortion was eliminated, and the focal plane spot energy was notably concentrated, as shown in Figs. 8(c) to 8(j). Referring to the original RMS of 0.837λ, the final RMSs after applying the SHWFS and PyWFS algorithms were 0.006λ and 0.004λ, respectively. The Strehl ratio (relative to the last frame), which represents the quality of the focal plane image, improved significantly and then remained stable. The SHWFS algorithm requires fewer iterations for system stabilization (≥95% final SR) due to the high linearity range, while the PyWFS algorithm achieves a smaller residual RMS. The contrast between the detection plane images before and after correction is shown in Fig. 9. Figure 9(a) displays the unprocessed detector plane image before correction utilized for determining the daytime HyWFS response using the PyWFS algorithm. The four subpupils were illuminated differently for the aberrated wavefront. Figure 9(b) shows the detector plane image processed for the SHWFS algorithm before correction. The location of each spot shifted when a wavefront aberration was present. After correction, spot shifting was reduced with the use of the SHWFS algorithm, and the intensity distributions of the four subpupils became more even when the PyWFS algorithm was used, as presented in Figs. 9(c) and 9(d). Multiple static waveforms were tested, and in all cases the waveforms were much flatter after the iterations, as listed in Table 1.
Fig. 8. Closed-loop performances of the daytime HyWFS with SHWFS and PyWFS algorithms. Before correction: (a) Wavefront image and (b) focal plane image. Correction results with SHWFS algorithm: (c) Wavefront image, (d) focal plane image, and plots of (e) RMS and (f) relative SR with iteration time. Correction results with PyWFS algorithm: (g) Wavefront image, (h) focal plane image, and plots of (i) RMS and (j) relative SR with iteration time.
Fig. 9. Daytime HyWFS images before and after correction. Before correction: (a) Unprocessed daytime HyWFS image and (b) daytime HyWFS image processed for SHWFS algorithm. After correction: (c) Unprocessed daytime HyWFS image and (d) daytime HyWFS image processed for SHWFS algorithm.
Table 1. Closed-loop correction results using SHWFS and PyWFS algorithms
The closed-loop results indicate that the daytime HyWFS approach with both algorithms is feasible for wavefront compensation in the AO system. The SHWFS algorithm can achieve a faster correction of large wavefronts, while the PyWFS algorithm is suitable for high-resolution phase measurements.
3. Daylight AO correction experiment
3.1 Field stop adjustment
To simulate daytime conditions, the relatively strong background light generated by the LED surface light source was mixed with the object light to form the incident light in daylight AO systems. The FS employed before the pyramid prism must be resized appropriately for experimental accuracy. The FS’s size needs to be within a certain threshold to avoid signal overlap in adjacent subapertures, while it also can’t be too small to block useful light. Figure 10 illustrates the experimental setup for the daytime HyWFS and the corresponding images with different FS sizes. When the FS was completely open, the background signal spanned all subapertures of the daytime HyWFS subpupil image, as shown in Fig. 10(b). Downsizing the FS to approximately 11.4 mm and 8.1 mm apertures resulted in varying degrees of signal overlap in adjacent subapertures, as displayed in Fig. 10(c) and Fig. 10(d). Optical analysis of the 4$F$ system indicated that the radii of the quarter-circle areas where the background signal was located were 41 and 29 pixels, respectively, consistent with the experimental images. For daylight experiments, the FS should be adjusted to encompass the entire mixed signal in each subaperture without overlap. This means the radius of the quarter-circle area in each subaperture should be limited to 15 pixels, and the corresponding FS diameter was calculated as 4.2 mm in this system.
Fig. 10. (a) Optical bench of the daytime HyWFS. The daytime HyWFS output images with (b) a fully open aperture, (c) an 11.4 mm aperture, and (d) an 8.1 mm aperture.
After adjusting the FS, daytime HyWFS output images were obtained with only object light, daylight, and mixed light, as shown in Figs. 11(a)–11(c). Without the lenslet array, the object signal and daylight noise would be distributed throughout the PyWFS subpupil images. By calculating the ratio of the mean object intensity and the mean daylight intensity, the SNR detected by the usual PyWFS was estimated as 0.81, implying that the object light was weaker than daylight. In contrast, the daytime HyWFS improved the SNR to 5.90, significantly enhancing the distinction between the object and daylight background signals.
Fig. 11. Daytime HyWFS output images with (a) the pure object signal, (b) the daylight signal, and (c) both object and daylight signals.
3.2 Daylight AO experiment results
Daylight AO corrections were conducted to validate the daytime HyWFS principle. The daylight closed-loop process with an initial RMS value of 0.837λ is presented in Fig. 12. Static wavefront aberration was deliberately introduced by the DM, and the aberrated object light was combined with the strong daylight as the incident light. After being extracted from the daylight signal using the background elimination algorithm, the object signal of interest in each subpupil was distributed in an 8$\times$8 circular spot array. For the SHWFS algorithm, the four subpupil images were summed, and the daytime HyWFS centroid locations of all effective subapertures were computed. The wavefront was reconstructed by multiplying the daytime HyWFS centroid displacement responses by the SHWFS reconstruction matrix. For the PyWFS algorithm, the object signal was binned into 8$\times$8 subapertures in each subpupil, and the daytime HyWFS slopes for effective subapertures were calculated. The wavefront was reconstructed by multiplying the daytime HyWFS slope difference responses by the PyWFS reconstruction matrix. The wavefront can be corrected after a series of closed-loop compensation procedures. The experimental results obtained using the SHWFS and PyWFS algorithms are highlighted in red and green, respectively, demonstrating reduced SHWFS centroid displacements and more even PyWFS intensity distributions after correction.
Fig. 12. Daylight closed-loop correction process with an initial RMS of 0.837λ based on the daytime HyWFS approach using both algorithms. The blue box indicates the main procedures. The red and green dashed frames indicate the correction results using the SHWFS and the PyWFS algorithms, respectively.
Detailed daylight correction results are illustrated in Fig. 13. After corrections with both algorithms, the wavefront distortion was eliminated, and the focal plane spot energy was concentrated. The daytime HyWFS with the SHWFS algorithm reached its sensitivity limit after 7 iterations, with a remaining RMS of approximately 0.061λ. Using the PyWFS algorithm, the system converged after 15 iterations, resulting in a residual RMS of 0.037λ. The extended linearity range using the SHWFS algorithm increases the temporal bandwidth and enables efficient correction, as large wavefronts can be estimated correctly and compensated for fewer iterations. The constrained linearity range using the PyWFS algorithm leads to underestimated wavefront amplitudes and more closed-loop iterations, whereas better correction quality can be achieved.
Fig. 13. Daylight closed-loop performances of the daytime HyWFS approach using SHWFS and PyWFS algorithms (Initial RMS = 0.837λ). Before correction: (a) Wavefront image and (b) focal plane image. Daylight correction results using SHWFS algorithm: (c) Wavefront image, (d) focal plane image, and plots of (e) RMS and (f) relative SR with iteration time. Daylight correction results using PyWFS algorithm: (g) Wavefront image, (h) focal plane image, and plots of (i) RMS and (j) relative SR with iteration time.
To further confirm the validity of the daytime HyWFS approach for daylight AO, another distorted wavefront with an RMS value of 1.123λ, which is large for astronomical AO systems, was introduced. The experimental results are presented in Fig. 14 and Fig. 15. The wavefront was successfully eliminated, and the final image exhibited a resolution close to the diffraction limit with either algorithm. Additional daylight correction results are listed in Table 2. The daylight closed-loop results affirm the feasibility of the daytime HyWFS approach using both signal calculation algorithms for real-time AO corrections under daytime conditions.
Fig. 14. Daylight closed-loop performances of the daytime HyWFS approach using SHWFS and PyWFS algorithms (Initial RMS = 1.123λ). Before correction: (a) Wavefront image and (b) focal plane image. Daylight correction results using SHWFS algorithm: (c) Wavefront image, (d) focal plane image, and plots of (e) RMS and (f) relative SR with iteration time. Daylight correction results using PyWFS algorithm: (g) Wavefront image, (h) focal plane image, and plots of (i) RMS and (j) relative SR with iteration time.
Fig. 15. Daytime HyWFS images before and after daylight correction (Initial RMS = 1.123λ). Before correction: (a) Unprocessed daytime HyWFS image and (b) daytime HyWFS image processed for SHWFS algorithm. After correction: (c) Unprocessed daytime HyWFS image, and (d) daytime HyWFS image processed for SHWFS algorithm.
Table 2. Daylight correction results using SHWFS and PyWFS algorithms
4. Conclusions
In this paper, a novel concept of wavefront sensing for real-time daylight AO observations, the daytime HyWFS approach, is demonstrated. First, the linearity ranges of daytime HyWFS with the SHWFS and PyWFS algorithms are presented by experiments, illustrating that the linearity range achieved with the SHWFS algorithm is wider than that with the PyWFS algorithm. The closed-loop results of multiple wavefronts substantiate the applicability of the daytime HyWFS to AO systems. Furthermore, the appropriate diameter of the FS for the daylight AO system was explained to be equal to the diameter of the daytime HyWFS subaperture through optical analysis. Subsequently, the daylight correction results indicate that the daytime HyWFS approach integrates the advantages of SHWFS and PyWFS for real-time daylight AO correction and allows for easy switching according to situations without any element movement, which is flexible for astronomical observations.
Compared to the usual PyWFS, the developed approach is applicable in much lower SNR conditions, such as visible observation in the daytime. Meanwhile, it performs rapid correction of large wavefronts using the SHWFS algorithm due to the high linearity range, essential for addressing strong turbulence in daylight AO. Moreover, it outperforms the traditional SHWFS as it achieves precise and sensitive compensation with real-time adjustable pupil sampling using the PyWFS algorithm, beneficial for daytime high-resolution imaging and weak object observation. In practical operations, the daytime HyWFS approach can first correct a large wavefront to a smaller one using the SHWFS algorithm and then perform precise compensation using the PyWFS algorithm.
In conclusion, the daytime HyWFS approach is proposed as an alternative for daytime natural guide star AO observations of solar-illuminated objects, enabling high-resolution daytime imaging of RSO using ground-based telescopes dedicated to SSA. Aware that actual astronomical AO observations may encounter several practical challenges, further studies should be conducted to successfully apply the proposed approach to our 4.0 m telescope.
Funding
National Key Research and Development Program of China (2022YFB3902000); Major Program of the National Natural Science Foundation of China (42192582); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0580000); Jilin Scientific and Technological Development Program (20230401097YY).
Acknowledgment
The authors would like to thank Dr. Hongzhuang Li from CIOMP for his advice about the lenslet array, and Dr. Wenlou Yuan from Osaka University for his help with establishing the design structure of the pyramid prism.
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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