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Abstract
The first non-defocus high transmittance non-fiber image slicer is presented. In order to solve the problem of image blur caused by the defocus between different sliced sub-images, an optical path compensation method based on stepped prism plate is proposed. Design results show that both the maximal defocus amount between the four sliced sub-images is reduced from 2.363 mm to nearly 0. The diameter of the dispersion spot on the focal plane is reduced from 98.47 μm to close to 0. The optical transmittance of the image slicer is up to 91.89%. This new image slicer is greatly valuable for high resolution and high transmittance spectrometer.
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1. Introduction
The image slicer makes all the acquired star images pass through the slit of the spectrometer by means of slicing and rearranging the image, so that all the starlight is possible to be converted into effective spectra, thus helping the instrument to obtain high spectral resolution and high light flux simultaneously [1]. In order to achieve high resolution, the slit of the astronomical spectrometer is usually set to very narrow, while the imaging diameter of the star is generally larger than the slit width of the spectrometer. This causes parts of the light blocked into the spectrometer and thus reduces the optical transmittance. The image slicer was proposed to solve this problem. By using the image slicer, the star image is possible to cut into several sub-images and then to fit the width of the slit. These sub-images are usually lined up in a vertical column and pass through the slit of the spectrometer, therefore the optical transmittance is improved while maintaining the high spectral resolution. Many high-resolution spectrometers (R > 30000) of large telescopes in the world are equipped with image slicers to meet the needs of scientific research, such as Keck I [10 m]-HIRES [2], VLT [8.2 m]-UVES [3], Subaru [8.2 m]-HDS [4,5], SALT [9 m]-HRS [6].
At present, the most widely used one is the Bowen-Walraven image slicer (BWIS) proposed by J.H. Walraven [7]. The Richardson type image slicer was also proposed [8], but it has a complicated structure (with cylindrical lens and several reflectors) and relatively low optical transmittance. The BWIS image slicer has the advantages of high transmittance, simple structure and stable system. However, because there is a thin solid parallel plate in its structure, it is very difficult and costly to process. Therefore, in 2012G. Avoila proposed a hollow image slicer (HIS) based on the principle of BWIS [9], which used two plane mirrors to form the reflection cavity, and significantly reduced the processing cost. However, the biggest disadvantage in these traditional non-fiber designs is that the sliced sub-images are realized by multiple reflections, the optical paths of the different sliced sub-images in the instrument are different, so that these sub-images cannot imaging onto the same plane. The sliced sub-images are characterized by only clear focal plane, blurred edges and gradual defocus. The amount of defocus will also accumulate with the increase of the number of sliced sub-images, resulting in serious blurring of edge image spots, which restricts increasing this number and the further improvement of spectral resolution. Francisco Diego proposed an improved “confocal image slicer” Bowen-Walraven image slicer [10]. However, because of the steep angle at which the light enters and leaves the image slicer device, the energy loss is about 14% for each time, producing the total optical transmittance less than 72%. There is no effective method to solve it in tradition. Optical fiber image slicers are possible to have no defocus amount between different sliced sub-images, however, their efficiency is generally 20% lower. This paper focuses on non-fiber image slicer.
Image slicer is also one of the core components of a new coherent-dispersion spectrometer (CODES) [11] for exoplanet exploration. CODES uses Sagnac common-path interferometer and grating spectrometer to obtain the spectral information of stars, and detects exoplanets by radial velocity method. It has the characteristics of high optical flux, high stability and flat image field. The star light introduced by the optical fiber passes through the interferometer to generate interference fringes, and then passes through an imaging module and reaches the image slicer. At this time, the interferometric image is cut into four stripes and grouped into a row, so that all of them can pass through the slit of the spectrometer and enter the subsequent grating spectrometer, so as to reduce the energy loss and obtain the aperture angle and field of view required by high spectral resolution. The maximal spectral resolution power within the spectral coverage 660-900 nm for CODES is ∼30000.
In this paper, based on the design of the hollow image slicer, the method of eliminating the defocus of the sliced sub-images by using the stepped compensation plate (SCP) is proposed. The theoretical analysis and optical design are carried out, and the four sliced sub-images with non-defocuses are realized, and the high transmittance is ensured.
2. Defocus characteristic analysis of typical Image slicer
2.1 Equivalent optical model
The structure of the BWIS consists of three parts: triangular prism, parallel plate and image slicing prism [12].The principle of the HIS is similar to BWIS. Both of them can form long image spots arranged along the image slicer’s optical edge. However, two planar mirrors are used in the HIS to replace the full reflective surfaces in the BWIS, and the edge of one mirror in the HIS are used to cut the image. Since HIS does not have to meet the total reflection condition as in the solid BWIS, the angle of incidence is no longer limited by it.
The basic idea of the BWIS and the HIS is that the beam is incident on the image slicer at a slow focal ratio. The star image is imaged near the optical cutting edge. The first sliced sub-image (with width D/M, D is the size of the star image, M is the number of sliced sub-images) is thereby separated; and the remaining un-sliced beams are reflected for even times in the reflection cavity. When the beam reaches the optical cutting edge again, another sub-image is separated [13]. The image cutting work is repeated. The equivalent optical model of these two image slicers is shown in Fig. 1. Because all the sliced sub-images are generated at the same optical cutting edge, they must be arranged along the optical cutting edge. At the same time, due to the different optical paths of all cutting beams reaching the edge, there is an optical path difference between different sliced sub-images. That is, defocus phenomenon occurs.
In Fig. 1, D is the diameter of the star image. θ is the incident angle of the beam incident on the reflection surface, d is the distance between the upper and lower optical surfaces. For the BWIS, d is the thickness of the parallel plate. The smaller d, the more difficult to processing, thus d should be carefully chose.. For the HIS, d is the distance between the two mirrors.
According to the above optical model, the best theoretical relationship between these parameters should be:
And the defocus amount (optical path difference) between two adjacent sliced sub-images can be deduced as follows:
It can be seen that the defocus amount of the image slicer is determined by both the incident star diameter and incident angle. The defocus amount is inversely proportional to the incidence angle on the image slicer. For a star spot with a diameter of 630.00 μm, the defocus can reach 1 mm at the incident angle of 30°. At the same time, if the optical path of the light in the image slicer is too long, the image spot will turn to widen, also resulting in energy loss. In order to minimize the optical path in the image slicer system to obtain a smaller defocus effect, the incident angle can be appropriately increased.
2.2 Factors that restrict the angle of incidence
Although Δl and d are gradually reduced with the increase of the incidence angle, the defocus amount does not always decrease with it, because in the actual design the sliced sub-images will also face the problem of spot dispersion.
Spot dispersion will make the sub-image spots sliced from the same object point fail to converging at the same point. For example, if F# is 20, the sub-image spot diameter will be diffused by 50 μm for every 1 mm optical path away from the focal plane. Related principle is shown in Fig. 2(a). The long dotted line represents the optical cutting edge, the large circle is the star image, the small circle is the dispersion spot when the object point is not in the focal plane, and the center of the circle is the object point. When the light beam propagates to the optical cutting edge, the left part of the dotted line in the diffusion spot passes through the image slicer, whereas the right part is reflected. After the beam propagates to the cutting edge again, the final image spot is shown in Fig. 2(b). Those points of the same color indicate that they come from the same object point.
Fig. 2. Left (a): segmentation under the condition of image spot dispersion. Right (b): object point repetition
Based on the above analysis, for the system with large F# and small number of slicing, a larger incidence angle can be considered to improve the slicing effect. For systems with small F# or large number of slicing, 45 degrees should be adopted to avoid the case of slicing dispersion spot. The table below shows the changes of optical parameters at different incident angles.
3. Design of image slicer in the CODES detection system
3.1 CODES system
The optical scheme of the CODES is shown in Fig. 3. The image slicer is a critical component. The partial parameters of the CODES system and the requirements for the image slicer are shown in Table 1 and Table 2. The input beam spot with a diameter of 630.00 μm is generated by the front optical system, and the beam spot is simulated by 32 object edge points, as shown in Fig. 4.
Table 1. Optical parameters change with incident angle/F24
Table 2. Input parameter requirements for the image slicer
3.2 HIS design
Since the lower processing cost and more flexible structure, the traditional HIS design is adopted in this paper as comparison. Reference [14] pointed out that the angle $\varphi$ between the optical cutting edge of the image slicer and the slit direction is:
Here q is the number of sliced sub-images. Angle $\varphi$ is the ideal angle. In practice, in order to avoid the influence of stray light, it is often required to have a certain distance between different sliced sub-images in the Sagittal plane. After repeated calculation and verification, the effect at angle 13°is better, and the designed image spot is shown in Fig. 5.
The traditional HIS is possible to divide the input circular image spot into four bar sub-image spots and arrange them on a straight line. But at the same time, the defocus amount between adjacent sliced sub-images is also obvious, which is up to 0.788 mm. According to the image spot diameter and the number of sliced sub-images, the maximum defocus amount was determined, i.e. 2.363 mm. When F# is 24, the diameter of the corresponding dispersion spot is 98.47 μm, the actual spot diameter is 158.50 μm. The actual spot diameter is 1.62 times of the theoretical one, so it cannot be clearly imaged. This is generally unacceptable in optical design, so under this system condition, the traditional design scheme can not achieve satisfied star image slicing effect.
3.3 Non-defocus design
In order to reduce defocus amount and limit image spot dispersion, the optical path should be optimized or reformed. The usual measure is to optimize the optical parameters of the image slicer in the optical design, such as adjusting incident focal ratio, material, number of sliced sub-images, incident angle, etc. But these can only minimize the defocus amount, unable to eliminate it. The best choice may be to compensate optical paths for different sliced sub-images. However, this is difficult to be realized inside the image slicer. Therefore, we propose a new design for the defocus compensation, the core of which is to add a stepped parallel prism plate, i.e. SCP, with each step corresponding to each sub-image. So that different sliced sub-images can be imaged at the same focal plane. According to the axial displacement formula of the ray after passing through a parallel plate:
where $\Delta l^{\prime}$s the axial displacement of the image plane after passing through the parallel plate, $d$s the thickness of the parallel plate, and $n$s the refractive index of the SCP.After careful design, the obtained sliced result is shown in Fig. 6. For the current imaging position deviation of 0.788 mm, when H-ZLAF92 glass is selected, the thickness of the SCP should be 1.576 mm, and the height should be slightly larger than the diameter of each sliced sub-image.
Fig. 6. Left: The stepped compensation plate (SCP); Right: The sliced effect after defocus compensation by using the SCP.
It can be seen that all sliced sub-images can be imaged on the same plane after adding the SCP, and the defocus amounts turn to almost zero, which well solved the core traditional defocus problem. Under the same conditions, the star image can be divided into four parts that it was unfulfilled, it is of great significance to further improve the resolution and transmittance of the spectrometer.
Although all the sliced sub-images can be imaged on the same plane by using the SCP, it can be seen from the above figure that it also introduces the stray light. The stray light is mainly caused by edge light overflow. In the process of sliced sub-images propagation, the SCP cannot completely envelop the rays. To eliminate this effect, we adopt blackening the bottom surface of the SCP (for visible - near infrared light) to absorb the spillover stray light.
In addition, due to the restriction of the propagation path of the sliced sub-images, the SCP has certain position and size requirements. In order to keep enough space for the actual installation and to avoid the mismatches of position and attitude between the SCP and the slicer, the last sliced sub-image spot do not have to pass through the SCP, thus three steps are only needed for the SCP.
After this engineering improvement, the image slicer with SCP can well meet the design requirements. The design structure and results of the new image slicer are shown in Fig. 7 and Fig. 8, respectively. Among them, the distance between the reflecting mirror and the cutting mirror is 1 mm; When F# is 24, the effective size of the four sliced sub-images is about 160.00 μm*630.00 μm.
3.4 Calculation of transmittance
The transmittance of the above design is analyzed in this part. The formula of optical transmittance is:
where T is that transmittance of the reflect surface, q is the number of split, and R is the reflectivity of the mirror of the plane mirror.When the surface is coated with high reflectance dielectric film, the reflectivity can reach 0.99, and the total transmittance of the system is about 97.05%. This image slicer divides the star image into four sub-images, thus each sub-image has a corresponding diffuse spot. Under the above simulation conditions, the image spot diameter is 630.00 μm and the sub-image width is 158.00 μm. The diameter of the dispersion spot of the first and fourth sub-images is 98.47 μm, and the energy loss caused by image spot dispersion accounts for about 7.77%. The diameter of the dispersion spot in the second and third sub-images is 29.60 μm, and the energy loss caused by the dispersion spot is 2.85%. The total energy loss caused by dispersion spot is about 5.31%, and thus the transmittance is 94.69%. Without considering the influence of tolerance, therefore the optical transmittance of image slicer is 97.05%×94.69%=91.89%.
Table 3. Optical Transmittance of this Image Slicer
Therefore, the total optical transmittance of the image slicer with SCP is 91.8% as shown in Table 3. This transmittance satisfies the design requirements of the CODES and is generally higher than other traditional image slicers. Generally, the transmittance of optical fiber image slicer and Richardson image slicer will not exceed 70%.
4. Conclusions
In the case of F# 24, it is a difficult design to divide the input image spot with a diameter of 630.00 μm into four sections. Due to this relatively large diameter and large number of sub-images, the defocus phenomenon is very obvious. According to the requirements of CODES system and based on the principle of HIS, the design method of image slicer with defocus compensation is presented in this paper, that is, the design of non-defocus optical structure and SCP. The material and length of the compensation plate are carefully selected and analyzed, which can make different sliced sub-images fall on the same plane, accurately eliminate the defocus amount, and solve the problems existing in the traditional image slicer. At the same time, we made a blackening design for the SCP, effectively prevent stray light. The whole design takes into account both cost and engineering requirements. The subsequent research work includes the specific design and analysis of the image slicer that satisfies more image segmentation spots, such as 5-6.
In this paper, the design of non-defocus method provides effective means for further improvements of the imaging quality and resolution of the astronomical spectrometer. This design method has universal and important application value, could provide important reference basis, and helps to achieve high quality astronomical observation and other remote sensing imaging.
Funding
National Natural Science Foundation of China (11727806, 42171464, 41827801); Key Research and Development Project of Hubei Province (2021BCA216, 2022BCA057).
Acknowledgments
We sincerely thank the editors and anonymous reviewers for their contributions to this paper.
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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