1. INTRODUCTION

Sun sensors are important components of the attitude and orbit control system in spacecraft [1], and can realize the orientation by measuring the angle between the sun’s rays and the sun sensor coordinate systems [2]. Sun sensors are mainly divided into analog and digital sun sensors. The analog sun sensor has a simple structure; however, it is not suitable for a high-accuracy attitude determination and control system [3,4]. Compared to the analog sun sensor, the digital sun sensor not only has a high accuracy, but it also can eliminate the effects of stray light. In 2002, the Jet Propulsion Laboratory utilized micro-electro-mechanical-system (MEMS) processes and an active pixel sensor CMOS to develop a smaller digital sun sensor with a low mass, compact size, and low power consumption [5,6]. Since then, micro-digital sun sensors have been widely studied, especially in the aspects of their large field of view (FOV), high precision, and centroid extraction algorithm, etc. [7 –13].

Currently, there are many methods being proposed and applied to improve the FOV and resolution of the sun sensor, such as the panoramic annular lens method [14,15], multi-FOV four-quadrant method [16,17], and a method involving multiple pinholes in a dome [18,19]. However, the aforementioned methods either make the system structure complicated, or increase the size and power consumption. In 2013, Xing et al. proposed a multiplexing image detector method based on a dedicated MEMS mask, which could enhance the resolution of the digital sun sensors without reducing the FOV and adding optical lenses or other unnecessary structures [20]. However, due to the diffraction, the images of adjacent apertures will generate interference phenomena, especially in the large FOV [21,22]. In order to solve this issue, Zhimin et al. [23] and Wei [24] et al. carried out diffraction simulations to determine the aperture array parameters on the mask. However, this is not available for the digital sun sensors with multiplexing image detector method, for the reason that the different sub-FOVs correspond to different aperture patterns. Therefore, the aperture sizes for different sub-FOVs need to be studied.

In this paper, we proposed a precision enhancement method for a multiplexing image detector-based digital sun sensor with varying and coded apertures, which were determined by diffraction images with different sub-FOVs. The experimental results indicate that the proposed method could solve the crosstalk and blur phenomena of the diffraction images of adjacent apertures, especially in the condition of a large FOV. Moreover, the precision of the sun sensor could be improved by three times to ${1.32}^{\prime \prime }(1\sigma )$ at a 50° incident sun angle along the $X$ axis. Additionally, the precision was more stable in the whole FOV, and the exposure time could be greatly reduced at a large incident angle.

2. VARYING AND CODED APERTURES METHOD FOR MULTIPLEXING IMAGE DETECTOR-BASED SUN SENSOR

Based on the multiplexing image detector method, it is possible to realize the measurements of multi-FOVs using a single image detector [18,20,25]. In the references, the sun sensor optical system consists of an image detector and a dedicated mask with the same apertures, which are not suitable for the multiplexing image detector. Therefore, we propose the varying and coded apertures method for the digital sun sensor according to the diffraction theory. The aperture sizes corresponding to the different sub-FOVs on the mask vary. In this paper, the mask is composed of $(2n+1)$ distinctive groups of aperture patterns in a line, as shown in Fig. 1(a).

 

Fig. 1. Schematic of the large FOV measurement with varying and coded apertures method. (a) Cross-section view. (b) Top view.

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In Fig. 1(a), $l_{\text{detector}}$ is the size of the image detector, $l_{\text{pattern}}$ is the center-to-center spacing between the two patterns that are at the edge of the mask, $d_m$ is the center-to-center spacing of the adjacent patterns, $l_m$ is the length of each aperture pattern, and $h$ is the distance between the mask plane and the image detector plane.

The layout of the mask pattern is shown in Fig. 1(b). Each group of patterns consists of three apertures that are aligned in a line. In the different groups, the distance between the three apertures ($L$, $R$) is disparate to make every sub-FOV unique. They are called $({\mathrm{FOV}}_0,{\mathrm{FOV}}_1,{\mathrm{FOV}}_{-1}\dots {\mathrm{FOV}}_n,{\mathrm{FOV}}_{-n})$. In the same group, the sizes of the three apertures ($S$) are identical, and the size is determined by the diffraction simulation. In the same line, $R$ is same and $L$ is different. Conversely, in the same column, $L$ is same and $R$ is different.

3. OPTICAL SYSTEM SIMULATION AND DESIGN FOR SUN SENSOR

A. Design for High Resolution and Large FOV

According to the above, the incident angle of the sun sensor can be roughly calculated with the equation below:

In this paper, the pixel pitch of the detector is 5.3 μm, and the size is $6.78\mathrm{mm}\times 5.43\mathrm{mm}$. In order to reach arc-sec class resolution, $h=15\mathrm{mm}$ is adopted according to Eq. (2). Meanwhile, to realize a $120°\times 120°$ FOV, a $45.2\mathrm{mm}\times 46.5\mathrm{mm}$ mask pattern area is required, based on Eq. (3).

B. Aperture Sizes Simulation and Design for Different Sub-FOVs

The incident angle can be calculated by extracting the central coordinates of the sun diffraction spots, which are projected on the image detector plane from the mask plane. The diffraction is related to the aperture size. The diffraction will decrease the spots’ centroid-extracting accuracy. Furthermore, it will decrease the calculation accuracy of the incident sun angle. Therefore, it is necessary to study the relationship between the apertures and the diffraction spots, and to optimize the aperture sizes of different sub-FOVs.

It was demonstrated in [25] that when the angle between the incident sun ray and the mask plane is 90° and $h$ is fixed, with the aperture size increasing in a certain range, the sizes of the image spots will decrease gradually. Meanwhile, when the sun’s ray is obliquely incident along the same direction with the same aperture size and $h$, with the increase of the incident sun angle, the image spots will stretch gradually in the same direction. Therefore, to acquire the optimum diffraction spots, the aperture sizes should be optimized for different sub-FOVs particularly based on the numerical simulations.

The diffraction changes under particular conditions. For the digital sun sensor, (1) the incident sun rays are visible light, (2) the aperture is square in shape, with a size of around $30\mathrm{pixels}\times 30\mathrm{pixels}$ ($1\mathrm{pixel}=5.3\mathrm{\mu m}$), and (3) the distance between the image detector plane and the mask plane is 15 mm. The above-mentioned three conditions conform to the scalar diffraction theory. Based on the Huygens–Fresnel diffraction integral formula, a numerical simulation was conducted to obtain the intensity distribution of the diffraction image.

To ensure the centroid extraction of the diffraction images, the aperture sizes on the mask of different sub-FOVs should satisfy the following two principles: (1) one aperture should correspond to only one diffraction spot on the image detector, namely, far-field diffraction, and (2) the main intensity distribution of two adjacent diffraction spots should not be overlaid. Meanwhile, the more centralized the intensity distribution is, the more precise the centroid extraction will be. As shown in Fig. 2, the intensity distributions of the diffraction images corresponding to different apertures and incident angles were derived. In the same figure, the incident angle is identical, and with the aperture sizes changing, the intensity distributions of the diffraction images are different. The aperture sizes are indicated in the inset with different colors, and all the dimensions are in pixels.

 

Fig. 2. Intensity distributions of diffraction images with different apertures and incident angles. (a) $\alpha =0°$. (b) $\alpha =30°$. (c) $\alpha =45°$. (d) $\alpha =60°$.

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According to the numerical simulation results shown in Fig. 2 and the two principles above, the particular aperture sizes corresponding to the disparate incident angles have been determined. When $\alpha =0°$, namely, when the sun ray was perpendicularly incident to the mask plane, as shown in Fig. 2(a), the aperture size of $28\mathrm{pixels}\times 28\mathrm{pixels}$ was chosen. Similarly, the aperture size of $30\mathrm{pixels}\times 30\mathrm{pixels}$ was chosen when $\alpha =30°$, the aperture size of $36\mathrm{pixels}\times 36\mathrm{pixels}$ was chosen when $\alpha =45°$, and the aperture size of $44\mathrm{pixels}\times 44\mathrm{pixels}$ was chosen when $\alpha =60°$, as shown in Figs. 2(b)–2(d). With the aperture size increasing, the maximum intensity of the diffraction spot will rise, and then it will reduce when the aperture size increases further, as shown in Figs. 2(b) and 2(d), for the reason that the far-field diffraction degrades into near-field diffraction.

Based on the simulation results, when $\alpha =0°\sim 30°$, the main intensity of diffraction spot was concentrated within 30 pixels in the same axis direction. Similarly, when $\alpha =45°$, the diffraction spot was concentrated within 40 pixels. When $\alpha =45°$, the diffraction spot was concentrated within 80 pixels.

C. Mask Pattern Design With Varying and Coded Apertures

In this paper, the mask pattern was designed according to the varying and coded apertures method, which was mentioned in section 2. In the whole FOV, the length of different groups of patterns ($l_m$) is fixed, and $l_m$ is determined by the diffraction spot size of the fringe sub-FOV, as shown in Fig. 3(b). According to the simulation result in section 3.B, $l_m$ is 360 pixels in the axis of abscissas, and 120 pixels in the axis of ordinates. $L_1$ and $L_2$ are the center distances between the three apertures. Each group of encoded apertures will be determined by $(L_1,L_2)$ exclusively and could be extracted from the sun spot on the image detector. Therefore, we can achieve the sun angles according to the determined encoded apertures. As for the coding principle, we encoded the uniform $L_2$ and disparate $L_1$ in the same line, and encoded the uniform $L_1$ and disparate $L_2$ in the same column. For instance, in the $X$-axis direction, the central groups are coded as [… (128 120), (124 120), (120 120), (122 120), (126 120)…], while in the $Y$-axis direction, the central groups are coded as [… (120 126), (120 122), (120 120), (120 124), (120 128)…].

 

Fig. 3. Layout of mask pattern. (a) Whole FOV view. (b) Sub-FOV view.

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To ensure the continuous coverage of the adjacent sub-FOVs, the sum of $d_m$ and $l_m$ must be less than $l_{\text{detector}}$. In our design, the margin of each sub-FOV in the $X$-axis direction is 120 pixels ($D_x$), while the margin in the $Y$-axis direction is 104 pixels ($D_y$), as shown in Fig. 3(b). So, the center-to-center spacing of the adjacent groups of patterns are both 800 pixels in directions of the $X$- and $Y$-axes. Therefore, the sub-FOV corresponding to each pattern and the pattern number to realize the $120°\times 120°$ FOV can be achieved.

As shown in Fig. 4, the adjacent sub-FOVs can realize continuous coverage, and the number of groups is $13\times 13$ in the two-axis direction. Therefore, the center-to-center spacings of the border patterns are both 50.88 mm in the two-axis direction.

 

Fig. 4. Sub-FOVs of different pattern groups. (a) $X$ axis. (b) $Y$ axis.

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4. EXPERIMENT AND ANALYSIS

In this paper, the sun sensor prototype, as shown in Fig. 5(a), consists of a mechanical structure, a circuit part, and a mask. The mask was fabricated by the MEMS processes. First, the Cr mask layer was sputtered on the glass; then, the photoresist, as the lithographic mask, was coated to form the multi-aperture shape. Last, we adopted the lithographic process to accomplish the mask fabrication. In order to achieve the prototype performance, the sun sensor was installed on a three-axis rotary table with positioning accuracy of 0.0001°, and the sun’s ray was simulated by a collimator, as shown in Fig. 5(b).

 

Fig. 5. Performance test. (a) Prototype. (b) Test platform.

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The test began with the parallel light adjusted perpendicularly to the mask plane, and the test step of FOV was 5° along the $X$ axis, the $Y$ axis and the area of $X>0$ and $Y>0$ (1/4 FOV). Then, we extracted the centroid coordinates of the sun spots and calculated the incident angles. Meanwhile, we did the contrast test with a mask composed of same aperture size. In the case of the same exposure time, the images of the 50° incident angle along the $X$ axis of two designs are shown in Figs. 6(a) and 6(b), and the images of the 45° oblique incident angle in $X$- and $Y$-axes directions of the two designs are shown in Figs. 6(c) and 6(d).

 

Fig. 6. Test images. (a) Image at 50° along the $X$ axis with varying aperture sizes on the mask. (b) Image at 50° along the $X$ axis with the same aperture size on the mask. (c) Image at 45° oblique incident angle in the $X$- and $Y$-axes directions with varying aperture sizes on the mask. (d) Image at 45° oblique incident angle in the $X$- and $Y$-axes directions with same the aperture size on the mask.

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As shown in Fig. 6, compared with the same aperture size design, the varying aperture sizes design can solve the overlap and distortion problem of the diffraction spots at the edge FOV efficiently. It can also reduce the exposure time and improve the extraction precision of the spot centroid tremendously. When the exposure time and threshold for the sun spot extraction employed for the two designs are the same, at a 50° incident angle along the $X$ axis, the histogram of the sun sensor error statistics for 100 times is shown in Fig. 7. It can be calculated that the extraction precision with varying aperture sizes design is improved to ${1.32}^{\prime \prime }(1\sigma )$; however, the extraction precision with the same aperture size design is ${4.52}^{\prime \prime }(1\sigma )$.

 

Fig. 7. Histogram of sun sensor error statistics for 100 times of the two designs.

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To further analyze the precision improvement, two prototypes with two different designs were tested. The sampling angles’ steps were set to 5° along the $X$ axis from 0° to 50°, and the same exposure time was applied for both prototypes at the same sampling angle. Once the images corresponding to the same aperture size design and the varying aperture sizes design were acquired, an optimized threshold was fixed for the sun spots’ extraction. The extraction precision result is shown in Fig. 8. The performance experiment indicates that, with the incident angle increasing, the extraction precision gets worse gradually, which conforms to the simulation analysis. Compared with the same aperture size design, the extraction precision is more stable in the whole FOV with the varying aperture sizes design. Meanwhile, compared with the small incident angle, the extraction precision of the varying aperture sizes design is much better at a large incident angle.

 

Fig. 8. Precision along the $X$ axis with same exposure time for the two designs.

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The performance experiment indicates that the actual measurement images are consistent with the design proposal and simulation results, and the extraction precision increases by three times that of the original design at 50° in the $X$-axis direction.

5. CONCLUSIONS

In this paper, a precision-enhanced method for a multiplexing image detector-based digital sun sensor with varying and coded apertures has been proposed to solve the images overlap and distortion, which influence the image centroid extraction precision. The aperture sizes of different sub-FOVs have been simulated and confirmed according to the Huygens–Fresnel diffraction integral formula. Meanwhile, the digital sun sensor with varying and coded apertures was designed and tested. The experimental results demonstrated that this method could effectively solve the image centroid extraction problem for the large FOV. Also, the extraction precision of the image centroid was more stable with the varying apertures method, and the precision at a 50° incident angle along the $X$ axis was ${1.32}^{\prime \prime }(1\sigma )$, which was three times better than that with the same aperture method.