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Nowadays sun sensors are being more widely used in satellites to determine the sunray orientation, thus development of a new version of sun sensor with lighter mass, lower power consumption and smaller size it of considerable interest. This paper introduces such a novel digital sun sensor, which is composed of a micro-electro-mechanical system (MEMS) mask with an

As an essential component of satellites, the sun sensor has been widely used to measure the incident angle of the sunrays in the satellite-fixed coordinates [

Recent years have seen substantial growth in the research on digital sun sensors and related products. Those sensors that adopt planar APS as focal plane detectors usually can determine two-axis sunray angles with higher accuracy and resolution [

Considering all the aforementioned shortcomings, such as high power consumption [

A linear CCD based sun sensor usually adopts the combination of an optical mask with a single slit on it and a linear CCD detector (see

By analyzing the location of the spot, the sun vector can be reconstructed and the incident angle _{c}

To maximize the merits of the linear CCD and accomplish the measurement of two-axis sunray angles, a novel scheme has been introduced in this paper. We put forward a mask with an

The special slit is composed of a central slit and two paralleling diagonal slits, which interconnect end to end, like the italic ‘

The principle of the novel digital sun sensor is based on the different shifts of the three detected sun spots. It is assumed that three sun spots denoted as _{0}, _{1} and _{2} are detected on the default situation (the sunray is parallel to the Z/Za-axis). Compared with the default situation, when an incident sunray deflects in the Xa-Za plane—where _{1} which denotes the distance between _{0} and _{0}′ contains the information related to the deflection angle in the Ya-Za plane while Δ_{2} which denotes the distance between _{1} and _{1}′ (or between _{2} and _{2}') contains the information related to the deflection angles both in Ya-Za plane and Xa-Za plane. Taking vector superposition into account, the two-axis sunray angles can be calculated as:
_{1} denotes the initial distance between the central sun spot and the origin of coordinates while _{2} denotes the initial distance between either sideways sun spot and the origin of coordinates; _{1m} denotes the measurement distance between the central sun spot and the origin of coordinates while _{2} denotes the measurement distance between either sideways sun spot and the origin of coordinates; and

Given the fact that Euler angles are more widely used to scale the attitude of a satellite, we could adapt the equations into the form of Euler angles (

On the basis of the analysis of fundamental geometrical relations, we have:

Furthermore, the main error of this digital sun sensor is the sunray refraction error caused by the glass protection layer of the CCD [_{1}, _{2}, _{3} denote the light refractive index of the vacuum, CCD protecting glass and air, respectively, and the superscript ′ indicates the ideal value without the refraction.

From the explanation about the principle and the geometrical relations, we have:

So the fundamental equations can be corrected with

The key process to correct the refraction error is to calculate the value of _{1} and _{3} with constant 1 into

Then the incident angle can be calculated through iteration as follows:

The initial incident angle for iteration can be obtained through the two-axis angles measured with the equation below:

To sum up, the correction coefficient

To optimize the features of the sun sensor, the relationship between the structural parameters and the system functional characteristics should be carefully considered. Therefore, the FOV and system resolution are analyzed in this section for the design of optical head, based on the

From

The first priority of our design is that

As for the optimization of system resolution, we introduce a first-order centroiding algorithm by having the pixel resolution of CCD subdivided from 1 pixel into 0.1 pixel [

From basic physical law, the sum of the serial rectangles’ gravitational potential energy equals the gravitational potential energy of the assembly. If we assume the gravitational potential energy along axis of grey value is zero and the unit area density is 1, then the total energy can be calculated as follows:
_{i}_{c}_{i}

Since the distance resolution of chosen CCD can be subdivided into 0.8 μm, the system resolution can be simulated as shown in

By employing the Toshiba CCD, which can provide a pixel resolution of 0.8 μm with the help of centroiding algorithm, the FOV is ±60° × ±60°, and system resolution is 0.02° when

To obtain the goals of larger FOV, smaller size and lower power, both hardware and software of the sun sensor must be designed scrupulously. It has been a great help to achieve the aimed FOV by using MEMS-based technology to fabricate the mask. The construction of the sun sensor prototype mainly consists of frames, circuit board and the mask with an

Besides, the mask is fabricated via MEMS processes to archive a thin mask layer for decreasing its adverse effect of the FOV, while it also has the capability to decay the incident sunray to keep the detector working at a proper intensity range [

The electrical design has been accomplished by integrating all the component devices into one circuit board. And the program is designed as what the program flowchart (see

In the test and calibration of the sun sensor, the set-up at ambient conditions serves as the testing system, which consists of a sun simulator and a three-axis gimbals rotary table (see

The sun simulator can send a parallel light beam and the rotating platform can provide different incident sunray angles with a position accuracy of 0.001°. The performance test indicates that the FOV of the sun sensor is larger than ±60° × ±60°, and the maximum error between the measured sun position in the form of incident angle and the setting position through the rotary table is less than 0.08 degrees of arc (see

The entire performance characteristics as well as physical parameters of the sun sensor have been summarized in

In this paper, a novel digital sun sensor to meet the requirements of the modern application of micro/nano-satellites has been proposed. This sun sensor relies on a MEMS mask with an

This work has been carried out in the State Key Laboratory of Precision Instrument Measurement, Tsinghua University under the financial support by the National 863 Project (No. 2008AA12A216) and China NSF project (No. 60807004). The authors also wish to acknowledge the contributions made by Wen Jiang for the efforts of amending the paper.

Schematic of digital sun sensor with single slit.

Light intensity distribution of digital sun sensor with single slit.

Principle schematic of digital sun sensor with N-shaped slit:

Illustration of angle definitions.

Illustration of the refraction error.

Simulation of resolution and FOV subject to

Illustration of the centroiding algorithm.

System resolution with respect to the incident angle.

Outline of sun sensor prototype.

Prototype of digital sun sensor with

Program flowchart.

Test system for the sun sensor.

Measurement error statistics of sun sensor performance test.

Performance of sun sensor.

| |
---|---|

FOV | ±60° × ±60° |

Accuracy | 0.08° (3σ) |

Resolution | 0.02° |

Size | 80 mm × 60 mm × 30 mm |

Mass | 133 g |

Power consumption | 300 mW |

Update rate | 14 Hz |