Study on the method of precision adjustment of star sensor

The star sensor is an optical device that measures star coordinates and outputs the altitude information with respect to inertial coordinates.¹ From the perspective of the altitude measurement accuracy, the conventional precision star sensor has an accuracy of 10″ order of magnitude, and the high precision star sensor has an accuracy of 3–5″ order of magnitude. Currently, mainstream products fall under these two levels, which are available as various models² in many research companies. The star sensor with an accuracy better than 1″ falls under the very high precision star sensor.³ The development of very high precision star sensors for high-resolution earth observation and astronomical observation tasks is of great significance.

The development of star sensors has a long history, and internationally renowned manufacturers include Sodern in France, Jena in Germany, and Selex Galileo in Italy. In China, there are also many star sensor research organizations. Through decades of technology accumulation, the star sensor development team of the Beijing Institute of Control Engineering has developed fifth-generation star sensors. Based on years of research accomplishments, designers have gained profound understanding of error models of star sensors; thus, they can further improve the measurement precision of star sensors.

The measurement errors of star sensors (Fig. 1) are divided into star position measurement error, bias stability, and bias error,⁴ and the position measurement error is further divided into spatial frequency error and temporal error. The position measurement error is a critical error source that should be restrained during star sensor development. The alignment precision of optical–mechanical structures is closely related to calibration residuals of the star sensor and positional deviations of mass center of star points.

The installation deviation depends on the precision of four benchmarks: surveying coordinate system, optical coordinate system, reference mirror coordinate system, and mechanical coordinate system.

The position of each coordinate system is shown in Fig. 2.

An established method for building a relationship for the four reference coordinate systems is to build the relationship between the reference mirror coordinate system and the mechanical coordinate system. This generates a high measurement precision and satisfactory repeatability. The alignment of the optical coordinate system and the surveying coordinate system is related to the interior alignment of detecting components and alignment between detecting components and the lens. The detecting component, which is complicatedly structured, has multiple assembly links and is thus a major controlled member of precision assembling adjusting. The positions of all components in a star sensor are presented in Fig. 3.

A detecting chip and chip-mounting flange form a detecting component. Considering that the detecting chip has no built-in installation interface, the detector is solidly connected to its mounting flange by pasting to guarantee installation precision. Then, relevant references for installation can be obtained by designing a detector-mounting flange; hence, interior alignment errors of detecting components are introduced. As absolute constructions, detecting components and optics lens respectively represent an optical reference coordinate system and a surveying coordinate system. In addition, their assembly is involved with the alignment error of components. The very high precision star sensor is taken for example, and the assembly relationship of its components is given in Fig. 4.

The improvement of imaging component alignment is important to elevate the calibration precision and overall measurement precision, and ultimately the star sensor measurement precision.

For general precision star sensors, no quantitative control is exerted upon the precision alignment indexes of all components during image component alignment. The machined surface of parts is used as the reference for assembling, and alignment precision is affected by mechanical precision. Subsequently, a complete machine calibration is performed to modify system error. Such an optical–mechanical structure alignment method is referred to as precision machining method. The assembly precision of image components applicable to such a method ranges from tens to dozens of minute of arc (′) component levels; therefore, the method is suitable for general precision star sensors.

For high precision star sensors, a mechanical fitting method is currently utilized to assemble and adjust imaging components. First, the pasting error between the detecting chip and its mounting flange is measured, and then the pasting error of the chip is compensated by making repairs and supplying replacements for the focusing ring. Then, the mechanical mounting face of an optical lens-mounting flange is selected as the reference for the assembly and adjustment of the detector components. Finally, a focusing test is conducted for the focusing ring compensated by coping. According to such an approach, the assembly precision of imaging components lies between three and five angular component levels. This means that the assembly precision of such components is high and can satisfy the precision requirement of high precision star sensors. However, the corresponding coping efficiency is low, but its rejection rate is high. Consequently, it is rather difficult to make repairs and supply replacements for the focusing ring. Comparison of common control methods for optical machine structures is given in Table I.

To further improve the assembly precision of imaging components and solve practical engineering problems, a new star sensor optical machining precision alignment method, simulation-aided optical alignment, is proposed in this paper. In line with this approach, the precision requirements of star sensors, considering the whole machine, are used as the input to obtain the alignment precision of imaging components by decomposition based on integrated precision simulation. Depending on the requirement decomposition, alignment schemes of different components have been formulated.

The component alignment scheme involves an optical alignment method, in which the optical axis of the optical lens is selected as the reference for alignment to paste the detecting chip, which results in a high precision. In addition, the positional relationship between the optical lens and the chip detector can be conveniently and rapidly adjusted to improve the alignment precision between the optical reference and measuring basis and consequently elevate the measurement accuracy of star sensors.

The advantages of this method are described as follows: The precision requirement of the whole machine is decomposed into a component level. With clear adjustment targets and short periods, engineering difficulty is controllable. Moreover, a suitable optical testing means is utilized to improve the assembly precision of imaging components to ≤2′. The difficulties of this approach lie in the accuracy requirement decomposition for optical–mechanical structures. Currently, no analysis software can establish the relation between the alignment precision of optical–mechanical structure and the single-star positioning error of the whole machine. In this case, integrated precision simulation should be conducted, considering the actual design conditions of star sensor hardware.

In this paper, we first analyze the assembly precision requirements of the very high precision star sensor, and then control the optical components by optical precision adjustment, so as to meet the precision requirements of the whole machine decomposition. Finally, through the star sensor calibration, the feasibility of the precision adjustment method of the optical machine structure is discussed.

For star sensors, the alignment error of an optical–mechanical structure is principally the space tilt error between the optical axis of the optical lens and the light-sensitive surface of the detecting chip. When the tilt error is excessively large, both the positional deviation of mass center of star points and the system calibration residual correspondingly increase, which further affects the position measurement precision of a single star of the star sensor. Therefore, the tilt error between the lens optical axis and the light-sensitive surface of the detecting chip is an important assembly factor and thus a critical control index.

The space tilt error between the optical axis of the optical lens and the light-sensitive surface of the detecting chip is embodied as a dip deviation between the image surface and the optical axis in a star sensor imaging model.⁵ Such deviation generates an image point offset error, which is shown in Fig. 5.

The image point Pα(xα_,yα) after the image plane is defined as⁶ 

where $r′=x′2+y′2+f2−2fx′sinα;rα=r′ff−x′sinα.$

After the image surface tilts, the distribution of defocused spots of image points changes accordingly, which further results in the deviation of the mass center position of star points regarding a star sensor. Such a deviation is a high-frequency system space deviation that cannot be modified by complete machine calibration. Considering the measurement precision of a very high precision star sensor, such a deviation is non-negligible.

The precision simulation for star sensors is an altitude calculation process specific to simulated star images. The precision simulation requires a digital simulated star image generated by fixed stars on a photoelectric detector via an optical system corresponding with the image-forming principle. In ideal cases, star images are gray-scale maps of defocused spots of two-dimensional Gaussian distribution, where x₀, y₀ refers to the mapping center of star points. A gray level design formula for pixel x_i, y_i is as follows.⁷ 

In Eq. (2), σ is related to the defocusing degree of the star sensor. At least 95% of a light energy often falls into a range of 3×3 pixel if σ < 0.671 (Fig. 6); A depends on the stellar magnitude of fixed star instrument, optical aperture, and detector response; therefore, it can be solved according to the fixed star catalogue, parameters of the optical system and photoelectric parameters of the detector.

The star point simulation model generated according to Eq. (2) is applicable to traditional precision simulation of star sensors. It leaves variations in defocused spots of star points generated by image surface tilt. Under this condition, Gaussian model fails to evaluate the assembly precision requirement of the star sensor imaging components.

The proposed star point model adopted by the simulation-aided optical alignment method uses CODE V to figure out the star point spot diagram of the required imaging position based on the optical path model parameters of a real star sensor optics. In this study, while generating the star point spot diagram, an error factor of image surface tilt was introduced. The star point spot diagram in this state was selected as the input to generate a digital star point image with image surface tilt error by combining the photoelectric parameters of the detector and the information in the fixed star catalogue. Moreover, the image surface tilt error was adjusted to analyze and obtain a certain level of sensitivity between star point positions and energy under different assembly errors conditions. Eventually, the assembly precision requirement of the imaging surface and optical axis is achieved by decomposition from the perspective of whole machine precision.

The influence of tilt angle between the optical axis and detector of a precision star sensor was analyzed.

The positional accuracy of star extraction conducted by the star sensor changes with the assembly error of the optical machine as shown in Fig. 7. When the tilt angle between the lens optical axis and the detector is below 100″, the positional accuracy of star points is about 1.8″; however, if the tilt angle exceeds 200″, the positional accuracy significantly rises. Figure 8 shows variations of the diameter of defocused spots with the assembly error of the optical machine in a certain field of the star sensor view. If the tilt angle described above is <100″, the diameter of defocused spots remains unchanged. However, as the angle of inclination increases, the diameter changes linearly.

Therefore, the tilt precision between the optical axis of the optical lens and the light-sensitive surface of the chip was defined as 100″, and it was used as the alignment precision of optical–mechanical structures for the very high precision star sensor.

The internal assembly precision of imaging components in a very high precision star sensor mainly includes the following aspects.

1. The alignment precision between the chip and its mounting flange.

   • The positional accuracy of the chip center relative to the mounting flange center.

   • The tilt precision of the light-sensitive surface normal of the chip relative to the installation surface normal of the mounting flange.

2. The alignment precision between the chip component (assembly of the chip and its mounting flange) and the lens optical axis.

   • The extension precision of the optical axis relative to the reference for installation of the lens.

   • The assembly precision of the mechanical reference of the chip component relative to that of the optical lens.

To satisfy the general assembly index standards for imaging components, that is, the tilt degree between the lens optical axis and the light-sensitive surface of the chip should not be >100″, the assembly accuracy mentioned in 1-b) and 2-a) and 2-b) should be controlled. As for 1-a), the assembly accuracy can be controlled according to the actual capacity of the testing equipment to mainly ensure that the design margin for the lens field of view is not exceeded (Table II).

According to the design form of the product, the optical axis of the optical system was used as the alignment reference to successively control the detecting chip alignment and imaging component alignment. Through the control over assembly precision of all working procedures, high-precision alignment of an optical–mechanical structure was eventually achieved.⁸ 

The optical alignment method of an optical–mechanical structure for very high precision star sensors is completed in three steps.

(1) Measurement of the lens optical axis orientation

A centrescope was utilized to measure the optical axis orientation in an optical system, and the lens optical axis was taken from the datum plane on the surface of the lens construction. Figure 9 shows the lens optical axis measurement system by a centrescope.

(2) Data transfer for lens optical axis

The reference information representing the optical axis of lens was transferred to an adjustable reference surface of the mounting flange construction of the chip, as shown in Fig. 10.

(3) Pasting of detecting chip

The detecting chip is fastened to the mounting flange of the detector by pasting. Using the optical axis datum of the mounting flange of the chip as reference, the bondline thickness of the pasted chip was adjusted so that the orientation of the detecting chip normal and the optical axis can be consistent with each other. Chip installation and testing diagram is given in Fig. 11.

Based on the above method, alignment testing was conducted for the extension of the lens optical axis and chip datum of the very high precision star sensor. Relevant test results signify that extension errors of the lens optical axis and the detecting chip normal are 0.2′ and 1.7″, respectively. The assembly error of the mechanical datum of the detecting element relative to that of the optical lens is the measuring error of the test equipment, which is <1″; thus, the decomposition index standards specified in Figs. 12 and 13 are satisfied.

A calibration test for the complete machine was carried out after the star sensor precision alignment for an optical–mechanical structure.⁹ The differences between the calibration precision after precision alignment and the calibration precision of a conventional alignment method were compared to evaluate the contribution of precision alignment to the overall measurement accuracy.

The star sensor calibration process is described as Fig. 14.¹⁰ A single star simulator served as the target light source to simulate fixed stars of infinity, and the star sensor realized the imaging of star points sent out from the simulator. By controlling a high-precision turntable, the formed star points covered the star sensor field of view. The positions of star points on the image plane of the star sensor were recorded when the turntable arrived at each test point, as well as the coordinates of angles formed by both axes of the turntable. The angular coordinates of the turntable were used as truth values of the object space measurement to process the turntable data and star point data measured by the star sensor. Finally, calibration coefficients were achieved to evaluate the associated calibration precision. Typical star sensor calibration vector diagram is given in Fig. 15.

Figure 16 presents the calibration precision generated by a conventional alignment method of a star sensor (1.2″). For comparison, the calibration residual of the precision alignment method is shown in Fig. 17. Improving the alignment precision of the optical–mechanical structure clearly contributes to the calibration precision of the complete machine. As demonstrated by the test results, the alignment precision improvement for the optical–mechanical structure significantly improves the calibration precision, which is vital for improving the precision of very high precision star sensors.

Compared to the existing conventional imaging component alignment methods, the proposed simulation-aided optical alignment approach of star sensors, which is targeted at optical–mechanical structures, has the following advantages.

1. First, by analyzing the precision requirements of the star sensor, considering the whole machine, the alignment indexes of all core components were obtained for the optical–mechanical structure through decomposition.

2. The optical axis of the optical system was used as the alignment reference of imaging components, and the orientation deviation from the optical axis of the optical system was compensated by pasting the detecting chip. The alignment precision of the method was below 2′, which is significantly better than the existing value. Meanwhile, it avoids much mechanical coping, which improves engineering efficiency and reduces implementation difficulty.

3. A centrescope was utilized for the first time to measure the optical axis of the optical system, and relevant references were introduced; this expands the application scope of the centrescope, which is usually used for precision alignment of lenses in an optical system, and solves precision alignment problems associated with components of optical system and those of the chip.

The approach is suitable for all high-precision imaging sensors. Because of the controllable alignment difficulty and short alignment period, it significantly contributes to the state consistency of productization. Its application in imaging component precision alignment can improve the measurement accuracy of products, especially very high precision star sensors. The approach can also to an extent enhance the performance stability for products of batch production; therefore, it can be commercialized and applied to the production and development processes of all imaging sensors.