Design of Optical System for Small Long-Life Star Sensor

ZHAO Chongyi,QIAN Xuemin,ZHOU Xiaojun

1 Anhui Institute of Optics and Fine Mechanics,Hefei Institutes of Physical Science,Chinese Academy of Sciences,Hefei 230031

2 School of Astronautics,Harbin Institute of Technology,Harbin 150001

3 Key Laboratory of Spectral Imaging Technology,Xi’an Institute of Optics and Precision Mechanics,Chinese Academy of Science,Xi’an 710119

Abstract:In order to realize a high-precision and continuous working function of a star sensor,we propose a new optical system design.Considering the difficulty of the manufacturing process,the entire optical system uses a complicated Petzval structure.In this paper,the key design elements of the optical system applied for star sensors are presented and the most important performance parameters are given.The ground test results show that the system can maintain excellent detection performance on a near-surface atmospheric platform.This study provides an optical system design scheme for a high-precision and continuous operating star sensor,as well as the theoretical basis for future in-atmosphere and continuous star detection technology.

Key words:star sensor,optical system,design,Petzval structure

1 INTRODUCTION

The star sensor is a high-precision,attitude-sensitive measuring instrument,which is generally used in the navigation for satellites,spacecraft,and rockets.It takes a star as a reference point to provide accurate spatial orientation and has the advantages of high precision,strong anti-interference,and independent operation.With the rapid development of navigation technology,the attitude measurement accuracy of star sensors has continuously improved,and the application range has been gradually expanded.In addition to applications on space platforms,in recent years,some institutions have begun to apply the star sensor technology on near-ground platforms such as aircraft,critical space vehicles,and warships.After experiencing the first-generation star sensors featuring small field of view high-star and the second-generation star sensors featuring autonomous navigation,star sensor technology has two new development trends:high-precision and continuous operation.

In view of this new trend of star sensor technology development,this paper proposes an optical system design scheme for a high-precision and continuous operating star sensor,which is designed mainly for use on the near-surface platforms in the atmosphere,providing a high-precision and daytime operational function.This paper provides a feasible method for improving the measurement accuracy of the star sensor,and promotes the development of all-day star detection technology in the atmosphere.

2 DESIGN SPECIFICATIONS

The basic working principle of the star sensor is as follows:(1)the light emitted by the star is imaged on the detector surface through the optical system;(2) the image is digitized by a signal processing circuit;(3) the direction of the star sensor’s optical axis in inertial space is determined;(4) combined with the carrier star sensor mounting angle,it can be used to instantaneously measure the three-axis attitude vector.The main technical parameters of the star sensor include:field and aperture,star detection sensitivity,number of available stars,measurement accuracy,integration time,data update rate,volume and quality.These parameters are interrelated and restrict each other,which determines the performance of the star sensor.

2.1 Basic Optical Indicator Requirements

The optical system designed in this paper adopts a transmissive image quasi-telecentric optical system,which has no vignetting and no glue surface over the whole field of view.The basic parameters of the optical system are shown in Table 1.

Table 1 Requisite performances of absolute angle encoder

2.2 Image Quality Requirements

Image quality requirements mainly include shape and energy distribution of diffuse spots,color deviation and absolute distortion.

Shape and energy distribution of diffuse spots:on the best image surface,the shape of the diffuse spot on the on-axis field should be close to a circle.In the operating spectral range,for the wavelength range of ±0.05 μm from the center wavelength,the energy concentration of the diffuse spot formed in the 0.8 field of view on the best image surface should satisfy:15 μm＜diameter (80% energy)＜45 μm.

Color deviation:in the range of 0.8 field of view,the color deviation of the monochromatic light in the test wavelength range with respect to the center design wavelength is less than 3 μm,i.e.|y -y0|≤3 μm,where y0 is the center of mass of the central wavelength dispersion of the optical lens in a certain field of view.

Absolute distortion:the deviation of the centroid position and the ideal position of each field of view at the center wavelength is defined as absolute distortion.In the 0.8 field of view,the absolute distortion should be no more than 8 μm.

3 DESIGN OF OPTICAL SYSTEM FOR STAR SENSOR

3.1 Structure Selection

This optical system has a large relative aperture,large field of view,and extremely high image quality.Based on the investigation of domestic and foreign data and the accumulation of our own experience,we proposed the aspheric surface design and global surface design scheme.The main features of this small long-life star sensor optical system include long life,large field of view,large relative aperture,small size of diffuse spot,small distortion,strict color deviation and light weight for the entire lens.

Option 1:Aspherical design.The optical system design is shown in Figure 1,where the first and sixth surfaces are low-order aspheric surfaces,and the rest are spherical surfaces.With this design based upon the imaging index and structural dimensions,the structural weight of the aspherical surface is 96 g.

Option 2:Global design.From the aspherical design,two spherical lenses are used to replace the thick lens of the aspherical design.After structure selection and reasonable optimization,we designed the global optical system as shown in Figure 2.Based on the requirements of imaging indicators and structural dimensions,we calculated that the global structural weight was 86 g.

Figure 1 Aspheric optical system structure

Figure 2 Petzval objective optical system structure

The aspheric surface can perfectly correct the spherical aberration of a point on the axis,and has corrective effects on off-axis aberrations such as coma,astigmatism and distortion,which is advantageous for simplifying the spherical optical system.However,since the aspheric surface has a varying radius of curvature,it cannot be processed and detected using a template like a spherical lens.For aspherical lenses,the processing and detection difficulty is considerably improved,and the production cycle is also greatly improved.Considering the relatively large thickness of the aspherical lens and the large weight of the optical system,we chose the second option,that is,a complicated Petzval optical structure.As shown in Figure 2 (aberration optimization has been performed),the entire optical system consists of 6 lenses without a cemented surface.The first lens uses JGS1 quartz material to improve the ability to suppress space irradiation.The optical system has a total length of 63.5 mm.

3.2 Aberration Balance and Optimization Design

The complicated optical structure was selected to reduce high-level aberrations on-and off-axis to meet the system aberration requirements.The increase in the number of lenses is proportional to the increase of the variable number of system correction aberrations,hence the total aberration can be reduced,so that the primary aberration is corrected and the remaining high-order aberrations are inevitably small.The reduction of the advanced aberrations of the system is conducive to improving the imaging quality or optical characteristics of the system.After repeated aberration balance and optimization design iterations,a material with high refractive index was selected to reduce the off-axis aberrations,so that the aberration of the whole field of view is flat,and the dispersion of each field of view is uniform.

A high refractive index and low dispersion lanthanum glass was selected as a positive lens to correct for chromatic aberration of magnification to satisfy the central color deviation requirement of speckle quality.This system adopts a fully-separated lens structure and abandons the usage of a glued surfaces to prevent debonding and blackening in the space environment.In order to reduce the size and weight of the system,the entrance pupil was designed on the first side.Considering the effect of irradiation,fused quartz was used as the first lens.The front and rear lens groups of the general Petzval type objective lens structure are separated by positive and negative optical foci.For increasing the curvature radius of the positive lens while keeping the optical focus constant,a positive focal power lens was introduced in front of the positive focal power lens to form a“positive positive and negative positive and negative”deformation structure.

3.3 Optical System Transmittance Calculation

The transmission of an optical system depends on the reflection loss of the surface of lens and the absorption of the material.This system requires a spectral transmittance of not less than 80% in the operating spectrum.The optical system has 6 lenses,12 faces,and the single-sided reflectance design needed to be controlled within 0.5%.

As the outermost film is directly exposed to various environments,if the denseness is poor or there are a large amount of voids,the possibility of absorbing moisture or impurities is greatly increased,so the performance of the optical element is easily deteriorated.Therefore,SiO2 was selected as the outermost film material.

Two kinds of membrane system designs are proposed based on the difference in substrate materials.When the substrate is JGS1 material,a three-layer broadband anti-reflection film system is adopted,and the basic structure is G/H2ML/A.The anti-reflection film curve is shown in Figure 3.It can be seen from the figure that the residual reflectance of the substrate surface is below 0.5%.When the substrate comprises other optical glass,the four-layer antireflection film system G/L1MHL2/A is used.Taking the substrate as H-LAK11 as an example,the anti-reflection film curve is shown in Figure 4,and the residual reflectance of the substrate surface is also below 0.5%.

Figure 3 Anti-reflection film curve of JGS1 at the base

Figure 4 Anti-reflection film curve of H-LAK11 at the base

When calculating the transmittance of the system,considering the processing technology,the transmittance of single-sided membrane system was calculated at 99%.At the same time,the material center thicknesses and corresponding absorption coefficients for all optical lens are listed in Table 2.According to Equation (1),we can calculate the total transmission rate of the system as 0.837.

Table 2 Material,centre thickness and absorption coefficient of optical glass

where

τ

,

τ

,

α

indicate the optical system transmittance,the sum of the transmittance of the lens surface,the sum of absorption of lens material,respectively.

3.4 Diffuse Spots and Energy Distribution

Table 3 shows the range of diffuse diameters formed with a monochromatic light with a wavelength interval of ±0.05 μm under certain conditions (0.8 field of view,+20°C,1 standard atmosphere) .Figure 5 (a-e) is a 80% energy distribution map with a 0.8 field of view.The diameter distribution of diffuse spot is between 15 μm and 45 μm in the 0.8 field of view.

Table 3 Diameter of the diffuse (0.8 field of view,+20°C,1 standard atmospheric pressure)

Figure 5 is the distribution of the diffuse spot in the full field of view (80% energy,at 20°C,1 standard atmosphere,in the 0.47-0.75 μm spectral range,centered at 0.62 μm).Figure 6 is a full field of view 100% energy point map in the 0.47 μm to 0.75 μm spectral range.Table 4 shows the diameter of the diffuse spot(80% energy) corresponding to different fields of view.

Figure 5 Distribution of the diffuse spot in the full field of view

Figure 6 in full field of view of 100% energy point map 0.47-0.75 μm

Table 4 Diameter of the diffuse spot corresponding to different fields of view

In summary,the diffuse spots and energy distribution match the requirements.

Since the star sensor works in an outer space environment,the high-and low-temperature variation is great,and this will have some influence on the imaging of the optical system.For the lens barrel and spacer of titanium alloy (TC4),the temperature variation will affect the interval variation of the optical system.For the optical system,the thermal expansion of structural material mainly affects the spacing size of the optical lens.Under vacuum conditions,we simulated the variation of the diffuse spots diameter with 80% energy in the temperature range of—50°C to 70°C,as shown in Table 5.

Table 5 Effect of temperature and pressure changes on the energy distribution of the optical system

It can be seen from Table 5 that the temperature variation has little effect on the optical system,while the pressure variation has a great effect on the optical system.When debugging on the ground,the best image can be artificially adjusted by 0.02 mm,that is,the back intercept is reduced by 0.02 mm,so that the diameter of the diffuse spots with 80% energy concentrated under vacuum conditions can be guaranteed within the required range.

3.5 Color Deviation

With 0.62 μm as the design center wavelength,the monochromatic light diffuse spot energy centroid position with wavelengths of 0.47 μm,0.50 μm,0.52 μm,0.57 μm,0.67 μm,and 0.71 μm was observed in five normalized fields of view of—0.8,—0.5,0,0.5,and 0.8.Table 6 shows the centroid position of the energy of the dispersion spot corresponding to different monochromatic light in different fields of view.Table 7 shows the deviation of each color light wavelength from the image height (energy center of mass) for 0.62 μm wavelength in each field of view.The results show that the color deviation of monochromatic light in the test wavelength range with respect to the central design wavelength is less than 3 μm.

3.6 Absolute Distortion

In this design,the absolute distortion is much less than 8 μm in 0.8 field of view.The simulated values and actual test values of the absolute distortion of the field of view in the normalized field of view such as ±0.5,±0.7,and ±0.8 are given.Table 8 lists the values of the centroid position,ideal position and their deviation values for the 0.5,0.7 and 0.8 fields of view.

Table 6 Centroid position of the energy of the diffuse spots

Table 7 Deviation of each color light

Table 8 The values of the centroid position and ideal position and their deviation values

3.7 Vignetting

This optical design is designed with no vignetting in the full field of view.The entire system design ensures no vignetting in the 0.8 field of view.Figure 7 is the vignetting diagram.

Figure 7 Optical system vignetting

3.8 Tolerance Analysis of Optical Systems

Optical system tolerances generally include the inherent deviations of optical components and the errors during assembly.The tolerance requirement of this system is different from that of general optical systems.Firstly,our assembly method was to adjust the center offset of each lens.Here we can ensure a certain adjustable range.We set the adjustable range as 0.04 mm,that is,the lens can be allowed to deviate by ±0.02 mm.Moreover,each element must have an independent structure for centeringand edging before assembly.Similarly,we also set a certain tolerance for the eccentricity namely 2'.In addition,the inherent deviation of the optical components,such as the overall surface deviation and local error,were added.Based upon the existing process,the overall surface deviation can be guaranteed to be 3 apertures,where the local error is within 0.4 apertures,and the center thickness is ±0.03 mm.The deviations of refractive index and Abbe number of the material were ±0.0005 and±0.5% respectively.We used ZEMAX for tolerance analysis,get the RMS spot radius error after the preliminary set tolerance analysis.

After the preliminary tolerance analysis,it can be concluded that the thickness tolerances of the surfaces 10,4,8,6,and 9 and the eccentricity of the fifth surface are large based on the RMS spot radius list.We then optimized the corresponding tolerance values in turn,and after adding the tolerance,the RMS spot radius changed from 0.010394 mm to 0.011104 mm,so the maximum percentage change of error was 6.8%.We selected 100 samples for tolerance evaluation,and listed the size of diffuse spots with tolerance and the extreme value of the focal length,as shown in Table 9 and Table 10.Table 9 is the list of the diameter of diffuse spots within the required field of view after tolerance,and Table 10 is the extreme value of the focal length with all tolerance.From the data in Table 10,it can be calculated that the tolerance of focal length is within the range of 0.2 mm,which meets the ±0.4 mm required for the mission.Based on the previous discussion,the variation in the diameter of diffuse spots and focal length met the index requirements after the tolerance.

Table 9 Maximum diameter of the diffuse spots corresponding to different fields of view

Table 10 The extreme values of the focal length with all tolerances

3.9 Optical System Ghost Analysis

Ghost analysis is particularly important in this system because all surfaces of the optical system must have some residual reflected light hence the star sensor receives weak light.Generally,the ghost effect is more likely to be formed on the surface near the imaging surface that is relatively concave.According to the analysis,the relatively large impact is due to the residual light reflected from the front surface of the protective window of the CCD (the 13th surface in this design) into the lens surface that can be received by CCD,thus affecting the image quality.The surface reflection can be received by the CCD,which affects the image quality.We have listed the ghost analysis diagrams of the 7th,9th,and 12th sides in the optical system relative to the 13th side.See Figure 8.

Figure 8 Ghost analysis diagrams

From the figures,it can be seen that the influence of ghost generated on the 9th side is larger than that on the 7th and 12th sides.Therefore,it is necessary to increase the surface transmittance of the 9th side as much as possible(≥99.5%) to reduce the influence of the ghost effect,so as to improve the comprehensive imaging ability of the entire optical system.

4 CONCLUSIONS AND PERSPECTIVES

4.1 Detection Method

The assembly process of the optical system is performed in a super clean room with a thousand-level cleanliness.The system is installed and adjusted piece by piece with a high-precision centering instrument to achieve the concentricity requirements of the optical system.

Firstly insertion of the lens into the lens barrel and ensuring good contact with the mounting end face in the lens barrel is performed.The gap between the lens and the inner wall of the lens barrel is Φ26H8/f7,and the maximum and minimum unilateral radial gaps are 0.037 mm and 0.01 mm,respectively.In order to satisfy an angle of less than 2’ between the optical axis of the optical system and the normal of the mounting flange surface,strict shape and position tolerance requirements are required for the end face of the lens and the inner end face in contact with the lens barrel.

The following is a finite element mechanical test of the overall structure of the star sensor to determine that the structure has sufficient strength and stiffness to ensure that the optical system can withstand severe environmental loads.

The acceleration test conditions were:a (x)=a (y)=a (z)=8 g.The test duration was 2 min after reaching the maximum.Loading and unloading rate was less than 0.5g/s.

4.2 Test Results

At room temperature,the accuracy was tested using the test method described in Section 4.1.The test results are shown in Table 11.It has been verified that the technical indicators of the small long-life star sensor optical system accord with the requirements.

Table 11 Technical indicators achieved by experimental verification

4.3 Conclusions

The star sensor designed in this paper has the characteristics of high precision and continuous performance,and is mainly used on near-surface platforms in the atmosphere.According to the advantages of long life,large field of view,large relative aperture,good optical performance and light weight,two schemes of aspheric design and global design were proposed.Considering the difficulty of the process,the complicated Petzval optical structure (global design) was finally adopted.At the same time,high refractive index and low dispersion materials were selected to greatly reduce the optical aberration.In addition,silicon dioxide with good compactness was selected as the outermost film material,and a multi-layer broadband anti-reflection film system was adopted,so that the transmittance of the optical system is greater than 83%.In this optical system,the diameter of thespeckle is small,the energy is concentrated,the color deviation,and the absolute distortion are small.At the beginning of the design,the entire lens was guaranteed to have no vignetting in the 0.8 field of view.In order to reduce the influence of ghosting,the transmittance of the key lens surface was improved,thereby improving the comprehensive imaging capability of the entire optical system.According to the simulation results of ZEMAX,the tolerance and temperature variation characteristics of the optical system are within the required range.After precision machining and assembly,the optical performance of the star sensor was tested at room temperature.The ground test results show that the center wavelength of the optical system is 0.62 μm,the receiving spectral range is 0.47-0.75 μm,and the transmittance is greater or equal to 80%.The color deviation was less than or equal to 2.9 μm.Under normal temperature and pressure and in 0.8 field of view,the diameter of dispersion spot with 80% energy concentration is 16-34 μm,and the absolute distortion was no more than 1.5 μm.Its excellent optical properties remain within the application requirements in the atmospheric environments with large temperature variations.

This design provides a new design scheme for the high-precision,continuous operation star sensors in the future,which fills the gap in the domestic continuous operation star sensors used on the near-ground platforms in the atmosphere,and lays the material foundation for this star detection technology for the star sensor in the atmosphere.