2011 International Conference on Electronic & Mechanical Engineering and Information Technology

Design and Simulation of CMOS Star Sensor Lens with Large Relative Aperture and Wide Field

Xing Zhong, and Guang Jin Changchun Institute of Optics, Fine Mechanics and Physics

Chinese Academy of Sciences Changchun, Jilin Province, China

ciomper@163.com

Abstract—A 50mm focal length, F/1.25, Gaussian type optical system is designed in this paper, which has 20°field of view. Actual star image adding optical cross-talk effect of CMOS(Complementary Metal Oxide Semiconductor),detector is simulated by non-sequential ray tracing in ZEMAX® optical design and analysis software to evaluate its performance. The distortion relative to image spot centriod is introduced and calculated by simulated star images, which is less than 0.03% of lens in this paper. Thermal adaptability is discussed by opt-mechanic thermal analysis, which shows the RMS spot radius of marginal filed changes less than 0.7um under 10 °C temperature gradient, and changes less than ljim during homogeneous temperature changing from -40°C to +40°C. The results of analyses and simulations show the design of this lens can achieve the requirement of high precision CMOS star sensor well.

Keywords—star sensor lens; optical system; energy centroid; thermal analysis

II. OPTICAL DESIGN

A. Spectral Band Detector's spectral response is an importance reference to

decide the wavelength in optical design work for lens of photoelectric systems. As this CMOS star sensor, its STAR1000 [5] detector's spectral response is shown in Figure 1. Output current which represent the response of CMOS is max when the irradiation light wavelength is 610nm~620nm. Spectral response drop rapidly in short wave, but slowly in long wave. Considering with the difficulty in optical design, working spectral range [6] of lens is set 450nm~900nm. Another reason of spectral range contained long wave is that stars in sky are almost looking "red".

I. INTRODUCTION

The research and fabrication of star sensor is developing with the conception of self-determination these years, and star sensor's output changes from star position to attitude angle. Wide field, small star chart storage, low detecting star magnitude is the trend of star sensor. Because of wide field, the brighter star can match the demand of amount stars to keep attitude measurement precise. CCD (Charge-coupled Device) Star sensors are widely used nowadays, but application of CMOS has extremely accelerated the development of star sensor industry [ 1 ] ~ . Compared with CCD star sensor, CMOS star sensor have many advantages such as good adaptability to radiation environment, simple electronics and low power cost[4].

As a precise angle measuring equipment, star sensor always has strict requirement at optical system, and works under rigorous environment. So it is necessary to deeply analyze and simulate the performance of optical system during design procedure. A large relative aperture and wide field lens for CMOS star sensor is designed in this paper. This F/1.25 lens which has 50mm focal length and 20° field works in a very wide spectral range from 450nm to 900nm, with low distortion, and it is very stable in thermal variable environment at the same time.

Fig. 1 Spectral response of STAR1000

B. System Type [7]~[9]

Petzval and Sonnar type objectives are usually used in large aperture optical systems, but their fields of view are narrow. Double Gauss type objectives can match the demand of large aperture and wide field well, its relative aperture can be 1/2-1/7. Axial aberrations such as coma, distortion and axial color are auto adjusted by symmetric configuration of double Gauss, and lateral aberrations are double of half the configuration. Astigmatic can be corrected by proper position of stop. So we choose complex double Gauss type objectives to achieve large relative aperture wide field, and keep spot radius and distortion of optical system well.

978-l-61284-088-8/ll/$26.00 ©2011 IEEE 3194 12-14 August, 2011

C. Optical Material Secondary spectrum must be considered in design of

F/1.25 high quality optical system working in 0.45um spectral band width. Exist of secondary spectrum course badly degeneration of modulate transfer function of optical system. For lens composed by n elements, chromatic aberration and secondary spectrum is corrected when:

®! + 0 2 + ®3 + ... + Ow = O

o1 o0 o,

0

- + -

0

- + - - + .

O

0

. + ̂ = 0

0 , — Pi +—Pl +—P, +- + —Pn = 0

(1)

(2)

(3) where 0j is element's power, vz is Abbe number, and pt is relative partial dispersion of material. Optical materials that match equations (1)~(3) are special, and their coefficient of thermal expansion or index is large. When temperature change At, influences of these two coefficients on radius, thickness and index of glass elements are given by:

AR = R0 • a • At

Ad = d0 • a • At

An = n0 - P - At

(4)

(5)

(6) where R is radius, d is thickness, n is index, a is coefficient of thermal expansion, and ft is coefficient of thermal index. So the position of focal plane and focal length are changed very much by temperature of environment when special glasses are adopted. For enhance the thermal adaptability of CMOS star sensor, normal glasses are used and combined in our design to correct secondary spectrum o

D. Design Result The 2D layout of optical system designed using ZEMAX

software is shown in Figure 2. Protecting plate of STAR1000 and Silica window are all involved in optical design. Design result mainly composed by ZK and ZF Chinese catalog glass. The total length of lens is 101mm, and weight of all glass elements is less than 240g.

corrected well[11], such as axial color relative to wavelength, distortion and coma relative to field. Spot radius of image should be controlled well at the same time. RMS spot radius of CMOS star lens in this paper are shown in Table 1.

Tab. 1 RMS spot radius

Field RMS spot radius

(u rn )

0° 9.94

2.5° 9.32

5° 8.09

7.5° 8.53

10° 14.11

Because the noise of CMOS is much more than CCD, fewer pixels are chosen to calculate centroid of image spot. 3 X 3 pixels are usually used [10]. So CMOS sensor requires the lens have very good energy concentration. Geometric encircled energy is shown in Figure 3. Above 90% energy can be included in 25um radius circle, and that's enough for centroid calculating.

Fig.3 Geometric encircled energy Fig.4 Distortion

Optical system's distortion is described by relative distortion:

g ( ^ ^ - / ' - t a n £ x l 0 0 %

/ ' • tan0 (?)

where y \ is intersection point height of chief ray and gauss image plane,/ ' is focal length. For star sensor lens, distortion can be processed as a system error[12]. It does not influence the clearance of image, but cause deviation of energy centroid of image spot, which can be partly calibrated through star sensor's software by testing data. However, distortion should be corrected well in optical design for testing the lens easily by observing stars on the ground without any calibrating software. Distortion of CMOS star sensor lens in this paper is shown in Figure 4. The max distortion occurs at marginal field, and is less than 0.1%.

Fig.2 2D layout of optical system

Star sensor is used for satellite's attitude sensing by measuring the angles of stars, so, position's accuracy of image spot in focal plane is the first assignment of optical system[ 0]. Aberrations which cause deviation of image spot and asymmetrically spread of image spot energy should be

III. SIMULATION OF STAR IMAGE

Actual star image acquired by STAR1000 CMOS detector using lens in this paper is simulated by non­sequential ray tracing in ZEMAX® optical design and analysis software, as shown in Figure 5. Pixel size is 15umxl5um. 16% Cross-talk on STAR1000 datasheet is also considered. Star image simulation results are shown in Figure 6.

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Fig.5 Non-sequential Analysis

Fig.6 star image simulation

Fig.7 Spot energy centroid distortion curve

V. THERMAL ANALYSIS

IV. ENERGY CENTROID DISTORTION

Distortion given by optical design is relative to chief ray. But distortion testing and calibration of lens for CMOS image are calculated from image spot centriod. So distortion relative to spot energy centriod is indicated by simulated image in this paper. Distortion relative to centriod of incident ray of field 6 is defined by:

^ - / ' • t a n A , Q(0) -xl00% (8)

/••tan0 where y0 is centroid height of image spot calculated from simulated star image F(x,y) composed by m^n pixels. For ideal simulation,^ is defined by:

YLnx,y>y y» =

x=l y=\

x=l y=\

(9)

Distortion relative to centriod on y axis is shown in Figure 7, which is a little different from optical distortion relative to chief ray. The distortion relative to image spot centriod of CMOS star sensor in this paper is less 0.03%. The max error cause by star image position will be 11 " without any process during initial performance tests of star sensor, and it's hopeful to be deduced under 5 " through calibration by software when using in space.

Fig. 8 Temperature distribution condition with temperature gradients

Analysis of temperature gradients influence is done in PATRAN software. Temperature distribution condition is shown in Figure 8. The mechanics is composed by titanic metal. Temperature difference on lens is 10°C changing fore-and-aft. RMS spot radius changing is acquired by opt-mechanic interface. The result is shown in Table 2. RMS spot radius of marginal filed changes less than 0.7um under 10°C temperature gradient, so CMOS star sensor with lens in this paper can work normally when there is 10°C temperature gradient.

Tab.2 10°C Temperature gradients influence (urn) Field

Initial RMS spot radius Changed RMS spot radius

0°

9.943

9.958

2.5°

9.316

9.183

5°

8.094

7.678

7.5°

8.525

8.182

10°

14.106

13.415

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B. Influence of Homogeneous Temperature Change RMS spot radius relative to homogeneous temperature

changing on lens is shown in Figure 9. Change of RMS spot radius is less than lum during ± 40 °C homogeneous temperature change.

Fig. 9 RMS spot radius of each fields vs. temperature

VI. CONCLUSIONS

F/1.25 CMOS star sensor lens is designed in this paper. The main characteristic of the optical system is with very small distortion in wide fields and wide spectral band, and good energy concentration at the same time. Simulation ray trace and opt-mechanic thermal analysis are done in this paper, which show star spot performance and environment adaptability of CMOS star sensor with lens. The results of analyses and simulations show the design of this lens can achieve the requirement of high precision CMOS star sensor. And the work in this paper can offer references to people developing CMOS star sensors.

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