- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Advances in Optical Technologies

Volume 2012 (2012), Article ID 485212, 4 pages

http://dx.doi.org/10.1155/2012/485212

## Study of Factors Making Space-Contaminated Optical System Unusable

^{1}Department of Physics, Harbin Institute of Technology, Harbin 150001, China^{2}School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

Received 4 April 2012; Revised 8 July 2012; Accepted 5 August 2012

Academic Editor: Zoran Ikonic

Copyright © 2012 Dakun Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Molecular and particulate contamination of space optical surfaces can be extremely detrimental to optical system performance. In order to determine whether optical system is unusable, we must do a lot of tests. For reducing experimental effort, computational criterion for unusable space optical system is put forward, which is based on experimentation and calculation by 2D-FDTD (finite-difference time domain). And then factors making optical system unusable are studied when distribution of light intensity is consistent with the criterion. Results show that small particulate is more detrimental to optical system than big one for particle with high permittivity is. The distribution of particles making optical system unusable is also obtained.

#### 1. Introduction

There are two types of contamination that affect optical performance: molecular and particulate contamination. Particulate contamination can occur through two phenomenons: obscuration and scattering effects. Particulate obscuration occurs when surface particles prevent light from reaching the underlying surface [1]. For particles with high permittivity, particulate obscuration plays a main role. Here, particulate with high permittivity is research subject.

Molecular and particulate contamination of spacecraft optical surfaces can be extremely detrimental to optical system performance [2]. Surface-deposited particles induce not only decreasing transmittance of optical system, but also reducing the image quality of optical system [3]. For system of space optical communication, contamination of optical surface can change the light intensity distribution [4].

As particles on optical surface accumulate, the space optical system will be unusable at last. Under what conditions the space optical system is unusable is concerned. As we know, particle size, the space between particles and absorbency of particles can influence quality of optical system. Then we should do a lot of experiments to ascertain whether optical system is unusable. In order to save money and time, a computational criterion for unusable space optical system is useful. In this paper, the criterion is put up. And then, for particle with high permittivity, factors making optical system unusable are studied.

#### 2. The Criterion for Unusable Optical System

Kahnert [5] has analyzed some of the most widely used numerical techniques in detail. In these models, FDTD can resolve scattering by inhomogeneous, anisotropic, and arbitrarily shaped charged or uncharged particles [6], so that it has been applied to such diverse applications as antenna scattering [7], analysis of microstrip circuits [8], absorption in tissue [9], optical absorption by biology cellula [10–13] or scattering by atmospheric ice crystals [14], irregular aggregates [15], multifaceted concave and convex particles [16], spheres with nonspherical inclusions [17], hexagonal columns with air bubble and soot inclusions [18] or clusters of particles with or without inclusions [19], consistent and rigorous analysis of infinite graphene layers is developed [20], electrically thin dispersive layers [21], calculation of reflection coefficient for the plane wave incident on planar periodic structures [22], light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium [23], an arbitrary beam’s interaction with an arbitrary dielectric surface [24], to name but a few examples. So FDTD is chosen. Because this calculation is only used to reduce experimental effort, rather than for exact simulation, 2D-FDTD is appropriate. And 2D-FDTD can also decrease calculation workload.

According to resolution test, when the diameter () of particulates is 0.3 mm, the maximal space () between particles, resulting in optical system being unusable, reaches 0.4 mm. In this case, far-field light intensity distribution calculated by 2D-FDTD is shown in Figure 1, and the relevant near-field distribution of light intensity is constant. Furthermore, light intensity distributions are also calculated when space between particles is less than 0.4 mm and diameter of particulates is more than 0.3 mm. Results show that both far-field light intensity distributionand near-field distribution are in accord with that of mm and mm [25]. Then a criterion for unusable optical system is put forward. That is to say, optical system can be thought unusable once near-field distribution of light intensity is constant and far-field light intensity distribution is like Figure 1. In [25], the resolution power is obtained by software HYRes 3.1, which is written by Olympus Corporation.

#### 3. Factors Making Optical System Unusable

As FDTD equations display, and are factors. and are different for different contaminants. That is to say, the kind of contaminant is a factor.

For the kind of contaminant (e.g., ), both the size of particulates and the space between particles are factors. Here, when distribution of light intensity is consistent with the criterion, the relationship between the maximal particle space and radius of particles is research emphasis.

##### 3.1. Relationship between Radius of Particles and the Maximal Particle Space

Here, relevant maximal space between particles () is obtained, firstly, for unusable optical system, when radius of particulates varies from 0.0325 mm to 1.25 mm (error is less than 1 *μ*m). See Figure 2.

From Figure 2, the relationship between radius of particles and maximal space between particles is linear on the whole, although there are some exceptions. That is to say, as radius of particulates increases, maximal space between particles increases linearly. This is reasonable because the diameter of the Airy disk varies inversely with the particle’s radius, the smaller the particles are, the larger the Airy disk is. Then the change of light intensity overlap is less susceptible to the particle size. in Figure 2 has smaller change with . As the particle size becomes bigger, diffraction image of one particle becomes sharper. Then changes with rapidly.

From the linear relationship between and , it may be deduced that total coverage of contaminant, which causes the optical system to be unusable, is equal for all size particles. Therefore, ratio of opaque part to all is calculated when radius of particles is different.

##### 3.2. Relationships between and

In order to study how total coverage of contaminant influences optical imaging system, is calculated when radius of particles, , is different. See Figure 3.

From Figure 3, total coverage of contaminant is not constant, which means total coverage of contaminant is not so important to imaging. It can also be seen from Figure 3 that the less radius of particles is, the less the quantity of contaminants which cause optical system to be unusable is. After reaches a certain size, moves up but slowly with the increasing of . So a smaller quantity of smaller than larger particulates on optical surface can induce optical system to become unusable. In a word, small particulates are more detrimental to optical system than large particulates.

So the small particle’s contamination prevention should be the most important of particle’s contamination prevention.

##### 3.3. Relationship between and –

Because of particle’s extinction, – may be an important parameter for transmissivity of optical system. And then, – is calculated correspondingly, when distribution of light intensity is consistent with the criterion. Results are plotted in Figure 4.

Result of Figure 4 is consistent with that of 3.1. Furthermore, there is an interesting fact in Figure 4, that is, – is always less than 0.36 mm. This means that according to the criterion put up in this paper, it is possible to obtain an exact value of resolution power from HYRes 3.1 when the space between particles is more than 0.36 mm, although resolution power of optical system will decrease somewhat. However, it is not quite clear why this value is 0.36 mm.

#### 4. Conclusions

In this paper, a criterion is put up based on test and calculation and it is used to determine whether optical system is usable or not in calculation. Then factors which may induce optical system unusable are studied. For particle with , the following results can be deduced when optical system is unusable: (1) maximum space between particles is linear with radius of particles approximately, (2) the smaller the radius of particles is, the smaller is the minimal coverage of particle, (3) small particles are more detrimental to optical system than large particles are, and (4) – is always less than 0.36 mm.

In conclusion, when distribution of light intensity is consistent with the criterion, the smaller the size of particulates is, the smaller the maximum space between particles is. But this is not to say that optical system will be unusable so long as the coverage of particulates reaches a value, whether the particles on optical surface are large or small. In fact, the lesser radius of particle is, the less minimal coverage of particles is, when optical system becomes unusable. That is, small particulates are more detrimental to optical system than large particulates. From the above study, if – is more than 0.36 mm, resolution power can be read out by HYRes 3.1.

The results are benefit to study relevant problem of similar structure, such as periodic arrays of left-handed metamaterials [26], monolayer and bilayer graphene deposited on a SiO_{2}/Si substrate [27], and multiwall carbon nanotubes [28]. And they may be of guidance for designs of some components, for example, design of graphene magnetic field sensors [29].

The paper presents that if near-field light intensity from FDTD is equal to the fixed value, optical system is hardly usable. However, the criterion is possibly not the best.

#### References

- K. D. Houston, “Comparative mirror cleaning study: a study on removing particulate contamination,” in
*Optical Systems Degradation, Contamination, and Stray Light: Effects, Measurements, and Control II*, vol. 6291 of*Proceedings of SPIE*, p. 629107, August 2006. View at Publisher · View at Google Scholar · View at Scopus - M. A. Folkman, L. A. Darnton, S. G. Silott, and M. E. Frink, “Optical scatter and contamination effects facility,” in
*Optical System Contamination: Effects, Measurement, Control II*, vol. 1329 of*Proceedings of SPIE*, pp. 221–232, July 1990. View at Scopus - D. Wu, Y. Zhou, and S. Guo, “Grain effect on imaging of spatial optical system,” in
*Fundamental Problems of Optoelectronics and Microelectronics III*, vol. 6595 of*Proceedings of SPIE*, p. 659529, September 2006. View at Publisher · View at Google Scholar · View at Scopus - D. Wu and Y. Zhou, “Relationship between antenna contamination and laser wavelength in optical communication,”
*Chinese Journal of Lasers*, vol. 36, no. 3, pp. 564–568, 2009. View at Publisher · View at Google Scholar · View at Scopus - F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,”
*Journal of Quantitative Spectroscopy and Radiative Transfer*, vol. 79-80, pp. 775–824, 2003. View at Publisher · View at Google Scholar · View at Scopus - W. Sun,
*Light scattering by nonspherical particles: numerical simulation and applications [Ph.D. dissertation]*, 2000. - W. V. Andrew, C. A. Balanis, P. A. Tirkas, J. Peng, and C. R. Birtcher, “Finite-difference time-domain analysis of HF antennas on helicopter airframes,”
*IEEE Transactions on Electromagnetic Compatibility*, vol. 39, no. 2, pp. 100–113, 1997. View at Google Scholar · View at Scopus - D. M. Sheen, S. M. Ali, M. D. Abouzahra, and J. A. Kong, “Application of the three-dimensional finite-difference time-domain method to the analysis of planar microstrip circuits,”
*IEEE Transactions on Microwave Theory and Techniques*, vol. 38, no. 7, pp. 849–857, 1990. View at Publisher · View at Google Scholar · View at Scopus - D. M. Sullivan, D. T. Borup, and O. P. Gandhi, “Use of the finite-difference time-domain method in calculating EM Absorption in human tissues,”
*IEEE Transactions on Biomedical Engineering*, vol. 34, no. 2, pp. 148–157, 1987. View at Google Scholar · View at Scopus - A. Dunn and R. Richards-Kortum, “Three-dimensional computation of light scatteing from cells,”
*IEEE Journal on Selected Topics in Quantum Electronics*, vol. 2, no. 4, pp. 898–905, 1996. View at Google Scholar · View at Scopus - A. Dunn, C. Smithpeter, A. J. Welch, and R. Richards-Kortum, “Finite-difference time-domain simulation of light scattering from single cells,”
*Journal of Biomedical Optics*, vol. 2, no. 3, pp. 262–266, 1997. View at Google Scholar · View at Scopus - R. Drezek, A. Dunn, and R. Richards-Kortum, “Light scattering from cells: finite-difference time-domain simulations and goniometric measurements,”
*Applied Optics*, vol. 38, no. 16, pp. 3651–3661, 1999. View at Google Scholar · View at Scopus - R. Drezek, A. Dunn, and R. Richards-Kortum, “A pulsed finite-difference time-domain (FDTD) method for calculating light scattering from biological cells over broad wavelength ranges,”
*Optics Express*, vol. 6, no. 7, pp. 147–157, 2000. View at Google Scholar · View at Scopus - P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,”
*Journal of the Optical Society of America A*, vol. 13, no. 10, pp. 2072–2085, 1996. View at Google Scholar · View at Scopus - G. Videen, W. Sun, and Q. Fu, “Light scattering from irregular tetrahedral aggregates,”
*Optics Communications*, vol. 156, no. 1–3, pp. 5–9, 1998. View at Google Scholar · View at Scopus - P. Yang, K. N. Liou, M. I. Mishchenko, and B. C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,”
*Applied Optics*, vol. 39, no. 21, pp. 3727–3737, 2000. View at Google Scholar · View at Scopus - M. I. Mishchenko, J. W. Hovenier, and L. D. Travis,
*Light Scattering by Nonspherical Particles: Theory, Measurements and Applications*, Academic, San Diego, Calif, USA, 2000. - P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,”
*Journal of the Optical Society of America A*, vol. 12, no. 1, pp. 162–176, 1995. View at Google Scholar · View at Scopus - W. Sun, Q. Fu, and Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,”
*Applied Optics*, vol. 38, no. 15, pp. 3141–3151, 1999. View at Google Scholar · View at Scopus - G. D. Bouzianas, N. V. Kantartzis, and T. D. Tsiboukis, “Subcell dispersive finite-difference time-domain schemes for infinite graphene-based structures,”
*IET Microwaves, Antennas & Propagation*, vol. 6, no. 4, pp. 377–386, 2012. View at Google Scholar - M. K. Kärkkäinen, “Subcell FDTD modeling of electrically thin dispersive layers,”
*IEEE Transactions on Microwave Theory and Techniques*, vol. 51, no. 6, pp. 1774–1780, 2003. View at Publisher · View at Google Scholar · View at Scopus - A. Aminian and Y. Rahmat-Samii, “Spectral FDTD: a novel technique for the analysis of oblique incident plane wave on periodic structures,”
*IEEE Transactions on Antennas and Propagation*, vol. 54, no. 6, pp. 1818–1825, 2006. View at Publisher · View at Google Scholar · View at Scopus - W. Sun, N. G. Loeb, and Q. Fu, “Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium,”
*Applied Optics*, vol. 41, no. 27, pp. 5728–5743, 2002. View at Google Scholar · View at Scopus - W. Sun, H. Pan, and G. Videen, “General finite-difference time-domain solution of an arbitrary electromagnetic source interaction with an arbitrary dielectric surface,”
*Applied Optics*, vol. 48, no. 31, pp. 6015–6025, 2009. View at Publisher · View at Google Scholar · View at Scopus - W. Dakun and Z. Yanping, “Performance test and analysis for imaging system of contaminated optical surface,”
*Acta Optica Sinica*, vol. 30, no. 2, pp. 411–415, 2010. View at Publisher · View at Google Scholar · View at Scopus - B. Bandlow, R. Schuhmann, G. Lubkowski, and T. Weiland, “Analysis of single-cell modeling of periodic metamaterial structures,”
*IEEE Transactions on Magnetics*, vol. 44, no. 6, pp. 1662–1665, 2008. View at Publisher · View at Google Scholar · View at Scopus - D. S. L. Abergel, A. Russell, and V. I. Fal'Ko, “Visibility of graphene flakes on a dielectric substrate,”
*Applied Physics Letters*, vol. 91, no. 6, Article ID 063125, 2007. View at Publisher · View at Google Scholar · View at Scopus - A. Maffucci, G. Miano, F. Villone, and W. Zamboni, “Analysis of multiwall carbon nanotubes using a three-dimensional integral formulation and a fluid model,”
*IEEE Transactions on Magnetics*, vol. 44, no. 6, pp. 1614–1617, 2008. View at Publisher · View at Google Scholar · View at Scopus - S. Pisana, P. M. Braganca, E. E. Marinero, and B. A. Gurney, “Graphene magnetic field sensors,”
*IEEE Transactions on Magnetics*, vol. 46, no. 6, pp. 1910–1913, 2010. View at Publisher · View at Google Scholar · View at Scopus