The Relationship of Point Spread Functions of Aberration and Diffraction Limited Lens of Matrix Imagers

Валентин Георгійович Колобродов, Богдан Юрійович Пінчук

Abstract


Background. Thermal imagers are widely used in many areas, but the priority is to use them for military purposes where the primary goal is focused on the identification and recognition of objects in difficult weather conditions. The quality of thermal imaging is estimated by the modulation transfer function (MTF), which is obtained by Fourier transform of the point spread function (PSF).

Objective. The aim of the paper is to get the ratio, which would have established a relationship between the PSF aberration and diffraction limited lens matrix imagers.

Methods. An approximation of the PSF in the form of a Gaussian function was proposed to consider as PSF limited lens aberration.

Results. Based on the analysis of functions of energy concentration, the relationship between the PSF for the abe­rration and diffraction limited lens was established. The formula, which summarizes all the formulas with cor­respondingly different conditionally selected levels, which determine the radius of the circle scattering PSF aberration of an optical system (AOS) was obtained.

Conclusions. Analysis of the resulting relationship for PSF aberration and diffraction-limited lens showed that pro­duced by PSF luminance highs differ in 2 times, on condition that the radius of the circle scattering AOS is minimum. The formula for calculating the minimum radius of the circle of confusion, in which AOS is considered diff­raction limited, is obtained.


Keywords


Thermal imager; Modulation transfer function; Point spread function; The radius of the circle scattering of lens

References


V.G. Kolobrodov et al., “The problems of designing coherent spectrum analyzers”, Proc. SPIE, vol. 9066, pp. 90660Z-1–90660N-7, 2013.

V.G. Kolobrodov et al., “The diffraction limit of an optical spectrum analyzer”, Proc. SPIE, vol. 9809, pp. 98090F-1–98090F-7, 2015.

V.G. Kolobrodov and М.І. Lykholyt, Design of Thermal Imaging and Television Observation Systems. Kyiv, Ukraine: NTUU KPI, 2007 (in Ukrainian).

V.G. Kolobrodov and G.S. Tymchyk, The Diffraction Theory of Optical Systems. Kyiv, Ukraine: NTUU KPI, 2011 (in Ukrainian).

M.M. Miroshnikov, Theoretical Basis of Optoelectronic Devices, 2nd ed. Leningrad, Mashinostroenie, 1983 (in Russian).

V.V. Tarasov and Y.G. Yakushenkov, Infrared Systems of Watching Type. Moscow, Russia: Logos, 2004 (in Russian).

Y.G. Yakushenkov, Theory and Calculation of Optoelectronic Devices, 5th ed. Moscow, Russia: Logos, 2004 (in Russian).

R.H. Vollmerhausen et al., Analysis and Evaluation of Sampled Imaging Systems. Washington: SPIE Press, 2010. doi:10.1117/3.853462

E. Grey and G.B. Mathews, Bessel Functions and Their Application to Physics and Mechanics. Moscow, USSR: Izdatel'stvo Inostrannoj Literatury, 1953 (in Russian).

V.G. Kolobrodov et al., “The point scattering function of the observation television system with matrix radiation detector”, Naukovi Visti NTUU KPI, no. 4, pp. 103–108, 2003 (in Ukrainian).

A.P. Prudnikov et al., Integrals and Series. Special Functions, 2nd ed. Moscow, Russia: Fizmatlit, 2003 (in Russian).

A.P. Prudnikov et al., Integrals and Series. Elementary Functions, 2nd ed. Moscow, Russia: Fizmatlit, 2002 (in Russian).


GOST Style Citations


  1. Kolobrodov V.G., Tymchyk G.S., Nguen Q.A. The problems of designing coherent spectrum analyzers // Proc. SPIE. – 2013. – 9066. – P. 90660Z-1–90660Z-7.
     
  2. Kolobrodov V.G., Tymchyk G.S., Kolobrodov M.S. The diffraction limit of an optical spectrum analyzer // Proc. SPIE. – 2015. – 9809. – P. 98090F-1–98090F-7.
     
  3. Колобродов В.Г., Лихоліт М.І. Проектування тепловізійних і телевізійних систем спостереження. – К.: НТУУ “КПІ”, 2007. – 364 с.
     
  4. Колобродов В.Г., Тимчик Г.С. Дифракційна теорія оптичних систем. – К.: НТУУ “КПІ”, 2011. − 148 с.
     
  5. Мирошников М.М. Теоретические основы оптико-электронных приборов. – 2-е изд., перераб. и доп. – Л.: Машиностроение, Ленинград. отд-ние, 1983. – 696 с.
     
  6. Тарасов В.В., Якушенков Ю.Г. Инфракрасные системы “смотрящего типа”. – М.: Логос, 2004. – 444 с.
     
  7. Якушенков Ю.Г. Теория и расчет оптико-электронных приборов. – 5-е изд., перераб. и доп. – М.: Логос, 2004. – 472 с.
     
  8. Vollmerhausen R.H., Reago D., Driggers R.G. Analysis and evaluation of sampled imaging systems. – Washington: SPIE Press, 2010. – 304 p. doi:10.1117/3.853462
     
  9. Грей Э., Мэтьюз Г.Б. Функции Бесселя и их приложения к физике и механике. – М.: Изд-во иностр. лит-ры, 1953. – 371 с.
     
  10. Колобродов В.Г., Протасов В.Г., Піронер Я.М. Функція розсіювання точки телевізійної системи спостереження з матричним приймачем випромінювання // Наукові вісті НТУУ “КПІ”. – 2003. – № 4. – С. 103–108.
     
  11. Прудников А.П., Брычков Ю.А., Маричев О.Ю. Интегралы и ряды. Специальные функции. – 2-е изд., исправ. – М.: Физматлит, 2003. – 664 с.
     
  12. Прудников А.П., Брычков Ю.А., Маричев О.Ю. Интегралы и ряды. Элементарные функции. – 2-е изд., исправ. – М.: Физматлит, 2002. – 632 с.




DOI: https://doi.org/10.20535/1810-0546.2016.5.72034

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