Method of Determination of RMS Exposure of Ex-tended Source Image by Microphotometry

Ігор Генріхович Чиж, Олександр Олексійович Голембовський


Background. Among the parameters and functions to assess the quality of images formed by optical systems RMS spot diagrams parameter is used. This option is usually defined by beam ray-tracing going through optical system. There is a fundamental ability to regenerate RMS by microphotometry of image of real point light sources. However, the RMS of the image is distorted due to finite size source. The problem is that the separation of RMS components values, which are caused by the parameters of the light source and the optical system aberrations.

Objective. The recovery of RMS aberration component based on the results of microphotometry of image of extended source of radiation generated with optical system to be tested.

Methods. The mathematical tools polar calculations were used, axial and centrifugal RMS from distribution function of illumination in the image of the extended light source, close to the spot. The calculations of mentioned RMS types are conducted by the radii formulas for moments of inertia that are known in theoretical mechanics. Analogue mass they contain is spatial density of luminous flux in the optical image source. In calculating of RMS the source length is included using Huygens- Steiner theorem.

Results. New mathematical observations for calculation of RMS including illumination distribution in the image of light sources are obtained. It was established that RMS of each type is Pythagorean sum of components, one of which is specified by the parameters of the source, and the other by the aberrations of the optical system. According to the results of the regenerated RMS from microphotometry of the image of source and the data on the source parameters aberrational component can be determined in each RMS type.

Conclusion. The study confirms the possibility of determining the aberration RMS of the optical system according to the results of microphotometry of image of extended light source. The method allows creating new photoelectrical hardware for measuring distances to objects, and to create new types of ophthalmic devices.


RMS image extended source; RMS operating spots; Microphotometry image light source


C. Kitelliu et al., Mechanicals. Moscow, USSR: Nauka, 1983, 255 p. (in Russian).

I. Chizh et al., Aberrometriya of Optical System of the Human Eye. Kyiv, Ukraine: NTUU KPI, 2013, 290 p. (in Ukrainian).

W. Lucosh, “Der Einflub der Aberrationen auf die optische Ubertragungsfunktion bei kleinen Orts-Frequenzen”, Optica Acta, vol. 10, no. 1, pp. 1–20, 1963.

I. Chizh, “Determination of the modulation transfer function of the optical system using Gaussian radii second points of the function of the scattering point”, Naukovi Visti NTUU KPI, no. 4, pp. 127–137, 2004 (in Ukrainian).

S. Marcos et al., “The depth-of-field of the human eye from objective and subjective measurements”, Vision Res., no. 3, pp. 78–85, 2010.

D. Atchinson et al., “Subjective depth-of-focus of the eye”, Optometry and Vision Sci., no. 7, pp. 511–520, 2014.

N. Sergienko et al., “The focus depth of focus pseudo phakic eyes”, Graefe’s Archive for Clinical and Experimental Ophthalmo­logy, no. 11, pp. 1623–1627, 2008 (in Russian).

GOST Style Citations

  1. Киттелью Ч., Найт У., Рудерман М. Механика. – М.: Наука, 1983. – 255 с.

  2. Аберометрія оптичної системи ока людини / І.Г. Чиж, Г.С. Тимчик, Т.О. Шиша, Н.Б. Афончина. – К.: НТУУ “КПІ”, 2013. – 290 с.

  3. Lukosz W. Der Einflub der Aberrationen auf die optische Ubertragungsfunktion bei kleinen Orts-Frequenzen // Optica Acta. – 1963. –  10, № 1. – P. 1–20.

  4. Чиж І.Г. Визначення модуляційної передавальної функції оптичної системи за допомогою радіусів других гаусових моментів від функції розсіювання точки // Наукові вісті НТУУ “КПІ”. – 2004. – № 4. – С. 127–137.

  5. Marcos S., Moreno E., Navarro R. The depth-of-field of the human eye from objective and subjective measurements // Vision Res. – 2010. – № 39. – P. 2039–2049.

  6. David A.A., Charman W N., Woods R. Subjective depth-of-focus of the eye // Optometry and Vision Sci. – 2014. – № 7. – P. 511–520.

  7. Сергиенко Н.М., Кондратенко Ю.Н., Тутченко Н.Н. Глубина фокуса в псевдофакических глазах // Graefe’s Archive for Clinical and Experimental Ophthalmology. – 2008. – № 11. – С. 1623–1627.



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