Systematic Error of the Optical Spectrum Analyzer

Валентин Георгійович Колобродов, Григорій Семенович Тимчик, Микита Сергійович Колобродов

Abstract


Background. Coherent optical spectrum analyzers are widely used in information processing systems. The principle of operation of spectrum analyzers is based on the scalar theory of Fresnel diffraction, which approximately describes the propagation of light in the paraxial range. This article examines the systematic error of the optical spectrum analyzer, which is caused by the Fresnel approximation.

Objective. The aim is the investigation of the optical spectrum analyzer systematic error, which is caused by the  Fresnel approximation, to determine the allowable errors of measurement of the spatial frequency of the signal spectrum.

Methods. On the basis of physical and mathematical model of coherent spectrum analyzer systematic error in determining the spatial frequency is investigated, which arises as a result of the transition from the propagation of light in free space to the Fresnel diffraction.

Results. An equation for calculating the absolute and relative measurement errors depending on the angle of diffraction of light is obtained, which allowed us to determine the limits of the spectral range for a given relative error of measurement of the spatial frequency. It is found that the Fresnel approximation within the diffraction angle from 0° to 10 ° provides a relative error less than 1,5 %. At the same time at a diffraction angle of 20°, it is 6,4 %.

Conclusions. There are fundamental limits to investigation of the application limits of the scalar theory of Fresnel  diffraction, which determine the spatial range, where is the Fresnel equation. At the same time, there is no investigation of the optical spectrum analyzer systematic error, which is caused by the Fresnel approximation. An equation for the absolute systematic error of measurement of the spatial frequency, depending from elements parameters of the spectrum analyzer is obtained. This equation can be used to optimize the parameters of the spectrum analyzer, as well as to compensate for systematic error by the computer processing of the output signal of the spectrum analyzer.


Keywords


Optical spectrum analyzer; Fresnel diffraction; Spatial frequency; Frequency measurement error

References


Applications of Optical Fourier Transforms, H. Stark, Ed. Moscow, USSR: Radio i svjaz', 1988, 536 p. (in Russian).

V.G. Kolobrodov and G.S. Tymchyk, Design of Diffractive Elements and System Optics.Kyiv,Ukraine: NTUU KPI, 2012, 200 p. (in Ukrainian).

B.E.A. Saleh and C.T. Malvin, Fundamentals of Photonics.New York: Wiley, 1991, 948 p.

V.G. Kolobrodov and G.S. Tymchyk. Applied Diffractive Optics. Kyiv, Ukraine: NTUU KPI, 2014, 312 p. (in Ukrainian).

L. Zhang et al., “Design of high resolution Fourier transform lens”, Proc. SPIE, vol. 6722, pp. 672211-1–672211-6, 2007.

V.G. Kolobrodov et al., “The problems of designing coherent spectrum analyzers”, Naukovi Visti NTUU KPI, no. 5, pp. 102–108, 2012 (in Ukrainian).

V.G. Kolobrodov et al., “Limiting characteristics of the optical spectrum analyzer”, Naukovi Visti NTUU KPI, no. 5, pp. 119–123, 2014 (in Ukrainian).


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DOI: https://doi.org/10.20535/1810-0546.2015.5.52607

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