# Mathematical model of digital optoelectronic spectrum analyzer

## DOI:

https://doi.org/10.20535/RADAP.2016.67.71-76## Keywords:

optoelectronic spectrum analyzer, spatial light modulators, matrix detector## Abstract

**Background**. Digital optoelectronic spectrum analyzer (DOSA) used for spatial-frequency analysis of two-dimensional signals occupies a significant place among optical information processing systems. Diaphragms and the photographic plates with transmission corresponding to investigating signals were used as an input transparency until recently. Such static transparents severely limit the possibility of input signals into spectrum analyzer, which vary in time and space. The appearance of the liquid-crystal spatial light modulators (SLM) allows to change transmission of input transparency in time and space with computer. At the same time there are no researches related to usage of such modulators in DOSA.

**Objective**. There is a justification for features of application of the matrix spatial light modulator in the optical spectrum analyzer.

Methods. The method for determining the light amplitude in the spectral field of DOSA analysis was developed by analyzing of physical-mathematical model of SLM.

**Results**. It was found that the distribution of the amplitude of the light field in the spectral analysis plane is equal to the sum of the maximums. There are some features of the sum: positions of the maximums are determined by period of SLM matrix structure, and width of the maximums – by the modulator size; the diffraction efficiency of each maximum is determined by ratio of the transparent area of the pixel to pixel’s total area.

**Conclusions**. Number of monographs and articles is devoted to the physical principles of coherent (laser) spectrum analyzers operation. At the same time there is practically no scientific and technical literature devoted to the research of the DOSA with spatial light modulators. Analysis of SLM mathematical model shows that the minimum distortion in the measurement of the signal spectrum will be in the case when amplitude distribution in the plane of analysis is forming with zero-order maximum only. The formula, which allows us to calculate the limit period of the SLM matrix structure was obtained, which provides the minimum error of the signal spectrum measurement.

## References

**Перечень ссылок**

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**References**

Okan K.E. (2007) * Diffraction, fourier optics and imaging*, Wiley & Sons, 428 p. DOI: 10.1002/0470085002

Bogatyreva V.V. and Dmitriev A.L. (2009) *Opticheskie metody obrabotki informatsii* [Optical Methods of Information Processing], St. Petersburg, SPbGUITMO, 74 p.

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Curatu G. and Harvey J.E. (2009) Analysis and design of wide-angle foveated optical system based on transmissive liquid crystal spatial modulators. * Optical Engineering*, Vol. 48, No 4, pp. 043001-1 - 043001-10. DOI: 10.1117/1.3122006

Kolobrodov V.H. and Lykholit M.I. (2007) *Proektuvannia teploviziinykh i televiziinykh system sposterezhennia* [Design of Thermal Imaging and Television Observation Systems], Kyiv, NTUU KPI, 364 p.

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, 0(67), pp. 71-76. doi: 10.20535/RADAP.2016.67.71-76.

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