# Influence of the Matrix Structure of the Modulator and Detector on the Optical Spectrum Analyzer Output Signal

## DOI:

https://doi.org/10.20535/RADAP.2018.72.78-85## Keywords:

digital optoelectronic spectrum analyzer, matrix light modulator, matrix detector, spatial spectrum of the image## Abstract

In this article, we investigate the physical and mathematical model of a coherent optical spectrum analyzer (COSA), which uses a matrix light modulator and a matrix detector as input and output devices. This model allows to define distortions in the output signal of the spectrum analyzer and the error in determining the signal spatial frequency. The study of this model showed that form of the signal at the COSA’s output depends on the pixels sizes of modulator and detector matrices, as well as on the aberrations of the Fourier lens entrance pupil diameter. The output signal is a convolution of an ideal input signal spectrum with a discrete spatial transmission spectrum of the modulator, which is followed by convolution with a discrete sensitivity of the matrix detector. This means that the spectrum of the signal under investigation is distorted by the spatial spectrum of the modulator and the matrix structure of the matrix detector. An important feature of the signal is its independence from the phase shift, which is caused by the displacement of the modulator center relative to the optical axis of the spectrum analyzer. The output signal of COSA consists of an infinite number of diffraction maximum, each of which has three maximum, the distance between which is proportional to the spatial frequency of the test signal. The position (frequency) of the maximum is determined by the pixel size, and their width by the size of the modulator. Obtain the formulas for determining the spatial frequency of the test signal, which differ substantially from the traditional formula and depend on the position of the central and lateral maximum in the diffraction maximum. The error in measuring the frequency depends on the size of the detector pixel, focal length of the Fourier lens, and the modulator matrix size. Developed the method for determining the error in measuring the spatial frequency of a harmonic signal. The error is defined as the difference between the true frequency corresponding to the position of the center of the diffraction maximum and the measured frequency corresponding to the position of the pixel center which has the maximum signal.## References

Kolobrodov V. G., Tymchyk G. S. (2014) *Prykladna dyfraktsiina optyka* [Applied Diffractive Optics]. Kyiv, NTUU KPI, 312 p.

Okan K.E. (2007) *Diffraction, Fourier Optics and Imaging*. Wiley & Sons, 428 p. DOI:10.1002/0470085002

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

Keysesent D. (1980) *Optical processing of information*. Mir Publ., Moscow, 350 p.

Kolobrodov V.H., Tymchyk H.S. and Kolobrodov M.S. (2015) *Koherentni optychni spektroanalizatory* [Coherent optical spectrum analyzer], Kyiv, Politekhnika Publ., 180,p.

Kolobrodov V.G., Tymchik G.S. and Nguyen Q.A. (2013) The problems of designing coherent spectrum analyzers. *Eleventh International Conference on Correlation Optics*. DOI: 10.1117/12.2049587

Kolobrodov V.G., Tymchik G.S. and Kolobrodov M.S. (2015) The diffraction limit of an optical spectrum analyzer. *Twelfth International Conference on Correlation Optics*. DOI: 10.1117/12.2228534

Harvey J.E. (2009) Analysis and design of wide-angle foveated optical systems based on transmissive liquid crystal spatial light modulators. *Optical Engineering*, Vol. 48, Iss. 4, pp. 043001. DOI: 10.1117/1.3122006

Kuz’min M.S. and Rogov S.A. (2015) Optical Fourier processor with a liquid-crystal information-input device. *Journal of Optical Technology*, Vol. 82, Iss. 3, pp. 147. DOI: 10.1364/jot.82.000147

Driggers R.G., Friedman M.H. and Nichols J. (2012) *Introduction to Infrared and Electro-Optical Systems*. Artech House, London, 534 p.

Vollmerhausen R.H., Reago D. and Driggers R.G. (2010) *Analysis and evaluation of sampled imaging systems*. SPIE, Washington, 288 p.

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, 0(72), pp. 78-85. doi: 10.20535/RADAP.2018.72.78-85.

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