Nanoobjects microscopy
Filtration of the digital holograms by Chebyshev polynomials to improve the quality of the obtained phase maps
H.A. Petrovska1, Yu.M. Kotsiuba2, V.M. Fitio1
1 Department of Photonics, Lviv Polytechnic National University,
C. Bandera str. 12, Lviv-71013, Ukraine.
E-mail: halyna.a.petrovska@lpnu.ua, v.m.fitio@gmail.com
2 Dep. № 1 Theory of wave processes and optical systems of diagnostics, Karpenko Physico-Mechanical institute of the NAS of Ukraine, 5, Naukova str., Lviv, 79060, Ukraine.
E-mail: jurok3x@gmail.com

Simulation of the filtration of the synthesized phase field by Chebyshev orthogonal polynomials in the one-dimensional case has shown high efficiency [1]. The proposed filter showed high quality, better than filters in the frequency domain.
This result prompted us to improve the proposed earlier filtration algorithm to use it for real digital holograms that are recorded on matrix photodetectors. First, a set of digital holograms with speckle noise was obtained using computer simulation. Next, we performed the filtering of the obtained images by Chebyshev polynomials using three different approaches. We suggest three filtering approaches in our work: one-dimensional filtering across the matrix rows, which are approximately parallel to interference fringes; one-dimensional filtering across the matrix columns, which are perpendicular to the interference fringes; two-dimensional filtering across both directions. The first case requires the least number of Chebyshev polynomials, and the third case requires the greatest number. The processing time is also the smallest in the first case.
Experimental studies have confirmed the main results of computer modeling. The quality/processing ratio of the digital hologram is the smallest in the first case.

1.	Fitio V., Kotsiuba Y., Petrovska H. Filtration of digital focused image hologram in spatial domain with Chebyshev polynomials // Nanotechnology and nanomaterials (NANO-2019): international research and practice conference, 27–30 August 2019, Lviv, Ukraine : book of abstracts. – 2019. –P. 524.