Nanoobjects microscopy

Filtration of the digital focused image hologram in spatial domain with Chebyshev polynomials
V.M. Fitio1, Y.M. Kotsiuba2, H.A. Petrovska1
1Photonics Department, Lviv Polytechnic National University. S.Bandera str., 12, Lviv-79013, Ukraine.
E-mail: halyna.a.petrovska@lpnu.ua
2Karpenko Physico-Mechanical institute of the NAS of Ukraine,
Dep. № 5 Optical-digital diagnostic systems.

In recent years, digital holographic interferometry is rapidly developing due to the matrix CCD photosensors with high resolution and speed. Digital holographic interferometry is widely used to study not only macro-objects, but also micro-objects and different phenomena [1]: the determination of surface roughness, the study of microdeformations, the quality of details in MEMS, the study of periodic microstructures, microscopy of living objects, etc. The main feature of digital interferometry is that it has two stages: the first stage is optical, and the second is digital. The sensitivity of digital holographic microscopy can be limited by both the parameters of a digital camera and the noise arising in the optical scheme [2].
The light reflected from the object is mainly diffused, that leads to the appearance of speckle modulation of a hologram, which is the source of noise in reconstructed phase maps. In work [3] an approach based on the filtering in the frequency domain was proposed, which has some limitation for complicated phase maps. In this work for partial elimination of speckle noise, and improvement the quality of phase map, a new method of filtration in spatial domain with Chebyshev polynomials. The following polynomials are orthogonal on the interval [-1, 1] with certain waging coefficient. The representation of the intensity distribution along the row (column) of matrix photodetector as a linear combination of low-order Chebyshev polynomials allows partial elimination of the speckle noise.
In our work, we first carried out a digital simulation of the proposed algorithm. After determining the optimal number of Chebyshev polynomials, experimental studies were carried out that confirmed the improvement of the quality of the retrieved phase map due to digital filtering with proposed method.

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