Noise reduction method using a variance map of the phase differences in digital holographic microscopy

Abstract

The phase reconstruction process in digital holographic microscopy involves a trade‐off between the phase error and the high‐spatial‐frequency components. In this reconstruction process, if the narrow region of the sideband is windowed in the Fourier domain, the phase error from the DC component will be reduced, but the high‐spatial‐frequency components will be lost. However, if the wide region is windowed, the 3D profile will include the high‐spatial‐frequency components, but the phase error will increase. To solve this trade‐off, we propose the high‐variance pixel averaging method, which uses the variance map of the reconstructed depth profiles of the windowed sidebands of different sizes in the Fourier domain to classify the phase error and the high‐spatial‐frequency components. Our proposed method calculates the average of the high‐variance pixels because they include the noise from the DC component. In addition, for the nonaveraged pixels, the reconstructed phase data created by the spatial frequency components of the widest window are used to include the high‐spatial‐frequency components. We explain the mathematical algorithm of our proposed method and compare it with conventional methods to verify its advantages.

Noise Filtering Method of Digital Holographic Microscopy for Obtaining an Accurate Three-Dimensional Profile of Object Using a Windowed Sideband Array (WiSA)

“…We compare these images with depth profiles of experimental results using the mean square error (MSE), signal-to-noise ratio (SNR), and peak signal-to-noise ratio (PSNR) [26]. We create images with height information of each 3D profile as intensity information and compare the noise of each image by the numerical analysis such as MSE, SNR, and PSNR values [24].…”

“…Figure 1a shows the process of windowing sidebands in Fourier domain. ± f O in Figure 1a denotes R * Oe j(φ O −φ R ) and RO * e −j(φ O −φ R ) in Equation ( 2) for each sideband [13,15,16,24]. That is, it can be seen through Equation ( 2) that the phase difference information is contained in the sideband of Fourier domain.…”

“…Therefore, φ O -φ R is the phase differences of the recorded hologram. This term can be symbolized as ∆φ, and we can obtain the depth information of the object from ∆φ by using follows [8,10,13,16,24]:…”

“…In addition, h is the height information of the object, K is the wavenumber, and ∆n is the refractive index difference between the object and surrounding medium. As a result, by using Equations ( 3) and ( 4), we can obtain the height information of the object from the recorded hologram [8,10,13,16,24]. Figure 1a,b show the problem for the image processing of DHM.…”

“…However, since Joseph Goodman proposed digital holography (DH) in 1967 [25], these disadvantages have been resolved and studied by more researchers. This digital holography technology is being applied to many research fields such as 3D image visualization [3,4], object recognition [ [5,6]], and digital holographic microscopy (DHM) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Among the mentioned technologies, DHM is widely used in many applications such as microstructure analysis [16,17], microbial research [18][19][20][21], and diagnosis of diseases using cell analysis [22,23] due to capability for obtaining 3D information of micro-objects.…”