Single-pixel edge enhancement of object via convolutional filtering with localized vortex phase

TL;DR

A novel and effective approach for enhancing and detecting the edges of object via convolutional filtering with a localized vortex phase, eliminating the extra single-pixel measurements required by the phase-shifting method.

Abstract

Microscopy is an essential tool in imaging research, and the edge-enhanced microscope by using the vortex filter is of particular interest as an optical information processing that highlights amplitude and phase edges of object in all directions. The application of this technique is not limited to the visible range, but edge enhancement of object in invisible wavelength is also crucial for near-infrared fluorescence and electronic circuit inspection through silicon semiconductors. One disadvantage of near-infrared imaging is that digital cameras such as CCD and CMOS become much more expensive than cameras for the visible spectrum. As an cost-effective method to implement invisible edge enhancement, the Fourier single-pixel imaging has already been proposed without using a camera, but using a single-pixel detector. However, this method requires 3 or 4 times more single-pixel measurements due to the three-phase or four-phase shift to detect optical complex amplitude in Fourier domain. In response, we propose a method for single-pixel edge enhancement of object via convolutional filtering with a localized vortex phase, eliminating the extra single-pixel measurements required by the phase-shifting method. Our simulation results show that the correlation coefficient between the ideal edges of an object and the edge enhanced by our proposed method is 0.95, indicating that our method is effective way to detect the edges. This novel and effective approach for enhancing and detecting the edges of object can be valuable in various invisible imaging applications.

Figures (9)

• Figure 1: The $4f$ system with a vortex filter for all-directional edge enhancement.
• Figure 2: Single-pixel edge-enhanced microscope via convolutional filtering. In $m$ different patterns, a white dot denotes the scanning path of patterns, while a red line denotes the patterns that have completed the scanning. For each scanning of a pattern, the photodiode measures the corresponding optical power as voltage data in time and the edge-enhanced image can be obtained by reshaping the temporal voltage data to a two-dimensional format.
• Figure 3: (a) Setup of super-pixel method. (b) Super-pixel with a size of $4 \times 4$ pixels exhibiting a phase difference of $2\pi/n^2$ in the $x$-direction and $2\pi/n$ in the $y$-direction. Two pixels in green are turned on with 100% reflectance while the other pixels are turned off with 0% reflectance. (c) Aperture with radius of $R$ placed at $(-\rho, 4 \rho)$ on the Fourier plane to extract the first-order diffraction of DMD. (d) The resultant field $E_\text{out}$ (red arrow) on the target plane is proportional to the sum of the phases on the pixels that are turned on.
• Figure 4: (a) Complex amplitude generated by all possible combinations of pixels corresponding to the super-pixel with $n=4$. (b) The desired complex amplitude distribution with $16 \times 16$ pixels. (c) The hologram with $64 \times 64$ pixels generated by replacing super-pixel $4 \times 4$ to the $16 \times 16$ desired complex function.
• Figure 5: (a) Radial dependence of the amplitude functions, $\frac{1}{r^2}$, $\frac{1}{r}$, $\frac{1}{\sqrt{r}}$ and $e^{-r^2/w^2}$ with $w=35$ µ m. (b-e) Corresponding complex amplitude distributions of the localized vortex phase.