Possibility to break through limitation of measurement range in dual-wavelength digital holography*

Abstract

By using the beat frequency technique, the dual-wavelength digital holography (DWDH) can greatly increase the measurement range of the system. However, the beat frequency technique has a limitation in measurement range. The measurement range is not larger than a synthetic wavelength. Here, to break through this limitation, we propose a novel DWDH method based on the constrained underdetermined equations, which consists of three parts: (i) prove that the constrained underdetermined equation has a unique integer solution, (ii) design an algorithm to search for the unique integer solution, (iii) introduce a third wavelength into the DWDH system, and design a corresponding algorithm to enhance the anti-noise performance of DWDH. As far as we know, it is the first time that we have discovered that the problem of DWDH can belong in a problem of contained underdetermined equations, and it is also the first time that we have given the mathematical proof for breaking through the limitation of the measurement range. A series of results is shown to test the theory and the corresponding algorithms. More importantly, since the principle of proposed DWDH is based on basic mathematical principles, it can be further extended to various fields, such as dual-wavelength microwave imaging and dual-wavelength coherent diffraction imaging.

Complex-amplitude Fourier single-pixel imaging via coherent structured illumination

“…Developing an efficient approach to recover the full complex-amplitude of an optical field has been one of the most attractive challenges in modern imaging science. Starting with early Zernike's phase contrast microscopy, [1] various complex-amplitude imaging techniques have been proposed, such as differential interference contrast microscopy, [2] Shack-Hartmann sensing, [3] coherent diffraction imaging, [4,5] digital holography, [6,7] Fourier ptychographic microscopy, [8] lensless ghost imaging, [9][10][11] and phase imaging techniques based on transport-of-intensity equation. [12] Single-pixel imaging (SPI) has attracted intensive interest as an innovative computational imaging technique in recent years.…”

Simultaneous dual-wavelength digital holographic microscopy as a tool for the analysis of keratoacanthoma skin samples

“…The DHM with dual-wavelength optical phase unwrapping (OPU) method is used to recover the optical phase images of a wide variety of objects [16][17][18][19]. Two, three [20], or more wavelengths can be used to increase the measurement range, which implies the generation of a synthetic wavelength (Λ) [21]. This synthetic wavelength is larger than the original wavelengths that generate it, and its value is calculated to be similar to the height variations of the object under study, a variable recorded in the hologram, e.g.…”