Objective Compared to traditional holography that relies on silver salt films, digital holography can reconstruct sample wavefront from holograms recorded by digital cameras via Fresnel transform as modern image processing. Therefore, digital holography is more convenient, fast and been widely studied and used in biological tissue imaging, particle tracking, encryption and measurements. Although refocusing is required, samples in digital holography can be focused at any depth for observation, whereas ordinary digital holography cannot provide sample tomographic structure. Optical diffraction tomography via angular scanning has been proposed as a method for obtaining tomographic imaging by combining computed tomography and holography; however, the optical system is complex and the spatial resolution is considerably limited by the accuracy and the range of the scanning mechanism. Multi-wavelength digital holography similar to optical coherence tomography has also been designed for tomographic imaging and it completely avoids the mechanical scanning in the imaging process. The samples, however, have different refractive indices for different wavelengths due to the dispersion effect. To address the shortcomings of traditional digital holographic tomography, this paper proposes a transmission mode K-domain transform-based digital holographic three-dimensional imaging method that requires only a single wavelength and one-dimensional sample scanning and is completely different from existing methods. Methods In transmission mode K-domain transform-based digital holographic three-dimensional imaging method, light sheet formed by a cylindrical lens is used to illuminate the sample and the off-axis hologram of the transmitted light is recorded via the interference between another reference light sheet. After the complex amplitude of the transmitted light is obtained using the traditional digital holographic reconstruction method, its spectrum is calculated and its low-frequency component is removed via high-pass filtering. Thus, the component of zero-order transmitted light is filtered out, and the high-order diffracted light is enhanced. Then the K-domain transformation is implemented on the spectrum space. The inverse Fourier transform is finally performed on the transformed spatial spectrum to obtain the tomographic sample structure illuminated by the light sheet through one-dimensional scanning. Because the low-frequency component has been removed, the reconstructed images are differential intensity images with intensities that are inverse to the bright field images. They do, however, retain the same structural information as the sample. Results and Disscusions According to theoretical analysis, the principle of transmission mode K-domain transform-based digital holographic three-dimensional imaging method is explained (Fig. 1) . Then, the characteristics of the method are analyzed by mathematical principle and physical model (Fig. 2) . Based on the analyses above, a high-pass filtering algorithm is proposed and its feasibility has been verified (Fig. 3 and Fig. 4). By filtering the low-frequency spatial spectrum of the transmitted light, the tomographic sample structure can be obtained accurately and swiftly via K-domain transforming and one-dimensional scanning. Furthermore, some low-frequency spatial spectrum loss does not affect axial resolution but slightly improves lateral resolution. As a result, even after filtering out some of the low-frequency components, the axial and lateral resolutions of the system are still primarily determined by the numerical aperture of the imaging system. But because the low-frequency components are filtered out, the image obtained is the differential image of the observed object in the transverse direction. The influence of high-pass filtering on reconstructed image quality is analyzed by a set of numerical simulation, and the necessity of high-pass filtering algorithm is proved (Fig. 5). Furthermore, numerical simulations (Fig. 6) and experiments (Fig. 7) in this paper are used to validate the feasibility of this transmission mode K-domain transformbased digital holographic three-dimensional imaging method. Conclusions This paper reports a transmission mode K-domain transform-based digital holographic three- dimensional imaging method, which is theoretically analysed and verified by both numerical simulations and experiments, to provide a simple and convenient tomographic imaging tool for the field of X-ray and electron beam microscopy, based on our previously proposed K-domain transform-based tomography. This paper reports a transmission mode K-domain transform-based digital holographic three-dimensional imaging method, which is theoretically analysed and verified by both numerical simulations and experiments, to provide a simple and convenient tomographic imaging tool for the field of X-ray and electron beam microscopy, based on our previously proposed K-domain transform-based tomography. It is proved that the method based on high-pass filtering can overcome the technical limitation that our previously proposed K-domain transforming based tomography can only work in the reflection light path. Furthermore, since this three-dimensional imaging method works in transmission mode, it has a much simpler optical alignment. Therefore, it can be adopted for ultra-high microscopic three-dimensional imaging with coherent synchrotron radiation. Furthermore, the illuminating light sheet is used to repeatedly scanning the sample, which can quickly generate a three-dimensional image of the entire sample quickly. As a result, the newly proposed transmission mode K-domain transform-based digital holographic three-dimensional imaging method can provide a simple and practical tomographic imaging tool for X-ray and electron beam short-wavelength microscopic imaging.
