Multiwavelength three-dimensional microscopy with spatially incoherent light, based on computational coherent superposition

Roadmap on computational methods in optical imaging and holography [invited]

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00340-024-08280-3.

Technology Selection for Inline Topography Measurement with Rover-Borne Laser Spectrometers

This work studies enhancing the capabilities of compact laser spectroscopes integrated into space-exploration rovers by adding 3D topography measurement techniques. Laser spectroscopy enables the in situ analysis of sample composition, aiding in the understanding of the geological history of extraterrestrial bodies. To complement spectroscopic data, the inclusion of 3D imaging is proposed to provide unprecedented contextual information. The morphological information aids material characterization and hence the constraining of rock and mineral histories. Assigning height information to lateral pixels creates topographies, which offer a more complete spatial dataset than contextual 2D imaging. To aid the integration of 3D measurement into future proposals for rover-based laser spectrometers, the relevant scientific, rover, and sample constraints are outlined. The candidate 3D technologies are discussed, and estimates of performance, weight, and power consumptions guide the down-selection process in three application examples. Technology choice is discussed from different perspectives. Inline microscopic fringe-projection profilometry, incoherent digital holography, and multiwavelength digital holography are found to be promising candidates for further development.

General phase-difference imaging of incoherent digital holography

The hologram formed by incoherent holography based on self-interference should preserve the phase difference information of the object, such as the phase difference between the mutually orthogonal polarizations of anisotropic object. How to decode this phase difference from this incoherent hologram, i.e., phase-difference imaging, is of great significance for studying the properties of the measured object. However, there is no general phase-difference imaging theory due to both diverse incoherent holography systems and the complicated reconstruction process from holograms based on the diffraction theory. To realize phase-difference image in incoherent holography, the relationship between the phase difference of the object and the image reconstructed by holograms is derived using a general physical model of incoherent holographic systems, and then the additional phase that will distort this relationship in actual holographic systems is analyzed and eliminated. Finally, the phase-difference imaging that is suitable for the most incoherent holographic systems is realized and the general theory is experimentally verified. This technology can be applied to phase-difference imaging of anisotropic objects, and has potential applications in materials science, biomedicine, polarized optics and other fields.

Extended autofocusing in dual-wavelength digital holography

In single-wavelength digital holography (DH), the phase wrapping phenomenon limits the total object depth that can be measured due to the requirement for well-resolved phase fringes. To address this limitation, dual-wavelength DH is proposed, enabling measurement of much deeper objects. In single-wavelength DH, because the object depth is limited, the depth of focus (DOF) of DH's optical system at a reconstruction distance is sufficient to cover the object depth. To date, many autofocusing algorithms have been proposed to obtain a correct reconstruction distance. However, in dual-wavelength DH, because the object depth is extended, the DOF at a reconstruction distance cannot cover the extended object depth. The extended object depth can span multiple DOFs, causing partially out of focus object depth. Therefore, in dual-wavelength DH, relying solely on autofocusing algorithms for a single distance is insufficient. But extended autofocusing algorithms, which can autofocus objects through multiple DOFs, are demanded. However, there are no such extended autofocusing algorithms in dual-wavelength DH. Therefore, we propose an extended autofocusing algorithm for dual-wavelength DH based on a correlation coefficient. The proposed algorithm is able to focus the whole object depth when the depth spans multiple DOFs. Through theoretical analysis, simulations, and experiments, the necessity and effectiveness of the proposed algorithm are verified.

Snapshot multi-frame parallel spectral holographic microscopy based on a reconfigurable optical comb

We present a snapshot multi-frame parallel holographic microscopy system through a reconfigurable optical comb source, which consists of a digital micromirror device (DMD) based spectrum filter system and a spectroscopic Michelson interferometric system. The proposed system allows arbitrarily tuning comb spacing and comb number, and the capturing of multi-frame images without overlap in one exposure. As a result, high-quality spectral holograms can be obtained with less acquisition time. The performance of the system is detailed in the experiment and 45-wavelengths holographic imaging for perovskite micro-platelets is conducted, which proves the system has the ability to realize high-performance four-dimensional (4D) imaging.

Roadmap on Recent Progress in FINCH Technology

Fresnel incoherent correlation holography (FINCH) was a milestone in incoherent holography. In this roadmap, two pathways, namely the development of FINCH and applications of FINCH explored by many prominent research groups, are discussed. The current state-of-the-art FINCH technology, challenges, and future perspectives of FINCH technology as recognized by a diverse group of researchers contributing to different facets of research in FINCH have been presented.

Phase-difference imaging based on FINCH

The diffraction theory was used to calculate the point spread function (PSF) of a typical Fresnel incoherent correlation holography (FINCH) system. It was found that the phase of the reconstructed image corresponds to the phase difference between the original points in two mutually perpendicular polarization directions. The experimental results show that the FINCH system with reasonable parameters can realize the phase-difference imaging of objects and measure the phase difference of cross-polarization directions in birefringent materials.

Incoherent color digital holography with computational coherent superposition for fluorescence imaging [Invited]

We present color fluorescence imaging using an incoherent digital holographic technique in which holographic multiplexing of multiple wavelengths is exploited. Self-interference incoherent digital holography with a single-path in-line configuration and the computational coherent superposition scheme are adopted to obtain color holographic three-dimensional information of self-luminous objects with a monochrome image sensor and no mechanical scanning. We perform not only simultaneous color three-dimensional sensing of multiple self-luminous objects but also color fluorescence imaging of stained biological samples. Color fluorescence imaging with an improved point spread function is also demonstrated experimentally by adopting a Fresnel incoherent correlation holography system.

Two-step phase-shifting interferometry for self-interference digital holography

We propose a phase-shifting interferometry technique using only two in-line phase-shifted self-interference holograms. There is no requirement for additional recording or estimation in the measurement. The proposed technique adopts a mathematical model for self-interference digital holography. The effectiveness of the proposed technique is demonstrated by experiments on incoherent digital holographic microscopy and color-multiplexed fluorescence digital holography with computational coherent superposition. Two-color-multiplexed four-step phase-shifting incoherent digital holography is realized for the first time, to the best of our knowledge, using the proposed technique.

Single-shot wavelength-selective quantitative phase microscopy by partial aperture imaging and polarization-phase-division multiplexing

We propose a single-shot wavelength-selective quantitative phase microscopy by annular white-light illumination, polarization-phase-division, and parallel phase-shifting. Compared to conventional multi-wavelength incoherence digital holography, the proposed microscopy presents the following merits: no switching of illumination or mechanical scanning, high spatiotemporal phase sensitivity, and single-shot reconstruction at each wavelength. Experiments validate these characteristics by quantitative phase imaging of gratings, cells, and tissues.

Partially coherent Pearcey-Gauss beams

We investigate the dynamics of partially coherent Pearcey-Gauss beams propagating in free space, theoretically and experimentally. They are produced by introducing the degree of coherence (DOC) function with Gaussian Schell-model correlation into the light source in the frequency domain. Under a nearly incoherent state, the oscillation of the sidelobe turns smooth, and the intensity distribution concentrates on the mainlobe. Particularly, partially coherent Pearcey-Gauss beams would maintain the inherent properties of autofocusing performance and inversion effect without diminishing the autofocusing distance and form-invariable propagation. Moreover, the opening angle and the shift of peak intensity of the beams can be controlled by the binary parabola in the spectrum distribution of the Pearcey function. Our experimental results are in great agreement with the theoretical analysis.

Randomly Multiplexed Diffractive Lens and Axicon for Spatial and Spectral Imaging

A new hybrid diffractive optical element (HDOE) was designed by randomly multiplexing an axicon and a Fresnel zone lens. The HDOE generates two mutually coherent waves, namely a conical wave and a spherical wave, for every on-axis point object in the object space. The resulting self-interference intensity distribution is recorded as the point spread function. A library of point spread functions are recorded in terms of the different locations and wavelengths of the on-axis point objects in the object space. A complicated object illuminated by a spatially incoherent multi-wavelength source generated an intensity pattern that was the sum of the shifted and scaled point spread intensity distributions corresponding to every spatially incoherent point and wavelength in the complicated object. The four-dimensional image of the object was reconstructed using computer processing of the object intensity distribution and the point spread function library.