Dual-wavelength Digital Holography Research Articles

Lensless single-shot dual-wavelength digital holography for industrial metrology

We demonstrate lensless single-shot dual-wavelength digital holography for high-speed 3D imaging in industrial inspection. Single-shot measurement is realized by combining off-axis digital holography and spatial frequency multiplexing of the two wavelengths on the detector. The system has 9.1 µm lateral resolution and a 50 µm unambiguous depth range. We determine the theoretical accuracy of off-axis dual-wavelength phase reconstruction for the case of shot-noise-limited detection. Experimental results show good agreement with the proposed model. The system is applied to industrial metrology of calibrated test samples and chip manufacturing.

Snapshot dual-wavelength digital holography with LED and laser hybrid illumination

To address the problem of the time-sharing recording of dual-wavelength low-coherence holograms while avoiding the use of customized achromatic optical elements, a snapshot dual-wavelength digital holography with LED and laser hybrid illumination is proposed. In this method, the parallel phase-shifting method is firstly employed to suppress zero-order and twin-image noise, and to record a LED hologram with low speckle noise and full field of view. Secondly, another laser hologram with a different center wavelength affected by speckle noise is recorded simultaneously using the spatial multiplexing technique. Finally, dual-wavelength wrapped phase images are reconstructed from a spatial multiplexing hologram, and then are combined to achieve low-noise phase unwrapping utilizing the iterative algorithm. Simulation and optical experiments on a reflective step with a depth of 1.38µm demonstrate that the proposed method can achieve single-shot and large-range height measurements while maintaining low-noise and full-field imaging.

Convenient dual-wavelength digital holography based on orthogonal polarization strategy with a Wollaston prism.

Dual-wavelength digital holography effectively expands the measurement range of digital holography, but it increases the complexity of optical system due to non-common-path of two wavelengths. Here, by using orthogonal polarization strategy, we present a dual-wavelength digital holography based on a Wollaston prism (DWDH-WP) to separate the reference beams of two wavelengths and realize the common-path of two wavelengths. A Wollaston prism is inset into the reference beam path of the off-axis digital holography system, so two orthogonal-polarized reference beams of two different wavelengths separated at different directions are generated. Then a dual-wavelength multiplexed interferogram with orthogonal interference fringes is captured by using a monochrome camera, in which both the polarization orientations and the interference fringe orientations of two wavelengths are orthogonal, so the spectral crosstalk of two wavelengths with arbitrary wavelength difference can be avoided. Compared with the existing DWDH method, the proposed DWDH-WP method can conveniently realize the common-path of the reference beams of two wavelengths, so it reveals obvious advantages in spectral separation, spectral crosstalk, system simplification, and adjustment flexibility. Both effectiveness and flexibility of the proposed DWDH-WP method are demonstrated by the phase measurement of the HeLa cell and vortex phase plate.

Synthetic-wavelength phase guided phase unwrapping method for dual-wavelength digital holography

Synthetic-wavelength phase guided phase unwrapping method for dual-wavelength digital holography

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.

Dual-wavelength off-axis digital holography inImageJ: toward real-time phase retrieval usingCUDA streams.

An ImageJ plug-in is developed to realize automatic real-time phase reconstruction for dual-wavelength digital holography (DH). This plug-in assembles the algorithms, including automatic phase reconstruction based on the division algorithm and post-processing. These algorithms are implemented and analyzed using a CPU and GPU, respectively. To hide the CPU-to-GPU data transfer latency, an optimization scheme using Compute Unified Device Architecture (CUDA) streams is proposed in ImageJ. Experimental results show that the proposed plug-in can perform faster reconstruction for dual-wavelength DH, resulting in frame rates up to 48fps even for one-megapixel digital holograms on a normal PC. In other words, the proposed plug-in can realize real-time phase reconstruction for dual-wavelength digital holographic videos.

Accelerated high-quality dual-wavelength digital holography using direct-retrieved synthetic-phases

Linear programming algorithm (LPA) using synthetic-phases can provide high quality quantitative phase imaging for dual-wavelength digital holography (dwDH). However, they are time-consuming owing to the complex process and heavy burden in computation. In this paper, an efficient LPA is developed to perform fast and accurate imaging for dwDH, in which both the additive and differential synthetic-phases are reconstructed in straightforward ways. After reconstructing the two synthetic-phases using multiplication-division and division-division multiplexing, respectively, the proposed method searches the optimal integer in one dimensional boundary condition to match the two synthetic-phases, and then yields the measured height map with high accuracy as well as fast speed. We demonstrate both the numerical and experimental results to evaluate the feasibility and effectiveness of the proposed method.

Quantitative phase reconstruction method based on an infrared-like single wave conversion in dual-wavelength phase-shift digital holography

Dual-wavelength digital holography has recently become a promising tool for achieving higher axial measurement ranges in microscopy. However, digital filtering, such as Fourier transform, or a separate hologram acquisition process is essential for retrieving the quantitative phase information of each respective wavelength. In this paper, a quantitative phase reconstruction method based on an infrared-like single wave conversion in dual-wavelength phase-shift digital holography, which does not require any of the processes mentioned above, has been proposed. Based on the proposed method, the quantitative phase information on the axial measurement specimen was simply obtained by only a phase-shift of a quarter of an infrared-like single wave which has the same magnitude of the synthetic wavelength. This approach simplifies not only the hologram acquisition process but also the numerical reconstruction process. The newly proposed theory is verified and evaluated using simulations and experimental validation.

Enlarged range of measurement method with strong noise resistance for dual-wavelength digital holography: erratum.

We present an erratum to our Letter [Opt. Lett.46, 4694 (2021)10.1364/OL.432135]. This erratum corrects an unintended error in the labels of Figs.5(h)-5(j). The corrections have no influence on the results and conclusions of the original Letter.

A review of the dual-wavelength technique for phase imaging and 3D topography

Optically transmissive and reflective objects may have varying surface profiles, which translate to arbitrary phase profiles for light either transmitted through or reflected from the object. For high-throughput applications, resolving arbitrary phases and absolute heights is a key problem. To extend the ability of measuring absolute phase jumps in existing 3D imaging techniques, the dual-wavelength concept, proposed in late 1800s, has been developed in the last few decades. By adopting an extra wavelength in measurements, a synthetic wavelength, usually larger than each of the single wavelengths, can be simulated to extract large phases or height variations from micron-level to tens of centimeters scale. We review a brief history of the developments in the dual-wavelength technique and present the methodology of this technique for using the phase difference and/or the phase sum. Various applications of the dual-wavelength technique are discussed, including height feature extraction from micron scale to centimeter scale in holography and interferometry, single-shot dual-wavelength digital holography for high-speed imaging, nanometer height resolution with fringe subdivision method, and applications in other novel phase imaging techniques and optical modalities. The noise sources for dual-wavelength techniques for phase imaging and 3D topography are discussed, and potential ways to reduce or remove the noise are mentioned.

Enhancement of image sharpness and height measurement using a low-speckle light source based on a patterned quantum dot film in dual-wavelength digital holography.

A dual-wavelength single light source based on a patterned quantum dot (QD) film was developed with a 405nm LED and bandpass filters to increase color conversion efficiency as well as to decouple the two peaks of dual-wavelength emitted from the QD film. A QD film was patterned laterally with two different sizes of QDs and was combined with bandpass filters to produce a high efficiency and low-speckle dual-wavelength light source. The experimental results showed that the developed dual-wavelength light source can decrease speckle noise to improve the reconstructed image sharpness and the accuracy on height measurement in dual-wavelength digital holography.

Enlarged range of measurement method with strong noise resistance for dual-wavelength digital holography.

A concise and powerful method for dual-wavelength digital holography (DWDH) is proposed. By designing a new algorithm, this proposed method bypasses the phase synthesis process and directly obtains the thickness distribution of the object. This method can enlarge the range of measurement with strong noise resistance. For example, noise analysis results show that the proposed method reduces the reconstruction error from 101 nm to 9 nm when the signal-to-noise ratio is equal to 30. Therefore, this method would prove useful for DWDH, and its effectiveness is verified by both numerical simulations and experimental results.

Parameter optimization of frequency sweeping digital holography for the measurement of ground optical surfaces

This paper describes the dependence of the precision of digital holographic methods on measurement parameters. The predominantly discussed parameters are illumination intensity and its homogeneity, surface microroughness, the influence of measurement geometry, as well as object shape, since most of them can be optimized by experimental arrangement. Frequency sweeping digital holography as well as dual-wavelength digital holography in the Fourier arrangement are tested and the results are discussed. It transpires that the methods are not very sensitive to object microroughness or overall reflectivity. Instead, it is the similarity of signal and reference waves that has the highest impact on measurement. After parameter optimization, the holographic methods can be advantageously used for ground surface measurements in optical workshops.

Possibility to break through limitation of measurement range in dual-wavelength digital holography* *Project supported by the Foundation of Science and Technology Department of Shaanxi Province, China (Grant No. 2018JQ6009), the Foundation of Education Department of Shaanxi Province, China (Grant No. 17JK1165), the Beijing Natural Science Foundation, China (Grant No. Z190004), the National Natural Science Foundation of China (Grant No. 61575197),

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.

Low-noise hierarchical phase unwrapping method for dual-wavelength digital holography using two synthetical wavelengths

Dual-wavelength digital holography can expand the unambiguous measurement depth in phase unwrapping by using a differential synthetic wavelength which is longer than the single illumination wavelength. However, the phase noise is significantly amplified due to the magnification of the differential synthetic wavelength, resulting in a lower measurement accuracy. On the other hand, a lower noise level can be achieved by using additive synthetic-wavelength which is shorter than the single illumination wavelength. However, the corresponding unambiguous measurement depth is greatly reduced due to the phase ambiguity. In this case, combining the merits of the differential synthetic-wavelength and the additive synthetic-wavelength, different low noise phase unwrapping algorithms have been developed in recent years. However, these algorithms are complex and time consuming because they need to calculate multiple intermediate variables or search for the constrained boundary conditions in two-dimensional space. Therefore, in this paper, we develop a hierarchical phase unwrapping algorithm by using the two synthetic wavelengths for dual-wavelength digital holography to realize low noise and fast unambiguous measurement with large depth. In this algorithm, the unwrapped phase difference obtained by the differential synthetic wavelength is used to guide the wrapped phase of one single wavelength to realize phase unwrapping, and then the optical path difference obtained by the single-wavelength unwrapped phase is employed to guide the wrapped phase sum, and thus realizing phase unwrapping. As a result, the phase noise is attenuated and the depth sensitivity is preserved for dual-wavelength phase unwrapping. After theoretical analysis, a series of simulation experiments is carried out on the reconstructed quality, anti-noise characteristics and speed through comparing with state-of-the-art dual-wavelength phase unwrapping algorithms, including the conventional algorithm, the linear programming algorithm and the direct linear programming algorithm. In this case, a flipping dual-wavelength common-path digital holography with orthogonal carrier is built to acquire multiplexed off-axis hologram in one shot and illustrate the operation of the algorithm with circular step target, and stability test of the setup. Both the simulation and experimental results show that the proposed method can be simplified and deterministic, resulting in a lower noise phase unwrapping in a time of 20.5 ms for a phase map of one megapixel. We expect that the proposed method can have practical applications in measurement that requires high accuracy, fast speed, and large depth.

Y4-Net: a deep learning solution to one-shot dual-wavelength digital holographic reconstruction.

In this Letter, a deep learning solution (Y4-Net, four output channels network) to one-shot dual-wavelength digital holography is proposed to simultaneously reconstruct the complex amplitude information of both wavelengths from a single digital hologram with high efficiency. In the meantime, by using single-wavelength results as network ground truth to train the Y4-Net, the challenging spectral overlapping problem in common-path situations is solved with high accuracy.

Autofocusing in dual-wavelength digital holography using correlation coefficient

An autofocusing method using correlation coefficient (CC) is proposed for dual-wavelength off-axis digital holography. The complex amplitudes of the object wave relative to the two wavelengths are first retrieved at different reconstruction distances, and the correlation degrees are then calculated between the two complex amplitudes. Considered the diffraction independency between the two wavelengths, the maximum CC is employed to automatically determine the focus plane. Our method can be applicable for the amplitude, phase, or both mixed sample. The experimental results demonstrate that the proposed method can enable automatically autofocusing with higher resolution in contrast to the state-of-the-art method.

Improved phase reconstruction using linear programming for dual-wavelength digital holography

Incorporating the advantages of the differential synthetic-wavelength and the additive synthetic-wavelength, we improve the linear programming algorithm for the phase reconstruction of dual-wavelength digital holography. Under the designated two dimensional boundary conditions, the improved linear programming algorithm is employed to search the optimal integer pair for the two aforementioned wavelengths. The convergence is determined by the square of height difference, in which the heights are obtained with the two aforementioned wavelengths, respectively. In comparison with other state-of-the-art approaches, our approach is straightforward to create phase unwrapping with similar or even better reconstruction quality. Both the numerical and experimental results were conducted to prove the feasibility and effectiveness of our approach.

Study on Quantitative Phase Imaging by Dual-Wavelength Digital Holography Microscopy

A dual-wavelength digital holographic microscopy with premagnification is proposed to obtain the object surface measurements over the large gradient. The quantitative phase images of specimens are captured in high precision by the processing of filtering and phase compensation. The phase images are acquired without phase unwrapping, which is necessary in traditional digital holographic microscopy; thereby the proposed system can greatly increase the speed of reconstruction. The results of numerical simulation and optical experiments demonstrated that the reconstructed speed increased by 37.9 times, and the relative error of measurement is 4% compared with the traditional holographic microscopy system. It means that the proposed system can directly acquire the higher quality quantitative phase distribution for specimens.

Generation of 3D digital models of the dental arches using optical scanning techniques

Due to a number of benefits mainly concerning orthodontic treatment planning and issues of documentation and sharing of patient records, digital models of the dental arches are more and more replacing conventional stone models in clinical orthodontics. To date, the most common approach for generating digital models of the dental arches comprises the digitization of stone models mostly by using optically-based desktop scanner systems. This indirect approach is sufficiently accurate and achieves a largely complete model surface with relatively low equipment acquisition costs. In the recent decade, however, intraoral scanners are becoming ever more established and proven in clinical practice. The great advantage of this direct approach for generating digital models is that the intermediate step of stone cast fabrication can be omitted which eliminates material and space requirements for casts. The various commercially available intraoral scanning systems are based on the application of different optical measurement techniques. Fringe (i.e., structured-light) projection and two or more camera systems lead to a bulky arrangement and to shadowing effects which limit the accessibility of undercuts and thin volume fractions such as incisal edges. Moreover, they usually require powder coating of the teeth. Confocal laser scanners eliminate these disadvantages, although the three-dimensional (3D) movement of the scanner handpiece is disadvantageous with regard to scanning speed, accuracy and reliability. Intraoral scans generally contain a source of risk for inaccuracy, because multiple single 3D images are assembled to a complete model. Recent studies, however, have shown that the trueness and precision of intraoral scanners of commercially available scanning systems is already sufficient for orthodontic applications. Current development of novel scanner technologies, e.g. based on multipoint chromatic confocal imaging and dual wavelength digital holography, will further improve the accuracy and clinical practicability of intraoral scanning. Hence, it is likely that in future intraoral scanning combined with 3D printing will completely replace conventional stone models of the dental arches.