Single-shot wavelength-multiplexing for off-axis digital holography with a spectral filter.

We present a single-shot wavelength-multiplexing technique for off-axis digital holography based on a spectral filter. Only a spectral filter is inserted between beam splitter and mirror in reflection off-axis digital holography (RODH). The spectral filter can transmit a well-defined wavelength band of light, while reject other unwanted radiation. By adjusting the filter and mirror separately, the propagation orientation of different reference beams of two wavelengths can be separated, and thus two off- axis holograms with different fringe directions are simultaneously captured by a monochrome camera. The wavefront interference analysis of using a spectral filter is discussed in detail. Our scheme is available for real-time wavelength-multiplexing but requires fewer optical elements and system modifications. Numerical simulation and experiment results of different types of spectral filters demonstrate the validity of proposed method.

Measurement of thermal effects of diode-pumped solid-state laser by using digital holography.

Thermal lensing is one of the most important factors that can affect the performance of high-power solid-state lasers, such as limiting the power scaling capability and deteriorating output beam quality. In this paper, a novel and accurate measurement of digital holography is proposed to determine the thermal lensing of diode-pumped solid-state lasers with high resolution. The digitally recorded hologram can reveal the phase change when light travels through the laser gain medium. From the phase map, we can obtain the index variations induced by temperature differences inside the laser crystal when it is pumped by laser diodes, as well as determine the focal length of the integrated thermal lensing focus length. There was much work on measuring the static laser medium thermal lens because there is no laser output from the cavity in the setup. Our experiment setup was able to achieve online measurement with laser output at the same time. The measuring result can provide an accurate guide for compensating the thermal lensing in laser design to achieve high-power output and good beam quality. Moreover, detailed index variations in the direction of the laser crystal cross-section can be numerically reconstructed, by which the thermal effects, pump uniformity, crystal uniformity, etc., can be revealed from the holography result.

Off-axis tilt compensation in common-path digital holographic microscopy based on hologram rotation.

We present a simple and effective compensation method for the off-axis tilt in common-path digital holographic microscopy (CPDHM) by introducing a rotating operation on the hologram. The proposed method mainly requires a digital reference hologram (DRH), which is a rotated version of the original one; it is assumed to be easy to obtain by rotating the specimen's hologram 180°. In this way, the off-axis tilt could be removed by subtracting the retrieved phase of DRH from the retrieved phase of the original hologram, but without any complex spectrum centering judgment, fitting procedures, or prior knowledge of the system. This highly automatic and efficient performance makes our approach available for real-time quantitative phase imaging (QPI), although it limits the field of view (FOV) of the specimen. Some experimental results of microlens array and phase plate demonstrate the feasibility and effectiveness of the proposed method.

Simple and flexible phase compensation for digital holographic microscopy with electrically tunable lens.

In a digital holographic microscopy (DHM) system, different microscope objectives (MOs) will introduce different phase distortions and thus lead to measurement errors. To address this problem, we present a simple and flexible method to compensate all phase distortions by introducing an electrically tunable lens (ETL) in the reference arm for a DHM system with multiple MOs. By exactly controlling the external currents of the ETL, we can change the reference wave front to match the wave front introduced by different MOs without complex alignment or additional numerical postprocessing manipulations. This method is suitable for quantitative real-time phase imaging especially when it refers to multiple MOs. To demonstrate the validity and effectiveness of our scheme, we did a series of simulations and carried out some real experiments with two different MOs (4× and 10×).

Linear programming phase unwrapping for dual-wavelength digital holography.

A linear programming phase unwrapping method in dual-wavelength digital holography is proposed and verified experimentally. The proposed method uses the square of height difference as a convergence standard and theoretically gives the boundary condition in a searching process. A simulation was performed by unwrapping step structures at different levels of Gaussian noise. As a result, our method is capable of recovering the discontinuities accurately. It is robust and straightforward. In the experiment, a microelectromechanical systems sample and a cylindrical lens were measured separately. The testing results were in good agreement with true values. Moreover, the proposed method is applicable not only in digital holography but also in other dual-wavelength interferometric techniques.

Quantitative measurement of thermal lensing in diode-side-pumped Nd:YAG laser by use of digital holographic interferometry.

Thermal lensing in diode-side-pumped Nd:YAG laser has been measured quantitatively using digital holographic interferometry. A series of holograms, carrying the information of the laser rod under different pump currents, are recorded with a CCD and reconstructed numerically. The optical path difference induced by the thermal lensing and the corresponding evolution process under different currents are obtained accordingly. Further, the thermal lensing diopters, induced aberrations, and its Zernike coefficients are calculated. The proposed method can be applied in the thermal lensing measurement and the optimization design of a laser resonator.

Focal length calibration of an electrically tunable lens by digital holography.

The electrically tunable lens (ETL) is a novel current-controlled adaptive optical component which can continuously tune its focus in a specific range via changing its surface curvature. To quantitatively characterize its tuning power, here we assume the ETL to be a pure phase object and present a novel calibration method to dynamically measure its wavefront by use of digital holographic microscopy (DHM). The least squares method is then used to fit the radius of curvature of the wavefront. The focal length is obtained by substituting the radius into the Zemax model of the ETL. The behavior curve between the focal length of the ETL and its driven current is drawn, and a quadratic mathematic model is set up to characterize it. To verify our model, an ETL and offset lens combination is proposed and applied to ETL-based transport of intensity equation (TIE) phase retrieval microscopy. The experimental result demonstrates the calibration works well in TIE phase retrieval in comparison with the phase measured by DHM.

Compact lensless digital holographic microscopy using a curved mirror for an enlarged working distance.

Digital holographic microscopy (DHM) has a wide range of applications from the analysis of microelectronic mechanical systems (MEMS) to the measurement of cells. We intend on making the system more compact to improve the portability of the device. A concave mirror has been presented to be used in a lensless DHM system to effectively enlarge the working distance and at the same time maintain the compact size of the whole system. A theoretical analysis of the phase compensation between the object wave and the wave reflected from curved reference mirrors is given. Experimental demonstrations of the curved reference mirrors used in the DHM system have been obtained to support our idea. This would change the overall size and adaptability of the DHM system and provide a better understanding of the effects of phase reflected off a curved mirror.

Close-range photogrammetry with light field camera: from disparity map to absolute distance.

A new approach to measure the 3D profile of a texture object is proposed utilizing light field imaging, in which three key steps are required: a disparity map is first obtained by detecting the slopes in the epipolar plane image with the multilabel technique; the intrinsic parameters of the light field camera are then extracted by camera calibration; at last, the relationship between disparity values and real distances is built up by depth calibration. In the last step, a linear calibration method is proposed to achieve accurate results. Furthermore, the depth error is also investigated and compensated for by reusing the checkerboard pattern. The experimental results are in good agreement with the 3D models, and also indicate that the light field imaging is a promising 3D measurement technique.

Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms.

A transport-of-intensity equation (TIE)-based phase retrieval method is proposed with putting an arbitrarily shaped aperture into the optical wavefield. In this arbitrarily shaped aperture, the TIE can be solved under nonuniform illuminations and even nonhomogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and nonuniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phase distribution under nonuniform illumination and nonhomogeneous boundary conditions within an arbitrarily shaped aperture, which enables the technique of TIE with hard aperture to become a more flexible phase retrieval tool in practical measurements.

Further investigation on the phase stitching and system errors in digital holography.

In this work, an improved phase stitching algorithm is proposed in digital holography (DH) based on a deduced phase errors model and a global optimization algorithm. In addition, to correct the relative rotation error between the coordinate systems of a CCD and xy-motion stages, we presented a simple and reliable image-based correction method. The experimental results obtained from our proposed method are compared with those calculated from the existing phase stitching method to verify the performance of the presented method. It is shown that our new proposed methods are robust and valid for measurement of a large microstructure element. As far as we know, the improved phase stitching algorithm and image-base correction method have not been discussed in DH, as we presented in this paper.

Boundary-artifact-free phase retrieval with the transport of intensity equation II: applications to microlens characterization.

Boundary conditions play a crucial role in the solution of the transport of intensity equation (TIE). If not appropriately handled, they can create significant boundary artifacts across the reconstruction result. In a previous paper [Opt. Express 22, 9220 (2014)], we presented a new boundary-artifact-free TIE phase retrieval method with use of discrete cosine transform (DCT). Here we report its experimental investigations with applications to the micro-optics characterization. The experimental setup is based on a tunable lens based 4f system attached to a non-modified inverted bright-field microscope. We establish inhomogeneous Neumann boundary values by placing a rectangular aperture in the intermediate image plane of the microscope. Then the boundary values are applied to solve the TIE with our DCT-based TIE solver. Experimental results on microlenses highlight the importance of boundary conditions that often overlooked in simplified models, and confirm that our approach effectively avoid the boundary error even when objects are located at the image borders. It is further demonstrated that our technique is non-interferometric, accurate, fast, full-field, and flexible, rendering it a promising metrological tool for the micro-optics inspection.

High-speed transport-of-intensity phase microscopy with an electrically tunable lens.

We present a high-speed transport-of-intensity equation (TIE) quantitative phase microscopy technique, named TL-TIE, by combining an electrically tunable lens with a conventional transmission microscope. This permits the specimen at different focus position to be imaged in rapid succession, with constant magnification and no physically moving parts. The simplified image stack collection significantly reduces the acquisition time, allows for the diffraction-limited through-focus intensity stack collection at 15 frames per second, making dynamic TIE phase imaging possible. The technique is demonstrated by profiling of microlens array using optimal frequency selection scheme, and time-lapse imaging of live breast cancer cells by inversion the defocused phase optical transfer function to correct the phase blurring in traditional TIE. Experimental results illustrate its outstanding capability of the technique for quantitative phase imaging, through a simple, non-interferometric, high-speed, high-resolution, and unwrapping-free approach with prosperous applications in micro-optics, life sciences and bio-photonics.

Noninterferometric single-shot quantitative phase microscopy.

We present a noninterferometric single-shot quantitative phase microscopy technique with the use of the transport of intensity equation (TIE). The optical configuration is based on a Michelson-like architecture attached to a nonmodified inverted transmission bright field microscope. Two laterally separated images from different focal planes can be obtained simultaneously by a single camera exposure, enabling the TIE phase recovery to be performed at frame rates that are only camera limited. Precise measurement of a microlens array validates the principle and demonstrates the accuracy of the method. Investigations of chemical-induced apoptosis and the phagocytosis process of macrophages are then presented, suggesting that the method developed can provide promising applications in the dynamic study of cellular processes.

Phase aberration compensation in digital holographic microscopy based on principal component analysis.

We present an effective, fast, and straightforward phase aberration compensation method in digital holographic microscopy based on principal component analysis. The proposed method decomposes the phase map into a set of values of uncorrelated variables called principal components, and then extracts the aberration terms from the first principal component obtained. It is effective, fully automatic, and does not require any prior knowledge of the object and the setup. The great performance and limited computational complexity make our approach a very attractive and promising technique for compensating phase aberration in digital holography under time-critical environments.

Trade-Off Analyses of Multiple Ecosystem Services and Their Drivers in the Shandong Yellow River Basin.

With the intensification of conflicts between different ecosystem services, how to achieve a win-win situation between socio-economic development and ecological protection is an important issue that needs to be addressed nowadays. In particular, how to better quantify and assess the intensity of ecosystem service trade-offs and their relative benefits, and to identify the influencing factors are issues that need to be studied in depth. Based on the INVEST model, this paper analyzed the evolution of spatial and temporal patterns of ecosystem services such as Carbon Storage (CS), Food Production (FP), Habitat Quality (HQ), and Water Yield (WY) in the Shandong Yellow River Basin (SYRB) in 2000, 2010 and 2020. Next, we quantitatively measured the trade-off intensity and revealed the key influencing factors of the trade-off intensity evolution using automatic linear models, root mean square deviation, and geographically weighted regressions. Subsequently, we further analyzed the impact of the correlation between environmental and socio-economic factors on the trade-off intensity of ecosystem services. The results indicated that the temporal and spatial changes of the four main ecosystem services in SYRB area were inconsistent. WY showed a fluctuating trend, with a large interannual gap. CS and FP are on the rise, while HQ is on the decline. Spatially, WY and HQ showed a decreasing distribution from the center to the periphery, while FP and CS showed a decreasing distribution from the southwest to the northeast. The location characteristics of SYRB's four ecosystem services and their trade-offs were obvious. FP had absolute location advantage in ecosystem service trade-offs. Most of the four ecosystem services showed significant trade-offs, and the trade-off intensity had significant spatial heterogeneity, but the trade-off between FP and CS was relatively weak. At the same time, there were also differences in the trends of trade-off intensities. Counties with low trade-off intensity were mostly located in mountainous areas; these areas are less disturbed by human activities, and most of them are areas without prominent services. Counties with high trade-off intensities were mostly concentrated in areas with relatively developed agriculture; these areas are more disturbed by human activities and are mostly prominent in FP. The trade-off intensity of ecosystem services in SYRB was affected by several factors together, and there were difference characteristics in the degree and direction of influence of each factor. Moreover, these influencing factors have gradually changed over 20 years. In terms of the spatial distribution at the county scale, the influence areas of the dominant drivers of different trade-off types varied greatly, among which the areas with NDVI, CON, and PRE as the dominant factors were the largest. In the future, in effectively balancing regional economic development and ecological environmental protection, quantifiable correspondence strategies should be developed from the administrative perspective of counties and regions based on comprehensive consideration of the locational advantages of each ecosystem service and changes in trade-offs.

Characterization and inspection of microlens array by single cube beam splitter microscopy.

The application of a single cube beam splitter (SCBS) microscope to micro-optics characterization is presented. The SCBS in the optical path, with a small angle between the optical axis and its central semireflecting layer, not only gives off-axis digital holograms but also provides dual-channel imaging. It is a unique and easy way to perform uniformity inspection across the entire microlens array. Experimental results on physical spherical phase compensation, single lens characterization, dual-channel imaging, and uniformity inspection are provided to demonstrate the unique properties of SCBS microscopy.

Transmission digital holographic microscopy based on a beam-splitter cube interferometer.

A new optical configuration for digital holographic microscopy is presented. Digital off-axis holograms are recorded by use of a single cube beam splitter in a nonconventional configuration to both split and combine a diverging spherical wavefront as it emerges from a single point source. Both the amplitude and the phase can then be reconstructed, yielding intensity and phase images with improved resolution. The novelty of the proposed configuration is its simplicity, minimal number of optical elements, insensitivity to vibration, and its inherent capability to compensate for the phase curvature that results from the illuminating wavefront in the case of microscopic samples.

Quasi-physical phase compensation in digital holographic microscopy.

In digital holographic microscopy, if an optical setup is well aligned, the phase curvature introduced by the microscope objective (MO) together with the illuminating wave to the object wave is a spherical phase curvature. It can be physically compensated by introducing the same spherical phase curvature in the reference beam. Digital holographic microscopy setups based on the Michelson interferometric configuration with MO and an adjustable lens are presented, which can well perform the quasi-physical phase compensation during the hologram recording. In the reflection mode, the adjustable lens serves as both the condensing lens and the compensation lens. When the spatial frequency spectra of the hologram become a point spectrum, one can see that the phase curvature introduced by imaging is quasi-physically compensated. A simple plane numerical reference wavefront used for the reconstruction can give the correct quantitative phase map of the test object. A theoretical analysis and experimental demonstration are given. The simplicity of the presented setup makes it easy to align it well at lower cost.

Pulse shaping properties of volume holographic gratings in anisotropic media.

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO(3) crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications.