Recent Advances and Current Trends in Transmission Tomographic Diffraction Microscopy.

Optical microscopy techniques are among the most used methods in biomedical sample characterization. In their more advanced realization, optical microscopes demonstrate resolution down to the nanometric scale. These methods rely on the use of fluorescent sample labeling in order to break the diffraction limit. However, fluorescent molecules' phototoxicity or photobleaching is not always compatible with the investigated samples. To overcome this limitation, quantitative phase imaging techniques have been proposed. Among these, holographic imaging has demonstrated its ability to image living microscopic samples without staining. However, for a 3D assessment of samples, tomographic acquisitions are needed. Tomographic Diffraction Microscopy (TDM) combines holographic acquisitions with tomographic reconstructions. Relying on a 3D synthetic aperture process, TDM allows for 3D quantitative measurements of the complex refractive index of the investigated sample. Since its initial proposition by Emil Wolf in 1969, the concept of TDM has found a lot of applications and has become one of the hot topics in biomedical imaging. This review focuses on recent achievements in TDM development. Current trends and perspectives of the technique are also discussed.

Jones tomographic diffractive microscopy with a polarized array sensor.

Tomographic diffractive microscopy (TDM) based on scalar light-field approximation is widely implemented. Samples exhibiting anisotropic structures, however, necessitate accounting for the vectorial nature of light, leading to 3-D quantitative polarimetric imaging. In this work, we have developed a high-numerical aperture (at both illumination and detection) Jones TDM system, with detection multiplexing via a polarized array sensor (PAS), for imaging optically birefringent samples at high resolution. The method is first studied through image simulations. To validate our setup, an experiment using a sample containing both birefringent and non-birefringent objects is performed. Araneus diadematus spider silk fiber and Pinna nobilis oyster shell crystals are finally studied, allowing us to assess both birefringence and fast-axis orientation maps.

3D differential interference contrast microscopy using polarisation-sensitive tomographic diffraction microscopy.

Tomographic diffraction microscopy (TDM) is a generalisation of digital holographic microscopy (DHM), for which the illumination angle onto the sample is fully controlled, which has become a tool of choice for 3D, high-resolution imaging of unlabelled samples. TDM makes it possible to obtain the optical field in both amplitude and phase for each illumination angle. Proper information reallocation eventually allows for 3D reconstruction of the complex refractive index map. On the other hand, polarisation array sensors (PAS) paves new way for TDM, as vectorial information assessment about the investigated sample. In this contribution, we show an alternative use of this polarisation information based on the phase sensitive nature of TDM. Here, we demonstrated that TDM coupled with PAS can lead to a 3D differential interference contrast (DIC) microscope with almost no experimental configuration modification.

Multimodal image reconstruction from tomographic diffraction microscopy data.

Tomographic diffraction microscopy (TDM) is a tool of choice for high-resolution, marker-less 3D imaging of biological samples. Based on a generalization of digital holographic microscopy with full control of the sample's illumination, TDM measures, from many illumination directions, the diffracted fields in both phase and amplitude. Photon budget associated to TDM imaging is low. Therefore, TDM is not limited by phototoxicity issues. The recorded information makes it possible to reconstruct 3D refractive index distribution (with both refraction and absorption contributions) of the object under scrutiny, without any staining. In this contribution, we show an alternate use of this information. A tutorial for multimodal image reconstruction is proposed. Both intensity contrasts and phase contrasts are proposed, from the image formation model to the final reconstruction with both 2D and 3D rendering, turning TDM into a kind of 'universal' digital microscope.

Optimizing sample illumination scanning for reflection and 4Pi tomographic diffractive microscopy.

Tomographic diffractive microscopy (TDM) is increasingly gaining attention, owing to its high-resolution, label-free imaging capability. Fast acquisitions necessitate limiting the number of holograms to be recorded. Reconstructions then rely on optimal Fourier space filling to retain image quality and resolution, that is, they rely on optimal scanning of the tomographic illuminations. In this work, we theoretically study reflection TDM, and then the 4Pi TDM, a combination of transmission and reflection systems. Image simulations are conducted to determine optimal angular sweeping. We found that three-dimensional uniform scanning fills Fourier space the best for both reflection and 4Pi configurations, providing a better refractive index estimation for the observed sample.

Optimizing sample illumination scanning in transmission tomographic diffractive microscopy.

Due to the sequential nature of data acquisition, it is preferable to limit the number of illuminations to be used in tomographic diffractive microscopy experiments, especially if fast imaging is foreseen. On the other hand, for high-quality, high-resolution imaging, the Fourier space has to be optimally filled. Up to now, the problem of optimal Fourier space filling has not been investigated in itself. In this paper, we perform a comparative study to analyze the effect of sample scanning patterns on Fourier space filling for a transmission setup. Optical transfer functions for several illumination patterns are studied. Simulation as well as experiments are conducted to compare associated image reconstructions. We found that 3D uniform angular sweeping best fills the Fourier space, leading to better quality images.

Versatile transmission/reflection tomographic diffractive microscopy approach.

Tomographic diffractive microscopy (TDM) has gained interest in recent years due to its ability to deliver high-resolution, three-dimensional images of unlabeled samples. It has been applied to transparent samples in transmission mode, as well as to surface studies in reflection mode. Mudry et al. [Opt. Lett.35, 1857 (2010)OPLEDP0146-959210.1364/OL.35.001857] introduced the concept of mirror-assisted TDM (MA-TDM), an elegant approach for achieving quasi-isotropic-resolution microscopic imaging, but which is still to be experimentally applied. In this work, we show that a simplified version of MA-TDM allows for transforming a reflective TDM setup into a more versatile instrument, also capable of observing transparent samples in transmission mode if using specific sample holders made out of a mirror and coated with a low-thickness transparent spacer.

Self-calibration for lensless color microscopy.

Lensless color microscopy (also called in-line digital color holography) is a recent quantitative 3D imaging method used in several areas including biomedical imaging and microfluidics. By targeting cost-effective and compact designs, the wavelength of the low-end sources used is known only imprecisely, in particular because of their dependence on temperature and power supply voltage. This imprecision is the source of biases during the reconstruction step. An additional source of error is the crosstalk phenomenon, i.e., the mixture in color sensors of signals originating from different color channels. We propose to use a parametric inverse problem approach to achieve self-calibration of a digital color holographic setup. This process provides an estimation of the central wavelengths and crosstalk. We show that taking the crosstalk phenomenon into account in the reconstruction step improves its accuracy.

Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography.

Common-path digital in-line holography is considered as a valuable 3D diagnostic technique for a wide range of applications. This configuration is cost effective and relatively immune to variation in the experimental environment. Nevertheless, due to its common-path geometry, the signal-to-noise ratio of the acquired hologram is weak as most of the detector (i.e., CCD/CMOS sensor) dynamics are occupied by the reference field signal, whose energy is orders of magnitude higher than the field scattered by the imaged object. As it is intrinsically impossible to modify the ratio of energy of reference to the object field, we propose a co-design approach (optics/data processing) to tackle this issue. The reference to the object field ratio is adjusted by adding a 4-f device to a conventional in-line holographic setup, making it possible to reduce the weight of the reference field while keeping the object field almost constant. Theoretical analysis of the Crámer-Rao lower bounds of the corresponding imaging model illustrates the advantages of this approach. These lower bounds can be asymptotically reached using a parametric inverse problem reconstruction. This implementation results in a 60% gain in axial localization accuracy (for 100 µm diameter spherical objects) compared to a classical in-line holography setup.

Holographic microscopy reconstruction in both object and image half-spaces with an undistorted three-dimensional grid.

We propose a holographic microscopy reconstruction method that propagates the hologram in the object half-space in the vicinity of the object. The calibration yields reconstructions with an undistorted reconstruction grid, i.e., with orthogonal x, y, and z axes and constant pixel pitch. The method is validated with a USAF target imaged by a ×60 microscope objective (MO), whose holograms are recorded and reconstructed for different USAF locations along the longitudinal axis: -75 to +75 µm. Since the reconstruction numerical phase mask, the reference phase curvature, and the MO form an afocal device, the reconstruction can be interpreted as occurring equivalently in the object or image half-space.

3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction.

In-line digital holography is a valuable tool for sizing, locating, and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, inverse problem approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with inverse problem approaches improves the estimation of particle size and 3D position. Here, we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D position are jointly optimized from video holograms acquired with a digital holographic microscopy setup based on a low-end microscope objective (×20, NA 0.5). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2×2×5 nm3 for position under additive white Gaussian noise assumption.

Digital holography super-resolution for accurate three-dimensional reconstruction of particle holograms.

In-line digital holography (DH) is used in many fields to locate and size micro or nano-objects spread in a volume. To reconstruct simple shaped objects, the optimal approach is to fit an imaging model to accurately estimate their position and their characteristic parameters. Increasing the accuracy of the reconstruction is a big issue in DH, particularly when the pixel is large or the signal-to-noise ratio is low. We suggest exploiting the information redundancy of videos to improve the reconstruction of the holograms by jointly estimating the position of the objects and the characteristic parameters. Using synthetic and experimental data, we checked experimentally that this approach can improve the accuracy of the reconstruction by a factor more than the square root of the image number.

In-line particle holography with an astigmatic beam: setup self-calibration using an "inverse problems" approach.

The use of digital in-line holography for the characterization of confined flows in cylindrical geometry confinements (e.g., cylindrical pipe or cylindrical capillaries) is discussed. Due to cylindrical geometry of the walls, the illuminating laser wave can be strongly astigmatic, which renders the use of classical reconstruction techniques impossible. Contrary to plane wave holography setup, the diffraction pattern of the particles strongly depends on the axial distance of the latter to the entry face of the confinement structure. To address this reconstruction issue, we propose to use an "inverse problems" approach. This approach amounts to finding the best match (least squares solution) between a diffraction pattern model and the captured hologram. For this purpose, a direct imaging model for astigmatic holograms, based on the use of transfer matrices, is presented and validated by comparing experimental and simulated holograms. The accuracy of the "inverse problems" reconstruction is then used to calibrate the experimental setup adjustable parameters. Finally, the approach is tested through experimental astigmatic hologram reconstruction, thus paving the way to its use in pipe flow studies.

Laser Doppler holographic microscopy in transmission: application to fish embryo imaging.

We have extended Laser Doppler holographic microscopy to transmission geometry. The technique is validated with living fish embryos imaged by a modified upright bio-microcope. By varying the frequency of the holographic reference beam, and the combination of frames used to calculate the hologram, multimodal imaging has been performed. Doppler images of the blood vessels for different Doppler shifts, images where the flow direction is coded in RGB colors or movies showing blood cells individual motion have been obtained as well. The ability to select the Fourier space zone that is used to calculate the signal, makes the method quantitative.

Phase-sensitive narrowband heterodyne holography.

We report on amplitude and phase imaging of out-of-plane sinusoidal surface vibration at nanometer scales with a heterodyne holographic interferometer. The originality of the proposed method is to make use of a multiplexed local oscillator to address several optical sidebands into the temporal bandwidth of a sensor array. This process is called coherent frequency-division multiplexing. It enables simultaneous recording and pixel-to-pixel division of sideband holograms, which permits quantitative wide-field mapping of optical phase-modulation depths. Additionally, a linear frequency chirp ensures the retrieval of the local mechanical phase shift of the vibration with respect to the excitation signal. The proposed approach is validated by quantitative motion characterization of the lamellophone of a musical box, behaving as a group of harmonic oscillators, under weak sinusoidal excitation. Images of the vibration amplitude versus excitation frequency show the resonance of the nanometric flexural response of one individual cantilever, at which a phase hop is measured.

Absolute measurement of small-amplitude vibrations by time-averaged heterodyne holography with a dual local oscillator.

We report a demonstration of the measurement of the ratio between an optical modulation sideband component and the nonshifted light component by time-averaged heterodyne holography in off-axis and frequency-shifting configuration, through coherent frequency-division multiplexing with a dual optical local oscillator. Experimental results of sinusoidal vibration sensing are reported. This technique enables absolute measurements of subnanometric out-of-plane vibration amplitudes.

Phase-resolved heterodyne holographic vibrometry with a strobe local oscillator.

We report a demonstration of phase-resolved vibrometry, in which out-of-plane sinusoidal motion is assessed by heterodyne holography. In heterodyne holography, the beam in the reference channel is an optical local oscillator (LO). It is frequency-shifted with respect to the illumination beam to enable frequency conversion within the sensor bandwidth. The proposed scheme introduces a strobe LO, where the reference beam is frequency-shifted and modulated in amplitude, to alleviate the issue of phase retrieval. The strobe LO is both tuned around the first optical modulation sideband at the vibration frequency, and modulated in amplitude to freeze selected mechanical vibration states sequentially. The phase map of the vibration can then be derived from the demodulation of successive vibration states.

Off-axis digital hologram reconstruction: some practical considerations.

Holographic rendering of off-axis intensity digital holograms is discussed. A review of some of the main numerical processing methods, based either on the Fourier transform interpretation of the propagation integral or on its linear system counterpart, is reported. Less common methods such as adjustable magnification reconstruction schemes and Fresnelet decomposition are presented and applied to the digital treatment of off-axis holograms. The influence of experimental parameters on the classical hologram reconstruction methods is assessed, offering guidelines for optimal image rendering regarding the hologram recording conditions.

Micropipe flow visualization using digital in-line holographic microscopy.

Digital in-line holography is used to visualize particle motion within a cylindrical micropipe. Analytical expression of the intensity distribution recorded in the CCD sensor plane is derived using the generalized Huygens-Fresnel integral associated with the ABCD matrices formalism. Holograms obtained in a 100microm in diameter micropipe are then reconstructed using fractional Fourier transformation. Astigmatism brought by the cylindrical micropipe is finally used to select a three dimensional region of interest in the microflow and thus to improve axial localization of objects located within a micropipe. Experimental results are presented and a short movie showing particle motion within a micropipe is given.

Digital in-line holography in thick optical systems: application to visualization in pipes.

We apply digital in-line holography to image opaque objects through a thick plano-concave pipe. Opaque fibers and opaque particles are considered. Analytical expression of the intensity distribution in the CCD sensor plane is derived using a generalized Fresnel transform. The proposed model has the ability to deal with various pipe shapes and thicknesses and compensates for the lack of versatility of classical digital in-line holography models. Holograms obtained with a 12 mm thick plano-concave pipe are then reconstructed using a fractional Fourier transform. This method allows us to get rid of astigmatism. Numerical and experimental results are presented.