Roadmap on digital holography [Invited].

This Roadmap article on digital holography provides an overview of a vast array of research activities in the field of digital holography. The paper consists of a series of 25 sections from the prominent experts in digital holography presenting various aspects of the field on sensing, 3D imaging and displays, virtual and augmented reality, microscopy, cell identification, tomography, label-free live cell imaging, and other applications. Each section represents the vision of its author to describe the significant progress, potential impact, important developments, and challenging issues in the field of digital holography.

Three-dimensional fluorescence imaging using the transport of intensity equation.

We propose a nonscanning three-dimensional (3-D) fluorescence imaging technique using the transport of intensity equation (TIE) and free-space Fresnel propagation. In this imaging technique, a phase distribution corresponding to defocused fluorescence images with a point-light-source-like shape is retrieved by a TIE-based phase retrieval algorithm. From the obtained phase distribution, and its corresponding amplitude distribution, of the defocused fluorescence image, various images at different distances can be reconstructed at the desired plane after Fresnel propagation of the complex wave function. Through the proposed imaging approach, the 3-D fluorescence imaging can be performed in multiple planes. The fluorescence intensity images are captured with the help of an electrically tunable lens; hence, the imaging technique is free from motion artifacts. We present experimental results corresponding to microbeads and a biological sample to demonstrate the proposed 3-D fluorescence imaging technique.

Single-pixel imaging of the retina through scattering media.

Imaging the retina of cataractous patients is useful to detect pathologies before the cataract surgery is performed. However, for conventional ophthalmoscopes, opacifications convert the lens into a scattering medium that may greatly deteriorate the retinal image. In this paper we show, as a proof of concept, that it is possible to surpass the limitations imposed by scattering applying to both, a model and a healthy eye, a newly developed ophthalmoscope based on single-pixel imaging. To this end, an instrument was built that incorporates two imaging modalities: conventional flood illumination and single-pixel based. Images of the retina were acquired firstly in an artificial eye and later in healthy living eyes with different elements which replicate the scattering produced by cataractous lenses. Comparison between both types of imaging modalities shows that, under high levels of scattering, the single-pixel ophthalmoscope outperforms standard imaging methods.

Low-cost single-pixel 3D imaging by using an LED array.

We propose a method to perform color imaging with a single photodiode by using light structured illumination generated with a low-cost color LED array. The LED array is used to generate a sequence of color Hadamard patterns which are projected onto the object by a simple optical system while the photodiode records the light intensity. A field programmable gate array (FPGA) controls the LED panel allowing us to obtain high refresh rates up to 10 kHz. The system is extended to 3D imaging by simply adding a low number of photodiodes at different locations. The 3D shape of the object is obtained by using a non-calibrated photometric stereo technique. Experimental results are provided for an LED array with 32 × 32 elements.

High sampling rate single-pixel digital holography system employing a DMD and phase-encoded patterns.

A single-pixel digital holography system with phase-encoded illumination using a digital micromirror device (DMD) as a spatial light modulator (SLM) is presented. The enhanced switching rate of DMDs, far exceeding the stringent frame-rate of liquid crystal SLMs, allows recording and reconstruction of complex amplitude distributions in just a few seconds. A single amplitude binary modulation device is used for concurrently displaying the phase-encoded sampling patterns, compensating the distortion of the wavefront, and applying phase-shifting, by means of computer generated holograms. Our detection system consists of a simple photodiode that sequentially records the irradiance fluctuations corresponding to the interference between object and reference beams. The system recovers phase and amplitude information even when a diffuser is placed in front of the photodiode.

Real-time acquisition of complex optical fields by binary amplitude modulation.

We describe, through simulations and experiments, a real-time wavefront acquisition technique using random binary amplitude masks and an iterative phase retrieval algorithm based on the Fresnel propagator. By using a digital micromirror device, it is possible to recover an unknown complex object by illuminating with this set of masks and simultaneously recording the resulting intensity patterns with a high-speed camera, making this technique suitable for dynamic applications.

Single-pixel digital holography with phase-encoded illumination.

We demonstrate imaging of complex amplitude objects through digital holography with phase-structured illumination and bucket detection. The object is sampled with a set of micro-structured phase patterns implemented onto a liquid-crystal spatial light modulator while a bucket detector sequentially records the irradiance fluctuations corresponding to the interference between object and reference beams. Our reconstruction algorithm retrieves the unknown phase information from the full set of photocurrent measurements. Interestingly, the sampling functions can be codified onto the reference beam, so they can be nonlocal with respect to the object. Finally, we show that the system is well-fitted for transmission of the object information through scattering media.

Image transmission through dynamic scattering media by single-pixel photodetection.

Smart control of light propagation through highly scattering media is a much desired goal with major technological implications. Since interaction of light with highly scattering media results in partial or complete depletion of ballistic photons, it is in principle impossible to transmit images through distances longer than the extinction length. Nevertheless, different methods for image transmission, focusing, and imaging through scattering media by means of wavefront control have been published over the past few years. In this paper we show that single-pixel optical systems, based on compressive detection, can also overcome the fundamental limitation imposed by multiple scattering to successfully transmit information. But, in contrast with the recently introduced schemes that use the transmission matrix technique, our approach does not require any a-priori calibration process that ultimately makes the present method suitable to use with dynamic scattering media. This represents an advantage over previous methods that rely on optical feedback wavefront control, especially for short speckle decorrelation times.

Generation of programmable 3D optical vortex structures through devil's vortex-lens arrays.

Different spatial distributions of optical vortices have been generated and characterized by implementing arrays of devil's vortex lenses in a reconfigurable spatial light modulator. A simple design procedure assigns the preferred position and topological charge value to each vortex in the structure, tuning the desired angular momentum. Distributions with charges and momenta of the opposite sign have been experimentally demonstrated. The angular velocity exhibited by the phase distribution around the focal plane has been visualized, showing an excellent agreement with the simulations. The practical limits of the method, with interest for applications involving particle transfer and manipulation, have been evaluated.

Diffractive digital lensless holographic microscopy with fine spectral tuning.

We experimentally demonstrate an all-diffractive optical setup for digital lensless holographic microscopy with easy wavelength line selection and micrometric resolution. In the proposed system, an ultrashort laser pulse is focused with a diffractive lens (DL) onto a pinhole of diameter close to its central wavelength to achieve a highly spatially coherent illumination cone as well as a spectral line with narrow width. To scan the complete spectrum of the light source the DL is displaced with respect to the pinhole plane. The proposed microscopy setup allows us to spectrally separate contributions from different sections of a sample, which may be attractive for several applications in life sciences.

Compressive holography with a single-pixel detector.

This Letter develops a framework for digital holography at optical wavelengths by merging phase-shifting interferometry with single-pixel optical imaging based on compressive sensing. The field diffracted by an input object is sampled by Hadamard patterns with a liquid crystal spatial light modulator. The concept of a single-pixel camera is then adapted to perform interferometric imaging of the sampled diffraction pattern by using a Mach-Zehnder interferometer. Phase-shifting techniques together with the application of a backward light propagation algorithm allow the complex amplitude of the object under scrutiny to be resolved. A proof-of-concept experiment evaluating the phase distribution of an ophthalmic lens with compressive phase-shifting holography is provided.

Femtosecond digital lensless holographic microscopy to image biological samples.

The use of femtosecond laser radiation in digital lensless holographic microscopy (DLHM) to image biological samples is presented. A mode-locked Ti:Sa laser that emits ultrashort pulses of 12 fs intensity FWHM, with 800 nm mean wavelength, at 75 MHz repetition rate is used as a light source. For comparison purposes, the light from a light-emitting diode is also used. A section of the head of a drosophila melanogaster fly is studied with both light sources. The experimental results show very different effects of the pinhole size on the spatial resolution with DLHM. Unaware phenomena on the field of the DLHM are analyzed.

Single-pixel polarimetric imaging.

We present an optical system that performs Stokes polarimetric imaging with a single-pixel detector. This fact is possible by applying the theory of compressive sampling to the data acquired by a commercial polarimeter without spatial resolution. The measurement process is governed by a spatial light modulator, which sequentially generates a set of preprogrammed light intensity patterns. Experimental results are presented and discussed for an object that provides an inhomogeneous polarization distribution.

Single-shot color digital holography based on the fractional Talbot effect.

We present a method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. A two-dimensional binary amplitude grating is used to generate Talbot periodic phase distributions in the reference beam. The interference patterns corresponding to the three chromatic channels are captured at once at different axial distances. In this scheme, one-shot recording and digital reconstruction allow for real-time measurement. Computer simulations and experimental results confirm the validity of our method.

Optical encryption based on computational ghost imaging.

Ghost imaging is an optical technique in which the information of an object is encoded in the correlation of the intensity fluctuations of light. The computational version of this fascinating phenomenon emulates, offline, the optical propagation through the reference arm, enabling 3D visualization of a complex object whose transmitted light is measured by a bucket detector. In this Letter, we show how computational ghost imaging can be used to encrypt and transmit object information to a remote party. Important features, such as key compressibility and vulnerability to eavesdropping, are experimentally analyzed.

Reconfigurable Shack-Hartmann sensor without moving elements.

We demonstrate wavefront sensing with variable measurement sensitivity and dynamic range by means of a programmable microlens array implemented onto an off-the-shelf twisted nematic liquid crystal display operating as a phase-only spatial light modulator. Electronic control of the optical power of a liquid lens inserted at the aperture stop of a telecentric relay system allows sensing reconfigurability without moving components. Results of laboratory experiments show the ability of the setup to detect both smooth and highly aberrated wavefronts with adequate sensitivity.

Single-shot digital holography by use of the fractional Talbot effect.

We present a method for recording in-line single-shot digital holograms based on the fractional Talbot effect. In our system, an image sensor records the interference between the light field scattered by the object and a properly codified parallel reference beam. A simple binary two-dimensional periodic grating is used to codify the reference beam generating a periodic three-step phase distribution over the sensor plane by fractional Talbot effect. This provides a method to perform single-shot phase-shifting interferometry at frame rates only limited by the sensor capabilities. Our technique is well adapted for dynamic wavefront sensing applications. Images of the object are digitally reconstructed from the digital hologram. Both computer simulations and experimental results are presented.

Optical filters with fractal transmission spectra based on diffractive optics.

The duality between the axial irradiance distribution originated by any circularly symmetric diffracting aperture under monochromatic illumination and its diffracted spectral intensity at a fixed on-axis point under broadband illumination is highlighted and experimentally investigated. Two applications are derived from this basic result. On the one hand, we suggest the use of a broadband source and a spectrometer for a single-shot measurement of the axial response of pupil filters. Second, we implement a spectral filter having a transmission spectrum with a fractal structure of frequencies. Experimental results and potential applications in synthetic spectra designs are provided.

High-visibility interference fringes with femtosecond laser radiation.

We propose and experimentally demonstrate an interferometer for femtosecond pulses with spectral bandwidth about 100 nm. The scheme is based on a Michelson interferometer with a dispersion compensating module. A diffractive lens serves the purpose of equalizing the optical-path-length difference for a wide range of frequencies. In this way, it is possible to register high-contrast interference fringes with micrometric resolution over the whole area of a commercial CCD sensor for broadband femtosecond pulses.

Spectral analysis of femtosecond pulse diffraction through binary diffractive optical elements: theory and experiment.

We report on the changes in the spectrum of a femtosecond pulse originated by diffraction of the ultrashort waveform through a circularly symmetric binary diffractive optical element. The analysis is performed in the framework of the Rayleigh-Sommerfeld formulation of the diffraction, where an analytical expression for the monochromatic amplitude distribution close to the optical axis is obtained. To corroborate our results, we experimentally measure the variations of the pulse spectrum within the collecting area of a spectrometer located at the output plane. Multiple splitting of the pulse spectrum in the vicinity of a focal position and a phase singularity are shown.