In order to measure the radial displacements of facets on surface of a growing spherical Cu_{2-δ}Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of fringes obtained applying digital laser interferometry method. Guided by the realistic experimental parameters (density and orientation of fringes), starting from 2-dimensional model interferograms and using unconventional custom designed Gaussian filtering window and unwrapping procedure of the retrieved phase, we have demonstrated that for considerable portion of parameter space the non-negligible inherent phase retrieval error is present solely due to non-integer number of fringes within the digitally recorded image (using CCD camera). Our results indicate the range of experimentally adjustable parameters for which the generated error is acceptably small. We also introduce a modification of the (last part) of the usual phase retrieval algorithm which significantly reduces the error in the case of small fringe density.
The method of digital processing of laser radiation interference pattern with the digital microscope and original two-beam interferometer with the phase Bragg grating as the amplitude beam splitter for a quantitative determination of the spatial and temporary coherence module of radiation is described. The digital processing of the interference pattern images was carried out with known software algorithms. Principles and functionality of a measurement procedures are demonstrated on measuring of the radiation coherence of several gas, solid-state and diode lasers.
It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the theoretical calculation of the lineshape, which gives a general closed--form expression for the spectrum in the time domain and is directly assimilable to the experimental interferogram. Error sources in Fourier integrals, apodization, peak fitting with standard interpolation functions, choice of background level, Stokes energy shifts, etc., are neatly avoided.
We report on phase-shifted holographic interferogram demodulation by singular value decomposition. Numerical processing of optically-acquired interferograms over several modulation periods was performed in two steps : 1- rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; 2- eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.
A single intensity-only holographic interferogram can records the full amplitude and phase information of optical field. However, current digital holography technologies cannot recover the lossless phase information from a single interferogram. In this paper, we provide an entirely new approach for the full-field quantitative phase imaging technology. We demonstrate that deep learning can be used to replace the entitative phase shifter, and quantitative phase imaging can obtain quantitative phase from a single interferogram in in-line holography. A deep-phase-shift network (DPS-net) is reporte…
We demonstrate swept-source optical coherence tomography in real-time by high throughput digital Fresnel hologram rendering from optically-acquired interferograms with a high-speed camera. The interferogram stream is spatially rescaled with respect to wavelength to compensate for field-of-view dilation inherent to discrete Fresnel transformation. Holograms are calculated from an input stream of 16-bit, 1024-by-1024-pixel interferograms recorded at up to 512 frames per second with a digital camera. All calculations are performed by a NVIDIA TITAN Xp graphics card on single-precision floating-po…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single shot interferogram. In the paper, a simple and effective method is presented without complex computation. The interference fringe is transferred to a phase distribution with a look-up-table. And then it is divided into different regions according to the parity of every pixel. The pixels in the same region have the same parity, which determines the wrapped pha…
We demonstrate the feasibility of high-quality digital holography of the human retina in real-time with a fast camera and commodity computer hardware. High throughput rendering of digital Fresnel holograms from optically-acquired inline interferograms is performed in conjunction with temporal demodulation by projection of hologram sequences onto a data-derived basis in order to discriminate local narrowband coherent detection contrasts, mostly due to blood flow and optical absorption, from spurious interferometric contributions. Digital holograms are calculated from a sustained input stream of…
Complex object wave recovery from single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of cross-term but this method suffers from poor resolution. For obtaining full pixel resolution, it is necessary to model the object wave recovery as an optimization problem. The optimization approach typically involves minimizing a cost function consisting of a data consistency term and one or more constraint terms. Despite its potential performance advantages, this m…
We demonstrate a 13-fold speed improvement in broadband cantilever-enhanced photoacoustic spectroscopy (CEPAS) by combining it with phase-controlled Fourier-transform spectroscopy (PC-FTS) instead of traditional Fourier-transform infrared spectroscopy (FTIR). PC-FTS is a modification of FTIR and capable of fundamentally faster interferogram acquisitions. The speed-improvement is beneficial for CEPAS, which is an especially sensitive version of the background-free photoacoustic spectroscopy technique. We used the PC-FTS-CEPAS technique to measure the absorption spectrum of methane in the mid-in…
We present a new technique for removing twin image in in-line digital Fourier holography using a combination of Fourier transformations. Instead of recording only a Fourier transform hologram of the object, we propose to record a combined Fourier transform hologram by simultaneously recording the hologram of the Fourier transform and the inverse Fourier transform of the object with suitable weighting coefficients. Twin image is eliminated by appropriate inverse combined Fourier transformation and proper choice of the weighting coefficients. An optical configuration is presented for recording c…
An approach reported recently by Alexandrov et al. on optical scatter imaging, termed digital Fourier microscopy (DFM), represents an adaptation of digital Fourier holography to selective imaging of biological matter. Holographic mode of recording of the sample optical scatter enables reconstruction of the sample image. Form-factor of the sample constituents provides a basis for discrimination of these constituents implemented via flexible digital Fourier filtering at the post processing stage. Like in the dark-field microscopy, the DFM image contrast appears to improve due to the suppressed o…
This paper presents an application of digital Fourier holography for selective imaging of scatterers with different sizes in turbid media such as biological tissues. A combination of Fourier holography and high-resolution digital recording, digital Fourier microscopy (DFM) permits crucial flexibility in applying filtering to highlight scatterers of interest in the tissue. The high-resolution digital hologram is a result of the collation of Fourier holographic frames to form a large-size composite hologram. It is expected that DFM has an improved signal-to-noise ratio as compared to conventiona…
The Differential Fourier Holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [1] the Differential Fourier Holography was successfully applied in many experiments to obtain amplitude and phase information about two-dimensional (2D) images. In this article we demonstrate numerically the possibility to apply the DFH also for investigation of unknown 3D Objects. The first simulation is made for a double-spiral structure plus a line as a reference object.
While numerous optical methods exist to probe the dynamics of biological or complex fluid samples, in recent years digital Fourier microscopy techniques, like differential dynamic microscopy, have emerged as ways to efficiently combine elements of imaging and scattering methods. Here, we demonstrate, through experiments and simulations, how point-spread function engineering can be used to extend the reach of differential dynamic microscopy.
Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular diversity illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3 to 0.7 with a 4X0.1 NA objective due to the constraint of planar geometry with weak illumination brightness and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500 to 1000 nm, …
We develop an error-free, nonuniform phase-stepping algorithm (nPSA) based on principal component analysis (PCA). PCA-based algorithms typically give phase-demodulation errors when applied to nonuniform phase-shifted interferograms. We present a straightforward way to correct those PCA phase-demodulation errors. We give mathematical formulas to fully analyze PCA-based nPSA (PCA-nPSA). These formulas give a) the PCA-nPSA frequency transfer function (FTF), b) its corrected Lissajous figure, c) the corrected PCA-nPSA formula, d) its harmonic robustness, and e) its signal-to-noise-ratio (SNR). We …
The integration of miniaturized optical spectrometers into mobile platforms will have an unprecedented impact on applications ranging from unmanned aerial vehicles (UAVs) to mobile phones. To address this demand, silicon photonics stands out as a platform capable of delivering compact and cost-effective devices. The Fourier transform spectrometer (FTS) is largely used in free-space spectroscopy, and its implementation in silicon photonics will contribute to bringing broadband operation and fine resolution to the chip scale. The implementation of an integrated silicon photonics FTS (Si-FTS) mus…
Optical spectrum analysis is the cornerstone of spectroscopic sensing, optical network performance monitoring, and hyperspectral imaging. While conventional high-performance spectrometers used to perform such analysis are often large benchtop instruments, on-chip spectrometers have recently emerged as a promising alternative with apparent Size, Weight, and Power (SWaP) advantages. Existing on-chip spectrometer designs, however, are limited in spectral channel count and signal-to-noise ratio (SNR). Here we demonstrate a transformative on-chip digital Fourier transform (dFT) spectrometer that ca…
Automated label-free quantitative imaging of biological samples can greatly benefit high throughput diseases diagnosis. Digital holographic microscopy (DHM) is a powerful quantitative label-free imaging tool that retrieves structural details of cellular samples non-invasively. In off-axis DHM, a proper spatial filtering window in Fourier space is crucial to the quality of reconstructed phase image. Here we describe a region-recognition approach that combines shape recognition with an iterative thresholding to extracts the optimal shape of frequency components. The region recognition technique …
360-degrees digitalization of three-dimensional (3D) solids using a projected light-strip is a well established technique. These profilometers project a light-strip over the solid under analysis while the solid is rotated a full revolution. Then a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based strip centroid estimation, we propose to use Fourier phase-demodulation. This 360-degrees profilometer first constructs a carrier-frequency fringe-pattern by closely adding individual lig…
Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system performance beyond the limit defined by its optical elements. The FPM technique applies a novel phase retrieval procedure to achieve both resolution enhancement and complex image recovery. In this letter, we compare FPM data to both theoretical prediction and phase-shifting digital holography measurement to show that its acquired phase maps are quantitative and artifact-free. We additionally explore the relationship between the achievable spatial and optic…
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schrödinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast al…
Fourier ptychography microscopy (FPM), sharing its roots with synthetic aperture technique and phase retrieval method, is a recently developed computational microscopic super-resolution technique. By turning on the light-emitting diode (LED) elements sequentially and acquiring the corresponding images that contain different spatial frequencies, FPM can achieve a wide field-of-view (FOV), high-spatial-resolution imaging, and phase recovery simultaneously. Conventional FPM assumes that the sample is sufficiently thin and strictly in focus. Nevertheless, even for a relatively thin sample, the non…
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from superimposition of the original signal with a reference beam. This approach can provide significant advantages in digital holography since it poses less stringent requirements on the reference beam. In particular, it does not require spatial separation between the sought signal and the reference beam. Moreover, the reference beam need not be known precisely, and…
We present a superpixel method for full spatial phase and amplitude control of a light beam using a digital micromirror device (DMD) combined with a spatial filter. We combine square regions of nearby micromirrors into superpixels by low pass filtering in a Fourier plane of the DMD. At each superpixel we are able to independently modulate the phase and the amplitude of light, while retaining a high resolution and the very high speed of a DMD. The method achieves a measured fidelity $F=0.98$ for a target field with fully independent phase and amplitude at a resolution of $8\times 8$ pixels per …
A new method for document watermarking based on the digital Fourier hologram is proposed. It applies the methods of digital image watermarking based on holographic principle presented previously in several papers into printed documents. Experimental results show that the proposed method can not only meet the demand on invisibility, robustness and non-reproducibility of the document watermark, and but also has other advantages compared with the conventional methods for document securities such as embossed hologram, Lippmann photograph and halftone modulation.
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as filtering, convolution, and correlation. Digital FFTs are limited in speed by the necessity of moving charge within logic gates. An analog temporal FFT in fiber optics has been demonstrated with highest data bandwidth. However, the implementation with discrete fiber optic FFT components is bulky. Here, we present and analyze a design of an optical FFT in Silic…
Phase noise or frequency noise is a key metrics to evaluate the short term stability of a laser. This property is of a great interest for the applications but delicate to characterize, especially for narrow line-width lasers. In this letter, we demonstrate a digital cross correlation scheme to characterize the absolute phase noise of sub-hertz line-width lasers. Three 1,542 nm ultra-stable lasers are used in this approach. For each measurement two lasers act as references to characterize a third one. Phase noise power spectral density from 0.5 Hz to 0.8 MHz Fourier frequencies can be derived f…
Exponential multi-graylevel computational-weighted dithering for high-quality binarized Fourier single-pixel imaging
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences（中国科学院非线性力学国家重点实验室，中国科学院力学研究所）；State Key Laboratory of Fire Science, University of Science and Technology of China（中国科学技术大学火灾科学国家重点实验室）
