Single pixel imaging at high pixel resolutions.

The usually reported pixel resolution of single pixel imaging (SPI) varies between 32 × 32 and 256 × 256 pixels falling far below imaging standards with classical methods. Low resolution results from the trade-off between the acceptable compression ratio, the limited DMD modulation frequency, and reasonable reconstruction time, and has not improved significantly during the decade of intensive research on SPI. In this paper we show that image measurement at the full resolution of the DMD, which lasts only a fraction of a second, is possible for sparse images or in a situation when the field of view is limited but is a priori unknown. We propose the sampling and reconstruction strategies that enable us to reconstruct sparse images at the resolution of 1024 × 768 within the time of 0.3s. Non-sparse images are reconstructed with less details. The compression ratio is on the order of 0.4% which corresponds to an acquisition frequency of 7Hz. Sampling is differential, binary, and non-adaptive, and includes information on multiple partitioning of the image which later allows us to determine the actual field of view. Reconstruction is based on the differential Fourier domain regularized inversion (D-FDRI). The proposed SPI framework is an alternative to both adaptive SPI, which is challenging to implement in real time, and to classical compressive sensing image recovery methods, which are very slow at high resolutions.

Differential real-time single-pixel imaging with Fourier domain regularization: applications to VIS-IR imaging and polarization imaging.

The speed and quality of single-pixel imaging (SPI) are fundamentally limited by image modulation frequency and by the levels of optical noise and compression noise. In an approach to come close to these limits, we introduce a SPI technique, which is inherently differential, and comprises a novel way of measuring the zeroth spatial frequency of images and makes use of varied thresholding of sampling patterns. With the proposed sampling, the entropy of the detection signal is increased in comparison to standard SPI protocols. Image reconstruction is obtained with a single matrix-vector product so the cost of the reconstruction method scales proportionally with the number of measured samples. A differential operator is included in the reconstruction and following the method is based on finding the generalized inversion of the modified measurement matrix with regularization in the Fourier domain. We demonstrate 256 × 256 SPI at up to 17 Hz at visible and near-infrared wavelength ranges using 2 polarization or spectral channels. A low bit-resolution data acquisition device with alternating-current-coupling can be used in the measurement indicating that the proposed method combines improved noise robustness with a differential removal of the direct current component of the signal.

Far-field signature of sub-wavelength microscopic objects.

Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically depends on the level of noise. This new path to superresolution has been recently investigated with use of compressed sensing and machine learning. We demonstrate a two-stage technique based on deconvolution and genetic optimization which enables the recovery of objects with features of 1/10 of the wavelength. We indicate that l1-norm based optimization in the Fourier domain unrelated to sparsity is more robust to noise than its l2-based counterpart. We also introduce an extremely fast general purpose restricted domain calculation method for Fourier transform based iterative algorithms operating on sparse data.

Single-pixel imaging with sampling distributed over simplex vertices.

We propose a method of reduction of experimental noise in single-pixel imaging by expressing the subsets of sampling patterns as linear combinations of vertices of a multidimensional regular simplex. This method also may be directly extended to complementary sampling. The modified measurement matrix contains nonnegative elements with patterns that may be directly displayed on intensity spatial light modulators. The measurement becomes theoretically independent of the ambient illumination, and in practice becomes more robust to the varying conditions of the experiment. We show how the optimal dimension of the simplex depends on the level of measurement noise. We present experimental results of single-pixel imaging using binarized sampling and real-time reconstruction with the Fourier domain regularized inversion method.

Real-time single-pixel video imaging with Fourier domain regularization.

We present a closed-form image reconstruction method for single-pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales proportionally with the number of measured samples. Regularization of the inverse problem is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters. The final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression, this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with measurement at a frame rate of 11 Hz for highly compressive measurements with a resolution of 256 × 256. To this end, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we can use binary rather than continuous sampling and reach similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine- or Morlet-based sampling with digital micromirror devices without advanced binarization methods.

Single-pixel imaging with Morlet wavelet correlated random patterns.

Single-pixel imaging is an indirect imaging technique which utilizes simplified optical hardware and advanced computational methods. It offers novel solutions for hyper-spectral imaging, polarimetric imaging, three-dimensional imaging, holographic imaging, optical encryption and imaging through scattering media. The main limitations for its use come from relatively high measurement and reconstruction times. In this paper we propose to reduce the required signal acquisition time by using a novel sampling scheme based on a random selection of Morlet wavelets convolved with white noise. While such functions exhibit random properties, they are locally determined by Morlet wavelet parameters. The proposed method is equivalent to random sampling of the properly selected part of the feature space, which maps the measured images accurately both in the spatial and spatial frequency domains. We compare both numerically and experimentally the image quality obtained with our sampling protocol against widely-used sampling with Walsh-Hadamard or noiselet functions. The results show considerable improvement over the former methods, enabling single-pixel imaging at low compression rates on the order of a few percent.

Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging.

Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper, we propose an efficient way of using complex-valued and nonbinary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows us to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.

Asymmetric transmission of radially polarized THz radiation through a double circular grating.

We report on unidirectional and asymmetric transmission of radially polarized THz radiation through a dual circular metallic grating with sub-wavelength slits. Unidirectional transmission is shown theoretically for a super-Gaussian incident beam, and an asymmetric transmission is demonstrated experimentally, when the radially polarized beam of 0.1 THz is obtained by converting a linearly polarized beam with a discontinuous phase retarder and a tapered waveguide. The dual grating does not include nonlinear materials, its operation is reciprocal, and analogous to that of some planar metallic gratings.

Asymmetric transmission of terahertz radiation through a double grating.

We report on experimental evidence of unidirectional transmission of terahertz waves through a pair of metallic gratings with different periods. The gratings are optimized for a broadband transmission in one direction, accompanied with a high extinction rate in the opposite direction. In contrast to previous studies, we show that the zero-order nonreciprocity cannot be achieved. Nonetheless, we confirm that the structure can be used successfully as an asymmetric filter.

Two-dimensional point spread matrix of layered metal-dielectric imaging elements.

We describe the change of the spatial distribution of the state of polarization occurring during two-dimensional (2D) imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarization of incident light is not preserved due to the difference in the amplitude transfer functions for the TM and TE polarizations. In effect, the transfer function and the point spread function (PSF) that characterize 2D imaging through a multilayer both have a matrix form, and cross-polarization coupling is observed for spatially modulated beams with a linear or circular incident polarization. The PSF in a matrix form is used to characterize the resolution of the superlens for different polarization states. We demonstrate how the 2D PSF may be used to design a simple diffractive nanoelement consisting of two radial slits. The structure assures the separation of nondiffracting radial beams originating from two slits in the mask and exhibits an interesting property of a backward power flow in between the two rings.

Multiscale analysis of subwavelength imaging with metal-dielectric multilayers.

Imaging with a layered superlens is a spatial filtering operation characterized by the point spread function (PSF). We show that in the same optical system the image of a narrow subwavelength Gaussian incident field may be surprisingly dissimilar to the PSF, and the width of the PSF is not a straightforward measure of the resolution. The FWHM or standard deviation of the PSF gives ambiguous information about the actual resolution, and imaging of objects smaller than the FWHM of the PSF is possible. A multiscale analysis of imaging gives good insight into the peculiar scale-dependent properties of subwavelength imaging.

Comparison of different methods for rigorous modeling of photonic crystal fibers.

We present a summary of the simulation exercise carried out within the EC Cost Action P11 on the rigorous modeling of photonic crystal fiber (PCF) with an elliptically deformed core and noncircular air holes with a high fill factor. The aim of the exercise is to calculate using different numerical methods and to compare several fiber characteristics, such as the spectral dependence of the phase and the group effective indices, the birefringence, the group velocity dispersion and the confinement losses. The simulations are performed using four rigorous approaches: the finite element method (FEM), the source model technique (SMT), the plane wave method (PWM), and the localized function method (LFM). Furthermore, we consider a simplified equivalent fiber method (EFM), in which the real structure of the holey fiber is replaced by an equivalent step index waveguide composed of an elliptical glass core surrounded by air cladding. All these methods are shown to converge well and to provide highly consistent estimations of the PCF characteristics. Qualitative arguments based on the general properties of the wave equation are applied to explain the physical mechanisms one can utilize to tailor the propagation characteristics of nonlinear PCFs.

PlaneWave Admittance Method- a novel approach for determining the electromagnetic modes in photonic structures.

In this article we present a novel approach for determining the electromagnetic modes of photonic multilayer structures. We combine the plane wave expansion method with the method of lines resulting in a fast and accurate computational technique which we named the plane wave admittance method. In addition, we incorporate perfectly matched layers at the boundaries parallel to the multilayer surfaces which allow for easy determination of leaky modes. The convergence of the method is verified for the case of photonic crystal slab showing very good agreement with the results obtained with full three-dimensional plane wave expansion method while the numerical effort is largely reduced. The numerical implementation of the method will be soon available on the web.