Phase-only Filter Research Articles

Wavelet-modified segmented phase-only filter for in-plane rotated object recognition

In this paper, we propose and implement a wavelet-modified segmented phase-only filter for in-plane rotated object recognition. The wavelet filter is combined with the segmented phase-only filter to significantly enhance the correlation capability of the optical processor. To verify the consistency of the results, we have calculated the performance measure parameters such as peak-to-correlation energy, peak-to-sidelobe ratio, discrimination ratio and signal-to-noise ratio and compared the performance with a conventional segmented phase-only filter. For carrying out the study, we have developed a dataset of different distorted objects such as alphabets, digits, vehicles, fighter planes. Through a series of experiments and case studies, we are able to prove that the proposed filter reduces the false alarm rate while increasing recognition capability.

Single-Shot 3D Incoherent Imaging Using Deterministic and Random Optical Fields with Lucy–Richardson–Rosen Algorithm

Coded aperture 3D imaging techniques have been rapidly evolving in recent years. The two main directions of evolution are in aperture engineering to generate the optimal optical field and in the development of a computational reconstruction method to reconstruct the object’s image from the intensity distribution with minimal noise. The goal is to find the ideal aperture–reconstruction method pair, and if not that, to optimize one to match the other for designing an imaging system with the required 3D imaging characteristics. The Lucy–Richardson–Rosen algorithm (LR2A), a recently developed computational reconstruction method, was found to perform better than its predecessors, such as matched filter, inverse filter, phase-only filter, Lucy–Richardson algorithm, and non-linear reconstruction (NLR), for certain apertures when the point spread function (PSF) is a real and symmetric function. For other cases of PSF, NLR performed better than the rest of the methods. In this tutorial, LR2A has been presented as a generalized approach for any optical field when the PSF is known along with MATLAB codes for reconstruction. The common problems and pitfalls in using LR2A have been discussed. Simulation and experimental studies for common optical fields such as spherical, Bessel, vortex beams, and exotic optical fields such as Airy, scattered, and self-rotating beams have been presented. From this study, it can be seen that it is possible to transfer the 3D imaging characteristics from non-imaging-type exotic fields to indirect imaging systems faithfully using LR2A. The application of LR2A to medical images such as colonoscopy images and cone beam computed tomography images with synthetic PSF has been demonstrated. We believe that the tutorial will provide a deeper understanding of computational reconstruction using LR2A.

Super-resolution and apodization with discrete adaptive optics.

High-resolution imaging is of great importance in various fields. The use of pupil phase-only filters (PPF) exceeds the diffraction limit of the imaging system in a simple way. When dealing with distorted wavefronts, however, PPF require that aberrations be compensated for. In this paper, we introduce a novel technique consisting of the use of discrete adaptive optics with PPFs so that the compensating device implements the PPF at the same time. Analysis of the theory for point spread function reshaping using PPFs has enabled us to develop a new approach to characterizing apodizing filters. A validation experiment has been carried out, the first of its kind to our knowledge, in which a number of PPFs were combined with two levels of compensation. Our experimental results are discussed.

Coupled two-core integrated waveguides modal analysis

We present a modal analysis of coupled two-core integrated waveguides fabricated by femtosecond laser writing as a function of the core-to-core distance, illuminating position and input light wavelength. In order to do that we use the correlation filter method, implementing the computer generated holograms in a phase-only spatial light modulator. Due to the two-core waveguide symmetry, we prove it is not necessary to encode the complex amplitude in a phase-only device as long as the cores are not strongly coupled. A comparison between experimental and numerical modal weights is presented, showing that simple phase-only match filters allow the modal decomposition of two-core waveguides output beams.

A Numerical Study of Optimization Methods for Phase-Only Optical Pulse-Shaping

The field of optical pulse-shaping and its applications is introduced, with a focus on time-domain approaches. A numerical investigation of all-fiber, time-domain, phase-only filtering is conducted for arbitrary temporal pulse synthesis. The theoretical phase modulation function required for generating use- specific target-intensity profiles is calculated using different optimization methods including a Brute Force Monte Carlo search, the Simulated Annealing method and the Genetic Algorithm method. The convergence speed, computational complexity and accuracy of these methods is compared under binary phase-only modulation, where the Genetic algorithm was found to outperform other methods.

High-resolution digital spatial control of a highly multimode laser

We developed a rapid and efficient method for generating laser outputs with arbitrary shaped distributions and properties that are needed for a variety of applications. It is based on simultaneously controlling the intensity, phase, and coherence distributions of the laser. The method involves a digital degenerate cavity laser in which a phase-only spatial light modulator and spatial filters are incorporated. As a result, a variety of unique and high-resolution arbitrary shaped laser beams were generated with either a low or a high spatial coherence and with a minimal change in the laser output power. By controlling the phase, intensity, and coherence distributions, a shaped laser beam was efficiently reshaped into a completely different shape after free space propagation. The generation of such laser beams could lead to new and interesting applications.

Investigation of temporal Talbot operation in a conventional optical tapped delay line structure.

We propose a novel scheme of temporal Talbot effect achieving optical pulse train repetition-rate multiplication in a conventional tapped delay line structure. While it is generally used for spectral amplitude filtering, we show that such architecture could also be configured for spectral phase-only filtering, as well as for a combination of amplitude and phase filtering regimes. We theoretically derive and numerically simulate the working principle of the concept, followed by a proof-of-principle experimental demonstration using an off-the-shelf Mach-Zehnder delay line interferometer, which corresponds to the simplest version of the proposed structure. We address the efficiency, and potential performance degradation in the presence of power imbalance and delay line length inaccuracy of the architecture, together with applied phase error.

On-Chip Sensor for Simultaneous Temperature and Refractive Index Measurements Based on a Dual-Passband Microwave Photonic Filter

We propose and experimentally demonstrate an on-chip optical sensor based on a dual-passband microwave photonic filter (MPF) incorporating a silicon photonic integrated microdisk resonator (MDR). Two whispering gallery modes supported by the MDR that are experiencing different wavelength shifts are employed for simultaneous temperature and refractive index (RI) measurements. To increase the interrogation speed and resolution, the MDR is incorporated in an MPF to produce two microwave passbands. By applying a broadband linearly chirped microwave waveform to the MPF, two filtered microwave waveforms with their temporal locations or equivalently central frequencies corresponding to the wavelength shifts of the notches are generated. The measurement of the temporal locations or equivalently the central frequencies is performed at high speed and high resolution using a digital signal processor. To increase the signal-to-noise ratio of the filtered microwave waveforms, a noise reduction algorithm based on phase-only filtering is proposed and employed. The on-chip optical sensing system is experimentally demonstrated. The sensing system can provide high temperature and RI interrogation resolutions of 2.4 × 10−5 °C and 9.1 × 10−8 RIU at a high interrogation speed of 1 MHz.

High-Speed and High-Resolution Interrogation of a Silicon Photonic Microdisk Sensor Based on Microwave Photonic Filtering

High-speed and high-resolution interrogation of a silicon photonic microdisk sensor based on microwave photonic filtering and advanced signal processing is proposed and experimentally demonstrated. An integrated microdisk resonator (MDR) with a high Q factor is used as a sensor which is interrogated by incorporating the MDR into a microwave photonic filter (MPF) consisting of a laser source, a phase modulator (PM), the MDR, and a photodetector (PD), with the central frequency of the MPF being a function of the resonant wavelength of the MDR. A broadband linearly chirped microwave waveform (LCMW) is applied to the input of the MPF to generate a filtered microwave waveform. By measuring the temporal location of the filtered microwave waveform, the sensing information is revealed. To increase the signal-to-noise ratio (SNR) of the filtered microwave waveform, a phase-only filter (POF) realized based on the LCMW is correlated with the filtered microwave waveform, to generate a compressed pulse, which is filtered using a Hamming window to remove the noise and recorrelated with the POF to recover the filtered microwave waveform. Since the SNR is significantly increased, the interrogation accuracy is improved. The use of the proposed sensor for temperature and refractive index (RI) sensing is performed. The experimental results show that the sensor has a sensitivity of 76.8 pm/°C and a resolution of 0.234 °C as a temperature sensor, and a sensitivity of 33.28 nm/RIU and a resolution of 1.32 × 10−3 RIU as an RI sensor. The interrogation speed is as high as 100 kHz.

Numerical modeling of two-photon focal modulation microscopy with a sinusoidal phase filter.

A spatiotemporal phase modulator (STPM) is theoretically investigated using the vectorial diffraction theory. The STPM is equivalent to a time-dependent phase-only pupil filter that alternates between a homogeneous filter and a stripe-shaped filter with a sinusoidal phase distribution. It is found that two-photon focal modulation microscopy (TPFMM) using this STPM can significantly suppress the background contribution from out-of-focus ballistic excitation and achieve almost the same resolution as two-photon microscopy. The modulation depth is also evaluated and a compromise exists between the signal-to-background ratio and signal-to-noise ratio. The theoretical investigations provide important insights into future implementations of TPFMM and its potential to further extend the penetration depth of nonlinear microscopy in imaging multiple-scattering biological tissues.

Super-resolution pupil filtering for visual performance enhancement using adaptive optics

Ocular aberration correction can significantly improve visual function of the human eye. However, even under ideal aberration correction conditions, pupil diffraction restricts the resolution of retinal images. Pupil filtering is a simple super-resolution (SR) method that can overcome this diffraction barrier. In this study, a 145-element piezoelectric deformable mirror was used as a pupil phase filter because of its programmability and high fitting accuracy. Continuous phase-only filters were designed based on Zernike polynomial series and fitted through closed-loop adaptive optics. SR results were validated using double-pass point spread function images. Contrast sensitivity was further assessed to verify the SR effect on visual function. An F-test was conducted for nested models to statistically compare different CSFs. These results indicated CSFs for the proposed SR filter were significantly higher than the diffraction correction (p < 0.05). As such, the proposed filter design could provide useful guidance for supernormal vision optical correction of the human eye.

Improved generation method utilizing a modified Fourier spectrum for Airy beams with the phase-only filter technique.

We present an improved method to generate Airy beams utilizing a liquid crystal on silicon (LCoS) device. In this method, the phase and amplitude information of a modified Fourier spectrum of an Airy beam together with a Fresnel holographic lens is encoded onto the LCoS using the phase-only filter technique; thus, a desired Airy beam is formed in the focal plane of the Fresnel holographic lens. In this paper, the principle of the proposed method is described in detail, and both the excellent numerical simulations and experimental results for verifying this method are demonstrated. It is shown that the new generation method is accurate and simple; in particular, the setup is more compact compared to the conventional Fourier transform method, which comprises only the input polarized laser and a LCoS device. This effective method will further promote investigations into the properties and applications of Airy beams.

Coded aperture correlation holography system with improved performance [Invited

Coded aperture correlation holography (COACH) is a recently introduced technique for recording incoherent digital holograms of general three-dimensional scenes. In COACH, a random-like coded phase mask (CPM) is used as a coded aperture. Even though the CPM is optimized to reduce background noise, there is still a substantial amount of noise, mitigating the performance of COACH. In order to reduce the noise, we first modify the hologram reconstruction method. Instead of computing the correlation between a complex hologram of the entire object and a hologram of a source point, in this study the numerical correlation is performed with a phase-only filter. In other words, the phase function of the Fourier transform of the source point hologram is used as the spatial filter in the correlation process. Furthermore, we propose and demonstrate two additional methods for reducing the background noise in COACH. The first is based on the integration of a quadratic phase function, as used in Fresnel incoherent correlation holography (FINCH), with the CPM of COACH. This hybrid COACH-FINCH system enables a dynamic trade-off between the amount of background noise and the axial resolution of the system. The second method is employed by recording COACH holograms with multiple independent CPMs and averaging over the reconstructed images. The results of the above two techniques are compared with FINCH and with a regular imaging system.

Differential processing for frequency chirp measurement using optical pulse synthesizer

In this study, we introduced an optical pulse synthesizer (OPS) to measure frequency chirps of optical pulses by differential processing. The OPS has a single-chip integrated structure of all elements for the differential filtering and enables stable measurement. Because the exact filter causes a large loss, we employed a phase-only filter, whose frequency response was only in phase. We measured chirp rates of pulses which were induced by propagating standard single mode fibers with different lengths. The retrieved chirp rates were comparable to calculated results. We simulated accuracy of the method and concluded that our experiment had phase control accuracy within ~0.07π.

Compressive phase-only filtering at extreme compression rates

We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter. The proposed method is based on two properties of phase-only filtering: such filtering is a unitary circulant transform, and the correlation plane it produces is usually sparse. Thanks to these properties, phase-only filters are perfectly compatible with the framework of compressive sensing. Moreover, the lasso-based recovery algorithm is very fast when phase-only filtering is used as the compression matrix. The proposed method can be seen as a generalization of the correlation-based pattern recognition technique, which is hereby applied directly to non-adaptively acquired compressed data. At the time of measurement, any prior knowledge of the target object for which the data will be scanned is not required. We show that images measured at extremely high compression rates may still contain sufficient information for target classification and localization, even if the compression rate is high enough, that visual recognition of the target in the reconstructed image is no longer possible. The method has been applied by us to highly undersampled measurements obtained from a single-pixel camera, with sampling based on randomly chosen Walsh–Hadamard patterns.

A convolution-based fractional transform

The fractional transforms are a class of powerful tool for the presentation of time–frequency domains in the field of signal processing. Based on the convolution algorithm of discrete fractional Fourier transform and gyrator transform, we propose a generalized framework defining a class of fractional transforms. By choosing various phase filters, the fractional transform can be employed for different computational tasks of information processing. The several properties of typical fractional transform are reserved in this definition scheme. Under the model of the convolution-based transform, fractional Fourier transform and gyrator transform are synthesized. Moreover, the transform can be implemented by an optical 4f system with phase-only filtering easily, which is a useful tool in the application of optical information processing. Numerical results are given for demonstrating the proposed transform and its application.

Road marking features extraction using the VIAPIX® system

Precise extraction of road marking features is a critical task for autonomous urban driving, augmented driver assistance, and robotics technologies. In this study, we consider an autonomous system allowing us lane detection for marked urban roads and analysis of their features. The task is to relate the georeferencing of road markings from images obtained using the VIAPIX® system. Based on inverse perspective mapping and color segmentation to detect all white objects existing on this road, the present algorithm enables us to examine these images automatically and rapidly and also to get information on road marks, their surface conditions, and their georeferencing. This algorithm allows detecting all road markings and identifying some of them by making use of a phase-only correlation filter (POF). We illustrate this algorithm and its robustness by applying it to a variety of relevant scenarios.

Programmable super-resolution pupil phase filter with a deformable mirror

Compared with binary diffractive super-resolving elements, programmable super-resolution pupil filters permit the analysis of various filter designs and allow the filters to be changed rapidly to modify the response of an optical system. In this Letter, a deformable mirror is employed as a programmable super-resolution pupil phase filter. Continuous phase-only filters based on the Zernike polynomial series are designed by the genetic algorithm and fitted through closed-loop adaptive optics with a piezoelectric deformable mirror. Experimental super-resolution results are in agreement with the theoretical predictions. This method has no polarization light requirement and is convenient for application.

Character recognition in degraded document images using morphological and phase-only filtering

Nowadays, new optical character recognition (OCR) algorithms for mobile devices are actively developed. Most of these algorithms work well with documents digitized under perfect conditions. When using mobile devices, document images are subject to various distortions, such as nonuniform and poor illumination, geometric distortions, low resolution, and sensor noise. In this paper, we propose a reliable method for recognition of contextually unrelated characters in degraded document images with the use of a bank of adaptive morphological and phase-only filters. With the help of computer simulation, the results of operation of traditional and proposed approaches to detection and classification of characters of the Latin alphabet in distorted document images are compared.

Pareto optimality between width of central lobe and peak sidelobe intensity in the far-field pattern of lossless phase-only filters for enhancement of transverse resolution.

Resolution capability of an optical imaging system can be enhanced by reducing the width of the central lobe of the point spread function. Attempts to achieve the same by pupil plane filtering give rise to a concomitant increase in sidelobe intensity. The mutual exclusivity between these two objectives may be considered as a multiobjective optimization problem that does not have a unique solution; rather, a class of trade-off solutions called Pareto optimal solutions may be generated. Pareto fronts in the synthesis of lossless phase-only pupil plane filters to achieve superresolution with prespecified lower limits for the Strehl ratio are explored by using the particle swarm optimization technique.