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Una herramienta para la caracterización de la calidad óptica de un sistema formador de imagen es el sensor de frente de onda Shack-Hartmann, muy empleado en óptica adaptativa. Exploraremos la historia, principios de funcionamiento y aplicaciones de este dispositivo y sus posibilidades para el astrónomo aficionado. En artículos anteriores (Astronomía 255 a 258), hemos hablado de las aberraciones ópticas, así como de su impacto en nuestras observaciones astronómicas y actividad fotográfica, con lo que a los objetos del cosmos se refiere. En este artículo introduciremos un tipo de dispositivos ampliamente utilizados por la comunidad científica, y que están empezando a irrumpir en el terreno del aficionado para la caracterización de estas aberraciones en nuestros telescopios, y nos centraremos en el más destacado de ellos: el sensor de frentes de onda Shack-Hartmann, o Hartmann-Shack.

The deflection of charged particles is an intuitive way to visualize an electromagnetic oscillation of coherent light. Here, we present a real-time ultrafast oscilloscope for time-frozen visualization of a terahertz (THz) optical wave by probing light-driven motion of relativistic electrons. We found the unique condition of subwavelength metal slit waveguide for preserving the distortion-free optical waveform during its propagation. Momentary stamping of the wave, transversely travelling inside a metal slit, on an ultrashort wide electron bunch enables the single-shot recording of an ultrafast optical waveform. As a proof-of-concept experiment, we successfully demonstrated to capture the entire field oscillation of a THz pulse with a sampling rate of 75.7 TS/s. Owing to the use of transversely-wide and longitudinally-short electron bunch and transversely travelling wave, the proposed “single-shot oscilloscope” will open up new avenue for developing the real-time petahertz (PHz) metrology., A travelling wave inside a metal slit can reveal its own waveform by probing deflecting motions of charged particles. Here, a real-time THz oscilloscope was demonstrated by utilizing the relativistic electrons and the subwavelength slit waveguide.

Silicon immersion gratings and grisms enable compact, high-throughput, near-infrared spectrographs. These instruments are used in ground-based efforts to characterize stellar and exoplanet atmospheres and in space-based observatories. Our grating fabrication technique uses x-ray crystallography to orient the crystal structure of silicon, followed by a specialized lithography and wet chemical etching to produce a blazed grating. The etching process takes advantage of the Silicon crystal structure and relative difference in etch rates between the [100] and [111] crystal planes. This allows us to produce parts that have phase uniformities of

In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number n to improve measurement precision. However, practical constraints prevent the arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by the saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains a considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to remarkably mitigate the detector saturation effect with low-cost apparatuses.

Inverse problem of Mueller polarimetry is defined as a determination of geometrical features of the metrological structures (i.e. 1D diffraction gratings) from its experimental Mueller polarimetric signature. This nonlinear problem was considered as an optimization problem in a multi-parametric space using the least square criterion and the Levenberg–Marquardt algorithm. We demonstrated that solving optimization problem with the experimental Mueller matrix spectra taken in conical diffraction configuration helps finding a global minimum and results in smaller variance values of reconstructed dimensions of the grating profile.

[EN]In this work we firstly study the influence of different parameters in the temporal characterization of ultrashort laser pulses with the recently developedamplitude swing technique. In this technique, the relative amplitude of two delayed replicas is varied while measuring their second-harmonic spectra. Herewe study the retrieval of noisy traces and the implications of having different delays or phase retardations (relative phases)between the two replicas. Then, we study the capability of the technique to characterize the pulses when the second-harmonic signal is spectrally uncalibrated or incomplete, presenting the analytical calculation of the marginal, which is used to calibrate the traces and to perform the pulse retrievals. We experimentally show the retrieval of different pulses using diverse delays and phase retardationsto perform the amplitude swing trace and demonstrate that, from an uncalibrated trace, both the pulse informationandthe response of the nonlinear process can be simultaneously retrieved.In sum, the amplitude swing technique is shown to be very robust against experimental constraints and limitations, showing a high degree of soundness., Spanish Ministerio de Economía y Competitividad (MINECO) (FIS2017-87970-R, EQC2018-004117-P), Consejería de Educación, Junta de Castilla y León (SA287P18) and FEDER Funds, Fundación General de la Universidad de Salamanca (PC_TCUE18-20_020).

[EN]We use self-calibrating dispersion scan to experimentally detect and quantify the presence of pulse train instabilities in ultrashort laser pulse trains. We numerically test our approach against two different types of pulse instability, namely second-order phase fluctuations and random phase instability, where the introduction of an adequate metric enables univocally quantifying the amount of instability. The approach is experimentally demonstrated with a supercontinuum fibre laser, where we observe and identify pulse train instabilities due to nonlinear propagation effects under anomalous dispersion conditions in the photonic crystal fibre used for spectral broadening. By replacing the latter with an all-normal dispersion fibre, we effectively correct the pulse train instability and increase the bandwidth of the generated coherent spectrum. This is further confirmed by temporal compression and measurement of the output pulses down to 15 fs using dispersion scan., The authors acknowledge funding from the Junta de Castilla y León (SA287P18) and FEDER funds; Spanish Ministerio de Economía y Competitividad (MINECO) (FIS2017-87970-R, EQC2018-004117-P, DI-15-07461, PTQ-15-07708); European EUREKA program CDTI-INNO-20171026; CCDR-N via the project Nanotechnology-based functional solutions (NORTE-01-0145-FEDER-000019); Fundação para a Ciência e a Tecnologia (FCT), Portugal (grants ‘UltraGraf’ M-ERA-NET2/0002/2016, M-ERA-NET2/0004/2016, UID/NAN/50024/2013, PTDC/FIS-OTI/32213/2017); Network of Extreme Conditions Laboratories - NECL and CCDR-N (NORTE-07-0124-FEDER-000070, NORTE-01-0145-FEDER-022096); PT2020 (program 05/SI/2017 – SI I&DT Empresarial - DI, grant no. 33573; program 04/SI/2019 Projetos de I&D Industrial à Escala Europeia, grant no. 045932). BA acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 798264.

Lisää oa-julkaisu, kun saatavilla. A sensitive photoacoustic detection approach employing a silicon cantilever is investigated for power measurement of electromagnetic radiation. The technique which is actuated by pressure waves generated through radiation-induced heat depicts high sensitivity for a considerably large spectral range from 325 nm to 1523 nm. The implemented method shows linear response in the measurement of radiation power from 15 nW to 6 mW demonstrating a dynamic range of almost six orders of magnitude. A numerical model has been developed to analyze and optimize the measurement sensitivity. The model allows studying different dimensions of the cantilever which is one of the key components of the radiation detection process. The numerical results are in good agreement with experimental results. The electromagnetic power detection technique shows future potential for industrial applications and scientific studies.

Wavefront sensors are applied for wavefront measurement, which is the basis for analyzing and testing optical systems. SPIE (OP300) 2021 is a special year for Tribute to Professor James C. Wyant who has great contributions and services to the fields of optical metrology and optics education, including the science and application of interferometry. This paper focuses mainly on recalling some interesting stories related to Prof. Wyant.

The complete Mueller polarimetry is particularly promising optical technique for the fast and non-contact characterization of complex media (e. g. layered, periodical, scattering, anisotropic and absorbing) as it provides information about all polarimetric properties of an object under study (diattenuation, birefringence, depolarization) and allows to characterize its scattering and absorption properties, surface topography and composition. We will present the results of our modeling and experimental studies in the domains of optical metrology, remote sensing and optical tissue diagnosis using number of custom-built Mueller polarimeters operating in both spectral and imaging modes and discuss further potential applications of Mueller polarimetry.

Metalenses have emerged as a new optical element or system in recent years, showing superior performance and abundant applications. However, the phase distribution of a metalens has not been measured directly up to now, hindering further quantitative evaluation of its performance. We have developed an interferometric imaging phase measurement system to measure the phase distribution of a metalens by taking only one photo of the interference pattern. Based on the measured phase distribution, we analyse the negative chromatic aberration effect of monochromatic metalenses and propose a feature size of metalenses. Different sensitivities of the phase response to wavelength between the Pancharatnam-Berry phase-based metalens and propagation phase-reliant metalens are directly observed in the experiment. Furthermore, through phase distribution analysis, it is found that the distance between the measured metalens and the brightest spot of focusing will deviate from the focal length when the metalens has a low nominal numerical aperture, even though the metalens is ideal without any fabrication error. We also use the measured phase distribution to quantitatively characterise the imaging performance of the metalens. Our phase measurement system will help not only designers optimise the designs of metalenses but also fabricants distinguish defects to improve the fabrication process, which will pave the way for metalenses in industrial applications.

We proposed a method to study the effects of azimuth and the incident angle on the accuracy and stability of rotating polarizer analyzer ellipsometer (RPAE) with bulk Au. The dielectric function was obtained at various incident angles in a range of 55°–80° and analyzed with the spectrum of the principal angle. The initial orientations of rotating polarizing elements were deviated by a series of angles to act as the azimuthal errors in various modes. The spectroscopic measurements were performed in a wavelength range of 300–800 nm with an interval of 10 nm. The repeatedly-measured ellipsometric parameters and determined dielectric constants were recorded monochromatically at wavelengths of 350, 550, and 750 nm. The mean absolute relative error was employed to evaluate quantitatively the performance of instrument. Apart from the RPAE, the experimental error analysis implemented in this work is also applicable to other rotating element ellipsometers.

There is a long history of using angle sensors to measure wavefront. The best example is the Shack-Hartmann sensor. Compared to other methods of wavefront sensing, angle-based approach is more broadly used in industrial applications and scientific research. Its wide adoption is attributed to its fully integrated setup, robustness, and fast speed. However, there is a long-standing issue in its low spatial resolution, which is limited by the size of the angle sensor. Here we report a angle-based wavefront sensor to overcome this challenge. It uses ultra-compact angle sensor built from flat optics. It is directly integrated on focal plane array. This wavefront sensor inherits all the benefits of the angle-based method. Moreover, it improves the spatial sampling density by over two orders of magnitude. The drastically improved resolution allows angle-based sensors to be used for quantitative phase imaging, enabling capabilities such as video-frame recording of high-resolution surface topography., Generally, wavefronts are measured using angle-based sensors like the Shack-Hartmann sensor. Here, the authors present an angle-sensitive device that uses flat optics integrated on a focal plane array for compact wavefront sensing with improved resolution.

Timescale comparison between optical atomic clocks over ground-to-space and terrestrial free-space laser links will have enormous benefits for fundamental and applied science, from measurements of fundamental constants and searches for dark matter, to geophysics and environmental monitoring. However, turbulence in the atmosphere creates phase noise on the laser signal, greatly degrading the precision of the measurements, and also induces scintillation and beam wander which cause periodic deep fades and loss of signal. We demonstrate phase stabilized optical frequency transfer over a 265 m horizontal point-to-point free-space link between optical terminals with active tip-tilt mirrors to suppress beam wander, in a compact, human-portable set-up. A phase stabilized 715 m underground optical fiber link between the two terminals is used to measure the performance of the free-space link. The active optics terminals enabled continuous, coherent transmission over periods of up to an hour. We achieve an 80 dB suppression of atmospheric phase noise to $3\times10^{-6}$ rad$^{2}$Hz$^{-1}$ at 1 Hz, and an ultimate fractional frequency stability of $1.6\times10^{-19}$ after 40 s of integration. At high frequency this performance is limited by the residual atmospheric noise after compensation and the frequency noise of the laser seen through the unequal delays of the free space and fiber links. Our long term stability is limited by the thermal shielding of the phase stabilization system. We achieve residual instabilities below those of the best optical atomic clocks, ensuring clock-limited frequency comparison over turbulent free-space links., Comment: 9 pages, 3 figures. In appendix: 4 pages, 2 figures

To fully exploit the advantages of fourth-generation synchrotron light sources, diffraction-limited-storage-rings (DLSR) and fully coherent free electron lasers (FELs), beamline mirrors and diffraction grating must be of exceptional quality. To achieve the required mirror and grating quality, the metrology instrumentation and methods used to characterize these challenging optics and, even more so, optical assemblies must also offer exceptional functionality and performance. One of the most widely used slope measuring instruments for characterizing x-ray optics is the long trace profiler (LTP). The easily reconfigurable mechanical design of the LTP allows optimization of the profiler arrangement to the specifics of a particular metrology task. Here, we discuss the optical schematic, design, and performance of an original multifunctional light beam source that provides functional flexibility of the LTP optical sensor. With this source, the LTP can be easily reconfigured for measurements of x-ray mirrors or diffraction gratings that have widely different source coherence requirements. Usage of a source with a low degree of coherence for mirror metrology helps to suppress the LTP systematic errors due to spurious interference effects in the LTP optical elements. A high-coherence narrow-band source is used for groove-density-distribution characterization of x-ray diffraction gratings. The systematic error and spatial resolution of the LTP with the different sources is also measured and analyzed.

Optical non-contact, interferometric measurement strategies for mold pins and plates provide an effective means for improving the consistency of the injection molding of small lenses for consumer devices. In this presentation, we describe high-precision interferometric metrology combined with motion systems and advanced software to address the wide range of length scales and metrology requirements of mold assemblies intended for high-volume production.

A low-power, passive integrated photonic heterodyne interferometer with one meter of on-chip delay is demonstrated for laser frequency stabilization applications with 30 parts-per-billion accuracy. This technology can be integrated with future space-borne optical metrology systems.

Measurement of surface roughness over a large area is a very challenging task due to the limitations with the existing techniques. Surface roughness measurement techniques including stylus and microscopy are limited by point-by-point data acquisition and a small field of view (FOV). In effect, any solution that would subdue these limitations would be characterized by its full-field nature, large FOV, and the ability to acquire and process data at high speeds. To meet these requirements, large area speckle imaging has been used to obtain areal surface roughness parameters through the processing of spectrally correlated speckle images. An automated optical system is developed for surface roughness evaluation of components with large and curved surface areas. In order to extract areal surface roughness parameters from the captured set of images, processing algorithms are developed. The methodology is first validated using a comparator plate containing areas having an average surface roughness (Ra) ranging between 0.2 µm and 0.6 µm. Further, statistical significance tests are conducted to determine the main factors affecting system performance. The measurement results are compared and validated using a 3D optical microscope. The results obtained from the blind tests performed on aerospace component surfaces as large as 450mm×210mm are also presented. Economic Development Board (EDB) Ministry of Education (MOE) National Research Foundation (NRF) Accepted version This work was conducted within the Rolls-Royce@NTU Corporate Lab MRT 4.2 project with support from the National Research Foundation (NRF) Singapore under the Corp Lab@University Scheme. The authors are also grateful for the support from COLE EDB funding. One of the authors, Patinharekandy Prabhathan contributed to this work during his role as a research fellow at Rolls-Royce@NTU Corporate Lab. Also, Aswin Haridas acknowledges NTU Singapore for the research scholarship received through NTU under the RSS scheme.

This paper addresses the effect and influence of wave optical aberrations and surface roughness on the chromatic confocal signal and resulting measurement errors. Two possible approaches exist for implementing chromatic confocal imaging based on either refraction or diffraction. Both concepts are compared and an expression for the expected chromatic longitudinal aberrations when using a diffractive optical element is derived. Since most chromatic confocal sensors are point sensors, the discussion on wave-optical aberrations is focused on spherical aberrations. Against common belief, the effect of spherical aberrations cannot be eliminated in the calibration process using for instance a piezo mounted mirror. It will be shown in the following that even a diffraction limited system with peak to valley spherical aberration smaller than 0.25 wavelength suffers from measurement errors. Experimental results will be shown to highlight this important issue. In order to develop a deeper understanding of the underlying physics, a wave-optical simulation environment has been realized. This wave-optical model furthermore enables the investigation of the influence of roughness. Herethereto the correct choice of numerical aperture when investigating a rough surface is based on a heuristic approach. Using the wave-optical simulations an explanation for the increased noise when employing a low numerical aperture to examine rough surfaces will be derived. Furthermore, a formula is presented to support the selection of the correct numerical aperture with regards to the roughness parameters of the surface under investigation., publishedVersion

Recent advances in digital holography in the far‐infrared region of the spectrum have demonstrated the potential use of digital holography in homeland security as a tool to observe hostile environments in which smoke, flames, and dust impair vision. However, to make this application practical, it is necessary to simplify the optical setup. Here, we show an off‐axis, self‐reference scheme that spills the reference beam out from the object beam itself and avoids the need for a complex interferometric arrangement. We demonstrate that this scheme allows the reconstruction of high‐quality holograms of objects captured under visible as well as far‐infrared light exposure. This could pave the way to the industrialization of holographic systems to enable users to see through fire. Moreover, the quantitative nature of the holographic signal is preserved. Thus, the reported results demonstrate the possibility to use this setup for optical metrology.

International audience; Interference microscopy is a non-destructive full-field imaging method, mainly used to measure the surface topography of different samples. In this work, two designs for improving the signal quality are described. The first consists of an original vertically orientated breadboard interferometer, in a Linnik configuration. The mechanical design of the arms allows the independent control and alignment of the coherence and the focal plane positions for optimizing fringe contrast. A low noise 16-bit camera is used to improve the sensitivity. The second interferometer is based on a Thorlabs tube system, with a Nikon Mirau Objective and a white LED, all controlled with IGOR Pro software or Labview, with the aim of being more compact, flexible and mobile. For both systems, an evaluation of the interferometric signal quality is performed, whereas the difference in lateral resolution by considering the 3D nature of the interferometric system, or only its 2D imaging abilities, is explored.

As light propagates along a waveguide, a fraction of the field can be reflected by Rayleigh scatterers. In high-quality-factor whispering-gallery-mode microresonators, this intrinsic backscattering is primarily caused by either surface or bulk material imperfections. For several types of microresonator-based experiments and applications, minimal backscattering in the cavity is of critical importance, and thus, the ability to suppress backscattering is essential. We demonstrate that the introduction of an additional scatterer into the near field of a high-quality-factor microresonator can coherently suppress the amount of backscattering in the microresonator by more than 30 dB. The method relies on controlling the scatterer position such that the intrinsic and scatterer-induced backpropagating fields destructively interfere. This technique is useful in microresonator applications where backscattering is currently limiting the performance of devices, such as ring-laser gyroscopes and dual frequency combs, which both suffer from injection locking. Moreover, these findings are of interest for integrated photonic circuits in which back reflections could negatively impact the stability of laser sources or other components., Comment: 7 pages, 4 figures, 2 supplemental pages

Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology Non-classical correlations in optical beams offer an unprecedented opportunity for surpassing the conventional limits of sensitivity and resolution in optical measurements and imaging, especially, but not only, when low photon flux, down to the single photon, is measured. We review the principles of quantum imaging and sensing techniques that exploit sub-Poissonian photon statistics and non-classical photon number correlation, presenting some state-of-the-art achievements in the field. These quantum photonics protocols have the potential to trigger major steps in many applications, such as microscopy and biophotonics, and represent an important opportunity for a new deal in radiometry and photometry., This work was supported by the Joint Research Project SIQUST (17FUN06). This project received funding from the European Metrology Programme for Innovation and Research (EMPIR) cofinanced by the Participating States and from the European Unions Horizon 2020 research and innovation programme.

Introducing a carrier into a fringe pattern makes the phase retrieval problem well-posed, and has become one of the pillar techniques in optical metrology. The carrier fringe pattern analysis for high-accuracy phase retrieval is hence important, for which, many well-known methods have been developed, such as the Fourier transform method, the windowed Fourier transform based methods (the windowed Fourier filtering and the windowed Fourier ridges), the spatial carrier phase-shifting method, and the sampling moire method. These methods were developed independently and seemingly different. The purpose of this paper is to reveal the close relationships between them, and to connect these methods into a tight-knit methodology family.

Next generation astronomical optics will enable science discoveries across all fields and impact the way we perceive the Universe in which we live. To build these systems, optical metrology tools have been developed that push the boundary of what is possible. We present a summary of a few key metrology technologies that we believe are critical for the coming generation of optical surfaces.

Light polarization, which is the direction of electromagnetic field oscillation, provides information that is highly different from that of spectral and intensity images and thus can enhance various fields of optical metrology. Polarization imaging can be also used by combining polarization and imaging, thereby providing polarization and spatial information. In university physics teaching, light polarization is limited to the understanding of the polarization state of a single beam and polarization imaging is rarely involved. Here we use the camera of a smartphone, a polarizer, and 3D printing components to create a simplified imaging polarimeter, thus showing the characteristics of polarization imaging and its application.

A full-field chromatic confocal microscopy (CCM) using a multispectral sensor was developed for quasi-one-shot microscopic 3D surface measurement. An innovative optical configuration employs a digital micromirror device (DMD) and a multispectral sensor is used to realize CCM with full-field area scanning. In the optical design, an area-scan type chromatic dispersive objective is specially designed to achieve measuring specification. Based on a self-developed chromatic dispersive objective, the FOV for one shot measurement can be reached to 1.8×1.3 mm2 which is immersive to microscopic profilometry. The spectral image captured by the multispectral sensor at each pinhole position has a unique spectrum pattern corresponding to its conjugate measured depth. A normalized cross-correlation (NCC) algorithm is developed to establish a spectrum-depth response curve with its corresponding spectrum pattern sets for accurate reconstruction of the tested 3D surface profile. With real test on standard targets, the measurement repeatability for a single surface depth is less than 0.6 μm.

Three dimensional-digital image correlation (3D-DIC) is a widely used optical metrology in the experimental mechanics community because of its reliability, practicality, and flexibility. Although the precision of digital image correlation (DIC) has been thoroughly studied theoretically and numerically, verification experiments have seldom been performed, especially for complex surfaces with a small field of view (FOV). In this work, the shape of a 1-yuan coin was measured using 3D-DIC; the shape was complex due to the presence of many fine details, and the FOV was relatively small because the coin diameter was only 25 mm. During the experiment, a novel strategy for speckle production was developed: white paint was simply sprayed onto the surface. Black paint was not used; instead, taking advantage of the reflective nature of the coin surface, polarized light and a Polaroid filter were introduced, and the polarization direction was carefully adjusted, ensuring that the spray pattern was extremely thin and that high-quality speckle images with significant contrast were captured. The three-dimensional coin shape was also successfully determined for comparison using a stylus profiler. The results demonstrate that 3D-DIC provides high precision in shape measurement even for complex surfaces with small FOV. The precision of 3D-DIC can reach 1/7000 of the field of view, corresponding to about 6 μm in this experiment.

The self-mixing interference (SMI) effect with multiway feedback is analyzed in this paper. The basic theory of SMI with multiway feedback external cavity (MFEC) can be derived from the theory of interference as well as the theory of laser self-mixing interference (LSMI). Based on the external cavity structure with MFEC, a SMI model with two feedback external cavity structure is proposed. The expressions of the phase and output power in the MFEC are deduced and some simulation analyses are made. It is found that the output signal of the SMI system with two external cavity is sinusoidal or sawtooth waves, which is similar to the signal of SMI with a low frequency sinusoidal phase modulation. The density of interference signal fringes is uneven in one period and the shape of the interference wave is determined by the intensity of the external feedback. Furthermore, a SMI with two feedback external cavity experiment system is considered, and the experiment verifies the simulations.

Newton’s rings are often encountered in interferometry, and in analyzing them, we can estimate the physical parameters, such as curvature radius and the rings’ center. The fractional Fourier transform (FRFT) is capable of estimating these physical parameters from the rings despite noise and obstacles, but there is still a small deviation between the estimated coordinates of the rings' center and the actual values. The least-squares fitting method is popularly used for its accuracy but it is easily affected by the initial values. Nevertheless, with the estimated results from the FRFT, it is easy to meet the requirements of initial values. In this paper, the proposed method combines the advantages of the fractional Fourier transform (FRFT) with the least-squares fitting method in analyzing Newton’s rings fringe patterns. Its performance is assessed by analyzing simulated and actual Newton’s rings images. The experimental results show that the proposed method is capable of estimating the parameters in the presence of noise and obstacles. Under the same conditions, the estimation results are better than those obtained with the original FRFT-based method, especially for the rings’ center. Some applications are shown to illustrate that the improved FRFT-based method is an important technique for interferometric measurements.

Active imagers capable of reconstructing 3-dimensional (3D) scenes in the presence of strong background noise are highly desirable for many sensing and imaging applications. A key to this capability is the time-resolving photon detection that distinguishes true signal photons from the noise. To this end, quantum parametric mode sorting (QPMS) can achieve signal to noise exceeding by far what is possible with typical linear optics filters, with outstanding performance in isolating temporally and spectrally overlapping noise. Here, we report a QPMS-based 3D imager with exceptional detection sensitivity and noise tolerance. With only 0.0006 detected signal photons per pulse, we reliably reconstruct the 3D profile of an obscured scene, despite 34-fold spectral-temporally overlapping noise photons, within the 6 ps detection window (amounting to 113,000 times noise per 20 ns detection period). Our results highlight a viable approach to suppress background noise and measurement errors of single photon imager operation in high-noise environments., Imagers capable of reconstructing three-dimensional scenes in the presence of strong background noise are desirable for many remote sensing and imaging applications. Here, the authors report an imager operating in photon-starved and noise-polluted environments through quantum parametric mode sorting.

Laser speckle has received extensive studies in its basic properties and wide applications. In the majority of research on speckle phenomena, these random optical fields have been treated as scalar optical fields, and the main interest has been in the statistical properties together with applications of the intensity distribution of the speckle patterns. In recent years, increasing attention has been paid to the statistical properties of random electric vector fields referred to as polarization speckle with spatially varying polarization state. Statistical phenomena of random electric vector fields with their close relevance to the theories of speckles, polarization and coherence theory have come to attract emerging interest due to their importance in a variety of areas for practical applications such as biomedical optics, remote sensing, astronomical observation and optical metrology. In this paper, we investigate the dynamic polarization speckle generated by a moving rough-surfaced retardation plate and present an exact analytical expression for the space-time lagged correlation for the stochastic fields within the framework of ABCD matrix theory (Canonical Transforms). General expressions are derived for the spot size, the mean polarization speckle size, the temporal coherence length, and the peak shift of the temporal correlation. Some interesting phenomena associated with dynamic polarization speckle have been predicted including polarization speckle boiling and polarization speckle translation. A general description of these phenomena has been given for arbitrary complex-valued ABCD optical systems.

It is well known that when a laser is reflected from a rough surface or transmitted through a diffusive medium, a speckle pattern will be formed at a given observation plane. Speckle is commonly produced by laser beams with a homogeneous intensity, for which, well-known relations have been derived, relating the speckle size to the area of illumination. Here we investigate the speckle generated by higher-order Laguerre-Gaussian (LG) modes, characterized by a non-uniform intensity distribution of concentric rings.We show that the ring-structure of the LG modes does not play any role in the speckle size, which happens to be the same as that obtained for a homogeneous intensity distribution. This allow us to provide with a simple expression that relates the speckle size to the spot size of the LG modes. Our findings will be of great relevance in many speckle-based applications., Comment: 5 pages, 5 figures