Off-axis Object Research Articles

REXPACO ASDI: joint unmixing and deconvolution of the circumstellar environment by angular and spectral differential imaging

ABSTRACT Angular and spectral differential imaging is an observational technique of choice to investigate the immediate vicinity of stars. By leveraging the relative angular motion and spectral scaling between on-axis and off-axis sources, post-processing techniques can separate residual star light from light emitted by surrounding objects such as circumstellar discs or point-like objects. This paper introduces a new algorithm that jointly unmixes these components and deconvolves disc images. The proposed algorithm is based on a statistical model of the residual star light, accounting for its spatial and spectral correlations. These correlations are crucial yet remain inadequately modelled by existing reconstruction algorithms. We employ dedicated shrinkage techniques to estimate the large number of parameters of our correlation model in a data-driven fashion. We show that the resulting separable model of the spatial and spectral covariances captures very accurately the star light, enabling its efficient suppression. We apply our method to data sets from the Very Large Telescope/Spectro-Polarimetry High-contrast Exoplanet REsearch instrument and compare its performance with standard algorithms (median subtraction, PCA, PACO). We demonstrate that considering the multiple correlations within the data significantly improves reconstruction quality, resulting in better preservation of both disc morphology and photometry. With its unique joint spectral modelling, the proposed algorithm can reconstruct discs with circular symmetry (e.g. rings, spirals) at intensities one million times fainter than the star, without needing additional reference data sets free from off-axis objects.

Reconstructing images of objects: method for reconstructing images from digital off-axis holograms based on a generative adversarial neural network

The reconstruction of object images that are located in 3D scene cross-sections using digital holography is described. The potential of generative adversarial networks for reconstructing cross-sections of 3D scenes composed of multiple layers of off-axis objects from holograms is investigated. Such scenes consist of a series of sections with objects that are not aligned with the camera’s axis. Digital holograms were used to reconstruct images of cross-sectional views of 3D scenes. It has been shown that the use of neural networks increases the speed and reconstruction quality, and reduces the image noise. A method for reconstructing images of objects using digital off-axis holograms and a generative adversarial neural network is proposed. The proposed method was tested on both numerically simulated and experimentally captured digital holograms. It was able to successfully reconstruct up to 8 cross-sections of a 3D scene from a single hologram. It was obtained that an average structural similarity index measure was equal to at least 0.73. Based on optically registered holograms, the method allowed us to reconstruct object image cross-sections of a 3D scene with a structural similarity index measure over cross-sections of a 3D scene of equal to 0.83. Therefore, the proposed technique provides the possibility for high-quality object image reconstruction and could be utilized in the analysis of micro- and macroobjects, including medical and biological applications, metrology, characterization of materials, surfaces, and volume media.

Characterization and design of a freeform holographic optical element

ObjectiveThe aberrations of a conventional lens holographic optical element (HOE) are considerable because of the off-axis recording and diffraction nature. A freeform HOE was introduced to alleviate these aberrations. To design and optimize the recording wavefront of a freeform HOE, it is important to figure out the imaging properties of an HOE. MethodsWe systematically derived a general characterization of the conjugate imaging equation of an elementary HOE recorded by two spherical wavefronts using the scalar diffraction theory. In our design, each patch of a freeform HOE is considered as an elementary HOE. The recording wavefronts of a freeform HOE is designed by determining each elementary HOE through the conjugate imaging equation. ResultsThe image position predicted by the imaging equation is consistent with that of the finite ray-tracing method. The error when the imaging equation is applied to off-axis object points and different reconstruction wavelengths is eliminated effectively through coordinate transformation. Furthermore, based on this equation, a freeform HOE with 3 × 3 tiling elementary HOEs is designed to eliminate distortion and astigmatism of the HOE imaging system. A holographic printer to fabricate this freeform HOE is recommended.

Design of a compact off-axis four-mirror objective system for a thermal camera.

The optical design of a compact off-axis four-mirror objective system (OFOS) of a thermal camera for a syndromic surveillance system that captures bioclinical signals, like temperature, directly related to the physical symptoms of the COVID-19 disease through thermal images is presented. The OFOS design works on wavelengths of 7.5-14 µm, with an f-number of 4, and a field of view (FOV) of 24×4 deg.

Locating optimal freeform surfaces for off-axis optical systems

One of the key tasks in designing off-axis optical systems is to place freeform surfaces in optimal locations. By analyzing the real ray paths, we introduce one simple method for locating freeform surfaces in off-axis systems. A four mirror off-axis microscope objective with freeform surfaces is designed to demonstrate the method, the result shows that our method is effective in identifying the optimal locations of freeform surfaces.

Optical Scanning Tilt Holography

Digital holography (DH) can record optical field of a three-dimensional (3-D) object, and the 3-D information can be retrieved and processed digitally. Thus, DH has application potential in 3-D sensing and metrology. However, it is hard for conventional DH to record the off-axis object light because of the limitation of the arrayed sensor. In this paper, optical scanning holography (OSH) is proposed to record the off-axis object light. OSH is a scanning-type and single-pixel holographic technique for 3-D imaging. Therefore, OSH can directly record the off-axis object light by using a small sampling pitch. This is, however, a waste of both bandwidth and recording time. For this reason, a new scheme called optical scanning tilt holography (OSTH) is proposed in this paper. In OSTH, the scanning beam is tilted related to the object axis, and thus the off-axis object light can be recorded by using a large sampling pitch. Although the horizontal resolution of OSTH is worse than that of OSH in normal scanning, the axial resolution of OSTH is better than that of OSH. In addition, the reconstruction plane of OSTH is always parallel to that of OSH in normal scanning. Therefore, there is no need of coordinate transformation post to the holographic recording. These features enable OSTH to be applied in depth sensing and stereoscopic imaging.

Analysis of an extraordinary electron beam moiré phenomena in a pulse-dilation framing camera

An extraordinary electron beam moiré phenomena (EBMP) is generated with a pulse-dilation framing camera. The intrinsic relationship between the extraordinary EBMP and the imaging curved plane of camera is theoretically analyzed. The experimental results and analysis show that the extraordinary EBMP and mesh appear simultaneously, the extraordinary EBMP has two inclination angles and the maximum inclined angle of both is 106.78°. Moreover, the Gaussian imaging plane of the off-axis object point is theoretically simulated by examining photoelectron trajectories, where the inclined angle between the axis and 25 mm off-axis is approximately 112°. The theoretical results are very similar to experimental results, that is a significant phenomenon that may possibly expand the use of EBMP in pulse-dilation framing cameras to new applications.

Theoretical Study of Refraction Effects of Plano Ophthalmic Prisms

Nominally plano prisms can have appreciable refractive errors that exceed the usual prescribing step of 0.25 D, particularly when an eye rotates to view off-axis objects. The purpose of this study was to determine theoretically the refractive power effects of nominally plano-refracting power prisms. Plano prisms with zero refraction were designed for the as-worn condition. A basic method was developed to determine refractive effects in the presence of pantoscopic tilt. A refined method was developed that considers the eye rotating behind the lens, and this and the basic method were compared with accurate raytracing. Plano prisms of 4 and 8 Δ were designed with astigmatic back surfaces to compensate for oblique incidence, and tangential and sagittal image vergence errors were investigated for base-up (BU) and base-down (BD) directions, 0 and -3.33 D object vergences, and pantoscopic tilts up to 10°. Basic and refined results did not differ from accurate results by more than 0.04 and 0.08 D, respectively. Errors for 8 Δ prisms were approximately twice those for 4 Δ prisms. Errors were approximately proportional to tilt. With 10° tilt, the errors ranged between -0.65 D/-0.23 D (8 Δ BD, -3.33 D object vergence) and +0.36 D/+0.15 D (8 Δ BU, 0 D object vergence). Sagittal errors were generally about one third of corresponding tangential errors. In the presence of tilt, BU prisms had positive errors, and BD prisms had similar, but negative, errors for distance objects. At -3.33 D object vergence with tilt, negative errors for BD were greater than positive errors for BU. When the eye rotates to look at objects at different positions, errors can increase beyond those occurring on-axis. When designed for nontilted conditions, but then subjected to tilt or to viewing off-axis objects, plano prisms can have errors exceeding the usual prescribing step of 0.25 D.

Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm

A method for calculating off-axis phase-only holograms of three-dimensional (3D) object using accelerated point-based Fresnel diffraction algorithm (PB-FDA) is proposed. The complex amplitude of the object points on the z-axis in hologram plane is calculated using Fresnel diffraction formula, called principal complex amplitudes (PCAs). The complex amplitudes of those off-axis object points of the same depth can be obtained by 2D shifting of PCAs. In order to improve the calculating speed of the PB-FDA, the convolution operation based on fast Fourier transform (FFT) is used to calculate the holograms rather than using the point-by-point spatial 2D shifting of the PCAs. The shortest recording distance of the PB-FDA is analyzed in order to remove the influence of multiple-order images in reconstructed images. The optimal recording distance of the PB-FDA is also analyzed to improve the quality of reconstructed images. Numerical reconstructions and optical reconstructions with a phase-only spatial light modulator (SLM) show that holographic 3D display is feasible with the proposed algorithm. The proposed PB-FDA can also avoid the influence of the zero-order image introduced by SLM in optical reconstructed images.

Design method of off-axis extreme ultraviolet lithographic objective system with a direct tilt process

An off-axis extreme ultraviolet (EUV) lithographic objective can achieve a high numerical aperture (NA) beyond 0.33 with only six mirrors due to the efficient separation of the ray path, which greatly improves the resolution and energy utilization. A method is developed to design an off-axis lithographic objective with six mirrors. The method starts with a coaxial system with ray vignetting caused by increase of the NA. To avoid the ray vignetting, a reasonable range of solution for the tilt angle of each mirror is determined by real ray calculation. A set of optimal solutions for tilt angles of mirrors, which corresponds to the minimal composite root-mean-square wavefront error, is found from the reasonable ranges of solutions by a search program. In this way, an initial off-axis configuration without ray vignetting can be directly obtained and it is suitable for further optimization. To demonstrate the practicability of the method, an off-axis design example is given which shows that the presented method provides an efficient process to get to initial configuration for off-axis EUV lithographic objective with six mirrors.

High-capacity imaging and rotationally insensitive object identification with correlated orbital angular momentum states

Using no conventional measurements in position space, information extraction rates exceeding one bit per photon are achieved by employing high-dimensional correlated orbital angular momentum (OAM) states for object recognition. The correlations are shown to be insensitive to axial rotation of the target object: The information structure of an object's joint OAM coincidence spectrum is unchanged even when the object undergoes random rotations between each measurement. Additionally, OAM correlations alone are shown to be sufficient for full image reconstruction of complex, off-axis objects, and novel object symmetries are observed in the phases of OAM-object interaction transition amplitudes. Variations in mutual information rates, due to off-axis translation in the beam field, are studied, and it is shown that object symmetry signatures and information rates are independent of environmental factors sufficiently far from the beam center. The results motivate dynamic scanning applications in contexts where symmetry and small numbers of noninvasive measurements are desired.

Optimization method for ultra-wide-angle and panoramic optical systems

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.

Guiding effects in waveguides with anti-symmetric refractive index layouts

This paper presents and analyzes configurations of waveguides composed by both, regular dielectrics and negative-index materials disposed in an anti-symmetric way with respect to the optical axis. In its basic form, the configuration includes two guiding layers and two cladding media, where both the cladding and the guiding pairs have opposite-signed refractive index. A geometrical analysis shows that paths are closed, hinting the possibility of localized modes or light trapping with zero ray velocity. The ray model shows also a quasi-perfect imaging effect for off-axis objects. A modal approach shows that trapping is broadband and the propagation constant spectrum is continuous. When cores are allowed different widths, control of the group velocity is possible. More general anti-symmetrically mirrored layouts are also addressed.

AN INTERFEROMETRIC STUDY OF THE FOMALHAUT INNER DEBRIS DISK. I. NEAR-INFRARED DETECTION OF HOT DUST WITH VLTI/VINCI

The innermost parts of dusty debris disks around main sequence stars are currently poorly known due to the high contrast and small angular separation with their parent stars. Using near-infrared interferometry, we aim to detect the signature of hot dust around the nearby A4 V star Fomalhaut, which has already been suggested to harbor a warm dust population in addition to a cold dust ring located at about 140 AU. Archival data obtained with the VINCI instrument at the VLTI are used to study the fringe visibility of the Fomalhaut system at projected baseline lengths ranging from 4 m to 140 m in the K band. A significant visibility deficit is observed at short baselines with respect to the expected visibility of the sole stellar photosphere. This is interpreted as the signature of resolved circumstellar emission, producing a relative flux of 0.88% +/- 0.12% with respect to the stellar photosphere. While our interferometric data cannot directly constrain the morphology of the excess emission source, complementary data from the literature allow us to discard an off-axis point-like object as the source of circumstellar emission. We argue that the thermal emission from hot dusty grains located within 6 AU from Fomalhaut is the most plausible explanation for the detected excess. Our study also provides a revised limb-darkened diameter for Fomalhaut (2.223 +/- 0.022 mas), taking into account the effect of the resolved circumstellar emission.

Analytical design of an Offner imaging spectrometer

We present the analytical design of an imaging spectrometer based on the three-concentric-mirror (Offner) configuration. The approach presented allows for the rapid design of this class of system. Likewise, high-optical-quality spectrometers are obtained without the use of aberration-corrected gratings, even for high speeds. Our approach is based on the calculation of both the meridional and the sagittal images of an off-axis object point. Thus, the meridional and sagittal curves are obtained in the whole spectral range. Making these curves tangent to each other for a given wavelength results in a significant decrease in astigmatism, which is the dominant residual aberration.RMS spot radii less than 5 mm are obtained for speeds as high as f/2.5 and a wavelength range of 0.4-1.0 microm. A design example is presented using a free interactive optical design tool.

Determination of pseudophakic accommodation with translation lenses using Purkinje image analysis

To determine pseudophakic accommodation of an accommodating posterior chamber intraocular lens (translation lens) using Purkinje image analysis and linear matrix methods in the paraxial space. A 2 x 2 system matrix was defined for each Purkinje image I to IV using refraction, translation and mirror matrices. Image size (m) and axial image position (z) was determined as an example for an off-axis object (a 0.2 m off-axis object located 0.5 m in front of the cornea.). First, our method was applied to the phakic relaxed (emmetropic) and accommodated (6.96 D) Le Grand eye. Secondly, for demonstration of the applicability of the calculation scheme to the pseudophakic eye, we provide a clinical example where we determine the accommodation amplitude of the translation lens (1 CU, HumanOptics, Erlangen, Germany) from photographed Purkinje images in the relaxed and accommodated state. From the biometric data: axial length 23.7 mm, corneal power 43.5, corneal thickness 550 microns, implanted intraocular lens (IOL) with a refractive power of 20.5 D (shape equi-biconvex, refractive index 1.46), and refractive indices of the cornea, aqueous and vitreous from the Le Grand model eye, we calculated the refractive state and the sizes of Purkinje images I and III initiated from two off-axis light sources. For the Le Grand model eye, Purkinje image II (z/m = 3.5850 mm/0.0064) is slightly smaller than and directly in front of image I (z/m = 3.8698 mm/0.0077). Purkinje image III (z/m = 10.6097 mm/0.0151) is nearly double the size of image I and during accommodation it moves from the vitreous into the crystalline lens. Purkinje IV (z/m = 4.3244 mm/-0.0059) is inverted, three quarters the size of image I, lies in the crystalline lens and moves slightly towards the retina. For the pseudophakic eye, pseudophakic accommodation of 1.10 D was calculated from the proportion of distances between both Purkinje images I and III in the relaxed (3.04) and accommodated (2.75) state, which is in contrast to the total subjective accommodation of 2.875 D evaluated with an accommodometer. We present a straightforward mathematical strategy for calculation of the Purkinje images I-IV. Results of our model calculation resemble the values provided by Le Grand. In addition, this approach yields a simple en bloc scheme for determination of pseudophakic accommodation in pseudophakic eyes with accommodative lenses (translation lenses) using Purkinje image photography.

120-nm lithography using off-axis TIR holography and 364 nm exposure wavelength

An extension of total internal reflection holographic lithography is presented that nearly doubles its resolution limit for patterns that are periodic or quasi-periodic in one direction. An off-axis object beam is employed to record the hologram from the photomask, the angle of the beam being such that essentially just the zero order and a first diffraction order are transmitted by the mask. A fully automated equipment based on this method has been developed which also implements a step-and-repeat procedure to enable a large array of patterns to be recorded in the hologram from a single pattern in the mask. Gratings and patterns with substantial deviations from the pure grating form, with resolutions down to 120 nm, have been printed using an exposure wavelength of 364 nm.

Fractional and integer Talbot effect for off-axis illumination and for finite object dimension in tapered GRIN media

Irradiance at fractional and integer Talbot images in tapered gradient-index (GRIN) media for ideal periodic objects is presented. Talbot effect for off-axis illumination and finite object dimension is investigated. Results have been applied to a hybrid structure composed by a divergent linear tapered GRIN medium and a sinusoidal amplitude grating to show transverse shift and finite-aperture diffractive effect on the Talbot images as well as the walk-off effect.

Corneal wave aberration from videokeratography: accuracy and limitations of the procedure.

A procedure to calculate the wave aberration of the human cornea from its surface shape measured by videokeratography is presented. The wave aberration was calculated as the difference in optical path between the marginal rays and the chief ray refracted at the surface, for both on- and off-axis objects. The corneal shape elevation map was obtained from videokeratography and fitted to a Zernike polynomial expansion through a Gram-Schmidt orthogonalization. The wave aberration was obtained also as a Zernike polynomial representation. The accuracy of the procedure was analyzed. For calibrated reference surface elevations, a root-mean-square error (RMSE) of 1 to 2 microm for an aperture 4-6 mm in diameter was obtained, and the RMSE associated with the experimental errors and with the fitting method was 0.2 microm. The procedure permits estimation of the corneal wave aberration from videokeratoscopic data with an accuracy of 0.05-0.2 microm for a pupil 4-6 mm in diameter, rendering the method adequate for many applications.

Resolution for off-axis illumination

The fundamental limit to resolution of a perfect lens for off-axis object points is considered. It has been shown previously that resolution decreases with illumination. Here it is shown that the relative decrease in resolution with illumination angle is reduced for lenses of higher numerical aperture. These results are of importance for optical systems that combine high aperture with large field of view, such as lithographic lenses.