Showing papers on "Point source published in 2014"

A 24 Micron Point Source Catalog of the Galactic Plane from Spitzer/MIPSGAL

Abstract: In this contribution, we describe the applied methods to construct a 24 micron based point source catalog derived from the image data of the MIPSGAL 24 micron Galactic Plane Survey and the corresponding data products. The high quality catalog product contains 933,818 sources, with a total of 1,353,228 in the full archive catalog. The source tables include positional and photometric informa- tion derived from the 24 micron images, source quality and confusion flags and coun- terpart photometry from matched 2MASS, GLIMPSE, and WISE point sources. Completeness decay data cubes are constructed at 1 arcminute angular resolution that describe the varying background levels over the MIPSGAL field and the ability to extract sources of a given magnitude from this background. The completeness decay cubes are included in the set of data products. We present the results of our efforts to verify the astrometric and photometric calibration of the catalog, and present several analyses of minor anomalies in these measurements to justify adopted mitigation strategies.

The NuSTAR spectrum of Mrk 335: extreme relativistic effects within two gravitational radii of the event horizon?

Abstract: We present 3–50keV NuSTAR observations of the active galactic nuclei Mrk 335 in a very low flux state. The spectrum is dominated by very strong features at the energies of the iron line at 5–7keV and Compton hump from 10–30keV. The source is variable during the observation, withthevariabilityconcentratedatlowenergies,whichsuggestingeitherarelativisticreflection oravariableabsorptionscenario.Inthiswork,wefocusonthereflectioninterpretation,making use of new relativistic reflection models that self consistently calculate the reflection fraction, relativistic blurring and angle-dependent reflection spectrum for different coronal heights to model the spectra. We find that the spectra can be well fitted with relativistic reflection, and that the lowest flux state spectrum is described by reflection alone, suggesting the effects of extreme light-bending occurring within ∼2 gravitational radii (RG) of the event horizon. The reflection fraction decreases sharply with increasing flux, consistent with a point source moving up to above 10 RG as the source brightens. We constrain the spin parameter to greater than 0.9 at the 3σ confidence level. By adding a spin-dependent upper limit on the reflection fraction to our models, we demonstrate that this can be a powerful way of constraining the spin parameter, particularly in reflection dominated states. We also calculate a detailed emissivity profile for the iron line, and find that it closely matches theoretical predictions for a compact source within a few RG of the black hole.

Extragalactic Foreground Contamination in Temperature-based CMB Lens Reconstruction

Abstract: We discuss the effect of unresolved point source contamination on estimates of the CMB lensing potential, from components such as the thermal Sunyaev-Zel'dovich effect, radio point sources, and the Cosmic Infrared Background. We classify the possible trispectra associated with such source populations, and construct estimators for the amplitude and scale-dependence of several of the major trispectra. We show how to propagate analytical models for these source trispectra to biases for lensing. We also construct a "source-hardened" lensing estimator which experiences significantly smaller biases when exposed to unresolved point sources than the standard quadratic lensing estimator. We demonstrate these ideas in practice using the sky simulations of Sehgal et al., for cosmic-variance limited experiments designed to mimic ACT, SPT, and Planck. We find that for radio sources and SZ the bias is significantly reduced, but for CIB it is essentially unchanged. However, by using the high-frequency, all-sky CIB measurements from Planck and Herschel it may be possible to suppress this contribution.

HerMES: point source catalogues from Herschel-SPIRE observations II

Abstract: The Herschel Multi-tiered Extragalactic Survey (HerMES) is the largest Guaranteed Time Key Programme on the Herschel Space Observatory. With a wedding cake survey strategy, it consists of nested fields with varying depth and area totalling similar to 380 deg(2). In this paper, we present deep point source catalogues extracted from Herschel-Spectral and Photometric Imaging Receiver (SPIRE) observations of all HerMES fields, except for the later addition of the 270 deg(2) HerMES Large-Mode Survey (HeLMS) field. These catalogues constitute the second Data Release (DR2) made in 2013 October. A sub-set of these catalogues, which consists of bright sources extracted from Herschel-SPIRE observations completed by 2010 May 1 (covering similar to 74 deg(2)) were released earlier in the first extensive data release in 2012 March. Two different methods are used to generate the point source catalogues, the SUSSEXTRACTOR point source extractor used in two earlier data releases (EDR and EDR2) and a new source detection and photometry method. The latter combines an iterative source detection algorithm, STARFINDER, and a De-blended SPIRE Photometry algorithm. We use end-to-end Herschel-SPIRE simulations with realistic number counts and clustering properties to characterize basic properties of the point source catalogues, such as the completeness, reliability, photometric and positional accuracy. Over 500 000 catalogue entries in HerMES fields (except HeLMS) are released to the public through the HeDAM (Herschel Database in Marseille) website (http://hedam.lam.fr/HerMES).

Retrieval techniques for airborne imaging of methane concentrations using high spatial and moderate spectral resolution: application to AVIRIS

Abstract: . Two quantitative retrieval techniques were evaluated to estimate methane (CH4) enhancement in concentrated plumes using high spatial and moderate spectral resolution data from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). An iterative maximum a posteriori differential optical absorption spectroscopy (IMAP-DOAS) algorithm performed well for an ocean scene containing natural CH4 emissions from the Coal Oil Point (COP) seep field near Santa Barbara, California. IMAP-DOAS retrieval precision errors are expected to equal between 0.31 to 0.61 ppm CH4 over the lowest atmospheric layer (height up to 1.04 km), corresponding to about a 30 to 60 ppm error for a 10 m thick plume. However, IMAP-DOAS results for a terrestrial scene were adversely influenced by the underlying land cover. A hybrid approach using singular value decomposition (SVD) was particularly effective for terrestrial surfaces because it could better account for spectral variability in surface reflectance. Using this approach, a CH4 plume was observed extending 0.1 km downwind of two hydrocarbon storage tanks at the Inglewood Oil Field in Los Angeles, California (USA) with a maximum near surface enhancement of 8.45 ppm above background. At COP, the distinct plume had a maximum enhancement of 2.85 ppm CH4 above background, and extended more than 1 km downwind of known seep locations. A sensitivity analysis also indicates CH4 sensitivity should be more than doubled for the next generation AVIRIS sensor (AVIRISng) due to improved spectral resolution and sampling. AVIRIS-like sensors offer the potential to better constrain emissions on local and regional scales, including sources of increasing concern like industrial point source emissions and fugitive CH4 from the oil and gas industry.

A deep Chandra ACIS survey of M83

Abstract: We have obtained a series of deep X-ray images of the nearby galaxy M83 using Chandra, with a total exposure of 729 ks. Combining the new data with earlier archival observations totaling 61 ks, we find 378 point sources within the D25 contour of the galaxy. We find 80 more sources, mostly background active galactic nuclei (AGNs), outside of the D25 contour. Of the X-ray sources, 47 have been detected in a new radio survey of M83 obtained using the Australia Telescope Compact Array. Of the X-ray sources, at least 87 seem likely to be supernova remnants (SNRs), based on a combination of their properties in X-rays and at other wavelengths. We attempt to classify the point source population of M83 through a combination of spectral and temporal analysis. As part of this effort, we carry out an initial spectral analysis of the 29 brightest X-ray sources. The soft X-ray sources in the disk, many of which are SNRs, are associated with the spiral arms, while the harder X-ray sources, mostly X-ray binaries (XRBs), do not appear to be. After eliminating AGNs, foreground stars, and identified SNRs from the sample, we construct the cumulative luminosity function (CLF) of XRBs brighter than 8 × 1035 erg s–1. Despite M83's relatively high star formation rate, the CLF indicates that most of the XRBs in the disk are low mass XRBs.

Directional Dipole Model for Subsurface Scattering

Abstract: Rendering translucent materials using Monte Carlo ray tracing is computationally expensive due to a large number of subsurface scattering events. Faster approaches are based on analytical models derived from diffusion theory. While such analytical models are efficient, they miss out on some translucency effects in the rendered result. We present an improved analytical model for subsurface scattering that captures translucency effects present in the reference solutions but remaining absent with existing models. The key difference is that our model is based on ray source diffusion, rather than point source diffusion. A ray source corresponds better to the light that refracts through the surface of a translucent material. Using this ray source, we are able to take the direction of the incident light ray and the direction toward the point of emergence into account. We use a dipole construction similar to that of the standard dipole model, but we now have positive and negative ray sources with a mirrored pair of directions. Our model is as computationally efficient as existing models while it includes single scattering without relying on a separate Monte Carlo simulation, and the rendered images are significantly closer to the references. Unlike some previous work, our model is fully analytic and requires no precomputation.

Designing optical free-form surfaces for extended sources

Abstract: LED lighting has been a strongly growing field for the last decade. The outstanding features of LED, like compactness and low operating temperature take the control of light distributions to a new level. Key for this is the development of sophisticated optical elements that distribute the light as intended. The optics design method known as tailoring relies on the point source assumption. This assumption holds as long as the optical element is large compared to the LED chip. With chip sizes of 1 mm² this is of no concern if each chip is endowed with its own optic. To increase the power of a luminaire, LED chips are arranged to form light engines that reach several cm in diameter. In order to save costs and space it is often desirable to use a single optical element for the light engine. At the same time the scale of the optics must not be increased in order to trivially keep the point source assumption valid. For such design tasks point source algorithms are of limited usefulness. New methods that take into account the extent of the light source have to be developed. We present two such extended source methods. The first method iteratively adapts the target light distribution that is fed into a points source method while the second method employs a full phase space description of the optical system.

High-Order Factorization Based High-Order Hybrid Fast Sweeping Methods for Point-Source Eikonal Equations

Abstract: The solution for the eikonal equation with a point-source condition has an upwind singularity at the source point as the eikonal solution behaves like a distance function at and near the source. As...

A framework for fast probabilistic centroid-moment-tensor determination—inversion of regional static displacement measurements

Abstract: The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(md), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)-a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as 'committees', we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 MW 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account.

The factorization method for cavities

Abstract: The inverse acoustic scattering of point sources by an impenetrable cavity is considered. The scattered fields incited by point source waves are measured on a closed curve inside the cavity. We prove the validity of the factorization method for reconstructing the shape of the cavity. Two explicit examples for circular cavities are given to show the feasibility and effectiveness of the factorization method. Finally, we present some numerical examples in 2D. The reconstructions are as satisfactory as the exterior scattering problems and change only slightly for different measurement curves, different boundary conditions and different wave numbers.

A search for point sources of EeV photons

Abstract: Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85{\deg} to +20{\deg}, in an energy range from 10^17.3 eV to 10^18.5 eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm^-2 s^-1, and no celestial direction exceeds 0.25 eV cm^-2 s^-1. These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.

Underwater optical wireless communications: depth-dependent beam refraction

Abstract: Global refractive gradients in seawater cause pointing problems for optical wireless communications. A refractive index depth profile of the Pacific Ocean was calculated from measured salinity, temperature, and pressure, determining the end points of a refracted and nonrefracted 200 m communication link. Numerical ray tracing was used with a point source for angles between 10° and 80° and transmission wavelengths of 500–650 nm; the maximum end-point difference found was 0.23 m. A 500 nm laser with a 0.57° full-angle FOV was traced; the nonrefracted receiver location was outside the FOV for all links angled >15° to the vertical. However, most pointing issues underwater are unlikely to be significant with suitable FOV choice and natural scattering of the source.

Quantum limits to optical point-source localization

Abstract: Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of microscopes that overcome a long-held belief about the resolution have revolutionized biological imaging. Termed "superresolution" microscopy, these techniques work by accurately locating optical point sources from far field. To investigate the fundamental localization limits, here I derive quantum lower bounds on the error of locating point sources in free space, taking full account of the quantum, nonparaxial, and vectoral nature of photons. These bounds are valid for any measurement technique, as long as it obeys quantum mechanics, and serve as general no-go theorems for the resolution of microscopes. To arrive at analytic results, I focus mainly on the cases of one and two classical monochromatic sources with an initial vacuum optical state. For one source, a lower bound on the root-mean-square position estimation error is on the order of $\lambda_0/\sqrt{N}$, where $\lambda_0$ is the free-space wavelength and $N$ is the average number of radiated photons. For two sources, owing to the statistical effect of nuisance parameters, the error bound diverges when their radiated fields overlap significantly. The use of squeezed light to enhance further the accuracy of locating one classical point source and the localization limits for partially coherent sources and single-photon sources are also discussed. The presented theory establishes a rigorous quantum statiscal inference framework for the study of superresolution microscopy and points to the possibility of using quantum techniques for true resolution enhancement.

An image-plane algorithm for JWST's non-redundant aperture mask data

Abstract: The high angular resolution technique of non-redundant masking (NRM) or aperture masking interferometry (AMI) has yielded images of faint protoplanetary companions of nearby stars from the ground. AMI on James Webb Space Telescope (JWST)'s Near Infrared Imager and Slitless Spectrograph (NIRISS) has a lower thermal background than ground-based facilites and does not suffer from atmospheric instability. NIRISS AMI images are likely to have 90 - 95% Strehl ratio between 2.77 and 4.8 micron. In this paper we quantify factors that limit the raw point source contrast of JWST NRM. We develop an analytic model of the NRM point spread function which includes different optical path delays (pistons) between mask holes and fit the model parameters with image plane data. It enables a straightforward way to exclude bad pixels, is suited to limited fields of view, and can incorporate effects such as intra-pixel sensitivity variations. We simulate various sources of noise to estimate their effect on the standard deviation of closure phase, sigma_CP (a proxy for binary point source contrast). If sigma_CP < 10^-4 radians --- a contrast ratio of 10 magnitudes --- young accreting gas giant planets (e.g. in the nearby Taurus star-forming region) could be imaged with JWST NIRISS. We show the feasibility of using NIRISS' NRM with the sub-Nyquist sampled F277W, which would enable some exoplanet chemistry characterization. In the presence of small piston errors, the dominant sources of closure phase error (depending on pixel sampling, and filter bandwidth) are flat field errors and unmodeled variations in intra-pixel sensitivity. The in-flight stability of NIRISS will determine how well these errors can be calibrated by observing a point source. Our results help develop efficient observing strategies for space-based NRM.

SPIRE point source photometry: within the Herschel interactive processing environment (HIPE)

Abstract: The different algorithms appropriate for point source photometry on data from the SPIRE instrument on-board the Herschel Space Observatory, within the Herschel Interactive Processing Environment (HIPE) are compared. Point source photometry of a large ensemble of standard calibration stars and dark sky observations is carried out using the 4 major methods within HIPE: SUSSEXtractor, DAOphot, the SPIRE Timeline Fitter and simple Aperture Photometry. Colour corrections and effective beam areas as a function of the assumed source spectral index are also included to produce a large number of photometric measurements per individual target, in each of the 3 SPIRE bands (250, 350, 500μm), to examine both the accuracy and repeatability of each of the 4 algorithms. It is concluded that for flux densities down to the level of 30mJy that the SPIRE Timeline Fitter is the method of choice. However, at least in the 250 and 350μm bands, all 4 methods provide photometric repeatability better than a few percent down to at approximately 100mJy. The DAOphot method appears in many cases to have a systematic offset of ∼8 % in all SPIRE bands which may be indicative of a sub-optimal aperture correction. In general, aperture photometry is the least reliable method, i.e. largest scatter between observations, especially in the longest wavelength band. At the faintest fluxes, <30mJy, SUSSEXtractor or DAOphot provide a better alternative to the Timeline Fitter.

Long-wave infrared digital holographic interferometry with diffuser or point source illuminations for measuring deformations of aspheric mirrors

Abstract: Long-wave infrared digital holographic interferometry with CO2 laser and microbolometer arrays has been developed for testing the large deformations of space reflectors. The setup considered is a Mach–Zehnder, associated to the digital holography reconstruction of the wavefront in the inline configuration with phase shifting. Two possibilities exist for illuminating the tested reflector: either with a point source (similarly to classical interferometry) or an extended source (with a diffuser). This paper presents the development of a modular setup which allows comparing both in the case of a parabolic mirror.

SPIRE Point Source Photometry

Abstract: The different algorithms appropriate for point source photometry on data from the SPIRE instrument on-board the Herschel Space Observatory, within the Herschel Interactive Processing Environment (HIPE) are compared. Point source photometry of a large ensemble of standard calibration stars and dark sky observations is carried out using the 4 major methods within HIPE: SUSSEXtractor, DAOphot, the SPIRE Timeline Fitter and simple Aperture Photometry. Colour corrections and effective beam areas as a function of the assumed source spectral index are also included to produce a large number of photometric measurements per individual target, in each of the 3 SPIRE bands (250, 350, 500um), to examine both the accuracy and repeatability of each of the 4 algorithms. It is concluded that for flux densities down to the level of 30mJy that the SPIRE Timeline Fitter is the method of choice. However, at least in the 250 and 350um bands, all 4 methods provide photometric repeatability better than a few percent down to at approximately 100mJy. The DAOphot method appears in many cases to have a systematic offset of ~8% in all SPIRE bands which may be indicative of a sub-optimal aperture correction. In general, aperture photometry is the least reliable method, i.e. largest scatter between observations, especially in the longest wavelength band. At the faintest fluxes, <30mJy, SUSSEXtractor or DAOphot provide a better alternative to the Timeline Fitter.

dart-ray: a 3D ray-tracing radiative transfer code for calculating the propagation of light in dusty galaxies

Abstract: We present DART-Ray, a new ray-tracing 3D dust radiative transfer (RT) code designed specifically to calculate radiation field energy density (RFED) distributions within dusty galaxy models with arbitrary geometries. In this paper, we introduce the basic algorithm implemented in . DART-Ray which is based on a pre-calculation of a lower limit for the RFED distribution. This pre-calculation allows us to estimate the extent of regions around the radiation sources within which these sources contribute significantly to the RFED. In this way, ray-tracing calculations can be restricted to take place only within these regions, thus substantially reducing the computational time compared to a complete ray-tracing RT calculation. Anisotropic scattering is included in the code and handled in a similar fashion. Furthermore, the code utilizes a Cartesian adaptive spatial grid and an iterative method has been implemented to optimize the angular densities of the rays originated from each emitting cell. In order to verify the accuracy of the RT calculations performed by DART-Ray, we present results of comparisons with solutions obtained using the dusty 1D RT code for a dust shell illuminated by a central point source and existing 2D RT calculations of disc galaxies with diffusely distributed stellar emission and dust opacity. Finally, we show the application of the code on a spiral galaxy model with logarithmic spiral arms in order to measure the effect of the spiral pattern on the attenuation and RFED. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

Astrophysical motivation for directed searches for a stochastic gravitational wave background

Abstract: The nearby Universe is expected to create an anisotropic stochastic gravitational-wave background (SGWB). Different algorithms have been developed and implemented to search for isotropic and anisotropic SGWBs. The aim of this paper is to quantify the advantage of an optimal anisotropic search, specifically comparing a point source with an isotropic background. Clusters of galaxies appear as point sources to a network of ground-based laser-interferometric detectors. The optimal search strategy for these sources is a ``directed radiometer search.'' We show that the flux of SGWBs created by the millisecond pulsars in the Virgo cluster produces a significantly stronger signal than the nearly isotropic background of unresolved sources of the same kind. We compute their strain power spectra for different cosmologies and the distribution of populations over redshifts. We conclude that a localized source, like the Virgo cluster, can be resolved from the isotropic background with very high significance using the directed-search algorithm. For backgrounds dominated by nearby sources, up to a redshift of about 3, we show that the directed search for a localized source can have a signal-to-noise ratio that is greater than that for the all-sky integrated isotropic search.

Solution for acoustic field of thermo-acoustic emission from arbitrary source

Abstract: In this work, an expression for acoustic field of thermo-acoustic (TA) emission from arbitrary source is presented by deriving the solutions of TA emission from spherical surface and point source in gas and then taking advantage of the point sources superposition and the surface heat distribution factor. Accordingly, the computational analysis of acoustic pressure field of TA emission is extended to three-dimensional cases. The theory developed in this work is in good agreement with the experimental results and applicable for solving many complex and important TA emission problems including nanothermophones and phased array and impulse-driven TA emissions.

“Stereo Compton cameras” for the 3-D localization of radioisotopes

Abstract: The Compton camera is a viable and convenient tool used to visualize the distribution of radioactive isotopes that emit gamma rays. After the nuclear disaster in Fukushima in 2011, there is a particularly urgent need to develop “gamma cameras”, which can visualize the distribution of such radioisotopes. In response, we propose a portable Compton camera, which comprises 3-D position-sensitive GAGG scintillators coupled with thin monolithic MPPC arrays. The pulse-height ratio of two MPPC-arrays allocated at both ends of the scintillator block determines the depth of interaction (DOI), which dramatically improves the position resolution of the scintillation detectors. We report on the detailed optimization of the detector design, based on Geant4 simulation. The results indicate that detection efficiency reaches up to 0.54%, or more than 10 times that of other cameras being tested in Fukushima, along with a moderate angular resolution of 8.1° (FWHM). By applying the triangular surveying method, we also propose a new concept for the stereo measurement of gamma rays by using two Compton cameras, thus enabling the 3-D positional measurement of radioactive isotopes for the first time. From one point source simulation data, we ensured that the source position and the distance to the same could be determined typically to within 2 meters׳ accuracy and we also confirmed that more than two sources are clearly separated by the event selection from two point sources of simulation data.

An image-plane algorithm for jwst's non-redundant aperture mask data

Abstract: The high angular resolution technique of non-redundant masking (NRM) or aperture masking interferometry (AMI) has yielded images of faint protoplanetary companions of nearby stars from the ground. AMI on James Webb Space Telescope (JWST)'s Near Infrared Imager and Slitless Spectrograph (NIRISS) has a lower thermal background than ground-based facilities and does not suffer from atmospheric instability. NIRISS AMI images are likely to have 90%-95% Strehl ratio between 2.77 and 4.8 μm. In this paper we quantify factors that limit the raw point source contrast of JWST NRM. We develop an analytic model of the NRM point spread function which includes different optical path delays (pistons) between mask holes and fit the model parameters with image plane data. It enables a straightforward way to exclude bad pixels, is suited to limited fields of view, and can incorporate effects such as intra-pixel sensitivity variations. We simulate various sources of noise to estimate their effect on the standard deviation of closure phase, σCP (a proxy for binary point source contrast). If σCP < 10–4 radians—a contrast ratio of 10 mag—young accreting gas giant planets (e.g., in the nearby Taurus star-forming region) could be imaged with JWST NIRISS. We show the feasibility of using NIRISS' NRM with the sub-Nyquist sampled F277W, which would enable some exoplanet chemistry characterization. In the presence of small piston errors, the dominant sources of closure phase error (depending on pixel sampling, and filter bandwidth) are flat field errors and unmodeled variations in intra-pixel sensitivity. The in-flight stability of NIRISS will determine how well these errors can be calibrated by observing a point source. Our results help develop efficient observing strategies for space-based NRM.

In-flight PSF calibration of the NuSTAR hard X-ray optics

Abstract: We present results of the point spread function (PSF) calibration of the hard X-ray optics of the Nuclear Spectroscopic Telescope Array (NuSTAR). Immediately post-launch, NuSTAR has observed bright point sources such as Cyg X-1, Vela X-1, and Her X-1 for the PSF calibration. We use the point source observations taken at several off-axis angles together with a ray-trace model to characterize the in-orbit angular response, and find that the ray-trace model alone does not fit the observed event distributions and applying empirical corrections to the ray-trace model improves the fit significantly. We describe the corrections applied to the ray-trace model and show that the uncertainties in the enclosed energy fraction (EEF) of the new PSF model is (approximately less than) 3% for extraction apertures of R (approximately greater than) 60″ with no significant energy dependence. We also show that the PSF of the NuSTAR optics has been stable over a period of ~300 days during its in-orbit operation.