Point Spread Function Profile Research Articles

PSFs of coadded images

We provide a detailed exploration of the connection between choice of coaddition schemes and the point-spread function (PSF) of the resulting coadded images. In particular, we investigate what properties of the coaddition algorithm lead to the final coadded image having a well-defined PSF. The key elements of this discussion are as follows: 1. We provide an illustration of how linear coaddition schemes can produce a coadd that lacks a well-defined PSF even for relatively simple scenarios and choices of weight functions. 2. We provide a more formal demonstration of the fact that a linear coadd only has a well-defined PSF in the case that either (a) each input image has the same PSF or (b) the coadd is produced with weights that are independent of the signal. 3. We discuss some reasons that two plausible nonlinear coaddition algorithms (median and clipped-mean) fail to produce a consistent PSF profile for stars. 4. We demonstrate that all nonlinear coaddition procedures fail to produce a well-defined PSF for extended objects. In the end, we conclude that, for any purpose where a well-defined PSF is desired, one should use a linear coaddition scheme with weights that do not correlate with the signal and are approximately uniform across typical objects of interest.

Gaia Early Data Release 3

Context. The unprecedented astrometric precision of the Gaia mission relies on accurate estimates of the locations of sources in the Gaia data stream. This is ultimately performed by point spread function (PSF) fitting, which in turn requires an accurate reconstruction of the PSF, including calibrations of all the major dependences. These include a strong colour dependence due to Gaia’s broad G band and a strong time dependence due to the evolving contamination levels and instrument focus. Accurate PSF reconstruction is also important for photometry. Gaia Early Data Release 3 (EDR3) will, for the first time, use a PSF calibration that models several of the strongest dependences, leading to signficantly reduced systematic errors. Aims. We describe the PSF model and calibration pipeline implemented for Gaia EDR3, including an analysis of the calibration results over the 34 months of data. We include a discussion of the limitations of the current pipeline and directions for future releases. This will be of use both to users of Gaia data and as a reference for other precision astrometry missions. Methods. We develop models of the 1D line spread function (LSF) and 2D PSF profiles based on a linear combination of basis components. These are designed for flexibility and performance, as well as to meet several mathematical criteria such as normalisation. We fit the models to selected primary sources in independent time ranges, using simple parameterisations for the colour and other dependences. Variation in time is smoothed by merging the independent calibrations in a square root information filter, with resets at certain mission events that induce a discontinuous change in the PSF. Results. The PSF calibration shows strong time and colour dependences that accurately reproduce the varying state of the Gaia astrometric instrument. Analysis of the residuals reveals both the performance and the limitations of the current models and calibration pipeline, and indicates the directions for future development. Conclusions. The PSF modelling and calibration carried out for Gaia EDR3 represents a major step forwards in the data processing and will lead to reduced systematic errors in the core mission data products. Further significant improvements are expected in the future data releases.

A Study of the Point-spread Function in SDSS Images

Abstract We use SDSS imaging data in the ugriz passbands to study the shape of the point-spread function (PSF) profile and the variation of its width with wavelength and time. We find that the PSF profile is well described by theoretical predictions based on von Kármán’s turbulence theory. The observed PSF radial profile can be parameterized by only two parameters, the profile’s full width at half maximum (FWHM) and a normalization of the contribution of an empirically determined “instrumental” PSF. The profile shape is very similar to the “double Gaussian plus power-law wing” decomposition used by the SDSS image-processing pipeline, but here it is successfully modeled with two free model parameters, rather than six as in the SDSS pipeline. The FWHM variation with wavelength follows the λ α power law, where α ≈ −0.3 and is correlated with the FWHM itself. The observed behavior is much better described by von Kármán’s turbulence theory, with the outer-scale parameter in the range of 5–100 m, than by Kolmogorov’s turbulence theory. We also measure the temporal and angular structure functions for FWHM and compare them to simulations and results from the literature. The angular structure function saturates at scales beyond 05−10. The power spectrum of the temporal behavior is found to be broadly consistent with a damped random-walk model with a characteristic timescale in the range of ∼5–30 minutes, though the data show a shallower high-frequency behavior. The latter is well fit by a single power law with an index in the range of −1.5 to −1.0. A hybrid model is likely needed to fully capture both the low-frequency and high-frequency behavior of the temporal variations of atmospheric seeing.

The optimal on-source region size for detections with counting-type telescopes

Source detection in counting type experiments such as Cherenkov telescopes often involves the application of the classical Eq. (17) from the paper of Li & Ma (1983) to discrete on- and off-source regions. The on-source region is typically a circular area with radius θ in which the signal is expected to appear with the shape of the instrument point spread function (PSF). This paper addresses the question of what is the θ that maximises the probability of detection for a given PSF width and background event density. In the high count number limit and assuming a Gaussian PSF profile, the optimum is found to be at ζ∞2≈2.51 times the squared PSF width σPSF392. While this number is shown to be a good choice in many cases, a dynamic formula for cases of lower count numbers, which favour larger on-source regions, is given. The recipe to get to this parametrisation can also be applied to cases with a non-Gaussian PSF. This result can standardise and simplify analysis procedures, reduce trials and eliminate the need for experience-based ad hoc cut definitions or expensive case-by-case Monte Carlo simulations.

The Effect of Detector Nonlinearity on WFIRST PSF Profiles for Weak Gravitational Lensing Measurements

Weak gravitational lensing (WL) is one of the most powerful techniques to learn about the dark sector of the universe. To extract the WL signal from astronomical observations, galaxy shapes must be measured and corrected for the point-spread function (PSF) of the imaging system with extreme accuracy. Future WL missions—such as NASA’s Wide-Field Infrared Survey Telescope (WFIRST)—will use a family of hybrid near-infrared complementary metal-oxide-semiconductor detectors (HAWAII-4RG) that are untested for accurate WL measurements. Like all image sensors, these devices are subject to conversion gain nonlinearities (voltage response to collected photo-charge) that bias the shape and size of bright objects such as reference stars that are used in PSF determination. We study this type of detector nonlinearity (NL) and show how to derive requirements on it from WFIRST PSF size and ellipticity requirements. We simulate the PSF optical profiles expected for WFIRST and measure the fractional error in the PSF size (ΔR/R) and the absolute error in the PSF ellipticity (Δe) as a function of star magnitude and the NL model. For our nominal NL model (a quadratic correction), we find that, uncalibrated, NL can induce an error of ΔR/R = 1 × 10−2 and Δe2 = 1.75 × 10−3 in the H158 bandpass for the brightest unsaturated stars in WFIRST. In addition, our simulations show that to limit the bias of ΔR/R and Δe in the H158 band to ∼10% of the estimated WFIRST error budget, the quadratic NL model parameter β must be calibrated to ∼1% and ∼2.4%, respectively. We present a fitting formula that can be used to estimate WFIRST detector NL requirements once a true PSF error budget is established.

Silicon-coated gold nanoparticles nanoscopy

This paper presents a method for modifying the point spread function (PSF) into a doughnut-like shape, through the utilization of the plasma dispersion effect (PDE) of silicon-coated gold nanoparticles. This modified PSF has spatial components smaller than the diffraction limit, and by scanning the sample with it, super-resolution can be achieved. The sample is illuminated using two laser beams. The first is the pump, with a wavelength in the visible region that creates a change in the refractive index of the silicon coating due to the PDE. This creates a change in the localized surface plasmon resonance wavelength. Since the pump beam has a Gaussian profile, the high intensity areas of the beam experience the highest refractive index change. When the second beam (i.e., the probe) illuminates the sample with a near-infrared wavelength, this change in the refractive index is transformed into a change in the PSF profile. The ordinary Gaussian shape is transformed into a doughnut shape, with higher spatial frequencies, which enables one to achieve super-resolution by scanning the specimen using this PSF. This is a step toward the creation of a nonfluorescent nanoscope.

Anisoplanatism effect on the E-ELT SCAO point spread function. A preserved coherent core across the field

Context. The science case studies and the optimized designing of the future adaptive optics-fed extremely large telescope instruments require the precise simulation of their adaptive optics system, potentially over their whole field of view, whatever the adaptive optics flavor the instruments will be equipped with.Aims. We simulate the anisoplanatism effect on the extremely large telescope single conjugate adaptive optics point spread function. Our interest in this expected degradation of the correction performance with respect to the off-axis distance is in terms of the point spread function Strehl ratio and profile.Methods. Adaptive optics simulations at the scale of extremely large telescopes are challenging given the large parameter space to explore for the adaptive optics dimensioning and the large number of degrees of freedom at play for a given set of simulation parameters. To address this problem, we have used three different simulation tools with increasing degree of fidelity compared to a real adaptive optics system. The first is based on analytical formulae and allowed us to derive the Strehl ratio degradation with the off-axis distance. The second is a Fourier-based code and provided us with both the Strehl ratio and the point spread function profile in the field. The last is an end-to-end code based on the graphical processing unit technology and also provided us with the Strehl ratio and the point spread function profile in the field.Results. The three tools we used demonstrated a fast execution time even at the extremely large telescope scale. Cross-checks between the different codes were performed and demonstrated the coherency of the results. In addition to the expected degradation of the adaptive optics performance with the field angle, we demonstrated that in the simulation conditions applicable to the E-ELT, the single conjugate adaptive optics point spread function remains topped with a coherent core even at off-axis distances as large as 60 arcsec and consequently very low Strehl ratios. We also studied the impact of the outer scale on the point spread function profile, demonstrating that the aforementioned Airy-like pattern is observable even when the outer scale is larger than the telescope diameter.Conclusions. These results could push for the preservation over a large field of the optical quality of any common path optics between the telescope and the instruments in single conjugate adaptive optics mode. This could offer some astrometric capabilities to these instruments operating in this adaptive optics mode.

Optical observations of comet 67P/Churyumov-Gerasimenko with the Nordic Optical Telescope

Context. 67P/Churyumov-Gerasimenko (67P) is a short-period Jupiter-family comet that was chosen as a target for the Rosetta mission by the European Space Agency (ESA). Monitoring of 67P with the Nordic Optical Telescope (NOT; La Palma, Spain) intends to aid this mission by providing ground-based reference information about the overall activity of the target and its astrometric position before the rendezvous. One motivation for our observations was to monitor sudden major increases in activity because they might have affected the Rosetta mission planning. None were observed. Ground-based photometric observations register the global activity of the comet, while the Rosetta spacecraft mostly measures local events. These data combined can lead to new insights into the comet behavior.Aims. The aim of this work is to perform the photometric and the astrometric monitoring of comet 67P with the NOT and to compare the results with the latest predictions for its position and activity. A new method of fitting extended-source components to the target surface brightness distribution was developed and applied to the data to estimate the size and contribution of the coma to the total brightness of the target.Methods. Comet 67P was monitored by the NOT in service mode during the period between 12.5.2013 and 11.11.2014. The very first observations were performed in the V band alone, but in the latest observations, the R band was used as well to estimate the color and nature of activity of the target. We applied a new method for estimating the coma size by deconvolving the point spread function profile from the image, which used Markov chain Monte Carlo and Bayesian statistics. This method will also be used for coma size estimations in further observations after the solar conjunction of 67P.Results. Photometric magnitudes in two colors were monitored during the period of observations. At the end of April 2014, the beginning of activity was observed. In late September 2014, a minor dip in cometary activity was measured. Otherwise, the activity of the comet was close to the expected values. For some of the observations, we were able to determine limits for the physical size and brightness of the coma by studying the surface brightness distribution of the target. The astrometric calibration results we obtained were consistent with the predictions of the ephemerides of the Minor Planet Center, but at the moment these results are superseded with the more precise astrometric data from the Rosetta spacecraft.

Aperture shape dependencies in extended depth of focus for imaging camera by wavefront coding

Optical transfer functions (OTFs) on various directional spatial frequency axes for cubic phase mask (CPM) with circular and square apertures are investigated. Although OTF has no zero points, it has a very close value to zero for a circular aperture at low frequencies on diagonal axis, which results in degradation of restored images. The reason for close-to-zero value in OTF is also analyzed in connection with point spread function profiles using Fourier slice theorem. To avoid close-to-zero condition, square aperture with CPM is indispensable in WFC. We optimized cubic coefficient α of CPM and coefficients of digital filter, and succeeded to get excellent de-blurred images at large depth of field.

Photon Counting Histogram Using Numerical Data of Point Spread Function

Photon counting histogram (PCH) is a fluorescence fluctuation method that can quantify the brightness and concentration of different fluorescent molecules in solution at a single molecule level using confocal optics. The current method assumes that the point spread function (PSF) of confocal optics is Gaussian function. However, this could be problematic when the actual PSF profile is not Gaussian. Here, we propose an improved PCH analysis method using numerical PSF data. This method does not require any analytical equation for the PSF profile, and can handle any arbitrary shape of PSF. We report a proof-of-concept estimation of this method using a model PSF.

Obtaining point spread function of penumbral encoding aperture with “expectation maximization” algorithm based on matched source-image pair experiment

A source penumbral image reconstruction method with linear mapping principle for geometrical optics is established. The ideal binary point spread function (PSF) can be obtained using a geometrical optics model. The system PSF with certain sharpness was obtained using a Monte Carlo (MC) model. Considering other factors besides the transportation of the x (gamma)-rays or particles (fusion neutrons) in the penumbral encoding aperture in MC model, such as the scattering background and the systematic error, the PSF from MC model "source-image pair matching" experiments with a large area standard oval shape source were processed. A method for correcting and calibrating the PSF by the expectation maximization adaptive algorithm was established and the optimized PSF with 22.30 microm sharpness was achieved. This is more consistent with the real system PSF despite the increased noise level of the two-dimensional PSF and large irregularity in the PSF profile.

Color Breakup Reduction by 180 Hz Stencil-FSC Method in Large-Sized Color Filter-Less LCDs

Field-sequential color (FSC) is a high optical throughput technique for future green liquid crystal displays (LCDs). However, the FSC-LCD faces a lethal issue, color breakup (CBU) which degrades image clarity and prevents high level LCD-TV productions. We proposed the 180 Hz Stencil Field-Sequential-Color method to redistribute intensities of the three primary color field-images to suppress CBU. By applying local color-backlight-dimming technology to FSC-LCDs, a low resolution colorful backlight panel combined with a high resolution color filter-less LC panel generated a green-based multi-color field-image which showed the most image luminance in the first field. Therefore, residual red and blue field-image intensities were reduced and effectively suppressed CBU when compared to field-rate increasing methods. In addition, to further implement hardware, the number of backlight divisions of 32×24 and a proper Gaussian point spread function profile were optimized via simulations while considering CBU reduction and image fidelity. Using optimized hardware parameters, the CBU phenomenon was suppressed by 50% of traditional RGB driving in simulation and was demonstrated on a 120 Hz 46-inch MVA LCD-TV.

Estimation of a super-resolved PSF for the data reduction of undersampled stellar observations

Context. Fitting photometry algorithms can be very effective provided that an accurate model of the instrumental point spread function (PSF) is available. When high-precision time-resolved photometry is required, however, the use of point-source star images as empirical PSF models can be unsatisfactory, due to the limits in their spatial resolution. Theoretically-derived models, on the other hand, are limited by the unavoidable assumption of simplifying hypothesis, while the use of analytical approximations is restricted to regularly-shaped PSFs. Aims. This work investigates an innovative technique for space-based fitting photometry, based on the reconstruction of an empirical but properly-resolved PSF. The aim is the exploitation of arbitrary star images, including those produced under intentional defocus. The cases of both MOST and COROT, the first space telescopes dedicated to time-resolved stellar photometry, are considered in the evaluation of the effectiveness and performances of the proposed methodology. Methods. PSF reconstruction is based on a set of star images, periodically acquired and presenting relative subpixel displacements due to motion of the acquisition system, in this case the jitter of the satellite attitude. Higher resolution is achieved through the solution of the inverse problem. The approach can be regarded as a special application of super-resolution techniques, though a specialised procedure is proposed to better meet the PSF determination problem specificities. The application of such a model to fitting photometry is illustrated by numerical simulations for COROT and on a complete set of observations from MOST. Results. We verify that, in both scenarios, significantly better resolved PSFs can be estimated, leading to corresponding improvements in photometric results. For COROT, indeed, subpixel reconstruction enabled the successful use of fitting algorithms despite its rather complex PSF profile, which could hardly be modeled otherwise. For MOST, whose direct-imaging PSF is closer to the ordinary, comparison to other models or photometry techniques were carried out and confirmed the potential of PSF reconstruction in real observational conditions.

Behavior of the point-spread function in photon-limited confocal microscopy.

We study the behavior of the point-spread function (PSF) of the confocal scanning optical microscope (CSOM) when the available optical energy density from the sample plane is low (<7.5 microJoule/micrometers2). The PSF profile is analyzed under three photon-limited imaging conditions: (1) reflection-type CSOM with a weak source and a perfectly reflecting sample, (2) reflection-type CSOM with a strong illumination source and a weak sample, and (3) fluorescence CSOM with a weak fluorescent sample. Linfoot's image quality criteria of fidelity, structural content, and correlation quality are used to assess the reproducibility of the PSF profile as a function of the photon number. Low photon numbers yield a PSF profile that is difficult to maintain from one location in the sample plane to another. The optical sectioning capability of the CSOM was found to deteriorate more quickly against light power reduction than its transverse resolving power. The signal-to-noise ratio of the scanned CSOM image improves exponentially with the photon number from the sample plane. The noise that is generated by an unstable PSF has an average amplitude that decreases exponentially with the photon number and is significant only at low photon numbers. The CSOM image quality deteriorates because of spurious high-frequency components, degradation in the PSF dynamic range, and varying resolving power.

Efficient Speckle Noise Attenuation in Faint Companion Imaging

ABSTRACTNumerical simulations are used to evaluate a technique to attenuate speckle noise and enhance faint companion images buried in a bright‐star point‐spread function (PSF). It is shown that when frames taken simultaneously at two different wavelengths are subtracted from one another, the general evolution of the PSF profile with wavelength limits the attenuation to A2∼2σ2ϕΔλ/λ, where σ2ϕ is the wave‐front phase variance and Δλ the bandpass separation. When images taken at three wavelengths are combined in a double difference, the residuals caused by speckle evolution are very strongly damped and attenuations A3∼A22 are obtained. Very strong attenuation of speckle noise can thereby be achieved in images taken with adaptive optics (σ2ϕ<1). With three filters spanning the CH4 bandhead at 1.59 μm in the spectrum of cool brown dwarfs or Jovian planets, speckle noise can be attenuated by a factor of ∼104. This technique makes it possible to reach the photon limit in searches for methanated companions of even the brightest stars in the sky at separations of less than λ/D.