Point Spread Function Patterns Research Articles

Simultaneous spectral differentiation of multiple fluorophores in super-resolution imaging using a glass phase plate.

By engineering the point-spread function (PSF) of single molecules, different fluorophore species can be imaged simultaneously and distinguished by their unique PSF patterns. Here, we insert a silicon-dioxide phase plate at the Fourier plane of the detection path of a wide-field fluorescence microscope to produce distinguishable PSFs (X-PSFs) at different wavelengths. We demonstrate that the resulting PSFs can be localized spatially and spectrally using a maximum-likelihood estimation algorithm and can be utilized for hyper-spectral super-resolution microscopy of biological samples. We produced superresolution images of fixed U2OS cells using X-PSFs for dSTORM imaging with simultaneous illumination of up to three fluorophore species. The species were distinguished only by the PSF pattern. We achieved ∼21-nm lateral localization precision (FWHM) and ∼17-nm axial precision (FWHM) with an average of 1,800 - 3,500 photons per PSF and a background as high as 130 - 400 photons per pixel. The modified PSF distinguished fluorescent probes with ∼80 nm separation between spectral peaks.

Frequency-Diverse Computational Automotive Radar Technique for Debris Detection

Frequency-diversity is a computational imaging technique that can offer all-electronic imaging systems by leveraging spatio-temporally incoherent radiation patterns as an enabling technology. This approach exhibits a significant contrast to conventional imaging modalities, such as synthetic aperture radars (SAR) and phased arrays in that the raster scanning requirement of a scene to be imaged (mechanical or electronic) can be broken and replaced by a quasi-random interrogation of the scene. This aspect of frequency-diverse computational imaging systems significantly simplifies the physical hardware requirements of conventional radars. Despite this advantage, the application of the frequency-diversity technique has been mostly limited to static imaging scenarios, where the position of the scene to be imaged remains fixed over the data acquisition cycle. This limitation hinders the frequency-diverse computational radars from being deployed for applications where the scene dynamics may vary over the data acquisition cycle, such as in automotive radars. In this paper, we demonstrate that by modifying the sensing matrix to account for the movement of the radar platform, frequency-diverse computational imaging radars can be successfully used in debris detection on roads. We show that operating within the frequency band of 77–81 GHz, the presented dynamic frequency-diverse radar technique can produce high fidelity point spread function (PSF) patterns eliminating the distortions caused by the motion of the radar. We also prove that the PSF patterns of the radar are in excellent agreement with theoretical diffraction limited resolution limits.

Point-Spread-Function (PSF) Characterization of a 340-GHz Imaging Radar Using Acoustic Levitation

In this paper, resolution characterization and beam analysis of a 340-GHz imaging radar are demonstrated by means of a point-spread-function (PSF) study by imaging an acoustically levitated point-like target. It is shown that at terahertz frequencies, conventional PSF measurement techniques are limited by the presence of strong scattering response of background objects, such as suspension threads, within the imaging field-of-view (FOV). Using acoustic levitation, it is possible to eliminate secondary objects within the FOV and achieve a pure PSF characterization of the radar. It is shown that the PSF patterns obtained using acoustic levitation exhibit high fidelity and are free from artifacts. We demonstrate this using a small water droplet suspended in air at the focus of the 340-GHz radar. The measured PSF characteristics of the radar are in excellent agreement with physical optics (PO) simulations and analytical results.

Atmospheric point spread function interpolation for weak lensing in short exposure imaging data

A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ($\simeq$15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, PSFent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, PSFent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than $\sim13'$, compared to polynomial fitting. We estimate that with PSFent and for stellar densities greater than $\simeq1/{\rm arcmin}^{2}$, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.

Image Ellipticity from Atmospheric Aberrations

We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a ray-tracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1 / sqrt(N)). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the ray-tracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not an accurate method of modeling PSF ellipticity induced by atmospheric turbulence unless some additional procedure is implemented to correctly account for the effects of high spatial frequency aberrations. The Fourier method, however, can be used directly to accurately model PSF ellipticity, which can give insights into errors in the statistics of field galaxy shapes used in studies of weak gravitational lensing.

PSF anisotropy and systematic errors in weak lensing surveys

Given the basic parameters of a cosmic shear weak lensing survey, how well can systematicerrors due to anisotropy in the point spread function (PSF) be corrected? The largestsource of error in this correction to date has been the interpolation of the PSF to thelocations of the galaxies. To address this error, we separate the PSF patterns intocomponents that recur in multiple exposures/pointings and those that vary randomlybetween different exposures (such as those due to the atmosphere). In an earlier study wedeveloped a principal component approach to correct the recurring PSF patterns. In thispaper we show how randomly varying PSF patterns can also be circumvented in themeasurement of shear correlations. For the two-point correlation function this is done bysimply using pairs of galaxy shapes measured in different exposures. Combiningthe two techniques allows us to tackle generic combinations of PSF anisotropypatterns. The second goal of this paper is to give a formalism for quantifyingresidual systematic errors due to PSF patterns. We show how the main PSFcorrections improve with increasing survey area (and thus can stay below the reducedstatistical errors), and we identify the residual errors which do not scale withsurvey area. Our formalism can be applied both to planned lensing surveys tooptimize survey strategy and to actual lensing data to quantify residual errors.