Bayesian photometric redshifts for weak-lensing applications

The next generation of weak gravitational lensing surveys are capable of generating good measurements of cosmological parameters, provided that, amongst other requirements, adequate redshift information is available for the background galaxies that are measured. It is frequently assumed that photometric redshift techniques provide the means to achieve this. Here, we compare Bayesian and frequentist approaches to photometric redshift estimation, particularly at faint magnitudes. We identify and discuss the biases that are inherent in the various methods, and describe an optimum Bayesian method for extracting redshift distributions from photometric data.     

Kernel regression for determining photometric redshifts from Sloan broad-band photometry

We present a new approach, namely kernel regression, to determine photometric redshifts for 399 929 galaxies in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS). Kernel regression is a weighted average of spectral redshifts of the neighbours for a query point, and higher weights are associated with points that are closer to the query point. One important design decision when using kernel regression is the choice of bandwidth. We apply 10-fold cross-validation to choose the optimal bandwidth, which is obtained as the cross-validation error approaches its minimum. The results show that the optimal bandwidth is different for different input patterns: the lowest rms error of photometric redshift estimation arrives at 0.019 using colour+eClass as the inputs, the lowest rms errors comes to 0.020 using ugriz +eClass as the inputs. Where eClass is a galaxy spectral type, and 0.021 using colour+ r as the inputs. Thus, in addition to parameters such as magnitude and colour, eClass is a valid parameter with which to predict photometric redshifts. Moreover, the results suggest that the accuracy of estimating photometric redshifts is improved when the sample is divided into early-type and late-type galaxies; in particular, for early-type galaxies, the rms scatter is 0.016 with colour+eClass as the inputs. In addition, kernel regression achieves high accuracy when predicting the photometric eClass  (σ_rms= 0.034)  using colour+ r as the input pattern. For kernel regression, the accuracy of the photometric redshifts does not always increase with the number of parameters considered, but is satisfactory only when appropriate parameters are chosen. Kernel regression is a comprehensible and accurate regression method. Experiments reveal the superiority of kernel regression over other empirical training approaches.     

A reliable cluster detection technique using photometric redshifts: introducing the 2TecX algorithm

We present a new cluster detection algorithm designed for finding high-redshift clusters using optical/infrared imaging data. The algorithm has two main characteristics. First, it utilizes each galaxy's full redshift probability function, instead of an estimate of the photometric redshift based on the peak of the probability function and an associated Gaussian error. Second, it identifies cluster candidates through cross-checking the results of two substantially different selection techniques (the name 2TecX representing the cross-check of the two techniques). These are adaptations of the Voronoi Tesselations and Friends-Of-Friends methods. Monte Carlo simulations of mock catalogues show that cross-checking the cluster candidates found by the two techniques significantly reduces the detection of spurious sources. Furthermore, we examine the selection effects and relative strengths and weaknesses of either method. The simulations also allow us to fine-tune the algorithm's parameters, and define completeness and mass limit as a function of redshift. We demonstrate that the algorithm isolates high-redshift clusters at a high level of efficiency and low contamination.     

Correcting systematic effects in a large set of photometric light curves

We suggest a new algorithm to remove systematic effects in a large set of light curves obtained by a photometric survey. The algorithm can remove systematic effects, such as those associated with atmospheric extinction, detector efficiency, or point spread function changes over the detector. The algorithm works without any prior knowledge of the effects, as long as they linearly appear in many stars of the sample. The approach, which was originally developed to remove atmospheric extinction effects, is based on a lower rank approximation of matrices, an approach which has already been suggested and used in chemometrics, for example. The proposed algorithm is especially useful in cases where the uncertainties of the measurements are unequal. For equal uncertainties, the algorithm reduces to the Principal Component Analysis (PCA) algorithm. We present a simulation to demonstrate the effectiveness of the proposed algorithm and we point out its potential, in the search for transit candidates in particular.     

Error analysis of the photometric redshift technique

We present a calculation of the systematic component of the error budget in the photometric redshift technique. We make use of it to describe a simple technique that allows the assignment of confidence limits to redshift measurements obtained through photometric methods. We show that our technique, through the calculation of a redshift probability function, gives complete information on the probable redshift of an object and its associated confidence intervals. This information can and must be used in the calculation of any observable quantity that makes use of the redshift.     

Transformations between 2MASS, SDSS and BVRI photometric systems: bridging the near-infrared and optical

We present colour transformations for the conversion of the Two Micron All Sky Survey (2MASS) photometric system to the Johnson–Cousins UBVRI system and further into the Sloan Digital Sky Survey (SDSS) ugriz system. We have taken SDSS gri magnitudes of stars measured with the 2.5-m telescope from SDSS Data Release 5 (DR5), and BVRI and   JHK _s   magnitudes from Stetson's catalogue and Cutri et al., respectively. We matched thousands of stars in the three photometric systems by their coordinates and obtained a homogeneous sample of 825 stars by the following constraints, which are not used in previous transformations: (1) the data are dereddened, (2) giants are omitted and (3) the sample stars selected are of the highest quality. We give metallicity, population type and transformations dependent on two colours. The transformations provide absolute magnitude and distance determinations which can be used in space density evaluations at short distances where some or all of the SDSS ugriz magnitudes are saturated. The combination of these densities with those evaluated at larger distances using SDSS ugriz photometry will supply accurate Galactic model parameters, particularly the local space densities for each population.     

Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real-space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated with the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large-scale distribution of galaxies.     

Difference imaging photometry of blended gravitational microlensing events with a numerical kernel

The numerical kernel approach to difference imaging has been implemented and applied to gravitational microlensing events observed by the PLANET collaboration. The effect of an error in the source-star coordinates is explored and a new algorithm is presented for determining the precise coordinates of the microlens in blended events, essential for accurate photometry of difference images. It is shown how the photometric reference flux need not be measured directly from the reference image but can be obtained from measurements of the difference images combined with the knowledge of the statistical flux uncertainties. The improved performance of the new algorithm, relative to isis2 , is demonstrated.     

Photometry from online Digitized Sky Survey plates

Online Digitized Sky Survey (DSS) material is often used to obtain information on newly discovered variable stars for older epochs (e.g. Nova progenitors, flare stars, etc.). We present here the results of an investigation of photometry on online DSS material in small fields calibrated by CCD sequences. We compared different source extraction mechanisms and found that even down near to the sensitivity limit, despite the H-compression used for the online material, photometry with an accuracy better than 0.1 mag rms is possible on DSS-II. Our investigation shows that the accuracy depends strongly on the source extraction method. The SuperCOSMOS scans, although retrieved with a higher spatial resolution, do not give us better results. The methods and parameters presented here allow the user to obtain good plate photometry in small fields down to the Schmidt plate survey limits with a few bright CCD calibrators, which may be calibrated with amateur-size telescopes. Especially for the events mentioned above, new field photometry for calibration purposes mostly exists, but the progenitors were not measured photometrically before. Also, the follow-up whether stellar concentrations are newly detected clusters or similar work may be done without using mid-size telescopes. The calibration presented here is a 'local' one for small fields. We show that the method presented here gives higher accuracies than 'global' calibrations of surveys (e.g. Guide Star Catalogue-II (GSC-II), SuperCOSMOS and the US Naval Observatory Astrometry Catalog B).     

A new algorithm for differential photometry: computing anoptimum artificial comparison star

Our new algorithm for differential photometry solves the problem of identifying proper comparison stars without a prior detailed study of the field of view. The comparison stars' variability is determined in a self‐consistent way, and their weighted average is used as a reference level. The maximum error in differential photometry using objects and reference stars of different spectral types is estimated. The results from these calculations show that the photometric band chosen greatly determines the level of accuracy achieved. Finally, an important application of high‐precision differential photometry are planetary transits. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photon counting strategies with low-light-level CCDs

Low light level charge-coupled devices (L3CCDs) have recently been developed, incorporating on-chip gain. They may be operated to give an effective readout noise of much less than one electron by implementing an on-chip gain process allowing the detection of individual photons. However, the gain mechanism is stochastic and so introduces significant extra noise into the system. In this paper we examine how best to process the output signal from an L3CCD so as to minimize the contribution of stochastic noise, while still maintaining photometric accuracy.
We achieve this by optimizing a transfer function that translates the digitized output signal levels from the L3CCD into a value approximating the photon input as closely as possible by applying thresholding techniques. We identify several thresholding strategies and quantify their impact on the photon counting accuracy and the effective signal-to-noise ratio.
We find that it is possible to eliminate the noise introduced by the gain process at the lowest light levels. Reduced improvements are achieved as the light level increases up to about 20 photon pixel⁻¹ and above this there is negligible improvement. Operating L3CCDs at very high speeds will keep the photon flux low, giving the best improvements in signal-to-noise ratio.     

Photometric redshifts of galaxies from SDSS and 2MASS

In order to find the physical parameters which determine the accuracy of pho- tometric redshifts, we compare the spectroscopic and photometric redshifts (photo-z's) for a large sample of ～ 80 000 SDSS-2MASS galaxies. Photo-z's in this paper are es- timated by using the artificial neural network photometric redshift method (ANNz). For a subset of～40000 randomly selected galaxies, we find that the photometric redshift recovers the spectroscopic redshifi distribution very well with rms of 0.016. Our main results are as follows: (1) Using magnitudes directly as input parameters produces more accurate photo-z's than using colors; (2) The inclusion of 2MASS (3, H, Ks) bands does not improve photo-z's significantly, which indicates that near infrared data might not be important for the low-redshift sample; (3) Adding the concentration index (essentially the steepness of the galaxy brightness profile) as an extra input can improve the photo-z's estimation up to～10 percent; (4) Dividing the sample into early- and late-type galaxies by using the concentration index, normal and abnormal galaxies by using the emission line flux ratios, and red and blue galaxies by using color index (g - r), we can improve the accuracy of photo-z's significantly; (5) Our analysis shows that the outliers (where there is a big difference between the spectroscopic and photometric redshifts) are mainly correlated with galaxy types, e.g., most outliers are late-type (blue) galaxies.     

Photometric redshifts with surface brightness priors

We use galaxy surface brightness as prior information to improve photometric redshift (photo- z ) estimation. We apply our template-based photo- z method to imaging data from the ground-based VVDS survey and the space-based GOODS field from HST , and use spectroscopic redshifts to test our photometric redshifts for different galaxy types and redshifts. We find that the surface brightness prior eliminates a large fraction of outliers by lifting the degeneracy between the Lyman and 4000-Å breaks. Bias and scatter are improved by about a factor of 2 with the prior in each redshift bin in the range  0.4 < z < 1.3  , for both the ground and space data. Ongoing and planned surveys from the ground and space will benefit, provided that care is taken in measurements of galaxy sizes and in the application of the prior. We discuss the image quality and signal-to-noise ratio requirements that enable the surface brightness prior to be successfully applied.     

The Sloan Digital Sky Survey monitor telescope pipeline

The photometric calibration of the Sloan Digital Sky Survey (SDSS) is a multi‐step process which involves data from three different telescopes: the 1.0‐m telescope at the US Naval Observatory (USNO), Flagstaff Station, Arizona (which was used to establish the SDSS standard star network); the SDSS 0.5‐m Photometric Telescope (PT) at the Apache Point Observatory (APO), NewMexico (which calculates nightly extinctions and calibrates secondary patch transfer fields); and the SDSS 2.5‐m telescope at APO (which obtains the imaging data for the SDSS proper). In this paper, we describe the Monitor Telescope Pipeline, MTPIPE, the software pipeline used in processing the data from the single‐CCD telescopes used in the photometric calibration of the SDSS (i.e., the USNO 1.0‐m and the PT). We also describe transformation equations that convert photometry on the USNO‐1.0m u ′g ′r ′i ′z ′ system to photometry the SDSS 2.5m ugriz system and the results of various validation tests of the MTPIPE software. Further, we discuss the semi‐automated PT factory, which runs MTPIPE in the day‐to‐day standard SDSS operations at Fermilab. Finally, we discuss the use of MTPIPE in current SDSS‐related projects, including the Southern u ′g ′r ′i ′z ′ Standard Star project, the u ′g ′r ′i ′z ′ Open Star Clusters project, and the SDSS extension (SDSS‐II). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stellar photometry and astrometry with discrete point spread functions

The key features of the matphot algorithm for precise and accurate stellar photometry and astrometry using discrete point spread functions (PSFs) are described. A discrete PSF is a sampled version of a continuous PSF, which describes the two-dimensional probability distribution of photons from a point source (star) just above the detector. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or an FITS (Flexible Image Transport System) image file. Discrete PSFs are shifted within an observational model using a 21-pixel-wide damped sinc function, and position-partial derivatives are computed using a five-point numerical differentiation formula. Precise and accurate stellar photometry and astrometry are achieved with undersampled CCD (charge-coupled device) observations by using supersampled discrete PSFs that are sampled two, three or more times more finely than the observational data. The precision and accuracy of the matphot algorithm is demonstrated by using the c -language mpd code to analyse simulated CCD stellar observations; measured performance is compared with a theoretical performance model. Detailed analysis of simulated Next Generation Space Telescope observations demonstrate that millipixel relative astrometry and mmag photometric precision is achievable with complicated space-based discrete PSFs.