Changeset 4900 for trunk/doc/psphot/psphot.tex
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- Aug 29, 2005, 4:37:55 PM (21 years ago)
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trunk/doc/psphot/psphot.tex (modified) (20 diffs)
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trunk/doc/psphot/psphot.tex
r4896 r4900 51 51 data rate. The prototype telescope alone is expected to produce 52 52 typically $\sim 700$ GB per night of imaging data. These images will 53 not be limited to high galactic lat titudes, so large numbers of53 not be limited to high galactic latitudes, so large numbers of 54 54 measurable stars can be expected in much of the data. The combination 55 55 of the high precision goals of the astrometric and photometric … … 83 83 \item Sextractor : pure aperture measurement with rudimentary 84 84 object subtraction. pro: fast, widely used, easy to automate. con: 85 poor object separation in crowded regions, psf-modelling is only85 poor object separation in crowded regions, PSF-modeling is only 86 86 beta (psfex), what models are available? 87 87 … … 89 89 con: IRAF-based, aperture photometry. 90 90 91 \item galfit : detailed galaxy model ling. not a multi-object PSF91 \item galfit : detailed galaxy modeling. not a multi-object PSF 92 92 analysis tool. con: does not provide a PSF model, not easily 93 93 automated. very detailed results in very slow processing. only a … … 112 112 Perl (or potentially Python). 113 113 114 \note{Discussion of the lessons learned from experience with previous 115 analysis programs. 1) Flexible PSF model: functional form should be 116 easily modified. 2) PSF variation is fundamental : PSF 117 representation should incorporate 2-D variations. 3) Speed fitting 118 with accurate parameter guesses. 3) Make good use of moment 119 information to speed analysis. 4) careful definition of PSF 120 validity tests. 5) careful analysis of aperture corrections. 6) 121 flexible non-PSF models. 7) Good code abstraction to simplify 122 modification. } 114 \note{Add discussion of the lessons learned from experience with previous 115 analysis programs} 116 117 \begin{itemize} 118 \item Flexible PSF model: functional form should be 119 easily modified. 120 \item PSF variation is fundamental : PSF representation should incorporate 2-D variations. 121 \item Speed fitting with accurate parameter guesses. 122 \item Make good use of moment information to speed analysis. 123 \item Careful definition of PSF validity tests. 124 \item Careful analysis of aperture corrections. 125 \item Flexible non-PSF models. 126 \item Good code abstraction to simplify modification. 127 \end{itemize} 123 128 124 129 \section{Description of the PSPhot analysis steps} … … 189 194 190 195 The noise image, if not supplied is constructed by default from the 191 flux image using the configuration supplied values of GAINand192 READ_NOISE to calculate the appropriate Poisson statistics for each 193 pixel. In this case, the image is assumed to represent the readout 194 from a single detector, with well-defined gain and read noise196 flux image using the configuration supplied values of \code{GAIN} and 197 \code{READ_NOISE} to calculate the appropriate Poisson statistics for 198 each pixel. In this case, the image is assumed to represent the 199 readout from a single detector, with well-defined gain and read noise 195 200 characteristics. In some obvious cases, this assumption will not be 196 201 valid. For example, if the input flux image is the result of an image 197 202 stack with significantly variable number of input measurements per 198 203 pixel, it will necessary to supply a noise image which accurately 199 represents the noise as a function of position in the image. 200 201 \subsubsection{In tial Object Detection}204 represents the noise as a function of position in the image. 205 206 \subsubsection{Initial Object Detection} 202 207 203 208 The objects are initially detected by finding the location of local … … 231 236 Once a collection of peaks have been identified, basic properties of 232 237 the objects are measured. First, the local sky flux is measured 233 (using Median? user-specifi emethod?) within a square annulus with238 (using Median? user-specific method?) within a square annulus with 234 239 user-defined dimensions (\code{INNER_RADIUS} and \code{OUTER_RADIUS}). 235 240 \note{rejection of some peaks based on the local sky measurement?}. … … 250 255 PSPhot uses an analytical model to represent the shape and flux of an 251 256 object. An important concept within the PSPhot code is the 252 distinction be wteen a model which describes an object on an image and257 distinction between a model which describes an object on an image and 253 258 a model with describes the point-spread-function across an image. 254 259 … … 258 263 ($x_o, y_o$), the elliptical shape parameters ($\sigma_x, \sigma_y, 259 264 \sigma_{xy}$), the model normalization ($I_o$) and the local value of 260 the background ($S$). A specific object will have a parti ular set of265 the background ($S$). A specific object will have a particular set of 261 266 values for these different parameters. 262 267 … … 278 283 each a function of the object centroid coordinates: 279 284 \begin{eqnarray} 280 \sigma_x & = & f 1(x,y) \\281 \sigma_y & = & f 2(x,y) \\282 \sigma_{xy} & = & f 3(x,y) \\285 \sigma_x & = & f_1(x,y) \\ 286 \sigma_y & = & f_2(x,y) \\ 287 \sigma_{xy} & = & f_3(x,y) \\ 283 288 \end{eqnarray} 284 289 … … 314 319 these types of circumstances are abstracted, and a method is provided 315 320 to return the necessary function to the higher-level software. For 316 example, each model type has its own function to define an in tial321 example, each model type has its own function to define an initial 317 322 guess for the model, or a function to determine the radius for a given 318 323 flux level. These are then registered as part of the model function 319 324 code. Another function is then used to return the appropriate 320 325 function for a specific model type. For example, the 321 psModelLookup_GetFunction will return the psModelLookup function for a 322 given model type. This mechanism makes it very easy to add new model 323 functions into the PSPhot code base. To add a new model function, the 324 programmer simply defines a new model name (a string), the set of all 325 necessary model lookup functions, and places the reference to the 326 model code at the appropriate location in the psModelInit.c routine. 327 It is not necessary to specify the PSF model functions independently 328 or the object model functions. Nor is it necessary to identify the 329 intended use of a given object model function (ie, PSF-like object, 330 galaxy, comet, etc). Any model can be used for the PSF model. The 331 code currently uses a fixed translation between the object model 332 parameters and the PSF model parameters. It also defines a specific 333 order for the 4 independent parameters. \note{it may also require 334 that two of the PSF-like parameters represent the shape in some way}. 326 \code{psModelLookup_GetFunction} will return the \code{psModelLookup} 327 function for a given model type. This mechanism makes it very easy to 328 add new model functions into the PSPhot code base. To add a new model 329 function, the programmer simply defines a new model name (a string), 330 the set of all necessary model lookup functions, and places the 331 reference to the model code at the appropriate location in the 332 psModelInit.c routine. It is not necessary to specify the PSF model 333 functions independently or the object model functions. Nor is it 334 necessary to identify the intended use of a given object model 335 function (ie, PSF-like object, galaxy, comet, etc). Any model can be 336 used for the PSF model. The code currently uses a fixed translation 337 between the object model parameters and the PSF model parameters. It 338 also defines a specific order for the 4 independent parameters. 339 \note{it may also require that two of the PSF-like parameters 340 represent the shape in some way}. 335 341 336 342 \subsubsection{PSF Object Candidate Selection} … … 339 345 identify a collection of objects in the image which are {\em likely} 340 346 to be PSF-like. PSPhot uses the object moments to make the initial 341 guess at a colle tion of PSF-like objects. At this point, the program342 has measured the second order moments for all objects identified th ier347 guess at a collection of PSF-like objects. At this point, the program 348 has measured the second order moments for all objects identified their 343 349 peaks, as well as an approximate signal-to-noise ratio. All objects 344 350 with a S/N ratio greater than a user-defined parameter are selected by … … 353 359 the bin size is approximately 0.1 image pixels. The binned $\sigma_x, 354 360 \sigma_y$ plane is then examined to find a peak which has a 355 significance greater than XXX. Unless the image is extremely spar ce,361 significance greater than XXX. Unless the image is extremely sparse, 356 362 such a peak will be well-defined and should represent the objects 357 363 which are all very similar in shape. Other objects in the image will 358 364 tend to land in very different locations, failing to produce a single 359 peak. To avoid detecting a peak from the unresol ed cosmic rays,365 peak. To avoid detecting a peak from the unresolved cosmic rays, 360 366 objects which have second-moments very close to 0 are ignored. The 361 367 only danger is if the PSF is very small and too many of these objects … … 381 387 iterative, and rejects the $3-\sigma$ outliers in each of three 382 388 passes. This fitting technique results in a robust measurement of the 383 variation of the PSF model paramete sras a function of position389 variation of the PSF model parameters as a function of position 384 390 without being excessively biased by individual objects which fail 385 391 drastically. Objects whose model parameters are rejected by this … … 400 406 the PSF objects. The difference between the aperture and fit 401 407 magnitudes ({\em ApResid}) is a critical parameter for any PSF 402 model ling software which uses an analytical model to represent the408 modeling software which uses an analytical model to represent the 403 409 flux distribution of the objects in an image. 404 410 … … 408 414 between two images. Whether the goal is calibration of a science 409 415 image taken at one location to a standard star image at another 410 location, or the goal is simply the repet ative photometry of the same416 location, or the goal is simply the repetitive photometry of the same 411 417 star at the same location in the image, it is always necessary to 412 418 compare the photometry between two images. If this measurement is to … … 450 456 Consider a typical bright object with a flux of (say) 40,000 counts in 451 457 an image of background 1000 counts per pixel, with FWHM of 4 pixels. 452 In principle, the flux of this object should be measur eable with an458 In principle, the flux of this object should be measurable with an 453 459 accuracy of roughly 0.57\% ($\frac{\sqrt{40000 + 1000 \times 454 460 12}}{40000}$). However, the measurement of the sky is limited at some … … 572 578 573 579 PSPhot will use the user-selected galaxy model to attempt the galaxy 574 model fits. In the configuration system, the KEYWORD GAL_MODEL is set575 to the model of interest. All suspected extended objects are fitted 576 with the model, allowing all of the parameters to float. The initial 577 parameter guesses are critical here to achieving convergence on the578 model fits in a reasonable time. The moments and the pixel flux 579 distribution are used to make the initial parameter guess. Many of 580 the object parameters can be accurately guessed from the first and580 model fits. In the configuration system, the keyword \code{GAL_MODEL} 581 is set to the model of interest. All suspected extended objects are 582 fitted with the model, allowing all of the parameters to float. The 583 initial parameter guesses are critical here to achieving convergence 584 on the model fits in a reasonable time. The moments and the pixel 585 flux distribution are used to make the initial parameter guess. Many 586 of the object parameters can be accurately guessed from the first and 581 587 second moments. The power-law slope can be guessed by measuring the 582 588 isophotal level at two elliptical radii and comparing the ratio to 583 that expected. 589 that expected. 584 590 585 591 For each of the galaxy models (in fact for all object models), a … … 642 648 Finally, PSPhot can simply ignore the fitting process and instead 643 649 glean information about the fainter sources on the basis of the peak 644 chara teristics. In this option, the image is smoothed with the PSF650 characteristics. In this option, the image is smoothed with the PSF 645 651 model, and the peak for each object is measured. The peak flux and 646 652 the local peak curvature theoretically give sufficient information to … … 675 681 will automatically result in inconsistent interpretation of the noise. 676 682 677 For a difference image, both positive and neg etive objects will be683 For a difference image, both positive and negative objects will be 678 684 present. The basic peak detection algorithm will only trigger for the 679 685 positive sources. One solution is to simply apply PSPhot to both the … … 703 709 a 30 second exposure. Even a main belt asteroid at roughly 1 AU would 704 710 have reflect motion of approximately 1 degree per day, equivalent to 705 1.25 arcsec in a 30 second exposure, and could be notic ably smeared711 1.25 arcsec in a 30 second exposure, and could be noticeably smeared 706 712 and non-PSF-like. A trailed-star model can be used to characterize 707 713 these types of objects. 2) Small offset stars, either due to
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