![]() In principle, one should also include contributions in the signal-to-noise for flat fielding uncertainties, noise in the bias and dark calibration files, and quantization noise. If, instead, the peak count rate comes out much greater than the background, the observation is photon noise limited, and the signal-to-noise should be computed as the square root of the signal S in electrons. Then Equation 6.5 above gives the signal-to-noise as 3.0: The sharpness for the WF camera in the best case, when the star is centered on a pixel, is given in Table 6.5 as 0.128. (We note that AB is approximately zero at this wavelength, so the spectral class is unimportant.) The expected peak count is 28 detected electrons using Table 5.4 (peak near pixel center), which is much less than B, requiring the use of Equation 6.5 for the background limited case. The total number of detected electrons from a star with V=28.19 is S=93 electrons, again using Equation 6.1. The equivalent background per pixel is then given as B=84.1+5.2 2+13.5=124.5. Therefore the total dark current (on which there will be shot noise) is only 13.5 electrons. From Table 4.2, the median dark current at -88 ☌ is 0.0045. From Table 4.4, the read noise for WF3 is 5.2 electrons. Note that the AB color correction required for the sky in the wavelength range of the filter is 0.0 from Table 6.2. The total sky background collected per pixel in 3000 seconds is given by Equation 6.1 as 84.1 electrons. The sky background in each pixel is 23.3+5=28.3, assuming an ecliptic latitude of 90° from Table 6.3, and the pixel area correction for the WFC given in that section. ![]() The efficiency of the filter is 0.02343 from Table 6.1. The calculation to check this goes as follows. The exposure time is represented by t.įor example, Table 2.2 lists the faintest V magnitude star, V=28.19, measurable with a signal-to-noise ratio of 3 in a 3000s integration in F569W in the Wide Field Cameras. Herein we will use " P" to represent count rates per pixel, and " R" to represent the total counts for an object. Where terms include the read out noise of the CCD ( readnoise), the dark current ( P dark), sky background count rate ( P sky), and the count rate of any diffuse background light from astrophysical sources ( P background). The average effective background counts per exposure and per pixel can be expanded to include various sources: In general, the lower "pixel corner" values should be used, so as to insure adequate SNR. Also, the location of the star on the pixel grid will be impossible to know in advance of the observation (i.e. We note that PSF fitting is equivalent to convolving the image with the PSF, and then measuring the peak counts for stellar objects. To estimate the signal-to-noise, multiply the signal-to-noise obtained, assuming all the flux is in one pixel, by the square root of the value in the table. The summation is tabulated for a few representative cases in Table 6.5. Where sharpness is effectively the reciprocal of the number of pixels contributing background noise. It is easy to show that the signal-to-noise ratio for optimal weights (which are proportional to the point spread function) is given by: read noise, dark current, or sky noise limited) the SNR is a function not only of the expected number of detected photons S from the source but also of the average effective background count rate B in each pixel, the point spread function, and the weights used to average the signal in the pixels affected by the source. Where S is the number of detected photons, and R object is given by the above Equations 6.2 through 6.4, and t is the exposure time. In the bright target limit, Poisson noise sets the SNR and Aperture photometry will tend to give lower SNR, especially for sources where the background is important, but nonetheless is widely used. The optimum SNR will be obtained when the pixels of the point source PSF are weighted in proportion to their expected intensity by PSF fitting. The SNR obtained for photometry of a point source will depend on the analysis technique used. Please see the Two-Gyro Mode Handbook for additional discussion. While this could potentially degrade the signal-to-noise ratio for point sources, we expect to see very little impact for WFPC2 due to its large pixel sizes. Two-Gyro Mode: At some future date HST may be operated with only two gyros, hence causing additional spacecraft jitter and degradation of the effective PSF.
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