TECHNICAL REPORT. Title: NIRCam Point Source SNR vs. Filter, Source Brightness and Readout Combinations

Transcription

1 When there is a discrepancy between the information in this technical report and information in JDox, assume JDox is correct. TECHNICAL REPORT Title: NIRCam Point Source SNR vs. Filter, Source Brightness and Readout Combinations Authors: M. Robberto Phone: Doc #: JWST-STScI , Date: June 21, 2010 Rev: - Release Date: 29 November Abstract I calculate the signal-to-noise achieved by NIRCam in imaging mode on point sources of different brightness (from 1 njy to 1 mjy), in all 29 NIRCam filters and for all 110 readout combinations. The calculation includes cosmic rays, realistic PSFs, flat-field, gain and digitization errors, and the current best understanding of the instrument background and total throughput (telescope included). The results provide the most accurate prediction to date of NIRCam point-source sensitivity for typical background values. Using these results, I select a subset of optimal readout combinations for each filter and flux level. Their overall frequency shows that ramps made by large groupaverages deliver, on average, the largest gain in signal-to-noise even in the presence of photon noise. This study may be useful for planning NIRCam observations in general. It may also allow to set the NIRCam readout combinations proposed by default by the JWST APT and possibly to simplify and/or optimize the current set of NIRCam readout patterns. 2.0 Introduction The goal of this report is to analyze how the signal-to-noise obtained in a NIRCam point source observation varies with the readout combinations, for all filters and over a wide range of source brightnesses. For readout combination I mean a combination of readout pattern (9 in total, from RAPID to DEEP8) and Ngroup (up to 10 typically, 20 for the DEEP2 and DEEP8 readout patterns). The method used follows the strategy developed in a number of previous studies. In particular, in Robberto (2010) I have estimated how the effective signal-to-noise per pixel depends on the readout combination for different photon rates, taking into account the effect of cosmic rays. This sets the basis for this study, where I calculate the signal-to-noise reached by co-adding all pixels falling within a given aperture extraction radius and accounting for all relevant noise sources. The calculation assumes the baseline parameters of the NIRCam Exposure Time Calculators (Rieke 2005) and NIRCam model PSFs calculated by J. Anderson (Anderson 2009), and is therefore supposed to be quite realistic. The calculation is performed for 29 NIRCam filters and 13 levels of source brightness, from 1 njy to 1 mjy, a range of 15 magnitudes appropriate for the large majority of Operated by the Association of Universities for Research in Astronomy, Inc., for the National Aeronautics and Space Administration under Contract NAS

2 NIRCam imaging programs. Each of these 29 13=377 combinations of filter and flux produces a PSF (background included) in units of counts/s which is sampled with each one of the 110 NIRCam readout combinations, Aperture photometry is then extracted using the classic formula of DAOPHOT and the associated signal-to-noise is derived. The super-sample of =41,470 signal-to-noise estimates is then analyzed to remove sub-optimal readout combinations. These are defined as the readout patterns which provide, for a given combination of filter and source brightness, one of the following three conditions: 1) a signal-to-noise lower than that obtained with a shorter integration time, 2) source saturation; or 3) exceedingly low signal-to-noise ratio. By analyzing the frequency of good vs. bad occurrence of each readout combination, I can flag those scarcely or never used, Eventually, these readout combiations could therefore not be offered to the general NIRCam user. The calculated signal-to-noise tables represent our current best understanding of NIRCam sensitivity in imaging mode for point sources and can be used for science planning and the development of ETC and APT. 3.0 Methods and parameters The main engine of the code is the procedure that calculates, given a certain photon rate, the noise, and therefore the effective signal-to-noise, associated to the 110 NIRCam readout combinations. This procedure has been documented in Robberto (2009a) and Robberto (2010) and I point to those documents for the details. Here I just remind that the procedure include the effect of cosmic rays, assumes a readout noise per single read of 20 electrons (or 20 counts, as gain equal to 1 is also assumed) and a linearity corrected ramp. The procedure uses the expression for the general signal-to-noise equation for the sampling of the ramp with groups of averaged frames, originally introduced by Rauscher et al (2007), rederived and correctly expressed in Robberto (2009b). The analytical treatment assumes that the sample/groups are uniformly weighted. Cosmic Rays are accounted for in a fully analytical way, and I make the assumption that they can all be identified and properly treated by ramp trimming and, when needed, by rejecting the affected datapoint (group of coadded samples). Other errors like 1/f, residual nonlinearity and bias drifts, etc. are supposed to be negligible and therefore ignored. This main computational routine, pixel-based, is called by a procedure that generates, for each filter, the PSF in counts/s. The PSFs are taken from a set of fits files provided by J. Anderson, giving the PSF in 24 NIRCam bandpasses. These PSFs have been calculated for a typical configuration of the JWST OTA (OPD01), less than optimal but still within JWST specifications. The PSFs are calculated with 8mas pixels, so I have rebinned them 4 times and 8 times to match the NIRCam short and long wavelength channels (32mas and 64mas pixel scale, respectively). Each PSF has been finally trimmed to a 64x64 pixel square array and normalized to 1 total count unit. I have then associated the PSFs to the full set of 29 flight NIRCam filters present in the Excel NIRCam Exposure Time Calculator (M. Rieke 2005), listed in Table 1. Filters F225N and F418N, also present in the Excel spreadsheet, have not been used as they are no longer present in the flight model

3 For convenience, I remind the naming convention for the filters: FXXXR assumes that XXX is the central wavelength in microns, whereas R = W (Wide), M (Medium), N (Narrow) stands for R=λ/Δλ~4,10, and 100, respectively. The two filters wih the 2 suffix (F150W2 and F322W2) have ultra-wide bandpass, i.e R~1.5 and R~2, respectively. Table 1 NIRCam filters FILTER F070W F090W F115W F140M F150W F150W2 F162M F64N F182M F187N F200W F210M F212N F250M F277W F300M F322W2 F323N F335M F356W F360M F405N F410M F430M F444W F460M F466N F470N F480M Short Wavelength Channel Long Wavelength Channel - 3 -

4 For filters lacking a corresponding Anderson s PSF, I have simply used the PSF closest in wavelength. The error associated to this rounding is comparable to the error introduced by neglecticing the chromatic dependence of the PSF on the source color for broad-band filters. Next I have set 13 flux levels for the point sources, distributed uniformly in logarithm between 1 njy and 1 mjy, as shown in Table 2. Table 2 Flux levels considered in the present study 1 njy 3.16 njy 10 njy 31.6 njy 100 njy 316 nj 1 µjy 3.16 µjy 10 µjy 31.6 µjy 100 µjy 316 µjy 1 mjy To convert physical fluxes to counts/s one has to assume an instrument model and transfer the photons from the telescope aperture to the detector accounting for all efficiency factors. I have used the parameters of the NIRCam Exposure Time Calculator of Rieke (2005). This is an Excel spreadsheet that tracks the allocation of performance parameters between NIRCam components and includes the background and source fluxes that NIRCam detector will see on orbit. In particular, it calculates the signal-to-noise achieavable in a given period of time taking into account the photoelectrons collected from the target source, from the zodiacal background, from the OTE and ISIM thermal emission, from the diffuse Milky Way background, from the scattered background, plus dark current and detector read noise. Some of these terms (Galaxy and OTE/ISIM) turn out to be negligible at all NIRCam wavelengths. The most convenient way to pick up the conversion factor is to use, for each filter, the ratio between the total noise in integration time (cell K14, divided by 10,000 as the integration time in the spreadsheet is set to 10,000s) and the noise in Jy/s (cell K16). This directly provides the conversion factor from Jy to counts/s. However, I have removed from this factor the effect of flat-field, contained in cell O14. This is because the flat-field error, being proportional to the signal falling on a pixel, has to be calculated in our case - 4 -

5 for each combination of readout combination and source flux, rather than treated as a constant factor. For each filter, the 13 fluxes have then been converted to counts/s and the PSF (previously normalized to 1) has been multiplied by this factor. Next I have added the total background, which is also filter dependent, taking the value from cell J11 of the Rieke (2005) Excel spreadsheet. Having calculated the PSF in counts/s, I have selected an aperture radius of 2.5 pixels, the same value adopted by the Excel spreadsheet, and selected the 19 pixels falling in the aperture (no attempt was made to account for fractional pixels). This is the same extraction radius used by Rieke (2005) and therefore allows for easy comparison. The count rates of each of these 19 pixels have been ingested into the main computational routine to obtain, for each pixel, the 110 equivalent noise values, one for each readout combination. The same procedure has been adopted for the sky, but in this case I have directly used the sky rate estimated by the spreadsheet (cell J11) rather than the value measured on the outer PSF annulus. This is because, as the source brightness and wavelength increase, the PSF wings contaminate more and more the sky measure in a surrounding annulus; to reduce this problem I should have varied the size of the sky annuus depending on the flux and PSF, but this would have made the comparison of the results less robust. Thus, for each combination of filter, flux and readout combination I calculate an integrated source flux which accounts for the PSF shape, a sky flux, and a sky variance which accounts for the readout combination and CR flux. These are the three ingredients that enter in the classic formula for the magnitude error used by DAOPHOT, which accounts for the scatter in the sky values, the random photon noise of the source and the uncertainty in the mean sky brightness. These terms, added in quadrature, provide the photometric error associated to the source flux measurement At the same time, I have also estimated the integrated counts of the brightest PSF pixel to monitor saturation. I have assumed a source saturated when its peak is higher than 100,000 electrons. A few final remarks about our treatment of flat-field, gain/digitization and bitshift errors: 1. The flat-field error has been treated by adding quadratically to the final pixel noise an extra noise term equal to 1/100 of the source signal (including background). 2. For simplicity, the calculation is performed assuming gain equal to 1. However, I have included the extra noise term associated with the choice of a different gain, which is given by (see e.g. g( e / adu) 12 and is therefore equal to if g(e/adu)=2. 3. At the same time, I have included the error due to the loss of resolution due to the bitshifts used to average the frames: when two numbers coded with 16 bit are averaged (coadded and divided by 2), one needs a 17 bit word to fully encode the - 5 -

6 result. Instead, if the result is stored in a 16-bit word, i.e. if the average loses the least significant bit, there is a loss of information. In practice, assuming gain=1, the Analog to Digital Conversion noise is 1/ 12 if one has no bitshifts, 2/ 12 if one averages N group = 2frames (i.e. 1 bitshift, which means 1 bit lost), 4/ 12 if one average N group = 4 frames (2 bitshifts, 2 bit lost) and 8/ 12 if one averages N group = 8frames (3 bitshifts, 3 bit lost). This error has to be compounded with the gain/digitization error, which adds another bit lost (see point 2 above), so that we have at the end an additive error equal to g( e / adu) N group 12 to be added quadratically to the readout noise (averaged over the N groupframes). I n practice, this corresponds to adding in quadrature a noise term equal to 0.577, 1.155, and for the cases with g=2 and N group = 1,2,4,8, respectively. These values have to be compared with the reduction in readout noise achieved by coadding the frames in a group. Assuming a readout noise (single read, ktc noise excluded) of 20 electrons, by coadding 1, 2, 4 and 8 frames we have 20.0, 14.1, 10.0, 7.1 electrons. Table 3 summarizes the situation; the last columns shows the total noise estimated by adding in quadrature the two terms. I have also added the case of N frames = 16, which has not been considered for NIRCam, to illustrate how the quantization/bitshift error becomes dominant when more than 8 frames are averaged in a 16 bit word. Table 3 Equivalent Readout noise for single sample, taking in account quanitization and bit shift errors N 20e / N frames frames 2( e / adu) N frames ( 15e / N frames ) (e/adu) N frames 2 1/ 2-6 -

7 4.0 Results For each filter, I have tabulated: 1. Source counts integrated within the aperture. They come from the nominal flux rate, distributed over the full PSF and sampled by the inner 19 pixels. For each filter and readout combination, they therefore scale directly with the exposure time 2. Photometric error, computed using the DAOPHOT formula. 3. Signal-to-noise ratio, from the ratio of Source over Error, i.e. points 1) and 2) above. 4. Peak value, for the brightest pixel in the PSF. Table 4 show a sample of the results, for the F200W filter. For each readout combination, Table 4 shows the corresponding integration time (from the reset), and the signal, noise, signal-to-noise and peak value calculated for our standard aperture of 2.5 pixel radius, for all 13 flux levels. As the signal depends only on the integration time, readout combinations having the same integration time produce the same signal. The same is true for the peak counts. The noise term (and therefore the signal to noise) cannot be calculated for ramps of only 1 read (no fit possible). These are marked with a NaN, as Not a Number is the output directly provided by the IDL routine used the perform the calclations. Note the readout combination nr 79, MEDIUM8-10 (highlighted with a yellow background), which provides a signal-to-noise ratio of about 3 for a 10 njy source in 1,000 seconds; this corresponds to SNR~10 for a 10 njy source in 10,000 seconds, the round reference value usually reported for NIRCAM sensitivity. Figure 1 shows the content of Table 3 as plots of the signal-to-noise achieved vs time. Similar tables for each filter and integration time are available for download from the SOCCER or NGIN web pages (see Appendix at the end of this document)

8 Table 4 Signal, Noise, Signal-to-Noise and peak value in electrons for a 2.5pixel aperture radius, F200W filter # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 0 RAPID counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max BRIGHT counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max RAPID counts noise SNR max BRIGH counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max SHALLOW counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max MEDIUM counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max DEEP counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max

9 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 7 RAPID counts noise SNR max BRIGHT counts noise SNR max RAPID counts noise SNR max SHALLOW counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max RAPID-5 53 counts noise SNR max BRIGHT counts noise SNR max BRIGH counts noise SNR max

10 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 14 RAPID counts noise SNR max RAPID counts noise SNR max BRIGHT counts noise SNR max SHALLOW counts noise SNR max RAPID counts noise SNR max BRIGH counts noise SNR max MEDIUM counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max

11 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 21 DEEP counts noise NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN SNR NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN max RAPID counts noise SNR max BRIGHT counts noise SNR max SHALLOW counts noise SNR max RAPID counts noise SNR max BRIGHT counts noise SNR max BRIGH counts noise SNR max

12 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 28 SHALLOW counts noise SNR max MEDIUM counts noise SNR max BRIGHT counts noise SNR max BRIGH counts noise SNR max SHALLOW counts noise SNR max BRIGHT counts noise SNR max BRIGHT counts noise SNR max

13 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 35 BRIGH counts noise SNR max SHALLOW counts noise SNR max MEDIUM counts noise SNR max BRIGHT counts noise SNR max SHALLOW counts noise SNR max BRIGH counts noise SNR max SHALLOW counts noise SNR max

14 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 42 MEDIUM counts noise SNR max DEEP counts noise SNR max BRIGH counts noise SNR max SHALLOW counts noise SNR max BRIGH counts noise SNR max SHALLOW counts noise SNR max MEDIUM counts noise SNR max

15 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 49 DEEP counts noise SNR max BRIGH counts noise SNR max SHALLOW counts noise SNR max SHALLOW counts noise SNR max MEDIUM counts noise SNR max SHALLOW counts noise SNR max SHALLOW counts noise SNR max

16 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 56 MEDIUM counts noise SNR max SHALLOW counts noise SNR max SHALLOW counts noise SNR max MEDIUM counts noise SNR max DEEP counts noise SNR max SHALLOW counts noise SNR max SHALLOW counts noise SNR max

17 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 63 MEDIUM counts noise SNR max DEEP counts noise SNR max SHALLOW counts noise SNR max MEDIUM counts noise SNR max MEDIUM counts noise SNR max MEDIUM counts noise SNR max DEEP counts noise SNR max

18 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 70 MEDIUM counts noise SNR max DEEP counts noise SNR max MEDIUM counts noise SNR max MEDIUM counts noise SNR max MEDIUM counts noise SNR max DEEP counts noise SNR max MEDIUM counts noise SNR max

19 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 77 DEEP counts noise SNR max MEDIUM counts noise SNR max MEDIUM counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max

20 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 84 DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max

21 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 91 DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max

22 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 98 DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max

23 # Readout Comb. time(s) 1nJy 3.16nJy 10nJy 31.6nJy 100nJy 316nJy 1uJy 3.16uJy 10uJy 31.6uJy 100uJy 316uJy 1mJy 105 DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR max DEEP counts noise SNR Max

24 Figure 1 Signal-to-Noise ratio vs. time estimated for the F200W filter. Dots indicate values corresponding to source saturation. Units to the right are njy. 5.0 Optimal readout combinations Having calculated all signal-to-noise values, I have extracted, for each filter and source brightness, the optimal readout combinations in the following way: 1) If a certain integration time is degenerate, i.e. if it can be achieved with more than one readout combination, the optimal readout combination is the one providing the highest signal-to-noise; if equal, I select the readout combination providing the largest number of groups (i.e. the more robust against cosmic rays). 2) If the signal-to-noise reached in a given time is lower than the signal-to-noise reached in a shorter time, that readout combination is not optimal. 3) If the source saturates, that readout combination is not optimal. Using these criteria a large number of readout combinations can be dropped. As an example, I show in Table 5 the equivalent of Table 4, limited to the signal-to-noise estimates, after the non-optimal readout combinations have been removed