Instrument Science Report NICMOS-015
Exposure Time & S/N Calculators for
NICMOS
C. J. Skinner
March 29, 1996
ABSTRACT
We describe a small suite of tools which have been developed to assist in the estimation of
S/N ratios and exposure times for NICMOS observations. Included are tools for determining S/N as a function of time for observing a known source, and tools for determining flux
as a function of time for a fixed S/N, and tools to determine, as a function of time, the
range of fluxes for which an observations is neither detector noise limited nor saturated.
All these tools are available in versions for either point sources or extended sources.
Finally, a similar set of tools is available for Multi-Object Spectroscopy using NICMOS’s
grisms. We provide a detailed description of the physical basis and techniques for each of
the tools, as well as a brief description of how to use them.
1. Scope and Purpose of these Tools
NICMOS will in mid-1997 add an important new capability to HST, namely IR imaging
and multi-object spectroscopy. This will open HST to a large community of atsronomers
who have not previously used it, as well as making available a variety of types of source
which in general were not previously accessible to HST (e.g. deeply embedded protostars). At its longest operating wavelengths, NICMOS will face an extremely bright
thermal background generated by the telescope optics, which will determine the limiting
sensitivity for many observations, while at intermediate wavelengths (in the region of 1.51.6µm) NICMOS will observe in a very low background. The parameters which will
determine the instrument’s sensitivity in these widely differing environments have not
needed to be determined previously for any other instruments, and the techniques for
observing in background limited conditions are probably not familiar to many HST users.
It was therefore felt desirable to generate software to assist in the process of proposal generation, as well as assisting staff at the Institute in the task of assessing feasibility and
limitations of various kinds of observation. Some time ago the Science Software Group at
the Institute began the task of incorporating into the IRAF HST instrument simulator
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package, SYNPHOT, the two new instruments to be installed during the Second Servicing
Mission, NICMOS and STIS. The intention of SYNPHOT, so far as NICMOS is concerned, is to be able to simulate all imaging observations. It is thus able to include in
simulated images objects with a variety of different sizes and morphologies, including
multiple and overlapping objects. As such, setting up the inputs for SYNPHOT can be
fairly lengthy and involved. Additionally SYNPHOT can only be run within the IRAF
environment. For many observers SYNPHOT therefore offers far more than is needed for
the purposes of Phase I (or in many cases even Phase II) proposals, while for some it has
undesirable limitations.
Both existing HST imagers (the FOC and WFPC2) have now provided simple, interactive
software tools to assist in proposal generation. While we feel there is certainly a need for
the more complicated capabilities that SYNPHOT provides, we believe that for many
users a simple set of interactive tools, providing relatively limited capability, is appropriate. We have therefore developed such a set of tools, and are in the process of making them
available via a WWW interface. These tools have been used by us to develop all the sensitivity information presented in the NICMOS Handbook. There are a number of elements
which are used by many or all of these tools, and in the next section we describe these and
their physical basis. In the following two sections we describe the available tools for imaging and then for Multi-Object Spectroscopy (MOS). Finally we describe briefly how to use
the tools.
System Throughput
S/N must always ultimately be dependent on the total throughput of the telescope plus
instrument system. A number of elements determine the throughput:
1. The reflectivity of all the reflecting optics in the system. These include the telescope primary and secondary mirrors, and all of the NICMOS fore-optics. At the
time of writing we do not know any of these values very well. We assume the
reflectivity of all the fore-optics to be 0.95 per surface, and better values should be
available well before launch. For the telescope mirrors we assume a reflectivity of
0.8 per mirror, which is likely to be an underestimate (perhaps by as much as a factor of two or three; the value is very uncertain).
2. Transmission of the dewar window. At the time of writing we do not know this
value, but assume a value of 0.9. All the parameters encompassed in items 1 and 2
are contained in a single data file, read by each of the tools. Inside the tools we
define the NICMOS optical efficiency as the product of all these terms. Note that
we have initially assumed all these values (optical element reflectivities and transmissions) to be independent of wavelength. This may not be a good approximation
in some cases.
3. Filter transmissions. NICMOS contains 48 imaging filters, 6 polarizing filters and
3 grisms distributed across three filter wheels. Each camera has access to only one
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filter wheel, which simplifies the code a little. Filter transmission measurements of
reasonable accuracy, of most of the flight filters, have been made available to us by
the IDT. The transmissions were measured for each filter at a wavelength spacing
of 0.001µm (1nm) across the full NICMOS operating waveband, and are stored in
a set of files. A data file is used to translate a given filter name into the name of the
file containing the filter transmission data. Each tool accesses this data file.
4. Detective Quantum Efficiency (DQE). The DQE is a strong function of wavelength, varying between about 0.1 at the shortest wavelengths to 0.8 at the longest.
The DQE has been measured by the IDT at about 0.1µm spacing across most of
the detector’s sensitivity range, and on a denser wavelength grid at the longest
wavelengths. These DQE data are stored in separate files, one for each of the flight
arrays.
Source Function
Any observation will detect photons from two basic sources - the astronomical target and
any general background emission. It is essential to account for both sources in order to
determine the photon statistics for the observation.
Initially, all the tools characterise the astronomical target by a black-body function. In
many cases this will be of adequate accuracy. A number of the terms treated in these calculations are functions of wavelength - for example the DQE and the Point Spread
Function. Across the bandwidths of the NICMOS broad-band filters either of these terms
may vary significantly, and thus the colour of the source inside the filter bandpass may significantly affect the outcome of the calculation. When the source spectrum contains strong
line emission, and the filter bandwidth is medium or broad, then the black-body approximation will be inadequate. In the near future we will probably add the possibility of
reading in an arbitrary spectrum to better represent some such sources.
The background for NICMOS may be regarded as comprising two distinct components:
1. Zodiacal Light. This is of course spatially dependent, and therefore difficult to represent with any accuracy. Following the IDT’s lead, we have adopted a simple
functional form for the Zodiacal background, based on early COBE data for a
position averaged for a 45o ecliptic latitude, where T is the Zodiacal dust tempera9 1.69
F ( λ ) = 1.09 ×10 λ
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+ 6.0 ×10 B ( λ, T )
ture, assumed to be 265K, and F(λ) is the spectral flux density in photons sec-1 cm2 µm-1.
2. Thermal background emission. This may in principle arise in many locations, but
we expect it to be dominated by two - the telescope primary and secondary mir-
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rors. The thermal emission will be determined by the areas of the mirrors, their
optical configurations, and their temperatures and emissivities. In the case of HST
the mirrors are heated in order to stabilise the telescope focus. We take their temperatures to be 293K, and their effective areas from the HST OTA Handbook. The
mirror emissivities are determined from the reflectivities discussed earlier: the sum
of the reflectivity and emissivity should be unity. As with the reflectivities, we have
taken the emissivities to be independent of wavelength, which may again be a poor
approximation.
The source function may be taken to be the sum of these three signals (source plus background) for the purposes of determining noise, but the signal we are interested in is only
the first term.
Image Scale
Two terms may be important here - the pixel size and the telescope Point Spread Function
(PSF). The pixel sizes are designed to be 0.043, 0.075 and 0.2 arcsec for Camera 1, 2 and
3 respectively, and we have adopted these figures. More accurate determinations will be
made soon after launch.
The telescope PSF is less easily determined. In principle it should be linearly proportional
to the observing wavelength. Naturally, for very broad bandwidth filters the PSF will vary
in size across the filter bandpass. In practise the PSF is also likely to vary somewhat with
position of the source on the camera field of view, and with the position of NICMOS’s
Field Offset Mechanism. To account for all these factors properly we would need to carry
out detailed ray-tracing of the HST plus NICMOS optical system. Instead we have simply
adopted a synthetic FOC PSF, calculated for a wavelength of 1.0µm using the tinytim program, which we scale linearly with wavelength. Work is currently underway at the ECF to
incorporate NICMOS into tinytim, so that soon we should be able to use a more accurate
PSF, and check the validity of a linear scaling with wavelength.
For extended sources the telescope PSF is unimportant for the purposes of these
calculations.
For the MOS case, the source is always assumed to be unresolved - grism observations of
an extended source would be at best extremely difficult to interpret. Even for a point souce
there will be non-negligible smearing in the dispersion direction due to the telescope PSF.
We assume that the spectrum is smeared in the cross-dispersion direction according to the
PSF as determined above, but for the purposes of this first-order calculation we ignore
spatial source smearing in the dispersion direction - in other words we take the PSF to be
entirely one dimensional. This approximation has a negligible effect for continuum
sources, but can make a significant difference in the case of narrow line emission or
absorption.
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Noise
A number of noise terms must be considered:
1. Poisson noise on the observed signal. This is trivially calculated as explained
above from the sum of the source plus background signals.
2. Dark current. For NICMOS the dark current is currently poorly determined
because it has proven too small to measure so far. The best estimates from the IDT
are that it is probably less than 0.1e-/sec, which means that Poisson noise on the
dark current becomes important only for rather long integrations.
3. Read noise. The read noise has been determined approximately by the IDT for
each of the three flight arrays, and we use their measurements, which are close to
30 electrons in each case. Slightly better measurements may become available
soon. It is important to bear in mind that for NICMOS it is possible to make multiple non-destructive reads, allowing a series of reads to be made to decrease the
effective read-noise. This is allowed for in the tools.
Unfortunately, there are a number of uncertainties regarding the latter two sources of
noise. First, the IDT have reported that the expected reduction in effective read noise due
to multiple reads does not extend to an indefinite number of reads - in fact, they report that
the noise may not decrease significantly beyond about ten reads. The reasons for this are
not clear. There is some suggestion that there may be some capacitive coupling between
the readout electronics and the pixels, such that the act of reading a pixel adds some noise
to the charge accumulated in the pixel itself. It is clear in any case that for NICMOS,
because the gain is set to roughly ten electrons per ADU, beyond an approximate effective
read noise of 10 electrons (corresponding to roughly 10 reads) quantization noise will
inhibit any further S/N gains. Secondly, the NICMOS detectors possess a feature known as
shading, which adds a large but time variable component to the signal. Its amplitude is
probably of order a few hundred electrons in the first few seconds after the pixel is reset. It
acts somewhat like a variable dark current, supplying several hundred e-/sec immediately
after reset, but dropping exponentially to zero within a minute. Tests so far have suggested
that the shading signal adds little noise to the final image, in which respect the shading
cannot be regarded simply as dark current. Exactly how much noise is associated with the
shading is not yet determined. These two effects leave some uncertainty in our noise determinations - initially we are therefore simply treating the noise as though it consists of a
constant 0.1e-/sec dark current, a read noise of roughly 30n-0.5 e- (for n reads), and Poisson noise on the observed signal.
Spectral Dispersion
For the MOS option, we need to determine what wavelength will be dispersed onto which
pixel. This depends on a variety of the grism parameters, including the wedge angle,
refractive index of the grism material, thickness and ruling spacing. For the NICMOS
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grisms we expect the dispersion to be approximately uniform across the spectrum. For
each grism, therefore, the spectral dispersion relation is simply
λ = Dn + λ o
where λ is the wavelength in µm, D is the dispersion, n is the number of pixels from the
central wavelength (i.e. it is a signed integer), and λo is the central wavelength in µm. We
do not yet have accurate measurements of the spectral dispersion, but instead use the
designed values for D and λo supplied by the IDT. We assume that the spectra will be
aligned with the dispersion directions exactly along columns of the array (in practise there
will of course be small alignment errors, but we assume these will be small enough that
our simple 1D approach here is not significantly compromised).
2. Descriptions of Imaging Tools
The following Table summarises the tools currently available, which are then described.
Table 1:
Name of tool
Type of source
Purpose
nicsn
Point
Calculate flux vs time for four different S/N values
nicsnx
Extended
Calculate flux vs time for four different S/N values
nicsat
Point
Calculate saturation and Poisson threshold fluxes vs time
nicsatx
Extended
Calculate saturation and Poisson threshold fluxes vs time
nicsauce
Point
Calculate S/N vs time for a fixed source flux
nicsaucex
Extended
Calculate S/N vs time for a fixed source flux
mossn
Point
Calculate flux vs time for different wavelengths in grism spectra
mossat
Point
Calculate saturation and Poisson threshold fluxes vs time in grism pectra
mossauce
Point
Calculate S/N vs time for fixed source flux in grism spectra
Flux vs Time for fixed S/N in Images
Two tools are available for this purpose, one for point sources (known as nicsn) and one
for extended sources (known as nicsnx).
The filter transmission curve, comprising of measurements every 0.001µm, is read in and
resampled so that for a narrow band filter we use only two wavelengths, for a medium
band filter we use 5, and for a broad band we use 10. By experiment we found that increasing the number of wavelengths had little effect on the results, while decreasing it in some
cases did produce a significant effect. The resampling was achieved by integrating under
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the bandpass across each resampled wavelength bin. The result is the filter transmission as
a function of wavelength, T(λ).
The NICMOS optical efficiency, εo, as defined earlier, is calculated as the product of the
transmissions of the telescope, fore-optics and dewar window.
In the nicsn program, the reference PSF as described earlier, sampled on a grid of 0.0005
arcsec pixels, is read in. For each wavelength this PSF is rescaled assuming that the PSF
diameter scales linearly with wavelength. Then the fraction of the PSF flux contained
inside the central pixel, assuming that the source is centered in that pixel, is calculated.
This parameter, f(λ), is the fraction of the flux in a point source which will be imaged onto
the brightest pixel.
In the nicsnx program on the other hand, the PSF is ignored entirely. Instead in this case
the extended source is assumed to have uniform surface brightness, yielding an identical
signal in any pixel. The parameter f(λ) is then set to the pixel area in arcsec2.
For each wavelength we now determine how many e-/sec are generated in the pixel per Jy
(which corresponds to the brightest pixel in nicsn, or to any pixel in nicsnx), which is
10 – 26 B ( λ, T c )
- Af ( λ )ε o T ( λ )Q ( λ )dλ
n r = ∫ ------------------ -----------------------hλ f B ( λ f , T c )
λ
(e ⁄ s)
where h is Planck’s constant, A the telescope primary mirror area (cm2), Q(λ) is the array
DQE at the wavelength λ (which is found by spline interpolation), and λf is the mean filter
wavelength in µm.
The background flux FB is calculated by integrating the background as described previously across the filter bandpass.
The S/N is denoted by S, the integration time by t (sec), the dark by d(t), and the effective
readnoise (i.e. the array readnoise divided by the square root of the number of the reads)
by Rn (e-). An array of integration times is defined, running logarithmically from 1.0 millisecond, which is the shortest possible integration time in Bright Object Mode, up to
86,400 seconds (which is 24 hours, quite a long integration time!). Four S/N values are
also chosen, the values currently being 10, 25, 50 and 100. Now the flux in Jy required to
obtain the desired S/N is determined as
S 2 t + S 4 t 2 + 4S 2 t 2 ( F B t + d ( t ) + R n 2 )
F υ = ---------------------------------------------------------------------------------------------------2t 2 n r
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where Fν is the point source flux in Jy, or the surface brightness in Jy/arcsec2, depending
on which code is in use.
Saturation and Read-Noise Limited Times
Programs have been written to determine the fluxes as functions of integration time for
which an observation will be read-noise limited or saturated. These are known as nicsat
and nicsatx. We define saturation here to mean that the potential well is sufficiently full
that the pixel departs by more than 2% from its linear operating regime.
These programs calculate the value nr exactly as defined above. We define the saturation
level, Ns, to be 2x105 electrons for each camera, based on preliminary information from
the IDT; this parameter is expected to be updated for each camera individually following
the SLTV tests in 1996. All other parameters are defined and denoted exactly as above.
The array of integration times is also set as before. Now the saturation flux is calculated as
Ns – FBt – d (t )
F s = -------------------------------------tn r
in either Jy or Jy/arcsec2 as appropriate.
The flux where the observation becomes Poisson noise dominated, FP, is defined as that
flux at which the Poisson noise on the signal is just greater than the detector noise (i.e.
noise on the dark current plus read noise). This flux is given by
(t ) + Rn2
 d-------------------------- – F B


t
F P = ---------------------------------------------nr
where d(t) is the total dark current in e- after time t seconds, and FB is the background signal in e-/sec.
Signal-to-noise vs Time for Individual Sources
For the case where the observer has an individual source to observe and wishes to determine the S/N obtained as a function of time for a given filter, we have developed a pair of
programs known as nicsauce and nicsaucex. These programs again calculate the values nr
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and FB exactly as for the nicsn program. An array of integration times t (seconds) is then
calculated identically to those for nicsn. Finally the S/N ratios are calculated for each time
as
Fνnrt
S = -----------------------------------------------------------nrt + FBt + Rn2 + d (t )
where all the symbols have the same meanings as before, and Fν is the source flux in Jy or
surface brightness in Jy/arcsec2.
3. Multi-Object Spectroscopy Tools
Flux vs Time for fixed S/N in Spectra
The purpose of this tool, known as mossn, is exactly analagous to that of nicsn. In this
case of course the S/N will be a function not only of source flux and integration time, but
also of wavelength. Therefore we have defined a set of three wavelengths for each grism,
spanning the usable wavelength range. The grism transmission curve is read in, and the
transmission T(λ) at each of the three wavelengths is determined by spline interpolation.
As discussed earlier, the PSF is assumed to be entirely 1D, and the fraction of the source
spectrum that will fall on the brightest pixel, f(λ), is calculated for each of the three wavelengths on this basis. In practise since the grisms are all in Camera 3 this fraction is for
most wavelengths not very much smaller than unity, so errors induced by the 1D approximation will usually be very small. Now the value nr can be calculated exactly as described
for nicsn, except that in this case it is calculated for each wavelength, rather than being
integrated over the filter passband as for the imaging tools:
10 – 26 B ( λ, T c )
( λ )ε o T ( λ )Q ( λ )
n r ( λ ) = ------------------ ------------------------DAf
hλ o B ( λ o, T c )
Fν being the source flux at the grism central wavelength in Jy. The background calculation
is not entirely intuitive for the MOS case. The equations used for thermal and Zodiacal
background emission are exactly as before. However, while the source flux is effectively
reduced in brightness by being dispersed across a significant area of the array, the background flux is not - because the source being viewed by every pixel on the array (including
areas which only see the background) is dispersed, each pixel will see a part of the spectrum from many other pixels, and thus in effect every pixel still sees the entire background
integrated over the grism bandpass. Thus the ratio of source to background fluxes is lower
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in the MOS case than in the imaging case.
For each of the three wavelengths the flux required to obtain a given S/N as a function of
time can now be calculated exactly as for the imaging case.
Saturation and Read Noise Limited Times for Spectra
The tool mossat is again exactly analagous to the imaging tool nicsat. All of the equations
are calculated exactly as for mossn. The only significant difference is that the saturation
and Poisson noise limited times are calculated only for the central wavelength of the spectrum, λo. The equations used to determine the fluxes as functions of time are then exactly
those quoted earlier for the nicsat and nicsatx programs.
Time vs Wavelength for Individual Sources
The tool mossauce is more or less analagous to nicsauce, but has wavelength as an additional variable. Therefore, instead of calculating simply the S/N as a function of time for a
given source flux, in this case we calculate the time to reach a pre-defined set of S/N values as a function of wavelength. All the terms can be calculated just as before, and the
time for each wavelength is calculated as
( n r F ν + F B + d c )S 2 + ( n r F υ + F B + d c ) 2 S 4 + 4 ( n r F υ ) 2 R n 2 S 2
t = --------------------------------------------------------------------------------------------------------------------------------------------------------------------2 ( n r F υ )2
4. Using the Tools
nicsn and nicsnx
Both codes have identical inputs. The user is asked first which camera to use, to which the
expected reply is 1, 2 or 3 for NICMOS Camreas 1, 2 or 3. Other responses are trapped
and the question repeated. Next the user is asked how many reads to make. Any integer
number can be entered in response, although in practise NICMOS will only make up to 25
reads. For a single read at the beginning and end of the exposure (the default mode for
NICMOS) the proper response would be 1. Now the user is asked for the colour temperature of the source to be modelled. Any number may be given in response, but the user
should be aware that for temperatures lower than 1000K it is possible that some of the filters may not adequately block all wavelengths longwards of the pass-band, which may
compromise the fidelity of photometry. Next the user is asked for the name of the filter to
be used. Any valid NICMOS filter can be entered, and at the moment the code does not
check to ensure that the requested filter is actually available in the requested Camera, only
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that the requested filter exists. For the F110W filter proper responses would be ‘f110w’ or
‘F110W’ - either upper or lower case can be used, but mixed case will cause an arror. In
the event that the code does not understand the filter name entered, the error will be
trapped and the code will ask again. The mean wavelength and filter transmission are calculated and written to the screen for information, as is the calculated filter bandwidth
(width at 2% transmission). Now all the results are calculated and written out. The output
consists of a two line header followed by five columns of data. The header lines begin with
the # character, which means they will be ignored by Supermongo. The first column is the
integration time in seconds, while the remaining columns are the fluxes in Jy required to
obtain a S/N of 10, 25, 50 and 100 respectively. The columns are all identified unambiguously in the header lines. The nicsn program runs in about 7 seconds on a SUN Sparc IPX,
while nicsnx runs in about a second. The difference is due to the large, heavily oversampled PSF used by nicsn.
nicsat and nicsatx
The inputs to these programs are identical to those for the previous pair. The output consists of a similar pair of header lines, followed by three columns. The first contains the
integration times, and the second and third contain the fluxes to saturate and to be photon
noise limited respectively. Again the columns are clearly labelled in the header. In the
event that it is not possible to observe for the given integration time and obtain the relevant
condition (i.e. to be photon noise limited, or not be saturated), the flux is set to 1.0E-37 Jy.
nicsauce and nicsaucex
These programs first request the Camera number, then the number of reads, the colour
temperature of the source to be observed and then the filter to use. Finally the code asks
for the flux or surface brightness of the object to be observed. This must be entered in Jy or
Jy/arcsec2. At present the programs require as input the flux (or surface brightness) in the
NICMOS filter to be used. It is the user’s responsibility to transform any known (e.g.
ground based fluxes) in whatever filter system to expected fluxes in the NICMOS filters. In
the future the capability of specifiying a flux in one of the standard photometric bands (i.e.
I, J, or K) and having the code transform this into a flux in the NICMOS filter may be
added.
mossn
The user is asked first to enter which grism to use, to which the valid replies are A, B or C
- in either upper or lower case. Any other reply is trapped, and the question repeated. The
camera number is always 3, so the appropriate PSF is immediately determined. Next the
user is prompted to enter the number of reads, to which valid replies are as for all the programs described previously. The output is similar to that from nicsn, but there are three
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lines of header information, and seven columns of data. The first column contains the
times, exactly as for nicsn. Then there are two groups of three columns. Each group contains the fluxes for three different wavelengths, which are identified in the header lines,
and the two groups are for two different S/N values, currently set to 10 and 100.
mossat
The inputs for this program are identical to those for mossn. The output is identical to that
for nicsat.
mossauce
This program prompts for the grism and number of reads as for the previous two programs. However mossauce also asks for the colour temperature of the source and its flux
at the grism central wavelength (in Jy). The output consists of two lines of header, followed by five columns. The first column is the wavelength in µm, and the remaining four
are the times (in seconds) required to reach a S/N of 10, 25, 50 and 100 respectively.
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