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Exposure Estimation

GHRS Instrument Handbook


Sensitivity

The sensitivity of the GHRS and HST's Optical Telescope Assembly (OTA), using the LSA, has been determined from observations of stars with known ultraviolet fluxes. The sensitivity is designated as Sl, and has units of (counts diode-1 sec-1) for each incident (erg cm-2 sec-1 Å). It varies as a function of wavelength for each grating. You must first estimate the intrinsic flux of your target and then multiply that by the appropriate value of Sl to yield an estimate of the count rate to be expected for a particular grating configuration at the chosen wavelength. Sensitivity curves for the first-order gratings are provided in Table 8.2 on page 106 and for the echelles in Table 8.3 on page 113 and Table 8.4 on page 113. The synphot tool in STSDAS can be useful for exposure estimation.

In the echelle configurations, the sensitivity varies with wavelength across each order. This behavior is characteristic of all echelle spectrographs, and is called the Blaze Function. The basic nature of the variation with wavelength is similar for all orders, and can be parameterized in terms of the product ml, where m is the order number and l is the wavelength (Å). The shape of the blaze function, normalized to a peak value of unity, and plotted as a function of ml is shown in Section on page 112. The sensitivity at any wavelength in any order can be estimated by multiplying the peak response of that order by the relative response shown. The blaze function, relative to the center of an order, falls as low as 0.25 at the end of the free spectral range and its effect should not be omitted in exposure calculations.

Reddening

Corrections for ultraviolet extinction in the interstellar medium are included in Section on page 114. These are standard values, and their applicability in specific situations is left to the judgment of the observer.

Background

There are several potential sources of background counts, including detector dark count, electrical interference or cross talk with devices either within the GHRS or the spacecraft, and effects caused by the charged particle radiation environment of the HST orbit.

The GHRS detectors themselves contribute little to the dark count. During "thermal vacuum" testing prior to launch, the detector dark count rates were observed to be approximately 0.0004 counts diode-1 sec-1. On-orbit, the background is caused primarily by Cerenkov radiation bursts induced in the faceplate of the Digicon by cosmic rays. This causes the actual background to range from 0.004 to about four times that, depending on the orbital position of HST. For planning purposes these mean values suffice: 0.011 counts s-1 diode-1 for D2 (Side 2) and 0.008 counts s-1 diode-1 for D1 (Side 1). The counts appear to be randomly distributed in time, so that the "noise" in the dark count is the square root of the total counts accumulated during the observation. If one is observing very faint objects with low count rates the background can influence the signal-to-noise ratio of the data. Formulae for making quantitative estimates of S/N are given in Section on page 35. At the present time there are no known sources of interference or cross talk which affect the detector count rates.

The GHRS is equipped with both hardware (automatic) and software capabilities to recognize and respond to cosmic ray and trapped particle events. You may invoke the software capability by specifying CENSOR = YES on an exposure line in Phase II. This causes rejection of individual segments of data if they included a specified number of photons arriving within a short (8 ms) interval, as happens with cosmic rays. Any rejected integration is repeated, so there is no loss of total exposure time. You should only use this anticoincidence rejection on faint targets, since on bright targets the interval between actual photon events will be small and real counts would be rejected. We recommend using CENSOR = YES only for count rates less than about 0.1 counts s-1 diode-1. The expected dark count reduction is ~10% (for more details on CENSOR, see Section on page 116).

For extremely faint sources for which the expected count rate is well below the expected dark level, it is possible to use a special commanding option called FLYLIM. This option, if pertinent to your needs, should be explored with a GHRS Instrument Scientist. See also Section on page 118. FLYLIM relies on the fact that much of the noise comes in bursts so that those spectra with overall counts above some threshold can be rejected. This then involves the risk of rejecting source counts as well if the source count rate has not been accurately predicted. An alternative to FLYLIM is to use RAPID mode. That results in some loss of data quality, but it is then possible to go back into the observations after the fact and to design algorithms optimized to extracting the best signal.

An external source of background which can potentially be a problem during the acquisition (and sometimes the observation) of faint targets is geocoronal Lyman-a. This problem and what to do about it are discussed in Section on page 99.

The final cause of background counts is passage through the dip in the Earth's Van Allen radiation belt called the South Atlantic Anomaly (SAA). SAA passage occurs on 7 of 15 daily orbits of HST. During the most central of these passages, dark count rates increase about two orders of magnitude, to about 1 count diode-1 sec-1. A contour around the SSA which corresponds to 0.02 cts/s/diode is known and no GHRS observations are scheduled when the HST is within this zone. We have now made it possible for the observer to specify a different SAA contour if they wish to do so. For example, observations of a very bright star may be less sensitive to background and so may tolerate an SAA contour that allows observations to be scheduled more flexibly.

Scattered light

The presence of stray and scattered light in a spectrograph is an effect which can influence the planning and execution of an observation, as well as the reduction and interpretation of the data. None of the optical configurations which include first order gratings has any serious problem with scattered light. The high quality of the imaging optics and holographic diffraction gratings and the effectiveness of the baffles have successfully minimized the stray light. On-orbit measurements indicate that it amounts to less than 10-3 when using the SSA, and at most a few times 10-3 when using the LSA (these are in units of the peak intensity).

In the echelle configuration, both the echelle and the cross-dispersers are ruled gratings. This fact, plus the presence of light from sixteen orders simultaneously on the photocathode, results in a detectable level of background radiation. The irradiance on the photocathode due to scattered light (measured as count rate per unit area) amounts to a few percent of the signal in the order. Two factors complicate this effect. The first is a geometrical effect caused by the fact that the science diodes are 400 mm tall, while the image of the spectrum is only about 55 mm high. Thus about 1/8 of the diode is illuminated by the spectrum+background, while the rest is measuring background, meaning that a weak background irradiance is multiplied to the point that a significant fraction (anywhere from 2 to 50%) of the gross count rate on a diode may be due to background. The measured scattered light background can be calculated from information in Table 8.3 on page 113 and Table 8.4 on page 113. It varies significantly with order number.

The second complication arises at the short wavelength ends of the echelle format. Below a wavelength of about 1800 Å with Echelle B (or 1250 Å with Echelle A), the spacing between orders is comparable to the length of the diodes, and it is difficult to make a clean measurement of a single order. The diode array has four large "corner diodes" which are long (1 mm) in the direction of the echelle's dispersion, but narrow (100 mm) in the cross-dispersion direction. These diodes may be used to sample the interorder background without the problem of contamination by in order light, but they do not provide any spatial resolution. The system will default to use of the corner diodes when that is appropriate. At a minimum, the time spent measuring the background should be about 10% of the time spent on the spectrum. If the goal is to achieve a very high signal-to-noise ratio in the net spectrum, it may be necessary to devote a greater fraction of time to the background measurement. Suggestions for estimating signal-to-noise ratios are made in the next section.

In order to reduce stray light, there is a shutter over the LSA which automatically closes whenever the SSA is being used for an observation. There is no shutter on the SSA. Thus a wavelength calibration exposure obtained with a bright star in the SSA will result in a combined spectrum of the two because the aperture for the wavelength calibration lamp (SC2) is displaced from the SSA in the same sense as the direction of dispersion. Usually you can subtract the stellar spectrum to recover the wavelength calibration. This contaminated calibration spectrum should be adequate for calibrating the wavelength zero point of your spectrum even with bright stars.

More detailed quantitative information on background and scattered light in the GHRS is provided in Section on page 107 and Section on page 115.

Signal-to-noise

There are several factors which influence the signal-to-noise ratio achieved, including statistical (Poisson) noise in the detected spectrum, dark count noise in the detector, scattered light in the spectrograph, diode to diode gain variations, and granularity in the photocathode sensitivity. For signal-to-noise ratios up to approximately 30, statistical fluctuations in the signal and background will dominate. Diode to diode variations are extremely small, and are accounted for in the routine calibration procedures. Cathode granularity will become important if a signal-to-noise ratio greater than 30 is to be achieved, and must be treated separately. There are also some photocathode blemishes with amplitudes greater than ~3%. For sources observed through the small aperture the sky background should not contribute significantly to the noise, except, perhaps, when observing at Lyman-a.

Photon Noise

The following equations may be used to estimate signal-to-noise ratio, depending on the relative importance of scattered light and dark count.

Case 1. Neither scattered light nor dark count are important.

Let:

Then

This formula would be appropriate for relatively bright objects observed with any first order grating.

Case 2. Dark count is important, scattered light is not.

Let:

Then

If the signal is less than about ten times the dark count rate, the factor in parentheses should be included in the estimate. This formula would be useful if STEP-PATT=5, for example, were used with a first order grating to measure a faint source (see Section on page 112).

Case 3. Scattered light is important, dark count is not.

Let:

Then

This formula gives a good estimate of the performance for observations with the echelle gratings. This formula assumes that the background bins are heavily smoothed. Most of the high frequency statistical noise in the background bins is thus suppressed.

Case 4. Both scattered light and dark count are important.

Let:

Then

There are two ways to use these formulae. If you need a certain S/N to do the scientific analysis, use the appropriate equation to solve for the required exposure time t. Alternately, you can decide to devote a fixed length of time to the observation, and use the equations to estimate what S/N will be achieved.

Fixed Pattern Noise

The formulae just presented suggest that the signal-to-noise ratio increases in proportion to the square root of the exposure time. These relations only hold true until S/N xbb 50 or so is reached. At higher signal levels the photocathode granularity described in Section on page 50 will become the limiting factor. For better S/N you need to use the FP-SPLIT option (see Section on page 50). Rather than merely averaging the four FP-SPLIT sub-exposures, the data analysis procedure solves for the two vectors representing photocathode granularity and the spectrum. S/N well in excess of 100 has been obtained this way on bright targets.

Achieving extremely high signal-to-noise (200 or more) is possible by obtaining a number of spectra, each with FP-SPLIT but at slightly different grating positions. See Lambert et al. (1994) for a discussion.

Example of Exposure Time Estimation

Here is a very simple example to illustrate how an integration time may be computed. Suppose that the goal is to obtain a spectrum of a 13th magnitude B0 star at 1900 Å, with the G160M grating and with a signal-to-noise of 25 per diode in the continuum. In this case we will assume that this star has not been previously observed in the ultraviolet so that there is no a priori knowledge of the UV flux.

To be specific, take the star to have a spectral type of B0I, V=12.89, and (B-V)=0.63. The calculation requires:

Sensitivity
Reddening
Background
Scattered light
Signal-to-noise
Photon Noise
Fixed Pattern Noise
Example of Exposure Time Estimation