4. Instrument Sensitivity

  The combined efficiency of the IMAPS optical system and the detector lead to a nominal effective area of about 4.5cm² for wavelengths longward of about 1000Å. For shorter wavelengths, the drop in efficiency follows the square of the relative decrease in the reflectivity of Al with a LiF overcoat (Lowrance & Carruthers 1981).

To calculate the sensitivity of IMAPS in practical astronomical applications, one must factor in several sources of noise that add to the Poisson statistical fluctuations in the number of detected photons:

1.

Scattered light from the gratings, principally from the echelle.

2.

Readout and dark-current noise from the CCD.

3.

The geocoronal Lyman-$\alpha$ background, some of which can pass through the mechanical collimator (§3.1).

Items (1) and (3) above are additional sources of uv light whose statistical fluctuations add to those of the desired spectral signal. For the purposes of estimating a net signal-to-noise ratio, these illuminations can be thought of as being perfectly uniform. Item (2) is a noise signal whose amplitude is independent of the uv illumination.

As a simplification to a more elaborate procedure discussed in §7.10, we may think of a spectrum being extracted by a slit that is 1 CCD pixel wide and 4 pixels tall, which covers the vertical extent of most of the intensity within an order widened by astigmatism from the echelle grating (§3.2). Within the 4 × 1 extraction rectangle, the rms readout noise is equivalent to 0.55 photons in an integration time lasting 1 second. This is equivalent to the statistical fluctuations in a hypothetical uniform background illumination of 0.30 s^-1 added to the spectrum's signal. For a continuum source (i.e., a hot star), the scattered light background is about equal to that of the spectrum itself. The diffuse Lyman-$\alpha$ background produces about 0.3 events s^-1 kR^-1 in an extraction rectangle near the top of our image format (at 1150Å), and it decreases by at the bottom (950Å) because of the increased baffling by the mechanical collimator.

For the energy gathered over a wavelength spanned by 1 CCD pixel in the horizontal (echelle dispersion) direction, one should expect to find the signal-to-noise ratio given by the relation,  

$${\rm SNR}={Nt^{1/2}\over\sqrt{2N+0.30+0.3I({\rm L}\alpha)_{\rm kR}}},$$ (1)

where t is the integration time in seconds, N is product of the instrument's effective area and the target's photon flux within a wavelength interval $\lambda/2.4\times 10^5$, and $I({\rm L}\alpha)_{\rm kR}$ is the intensity of the geocoronal emission expressed in kiloRayleighs. As a rough guide, $I({\rm L}\alpha)_{\rm kR}$ is about 2 at night and 20 on the daytime side of an orbit. However, there is a strong dependence on solar activity and viewing geometry. Useful guidance on typical values for the geocoronal emission are given by Meier & Mange (1970, 1973) . Fig. 3 shows a plot of the outcome of Eq. 1 for an integration time of 300 seconds per echelle position. In a typical orbit, one can expect to obtain about 1 to 3 times this amount of on-target time for a given object in the sky. Two curves are shown: one for $I({\rm L}\alpha)_{\rm kR}$ = 2 and the other for $I({\rm L}\alpha)_{\rm kR}$ = 20. As an example, the star $\pi$ Sco has a flux equal to 630 photons ${\rm cm}^{-2}~{\rm s}^{-1}~{\rm \AA}^{-1}$ at 1050Å, and thus at this wavelength we could expect a SNR = 40. This is about twice the SNR of the $\pi$ Sco spectrum that was obtained by Jenkins, et al. (1989) on the relatively brief 5-minute observing time of a sounding rocket flight (§2).

 

Figure: 3 Expected signal-to-noise ratios for spectra recorded by IMAPS in 300 s, as a function of the target's continuum intensity. The two curves show the outcome of Eq.1  for two values of the geocoronal Lyman-$\alpha$ diffuse background emission, $I({\rm L}\alpha)_{\rm kR}$. Numbers at the top of the plot show the approximate fluxes of stars of various spectral types and V magnitudes.