Photon Noise

A far-infrared astronomical system will also be limited by photon noise. The cosmic background at infrared wavelengths can be broken down into a number of important components. At shorter wavelengths scattered solar radiation and thermal emission from zodiacal dust dominate, while beyond 40m emission from cold galactic dust must be included. Each of these components has a distinctive positional dependence on the sky, and large variations in the relative contributions are present. To investigate a case appropriate for extragalactic astronomy, we have taken the COBE Diffuse Infrared Background Experiment (DIRBE) measurements of the South Galactic Pole (Hauser et al. 1991). The noise from this background is computed in a conventional manner (e.g., Rieke 1994); because the astronomical backgrounds are due to very dilute graybodies, the Boson correction can be ignored (van Vliet 1967).

Since the focal plane fully samples the point spread function, the signal is spread over a number of pixels. Therefore, we combine the measurements from the number of pixels needed to synthesize a point source, quadratically adding the noise. An additional noise penalty of a factor of 1.1 was added to allow for noise in the flat field. We have assumed a diffraction limited beam (for a telescope with 15 areal obscuration) and have computed the net signal in apertures centered on the source after subtraction of the average surface brightness in a reference area between 1 and 2.5 . The result is that the signal to noise for a point source is 8.2 times worse than that computed for a single 0.4 pixel (assuming all the signal fell on the single pixel) if the signal is measured in a 0.8 beam and 7.1 times worse if measured in a 1.2 beam. The latter beam size has the maximum ratio of signal to noise if photon noise alone is considered; however, to maximize the ratio of signal to noise that can be achieved in a confusion-limited situation, we will use the former beam size in the following.

Some degradation of the photon noise will occur in space because cosmic rays striking the detector will limit the integration times. A discussion of the extent of this effect is given by Herter (1990). The results depend on detector geometry, read noise, and the method of operation of the readout. We assume appropriate parameters for the far infrared arrays under development for SIRTF (Young et al. 1993), i.e., that a cosmic ray hit destroys all information in the integration after the hit, a hit affects the pixels on either side of the hit one so that the resulting net pixel area is 0.13 cm, and the read noise is 50 electrons; the result is that the pure background-limited photon noise will be degraded by a factor of 1.5.

The photon noise limits in Table I are computed according to the description above and include the degradation by cosmic radiation. Of course, for a diffraction limited telescope, these detection limits scale as .