1 Introduction

Observations at hard X-ray and gamma-ray energies are severely constrained by the limited sensitivity and poor angular resolution of the present generation of instrumentation. The sensitivity could be enormously improved if gamma-ray radiation could be concentrated from a large collection area onto a small, low background detector, as is done with grazing incidence optics at lower energies in, for example, the Chandra and XMM-Newton observatories. Similarly, if a diffraction-limited gamma-ray optical system, even of modest diameter (a few metres), could be constructed, then the angular resolution achievable would be a fraction of one micro arcsecond ($\mu''$). This would be better than that achievable in any other waveband and would be sufficient to resolve the structure in the emitting region immediately surrounding the event horizon of massive black holes in the nucleii of nearby galaxies.

The object of this paper is to point out that in principle simple diffractive optics in the form of a Phase Fresnel Lens can simultaneously achieve both of these advances. This idea has been briefly introduced (Skinner 2001b) but is here examined in detail. The background to the problem of obtaining high sensitivity and ultra-high angular resolution observations is first discussed (Sect. 2) and the concept of utilising diffractive optics at gamma-rays is then introduced (Sect. 3), along with some specific considerations for astronomical applications (Sect. 4). The practical problems are discussed in Sect. 5 and the performance anticipated and the science which it would make possible are reviewed in Sect. 6. In a companion paper (Skinner 2001a, Paper II) some variations of the proposed configuration, which offer advantages in particular circumstances, will be discussed.