Laue lenses

The sky between about 100 keV and 1 MeV is still poorly ex­plored, al­though it holds open ques­tions such as the origin of the 511 keV po­si­tron-annihila­tion line from the Ga­lac­tic Centre and the physics of su­per­no­va explo­sions. At these en­er­gies mirrors no longer reflect and refrac­tion is neg­li­gi­ble, so tele­scopes collect photons di­rect­ly on large de­tec­tors, whose back­ground grows with their size. A lens that con­cen­trat­ed the photons on a small de­tec­tor would greatly improve the sen­si­tiv­i­ty; only diffrac­tion in crys­tals can make one.

A crystal re­flects photons of wave­length λ when they meet its planes, of spacing d, at the Bragg angle

2d sin θ_B = λ

For 100 keV photons on silicon (111) planes θ_B is about 1.1°. In transmis­sion, or Laue, ge­om­e­try the photons cross the crystal and leave it de­flect­ed by 2θ_B.

A Laue lens places many crys­tals on con­cen­tric rings, each tilted to dif­fract towards a common focus. Since the deflec­tion is 2θ_B and θ_B falls as the energy rises, outer rings focus lower en­er­gies and inner rings higher ones.

The ef­fi­cien­cy depends on the crys­tals. In a mosaic crystal, made of slight­ly mis­aligned blocks, photons are dif­fract­ed back and forth and at most half leave in the dif­fract­ed direc­tion. In a crystal with curved diffract­ing planes the Bragg condi­tion changes con­tin­u­ous­ly across the thick­ness, so photons are not dif­fract­ed back: the ef­fi­cien­cy can exceed 50%, and the cur­va­ture also con­cen­trates the dif­fract­ed beam into a smaller spot.

We bend silicon and ger­ma­nium plates without holders: stressed thin films, surface grooves, sandblast­ing or carbon-fibre layers curve the plate, and the quasi-mosaic effect, which follows from the an­iso­trop­ic elas­tic­i­ty of the crystal, curves the diffract­ing planes inside it. To fix the crys­tals in the lens we are replac­ing space-qual­i­fied resins with anodic bonding, for higher ef­fi­cien­cy and more ac­cu­rate orienta­tion.