is the rays from this annular region, shown by continuous lines in Fig. 1, 
which produce the required "axicon image". Such images are produced by a 
converging wavefront which is locally conical, and they consist of a central 
bright rod-like image which is surrounded by numerous concentric diffraction 
rings of almost regular spacing and gradually decaying intensity. : I£ 6 is 
the angular radius of the effective annular source and À is the wavelength, 
then the intensity at radius r is proportional to a (27rsin0/A), but remains 
substantially unchanged as it is propagated along the axis. See Fig. 3 for a 
logarithmic plot which indicates the photographic density that might be 
expected from a suitably exposed negative. 
Axicons were invented (McCleod 1954) for use in alignment where a 
Single axis needs to be accurately defined. The commonest type of axicon 
imaging element is a conical reflecting or refracting surface, or a circular 
diffraction grating (Dyson 1958). It was however realised by 1958 that the 
spherical aberration generated by wholly spherical surfaces could also 
Serve to produce an approximately conical wavefront and hence to define a 
single axis in space (Steel 1958, see also Burch 1958). 
DESIGN OF CENTRAX CAMERA LENS 
In order to obtain a "monocentric axicon", an element which performs 
the job of defining an axis equally well in all directions, it would not 
  
be satisfactory merely to split the lens in half and insert an annular 
amplitude mask, because such a mask would appear foreshortened rather than 
circular from most directions. (In principle a central opaque sphere 
could form the inside of a truly symmetrical amplitude mask, but generating 
the outside of such a mask seems to present problems). On the other hand 
there seems to be no difficulty in generating a spherically symmetric 
"phase mask" using the spherical aberration produced by high angle incidence 
on a transparent inner sphere. 
A prototype lens of this type has now been designed and constructed; 
since its purpose is to define a multitude of axes, all passing through a 
common centre, the term CENTRAX is proposed as a suitable acronym. Table 
I and Fig. 2 give optical and mechanical data of its construction. Fig. 4 
indicates the calculated wavefront error that is generated for various 
object points; the curves represent a variable amount of wavefront 
curvature (the paraxial focus error) combined with substantial 4th order 
92