The goal became to find a surface geometry which would permit designers the
predictability of diffusion from MLS diffusers with a wider bandwidth.
The new system
was again introduced by Schroeder in 1975 in a paper describing the implementation of
the quadratic residue diffuser or Schroeder diffuser ? a device which
has since been widely accepted as one of the de facto standards for easily creating
diffusive surfaces.
Rather than relying on alternating reflecting coefficient patterns, this
method considers the wall to be a flat surface with varying impedance according to
location. This is accomplished using wells of various specific depths arranged in a
periodic sequence based on residues of a quadratic function.
s_{n} = n^{2} mod(p)
where sn is the sequence of relative depths of the wells, n is a number in the sequence of
nonnegative consecutive integers {0, 1, 2, 3 ...} denoting the well number, and p is a
nonnegative odd prime number.
For example, for modulo 17, the series is
0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9, 16, 8, 2, 15 ...
The actual depths of the wells are dependent on the design wavelength of the diffuser. In
order to calculate these depths, Schroeder suggests the function
dn = sn * (DF / 2 p)
where dn is the depth of well n and DF is the design wavelength.
The widths of these wells w should be constant and small compared to the design
wavelength
(no greater than DF / 2; Schroeder suggests 0.137 * DF)
