Halftone contact screen and photographic method of making the screen

The halftone contact screen consisting of a substantially plane medium whose optical density varies in a pattern:

• in which said pattern consists of a rectangular array of a large number of small abutting square areas (a "rectangular array of areas" being understood as defined in this disclosure) each of uniform density;
• in which the density of said square areas is described by a random variable whose cumulative distribution function is equal to a real-valued and positive (with values between 0 and 1 inclusive), increasing function P(d) of density d;
• that is to say, the probability that the density of an arbitrary one of said square areas is less than or equal to density d is equal to P(d);
• in which the knowledge of the density of one square area constitutes a minimum of information as to the density of any other square area, that is to say, if
• a. N is the number of the square areas of said array,
• b. the square areas are numbered 1 to N in an arbitrary order,
• c. X is said random variable, defined on the positive integers between 1 and N inclusive, whose value at k, k a positive integer between 1 and N inclusive, is the density of the square area numbered k,
• d. Y is the random variable defined by Y(k)=X[Rem(k+n, N)], where n is an arbitrary fixed positive integer between 1 and N-1 inclusive and Rem (k+n, N) is the remainder when k+n is divided by N--i.e., k+n if k+n.ltoreq.N and k+n-N if k+n>N--except when k+n=N, when it is N,
• then X and Y are independent random variables;
• and in which said function P(d) of density is (exp [-ln 10 R(C-d)]-R.sub.B)/(R.sub.W -R.sub.B), where
• C is a positive constant real number
• R.sub.B is equal to the reflectance of printing paper when said paper is inked
• R.sub.W is equal to the reflectance of said paper when uninked
• R(d') is an arbitrarily-chosen positive, real-valued, increasing function defined on the positive real numbers d'
• (so that, in accordance with the argument set out above in this disclosure, C being made the "critical density" as this is defined above in this disclosure, R(d') is the "reproduction curve," that is to say, the graph of the integrated density of the positive facsimile printed on said paper as a function of the copy density d').