Optimal reconstruction of tone reproduction curve

In a printing machine having a moving imaging surface, a projecting system for modulating a beam and projecting an image onto the imaging surface, a developer for application of toner to the image projected onto the imaging surface for transfer of the image to a medium, a method of machine control comprising the steps of;

• providing a look up table for reconstructing a tone reproduction curve (TRC), sensing a discrete number of machine samples,
• responding in a matrix multiplier to the sensed samples and to the look up table to reproduce the tone reproduction curve, and
• responding to the tone reproduction curve to adjust machine quality, the look up table comprising a covariance matrix of elements determined by
• denoting a matrix resulting from an N set of output tone reproduction curve measurements, as
• .OMEGA.:=›C.sub.1 C.sub.2 . . . C.sub.N !.epsilon.R.sup.n.times.N,
• where C.sub.1, C.sub.2 . . . etc., are the vectors of elements containing n TRC samples covering a whole TRC space wherein n is a positive integer used to represent TRC samples, N represents TRC measurements obtained from input/out experiments, and R represents Euclidean spaces,
• specifying an associated sample covariance matrix as
• .SIGMA.:=1/N.OMEGA..OMEGA..sup.T,
• wherein T represents the transpose of the matrix,
• assuming a fixed set of sample points and defining a TRC vector c as
• c:=.PI..sup.T C
• where each column of .PI. denoting a matrix with each column vector containing zeros with a single unity value placed in the slot corresponding to the quantized value at which the TRC is sampled by the sensor, is a vector of zeros with a single unity value in a slot corresponding to the quantized value at which the TRC is to be sampled, and C corresponds to all the elements of the TRC,
• providing a least squares optimal reconstruction, .PI..sup.+ denoting a matrix used as a look up table as the sensor complement in the TRC reconstruction process, with respect to a given set of N sample vectors that form the columns of .OMEGA. defined as
• C:=.PI..sup.+ .PI..sup.T C
• obtaining .PI..sup.+ by minimizing the Frobenius norm of
• .OMEGA.-.PI..sup.+ .PI..sup.T .OMEGA.
• resulting in a matrix look up table for use in a TRC reconstruction process defined by
• .PI..sup.+ =.SIGMA..PI.(.PI..sup.T .SIGMA..PI.).sup.-1.

A smart sensor for use in adjusting quality in an imaging machine comprising;

• a look up table for reconstructing a tone reproduction curve (TRC), means for measuring machine parameters, and
• a matrix multiplier responsive to the machine parameters and to the look up table to reproduce the tone reproduction curve, the look up table comprising a covariance matrix of elements determined by
• denoting a matrix resulting from an N set of output tone reproduction curve measurements, as
• .OMEGA.:=›C.sub.1 C.sub.2 . . . C.sub.N !.epsilon.R.sup.n.times.N,
• where C.sub.1, C.sub.2 . . . etc., are the vectors of elements containing n TRC samples covering a whole TRC space wherein n is a positive integer used to represent TRC samples, N represents TRC measurements obtained from input/out experiments, and R represents Euclidean spaces,
• assuming a fixed set of sample points and defining a TRC vector c as
• c:=.PI..sup.T C
• where each column of .PI. denoting a matrix with each column vector containing zeros with a single unity value placed in the slot corresponding to the quantized value at which the TRC is sampled by the sensor, is a vector of zeros with a single unity value in a slot corresponding to the quantized value at which the TRC is to be sampled, and C corresponds to all the elements of the TRC,
• providing a least squares optimal reconstruction, .PI..sup.+ denoting a matrix used as a look up table as the sensor complement in the TRC reconstruction process, with respect to a given set of N sample vectors that form the columns of .OMEGA. defined as
• C:=.PI..sup.+ .PI..sup.T C
• resulting in a matrix look up table for use in a TRC reconstruction process defined by
• .PI..sup.+ =.SIGMA..PI.(.PI..sup.T .SIGMA..PI.).sup.-1.

A smart sensor system for use in adjusting control parameters in an imaging machine comprising;

• a look up table for reconstructing said control parameters,
• a sensor for obtaining control parameter data, and a matrix multiplier responsive to minimal sensor measurements and to the look up table to reconstruct the control parameters, the look up table comprising a covariance matrix of elements determined by denoting a matrix resulting from an N set of output tone reproduction curve measurements, as
• .OMEGA.:=›C.sub.1 C.sub.2 . . . C.sub.N !.epsilon.R.sup.n.times.N,
• where C.sub.1, C.sub.2 . . . etc., are the vectors of elements containing n TRC samples covering a whole TRC space wherein n is a positive integer used to represent TRC samples, N represents TRC measurements obtained from input/out experiments, and R represents Euclidean spaces.

A smart sensor system for use in adjusting control parameters in an imaging machine comprising;

• a look up table for reconstructing said control parameters,
• a sensor for obtaining control parameter data,
• a matrix multiplier responsive to sensor measurements and to the look up table to reconstruct the control parameters, and
• a control responding to the reconstructed control parameters to adjust machine quality wherein said given control parameters include a tone reproduction curve.