Spectral modeling of photographic printing based on dye concentration

A method of predicting a reflectance spectrum of a photographic print based on a photographic negative, comprising:

• estimating a film spectral transmittance of a photographic negative;
• estimating an exposure illumination spectrum of a printing illuminant over time;
• estimating spectral sensitivities of photographic paper corresponding to the photographic print;
• estimating dye concentrations based on the film spectral transmittance, the exposure illumination spectrum, and the spectral sensitivities;
• converting the estimated dye concentrations to a predicted reflectance spectrum of the photographic print corresponding to the photographic negative.

A method of predicting a reflectance spectrum of a photographic print based on a photographic negative, comprising:

• estimating a film spectral transmittance of a photographic negative using a scanner and film model;
• estimating an exposure illumination spectrum of a printing illuminant over time using a photographic printer model;
• estimating spectral sensitivities of photographic paper corresponding to the photographic print using a photographic paper model;
• estimating dye concentrations based on the film spectral transmittance, the exposure illumination spectrum, and the spectral sensitivities using the photographic paper model;
• converting the estimated dye concentrations to a predicted reflectance spectrum of the photographic print using the photographic paper model.

A method of modeling spectral characteristics of a photographic print based on a photographic negative, comprising:

• converting digital values representative of the photographic negative to a film transmittance spectrum;
• determining an exposure illumination spectrum for generation of the photographic print;
• determining paper spectral sensitivities of a photographic paper for generation of the photographic print;
• generating log integrated exposures based on a time integrated spectral product of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• generating dye concentrations based on the log integrated exposures;
• and
• generating a predicted reflectance spectrum based on the dye concentrations.

A method of modeling spectral characteristics of a photographic print based on a photographic negative, comprising:

• converting digital values representative of the photographic negative to a film transmittance spectrum using a selected photographic negative model;
• determining an exposure illumination spectrum for generation of the photographic print using a selected illuminant model and a selected print filter model;
• determining paper spectral sensitivities of a photographic paper for generation of the photographic print using a selected photographic paper model;
• generating log integrated exposures based on a time integrated spectral product of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• generating dye concentrations based on the log integrated exposures;
• and
• generating a predicted reflectance spectrum based on the dye concentrations using a selected paper dye model and the selected photographic paper model.

A method of modeling spectral characteristics of a photographic print based on a photographic negative, comprising:

• converting digital values from scanning a photographic negative to a film transmittance spectrum using a photographic negative film model corresponding to a media of the photographic negative, by iteratively updating media coordinates corresponding to an estimated spectrum until a stopping criterion is met, where the media coordinates are in a colorant space of a sample scanned by an image acquisition device;
• estimating an exposure illumination spectrum over time using an exposure schedule;
• estimating paper spectral sensitivities of a photographic paper corresponding to the photographic print;
• integrating spectral products of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• converting the integrated spectral products into log integrated exposures;
• converting the log integrated exposures to dye concentrations;
• and
• converting the dye concentrations to a predicted reflectance spectrum.

A method of modeling spectral characteristics of a photographic print based on a photographic negative, comprising:

• converting digital values from scanning a photographic negative to a film transmittance spectrum using a photographic negative film model corresponding to a media of the photographic negative;
• estimating an exposure illumination spectrum over time using an exposure schedule;
• estimating paper spectral sensitivities of a photographic paper corresponding to the photographic print;
• integrating spectral products of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• converting the integrated spectral products into log integrated exposures;
• iteratively adjusting the derived spectral sensitivities and log integrated exposures until a spectral sensitivity stopping criterion is met;
• converting the log integrated exposures to dye concentrations;
• and
• converting the dye concentrations to a predicted reflectance spectrum.

A method of modeling spectral characteristics of a photographic print based on a photographic negative, comprising:

• converting digital values from scanning a photographic negative to a film transmittance spectrum using a photographic negative film model corresponding to a media of the photographic negative;
• estimating an exposure illumination spectrum over time using an exposure schedule;
• estimating paper spectral sensitivities of a photographic paper corresponding to the photographic print;
• integrating spectral products of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• converting the integrated spectral products into log integrated exposures;
• estimating dye absorption curves for the photographic paper, where estimating the dye absorption curves comprises:
• measuring a paper base spectrum of the photographic paper;
• measuring a paper target spectrum of a paper target having steps in each of the photographic paper's colorant channels;
• converting the paper base spectrum and the paper target spectrum to absorption spectra;
• and
• applying factor analysis and target rotation to the absorption spectra to produce dye absorption curves;
• converting the log integrated exposures to dye concentrations based on the dye absorption curves;
• and
• converting the dye concentrations to a predicted reflectance spectrum.

A computer program, residing on a computer-readable medium, for modeling spectral characteristics of a photographic print based on a photographic negative, the computer program comprising instructions for causing a computer to:

• convert digital values from scanning a photographic negative to a film transmittance spectrum using a photographic negative film model corresponding to a media of the photographic negative;
• estimate an exposure illumination spectrum over time using an exposure schedule;
• estimate paper spectral sensitivities of a photographic paper corresponding to the photographic print;
• integrate over time spectral products of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• convert the integrated spectral products into log integrated exposures;
• convert the log integrated exposures to dye concentrations;
• and
• convert the dye concentrations to a predicted reflectance spectrum.

In a computer system, a spectral model for modeling spectral characteristics of a photographic print based on a photographic negative, comprising:

• means for converting digital values from scanning a photographic negative to a film transmittance spectrum using a photographic negative film model corresponding to a media of the photographic negative;
• means for estimating an exposure illumination spectrum over time using an exposure schedule;
• means for estimating paper spectral sensitivities of a photographic paper corresponding to the photographic print;
• means for integrating over time spectral products of the film transmittance spectrum, the exposure illumination spectrum, and the paper spectral sensitivities;
• means for converting the integrated spectral products into log integrated exposures;
• means for converting the log integrated exposures to dye concentrations;
• and
• means for converting the dye concentrations to a predicted reflectance spectrum.