A Conditional Model for Integrating Tone Response and Gray Balance in Print Calibration

Ronen Dolev | 2026

1. Abstract

Print calibration requires attention to both the response of individual color channels and the color produced when those channels are printed in combination. This article introduces the Conditional Tone and Gray-Balance Optimization (CTGBO) Model, an author-proposed framework for selecting CMYK corrections from tone and gray-patch measurements. The framework builds on established methods: converting optical density to apparent tone area using Murray–Davies, inverting a measured response curve, calculating color targets from an ICC profile, and evaluating color differences using CIEDE2000. The proposed measurement set comprises 11 tone points per channel and seven gray patches with explicitly defined CMYK recipes. A tone-correction lookup table (LUT) is calculated first. When the conditional combined mode is enabled, four correction-strength factors are then selected using an objective function that balances tone-response error against predicted color differences in the gray patches. The predicted color change comes from the difference between two ICC-profile predictions and is added to the original measurement. Previous work describes approaches that combine tone curves and gray balance, calibration against a reference profile, and local correction of color predictions. CTGBO proposes a particular, transparent formulation of this combination, with few decision variables and explicit correction constraints. Prediction from a reference profile is a conditional assumption whose reliability depends on the press's local response. This article defines the calculation, its limitations, and a validation protocol. No experimental results demonstrating a production improvement are presented here; every combined correction requires a trial print and subsequent measurement.

2. The Problem with Single-Metric Correction

An operator may adjust solid-ink densities and match tone curves to a defined target while still obtaining grays with a reddish, greenish, or bluish cast. Conversely, adjusting the relative CMY contributions may improve gray balance while moving an individual channel farther away from its desired tone-response curve. Measurements from a single-color step wedge do not describe all interactions that occur in overprinted color combinations. The limitations of one-dimensional correction curves are well documented, and work on two-dimensional calibration has investigated control methods beyond these curves [19].

Operationally, the problem is deciding which correction to apply when different metrics suggest different priorities. A full tone-based correction may be a strong candidate, but its effect on grays also deserves examination. CTGBO proposes a numerical, explicitly defined comparison rather than relying solely on visual inspection of graphs or undocumented manual curve adjustments.

The proposal applies to a press in a specified production state, with defined substrate, inks, screening, measurement conditions, and processing path. It does not attempt to compensate for every mechanical or materials-related fault through a LUT. Before calculating a correction, the printing process must be sufficiently stable and its measurements representative.

3. What Optical Density, Tone Area, and Gray Balance Measure

Optical density (OD) is a logarithmic description of measured reflectance response under specified density-measurement conditions. In the proposed application, paper, tint, and solid densities are used to calculate apparent tone area. This is an effective densitometric quantity; it must not automatically be interpreted as the geometric dot-area percentage observed under a microscope. Murray–Davies is based on a reflectance mixture of substrate and ink, whereas light scattering and print structure may cause departures from this simplified description [4, 5].

If the measuring instrument already supplies apparent tone area, that value can be entered directly, provided its calculation method and instrument settings are known. OD and tone area derived from that same OD are not independent sources of information. In this framework, they are alternative input routes to the same response curve.

Gray-patch measurements describe the resulting combined color in CIELAB: lightness and chromatic components relative to the measurement conditions. Tone area is expressed as a percentage; Δ E_00 is a color-difference metric. Combining them in an objective function requires explicit normalization rather than treating the raw numbers as though they had the same meaning.

4. Proposed Measurement Set

For each of the C, M, Y, and K channels, the following nominal input points are measured:

x_j ∈ {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}%

The resulting set contains 44 tone values. The 0% point represents the paper, and the 100% point is the solid. For OD measurements, each channel must use its appropriate density response with consistent Density Status, polarization condition, measurement geometry, and backing. The paper must also be measured using the density response applicable to that channel; its density need not be identical across all density-response functions.

Seven gray patches form the second measurement group. Each patch supplies L*, a*, and b*: seven color measurements and 21 numerical components. The following working recipes are provided as part of the author’s model definition. They are experimental-chart recipes, not a table attributed to a standard or external organization without a specific supporting source.

The labels L90–L30 identify measurement regions. The target LAB for each patch is calculated from its recipe and the selected profile. The calculated L* should not be assumed to equal the number in the patch name, nor must its a* and b* be zero.

For FOGRA55, these recipes are submitted as CMYK inputs, with the three additional channels set to zero. Fogra defines FOGRA55 as a seven-channel CMYKOGV color-exchange space, whose CMYK portion corresponds to FOGRA51, including gray balance. The actual channel order in the profile must be respected. Using this profile does not imply that the algorithm described here also calibrates O, G, or V curves [9].

5. Scientific Basis, Reference Conditions, and Prior Work

CIELAB is defined in ISO/CIE 11664-4:2019, and the CIEDE2000 color-difference formula in ISO/CIE 11664-6:2022. ISO 13655:2017 addresses spectral measurement and colorimetric computation in graphic technology. Within the ISO 12647 series, Part 1 covers parameters and measurement methods, Part 2 concerns offset lithography, and Part 7 concerns digital proofing that simulates characterization conditions. Citing these standards establishes professional context; it does not certify CTGBO under them [1–3, 12–14].

Characterization data relate device values, such as CMYK combinations, to colorimetric outcomes. An ICC profile is a computational representation built from data and profile-generation choices; a characterization-data identifier and an ICC profile filename are not the same identifier. Fogra publishes characterization data for various printing conditions, while PRINTING United Alliance provides resources for GRACoL and CRPC [6–10].

The proposed reference specification includes the following condition–measurement pairs:

The association of FOGRA51/52 with M1 is documented by ICC and ECI sources; ECI documentation treats FOGRA39 as M0. Fogra describes FOGRA55 in relation to FOGRA51 and M1-based color data. The distinction between the M0-based GRACoL 2006 condition and the later M1-based CRPC family is addressed in SGIA technical material [8–11, 22].

In the proposed implementation, M0-to-M1 conversion is never implicit. If the measurement condition is incompatible with the reference or is unknown, processing stops. The backing and reference-data version must also be identified; selecting a generic profile name is insufficient. The selected profile supplies LAB targets for the gray patches, but does not automatically import an official TVI curve for tone correction. The tone target is defined separately.

The idea of jointly considering tone response and gray balance is already documented. In 2004, Birkett and Spontelli studied blending curves based on separate-color step wedges and combined CMY printing. Heidelberg describes improving gray balance using measurements and a reference profile while keeping dot gain within permitted limits. G7 and G7+ address tonality and gray balance. Mestha and colleagues described a calibration control loop using measured LAB and local sensitivity. Esko describes local refinement of profile predictions against measurements for spot-color correction [15–18, 20].

CTGBO is the author’s proposed formulation of these existing ingredients. It is not an official model of Fogra, GRACoL, Esko, GMG, ColorLogic, or HP. This article does not claim worldwide priority, industrial adoption, or an experimentally demonstrated advantage.

6. Converting Optical Density to Apparent Tone Area

For each channel, the Murray–Davies calculation accounts for paper density:

A(D) = 100 × [1 − 10^(−(D − D_p))] / [1 − 10^(−(D_s − D_p))]

Here, D denotes tint density, D_p paper density, and D_s solid density; A is expressed as a percentage. The formula follows from the ratio of tint, ink, and paper reflectances and the logarithmic relationship between density and reflectance [4, 5].

Subtracting the paper density defines the tint relative to the substrate on which it is printed. At D=D_p, A=0; at D=D_s, A=100. If the instrument has already been zeroed on paper, the corresponding relative densities must be used with D_p=0; paper density must not be subtracted twice.

The normalization also highlights an important limitation: the solid is assigned 100% tone area even if its density or color is unsuitable for production. Therefore, matching the A curve does not establish that ink-film thickness, solid color, or gamut are correct. Murray–Davies is neither a complete color characterization nor a complete model of optical light scattering; it provides apparent tone area under the stated assumptions.

Data are accepted only when D_s>D_p and every tint density lies between the paper and solid values. An out-of-range measurement must trigger inspection of the reading or printed patch rather than automatic clipping that conceals the anomaly.

7. Building the Response Curve and Defining the Target

For each channel c, a measured response curve M_c(x) relates nominal input to apparent tone area. Piecewise-linear interpolation is used between measurement points. A graph may be displayed as a smooth line, but the numerical calculation remains based on the linear segments.

Two types of targets are supported. For a linear apparent-tone-area target:

T_c(i) = i

A 40% input therefore targets 40% apparent tone area. This is an explicitly selected calibration target; do not confuse it with a FOGRA or ISO TVI curve. The second option is a manually specified, approved target curve from a customer specification, a production condition, an applicable standard requirement, or external characterization.

Both the measured and target curves must start at 0, end at 100, and contain no missing or non-finite values. For the inverse defined here to be unique, the measured curve must be strictly increasing between successive points. A flat segment maps multiple inputs to the same output and requires remeasurement or an additional inversion rule; such a rule is not silently introduced in this model. The target curve must also retain a valid monotonic ordering.

8. Calculating the Tone LUT and Limiting Its Change

The unconstrained correction is obtained by inverting the measured response:

U_c(i) = M_c⁻¹(T_c(i))

If the target lies between M_c(x_j) and M_c(x_j+1), then:

U_c(i) = x_j + [T_c(i) − M_c(x_j)] / [M_c(x_(j+1)) − M_c(x_j)] × (x_(j+1) − x_j)

No extrapolation outside the measured domain is permitted. After inversion, the Maximum Change constraint, denoted L and measured in percentage points, is applied:

B_c(i) = clip[U_c(i), max(0, i − L), min(100, i + L)]

B_c is the limited tone LUT used below. This bound is intended to reduce extreme corrections caused by a defective patch, noise, or unstable response. It does not remove measurement error and cannot replace data validation. When the bound is active, the target may not be reached even within the model.

The tone-fit metric for any LUT Q is:

RMS_tone(Q) = √{(1/N) × Σ[c ∈ {C,M,Y,K}] × Σ[i ∈ {10, 20, …, 90}] [M_c(Q_c(i)) − T_c(i)]²}

Here N=36. The 0% and 100% points are fixed endpoints and are excluded from the interior-point metric. The error is reported in percentage points of apparent tone area and describes curve fit, not overall color accuracy.

9. Generating Gray Targets from an ICC Profile

Let P_i denote the original CMYK recipe for gray patch i. Its target LAB is calculated using the selected reference profile. The proposed implementation specifies ICC-Absolute Colorimetric, D50 illumination, and the CIE 1931 2° standard observer, without Black Point Compensation. These are explicit computation-path choices. The profile and color-management engine must be recorded; selecting the reference name alone is not sufficient. The ICC specification defines the profile connection space (PCS) and rendering intents, including the distinction between media-relative and ICC-absolute colorimetry [6].

The computed LAB value is a target under the reference condition, not a measurement of the particular press. The reference may incorporate substrate coloration and grays for which a* and b* are nonzero. It must not be replaced by an idealized neutral gray without an explicit decision.

The original recipes P_i must be preserved when printing the measurement chart. An undocumented transformation through another profile, a changed separation, or a change in K makes the relationship between printed color and intended recipe unknown. The LUT insertion point in the print-processing pipeline must also be documented. If an existing calibration is already in place, it must remain unchanged between initial measurement and trial, and the new LUT must operate at the input point assumed by the model.

10. Evaluating Gray Patches with CIEDE2000

For each patch, the component differences are displayed as:

ΔL_i* = L_(measured,i)* − L_(target,i)*

Δa_i* = a_(measured,i)* − a_(target,i)*; Δb_i* = b_(measured,i)* − b_(target,i)*

Δ L* identifies lightness deviation; Δ a* describes the green–red axis; and Δ b* describes the blue–yellow axis. Δ E_00 is calculated with CIEDE2000, which applies lightness, chroma, and hue weighting and an interaction term. It must not be computed as the simple Euclidean length of the three LAB component differences. The formula is specified in ISO/CIE 11664-6:2022; Sharma, Wu, and Dalal also provide supplementary test data for implementation verification [2, 21].

Report the measured LAB, target LAB, and ΔE00 for each patch separately. An average may hide deterioration in an individual patch. This article does not impose a universal pass/fail threshold; acceptance limits follow an agreed specification. In the normal operating mode, gray measurements are used for evaluation and reporting, while the tone LUT is derived from CMYK tone measurements alone. Gray patches participate in selecting correction strength only when the combined mode is explicitly activated.

11. CTGBO: Four Correction Strengths Applied to the Base Curves

Rather than fitting every LUT point independently, the proposal selects four variables:

s = (s_C, s_M, s_Y, s_K), 0 ≤ s_c ≤ 1

A candidate curve is defined for each channel:

Q_(c,s)(i) = i + s_c × [B_c(i) − i]

When s_c=0, the channel retains an identity mapping. When s_c=1, the full limited tone LUT is applied. Intermediate values apply a corresponding fraction of the correction. The Maximum Change bound is preserved because the candidate lies between identity and the limited base curve.

The 44-value table has eight fixed endpoints and 36 interior points. Reducing these to four channel-wide strengths substantially restricts the fitting freedom. The intention is to avoid overly flexible fitting from a small gray-patch dataset; experimental work is needed to determine whether this choice actually improves stability and reduces sensitivity to noise.

This parameterization also limits the solution. It can weaken the tone correction but cannot reverse its direction or extend it beyond the full correction. If B_c(i)=i, changing s_c has no effect at that point. A single factor for each channel also prevents independent correction of highlights, midtones, and shadows. These are deliberate restrictions of the search space and should be reported explicitly.

12. Conditional Prediction of the Correction’s Effect on Gray Patches

For each original gray recipe P_i, the corrected recipe is first calculated by applying the four candidate curves:

P'_(i,c) = Q_(c,s)(P_(i,c))

If a recipe value P_(i,c) falls between LUT points, linear interpolation is used. Let F denote the colorimetric transformation of the reference ICC profile. The proposed prediction is:

LAB̂_i(s) = LAB_(measured,i) + F(P'_i) − F(P_i)

The corresponding predicted color difference is:

ΔÊ_(00,i)(s) = ΔE_00[LAB̂_i(s), LAB_(target,i)]

The actual measurement provides the starting point, while the profile estimates how color changes when the recipe changes. This is a local-response assumption: the change predicted by the reference profile must be a useful approximation to the change on the actual press, even when the two differ in their absolute color predictions.

The expression can also be written as F(P'_i)+[LAB_(measured,i)-F(P_i)]. In other words, the profile prediction is corrected by a local measurement offset. If the actual press response is G and its residual relative to the reference is e(P)=G(P)−F(P), then, neglecting measurement noise, the prediction error is e(P)-e(P'). A constant residual cancels; a residual that changes rapidly near the recipe produces prediction error.

Consequently, a good profile match at the original point is not enough. The predicted color change must also be tested for accuracy. Esko’s precedent for local profile adjustment and published local-control models provide useful context, but neither validates the assumption for an arbitrary press and reference profile [17, 18].

13. The Objective Function and the Meaning of Its Weight

For each candidate, tone RMS is recalculated using Q_(c,s). A constant RMS value from the full tone correction must not be used when comparing candidates. The mean predicted gray-patch color difference is:

Mean ΔE_gray(s) = (1/7) × Σ[i = 1…7] ΔÊ_(00,i)(s)

The proposed objective is:

J(s; w) = (1 − w) × [RMS_tone(Q_s) / 10]² + w × [Mean ΔE_gray(s) / 3]², 0 ≤ w ≤ 1

A lower weight favors tone fidelity; a higher weight favors agreement between gray patches and their reference colors. At the endpoints, w=0 ignores the gray metric in the objective, while w=1 ignores the tone error in the objective, although the candidate constraints remain in force. Because Δ E_00 includes lightness differences, the gray metric describes color accuracy of gray-patch samples, not merely their chromatic neutrality.

The denominators of 10 percentage points and 3 units of Δ E_00 are normalization constants selected for this particular objective function. They are not tolerances or pass/fail limits. Altering either changes the effective balance between the metrics even with w unchanged; all three values therefore need to be documented together.

The report must display J, tone RMS, and Δ E_00 for each individual patch. A candidate with a lower overall J may still worsen a particular tone or gray patch. An average-based objective does not guarantee protection of the worst case.

14. Search Procedure and Validation Checks

The bounded local search is initialized at three points:

(0, 0, 0, 0); (1, 1, 1, 1); (0.5, 0.5, 0.5, 0.5)

The step sizes are 0.5, 0.25, 0.10, 0.05, and 0.02. At each stage, positive and negative movements in each channel are examined while keeping all strengths between 0 and 1. The algorithm moves to a valid candidate that improves J, repeats the search at that step size, and proceeds to the next smaller step when no further improvement is found. The best result across all initialization points is retained.

This is a bounded local search, not a guarantee of a global optimum. The identity solution is retained as a candidate. Therefore, provided it satisfies the constraints and all candidates are evaluated on the same numerical path, the selected solution should not have a worse J than the baseline, within a specified numerical tolerance. This refers to the computed objective, not a guarantee of improvement in the actual print.

The proposed implementation must reject non-finite OD values, a solid density no greater than paper density, out-of-range tints, non-increasing measured curves, invalid targets, and incomplete LAB data. It must also stop when measurement mode is incompatible, the origin of CMYK values is unknown or transformed, a profile is missing, or the conversion path cannot support the profile’s channel count. A seven-channel profile must not silently be replaced by a four-channel profile.

Every candidate LUT must stay between 0 and 100, preserve endpoints and the Maximum Change constraint, and remain monotonic. For each gray patch, the total area coverage (TAC) is also calculated:

TAC_i(s) = Σ[c] P'_(i,c)

A candidate exceeding the approved ink limit for the production condition and profile is rejected. The limit must be stored as part of the approved reference configuration rather than assuming every ICC file exposes it as a direct field. The test covers only the seven gray recipes; it does not establish that a complete page, image, or job complies with the TAC limit.

15. Illustrative Numerical Example Only

All measurements and aggregate performance figures in this section are synthetic. They are not press results, official target values, or the output of a particular ICC-profile conversion.

Assume that the C channel has paper density D_p=0.05 and solid density D_s=1.45, with the following tint densities:

For a linear target, a 50% nominal input requires 50% apparent tone area. Inverting the relevant segment gives:

U_C(50) = 40 + [(50 − 45.580458) / (57.625764 − 45.580458)] × 10 ≈ 43.6691

With L = 10, the Maximum Change limit does not bind at this point. For s_C=0.6, the candidate becomes:

Q_(C,s)(50) = 50 + 0.6 × (43.6691 − 50) ≈ 46.2015

This partial correction produces a higher input than the full correction. If selected, it is expected to reduce tone accuracy at that point. This trade-off can be justified in the combined calculation if other metrics improve under the chosen weighting.

To illustrate only the computation of J, assume the following aggregate metrics for the entire measurement set, with w=0.5:

The tone RMS and gray Δ E_00 values in this table are assumptions for illustration; only J is calculated from them. They are not outputs of an optimization run on a complete measurement set. The example shows how a strong tone-only correction may lose under a combined objective and how another candidate may be chosen despite its higher tone RMS. Only a printed trial can establish whether the prediction occurs in practice.

16. Recommended Operational Workflow

1. Select a reference printing condition, a uniquely identified profile file, the measurement condition, and backing; define the tone target and Maximum Change independently.
2. Stabilize the press, substrate, and environment, and record the existing calibration state and the correction insertion point.
3. Print the chart, preserving the original recipes and the documented processing path.
4. Measure paper, solid, and tints for every channel, followed by the LAB values of all seven gray patches.
5. Validate the inputs, convert OD to apparent tone area when necessary, and construct the response curves.
6. Calculate the tone LUT and evaluate the gray measurements against ICC-derived targets.
7. Choose between a tone-only trial and explicit activation of the combined search; retain all comparison metrics.
8. Print a trial using the selected LUT and remeasure under the same conditions.
9. Compare before and after: tone curves, tone RMS, LAB, and Δ E_00 for every gray patch, together with additional color patches relevant to the job.
10. Approve the correction for the tested conditions, reject it, or begin another iteration from updated measurements.

The report should retain the date, press, substrate, ink set, screening, instrument settings, profile file and version, color-management engine, complete original inputs, targets, L, w, correction factors, and exported LUT. Displaying two decimal places may aid readability, but internal calculations should retain full numerical precision. Exporting LUT values with four decimal places preserves more information than the display without implying measurement accuracy that has not been demonstrated.

17. Limitations and Professional Risks

A reference profile does not characterize the specific press. Pigments, substrates, ink sequence, and layer interactions may alter the local response. The same CMYK change can therefore yield a different LAB change than the reference profile predicts. Calibration with four one-dimensional curves cannot fully control every color combination, and the four-strength parameterization limits that control further [18, 19].

Densitometric accuracy is not the same as geometric dot-area accuracy. Murray–Davies does not fully model light scattering in the substrate and printed layer. Changes in substrate, inks, screening, blanket, drying or curing, temperature, or press condition may invalidate a previously derived correction. Every correction should be tied to a documented production state.

Seven gray patches cannot replace a complete characterization chart. Improvement in those patches does not establish improvement in saturated colors, brand colors, skin tones, or every possible gray. Where gray recipes include K, multiple channels may partly explain the same deviation; K cannot correct a patch whose recipe has K=0 while the LUT endpoint remains zero.

The search does not guarantee a global optimum, and the objective permits trade-offs between metrics and between individual patches. Any combined output should be labeled Conditional Correction or Estimated Correction. The application’s “Load illustrated example” data are synthetic demonstration data only. Selecting FOGRA or GRACoL does not establish conformity with a standard. The model itself confers no conformance or certification and cannot replace a trial print followed by measurement.

18. Proposed Experimental Validation Protocol

Validation must address two different questions: Is the predicted color change useful? And does selecting a combined correction improve the outcome relative to alternatives?

First, measure instrument repeatability on stable patches with at least three repetitions. Also measure variation across positions and sheets so that instrument noise can be distinguished from print-process variation. Substrate, backing, M condition, polarization, and Density Status must remain unchanged throughout the experiment. The minimum number of repetitions is a starting point, not a guarantee of adequate statistical power.

To validate prediction, print original gray recipes and recipes with small, known, permissible CMYK perturbations. Compare the predicted LAB change with the measured LAB change. Both the direction and magnitude of the change should be evaluated, not only the absolute Δ E_00 to the target. This test identifies where a reference profile provides useful local sensitivity and where the assumption fails.

To assess correction performance, print three separate series: Baseline, Tone-only, and Conditional LUT. Preferably repeat the conditions in blocks or an interleaved order so that press drift over time is not mistakenly attributed to a method. To substantiate an advantage over existing solutions, include a comparator using an established gray-balance calibration method whenever possible.

In every series, measure tone RMS and Δ E_00 for every gray patch. Report mean, median, maximum, and standard deviation, specifying whether the standard deviation describes variation among patches, repeats, or separate runs. Include validation patches that were not used for optimization: additional grays and relevant chromatic colors. Improvement in the seven patches used to select a solution is a fit check; independent patches are needed to assess generalization.

Finally, evaluate several values of w, stability over time, and reproducibility between runs. A claim of advantage requires consistent improvement relative to measurement and process variability, while also accounting for possible deterioration in particular cases. Demonstration data or a single successful run cannot establish such a conclusion.

19. Conclusions

CTGBO proposes a selection layer above established tone calibration: four channel-level application strengths are evaluated against measured tone response and their predicted influence on gray patches. The calculation is built on Murray–Davies, measured response curves, ICC color transformations, and CIEDE2000. The combined consideration of tone control and gray balance is not new; Ronen Dolev’s proposal supplies a particular parameterization, prediction rule, and objective function for that combination.

Its proposed operational value is an explainable correction decision: which candidate was chosen, how much correction is applied to each channel, and what trade-off is predicted between the metrics. Any production advantage will depend on the accuracy of local-change prediction and the results of repeated trials. Publishing the assumptions, constraints, and measurements allows the proposal to be examined professionally, the calculation to be reproduced, and its usefulness under particular printing conditions to be determined.

20. References

Sources were reviewed on 31 October 2026. Formulas, decision rules, and protocols expressly defined as the CTGBO proposal are part of the author’s proposed framework and must not be attributed to the standards bodies. The ISO/CIE catalog entries identify editions and scope; citing them does not imply a complete compliance assessment of their provisions.

1. CIE. ISO/CIE 11664-4:2019 — Colorimetry, Part 4: CIE 1976 Lab color space. Official standards catalog. Online source: https://www.cie.co.at/publications/international-standards
2. CIE. ISO/CIE 11664-6:2022 — Colorimetry, Part 6: CIEDE2000 color-difference formula. Official publication. Online source: https://www.cie.co.at/publications/colorimetry-part-6-ciede2000-colour-difference-formula-1
3. ISO. ISO 13655:2017 — Graphic technology: Spectral measurement and colorimetric computation for graphic arts images. Standard catalog entry. Online source: https://www.iso.org/standard/65430.html
4. Murray, Alexander. Monochrome reproduction in photoengraving. Journal of the Franklin Institute, 221(6), 721–744, 1936. Publisher’s record. DOI: 10.1016/S0016-0032(36)90524-0. Online source: https://www.sciencedirect.com/science/article/abs/pii/S0016003236905240
5. Arney, J. S., P. G. Engeldrum, and H. Zeng. An Expanded Murray-Davies Model of Tone Reproduction in Halftone Imaging. IS&T, Recent Progress in Digital Halftoning II. Online source: https://www.imaging.org/common/uploaded%20files/pdfs/Papers/1999/RP-0-93/1808.pdf
6. International Color Consortium. ICC.1:2022, Profile version 4.4, including documentation of the PCS and rendering intents. Specifications; Introduction to ICC profiles; Colorimetry data. Online sources: https://www.color.org/icc_specs2/ | https://www.color.org/getting-started/ | https://registry.color.org/colorimetry-data/
7. Fogra. Characterization data for relevant printing conditions. Official characterization datasets. Online source: https://fogra.org/en/downloads/work-tools/characterisation-data
8. International Color Consortium. What is FOGRA39? Background on FOGRA39 and FOGRA51/52. Online source: https://www.color.org/fogra39/
9. Fogra. Professional color communication in multiprimary printing, project 13.003. FOGRA55 definition and reference materials. Online source: https://fogra.org/en/research/prepress-technology/multiprimary-printing-13003
10. PRINTING United Alliance. GRACoL — Profiles and Datasets. Official GRACoL resources. Online source: https://www.printing.org/library/standards/specifications-for-print-production/gracol
11. Gillespie, Dan. Color Verification: What It Is and Why You Should Be Doing It. SGIA Journal, September/October 2018, pp. 43–46. Article, PRINTING United Alliance. Online source: https://www.printing.org/docs/default-source/default-document-library/journal/gillespie-0.pdf?sfvrsn=46c003fc_0
12. ISO. ISO 12647-1:2013 — Parameters and measurement methods. Standard catalog entry. Online source: https://www.iso.org/standard/57816.html
13. ISO. ISO 12647-2:2013 — Offset lithographic processes. Standard catalog entry. Online source: https://www.iso.org/standard/57833.html
14. ISO. ISO 12647-7:2016 — Proofing processes working directly from digital data. Standard catalog entry. Online source: https://www.iso.org/standard/66426.html
15. Birkett, William B., and Charles Spontelli. Improving Print Standards by Specifying Isometric Tone Reproduction for the Overall Process. TAGA, 2004. Paper; authors’ presentation, 20 April 2004. Online sources: https://www.printing.org/docs/default-source/publications/t040453.pdf | https://www.optimalmethod.org/resources/TAGA_2004_Presentation_Web.pdf
16. Heidelberg. Prinect gray balance optimization and correction. Gray balance optimization; Curve Modification — Correction of Gray Balance. Online sources: https://onlinehelp.prinect-lounge.com/Prinect_Color_Toolbox/Version2020/en/Prinect/tools/tools-16.htm | https://onlinehelp.prinect-lounge.com/Prinect_Calibration_Manager/Version_CR/en/Prinect/processcalibration/processcalibration-15.htm
17. Esko. Color Engine Pilot 14.1 User Guide, printed pp. 104–106: Refining the Values from the Destination Profile. Official user guide. Online source: https://docs.esko.com/docs/en-us/colorenginepilot/14.1/userguide/ColorEnginePilot141.pdf
18. Mestha, Lalit K., R. Enrique Viturro, Yao Rong Wang, and Sohail A. Dianat. Gray Balance Control Loop for Digital Color Printing Systems. NIP21, 2005, pp. 499–504. Publisher’s record. DOI: 10.2352/ISSN.2169-4451.2005.21.1.art00044_2. Online source: https://library.imaging.org/print4fab/articles/21/1/art00044_2
19. Monga, Vishal, and Raja Bala. Two-dimensional color correction: Recent advances. CIC15, 2007, pp. 48–53. Publisher’s abstract. DOI: 10.2352/CIC.2007.15.1.art00010. Online source: https://library.imaging.org/cic/articles/15/1/art00010
20. PRINTING United Alliance. G7 System Certification; Just Announced: G7+, 2024. Online sources: https://www.printing.org/library/technical-excellence/certifications/g7-system-certification | https://www.printing.org/content/2024/01/23/what-is-g7plus
21. Sharma, Gaurav, Wencheng Wu, and Edul N. Dalal. The CIEDE2000 Color-Difference Formula: Implementation Notes, Supplementary Test Data, and Mathematical Observations. Color Research and Application, 30(1), 21–30, 2005. Paper, test data, and tools are available at the author’s site. This research supports implementation testing, not an official CIE implementation. Online source: https://hajim.rochester.edu/ece/sites/gsharma/ciede2000/
22. European Color Initiative. How to create characterization data for a printing standard — let’s make FOGRA51!, presentation, TAGA 2016. Original presentation; ECI offset conditions and profiles. Online sources: https://eci.org/lib/exe/hanno_hoffstadt_taga2016_v2.pdf | https://eci.org/doku.php_id%3Den_colorstandards_offset.html