Commercial Offset/Flexo Printing, ISO 12647 Colorimetry & Pressroom Densitometry
Murray-Davies Halftone Dot Area & Dot Gain (TVI) Formula
Calculate Tint Patch Paper-Relative Reflectance R_t (%), Solid-Ink Patch Reflectance R_s (%), Murray-Davies Apparent Printed Dot Area (%A), and Tone Value Increase / Dot Gain TVI (%).
Why a 50% digital CTP plate screen prints as 66% apparent dot area—from BOTH blanket ink squeeze AND optical paper light trapping!
Pressroom spectrophotometers and reflection densitometers zeroed on unprinted paper substrate measure logarithmic Optical Density D = -LOG10(R) (so Paper-Relative Reflectance R = 10^(-D)) on a 100% Solid-Ink Control Bar Patch (`D_s`, e.g. 1.45 for Cyan/Black) and an adjacent Midtone Tint Patch (`D_t`, e.g. 0.44 on a 50% digital plate screen)! Alexander Murray and Edward Davies derived the ISO 12647 industry-standard Apparent Halftone Dot Area equation from linear reflectance partitioning between ink coverage `a` (`R_s = 10^(-D_s)`) and uninked paper `1 - a` (`R_p = 1`): `%A_MD = ((1 - 10^(-D_t)) / (1 - 10^(-D_s))) * 100`! Subtracting Nominal Digital Plate Percentage `%A_plate` yields Tone Value Increase (`TVI`, traditionally called Dot Gain = `%A_MD - %A_plate`), capturing BOTH mechanical rubber-blanket ink spread AND Yule-Nielsen internal paper photon scattering!
Verify on an ISO 12647-2 Coated-Stock Offset Press Sheet—Nominal_Plate_Tint = 50.0% (B2), Paper_Zeroed_Tint_Density D_t = 0.44 (B3 -> Tint Reflectance = 36.31% in E2), and Solid_Ink_Patch_Density D_s = 1.45 (B4 -> Solid Reflectance = 3.55% in E3): Murray-Davies Apparent Dot Area equals `((1 - 0.36308) / (1 - 0.03548)) * 100 = 66.04%` (E4), giving Midtone Dot Gain / TVI = `+16.04%` (right inside the ~14%–17% ISO coated CMYK target!, E5)!
| ISO 12647 Press Densitometry KPI (50% Plate Tint, Dt=0.44, Solid Ds=1.45) | Formula | Verified Output |
|---|---|---|
| Tint Patch Reflectance Rt (%) | (10 ^ (-Tint_Density_Dt)) * 100 | 36.31% (28.84% @ over-inked Dt=0.54) |
| Solid Ink Reflectance Rs (%) | (10 ^ (-Solid_Density_Ds)) * 100 | 3.55% |
| Murray-Davies Dot Area (%A) | ((1 - 10^(-Dt)) / (1 - 10^(-Ds))) * 100 | 66.04% (73.78% @ Dt = 0.54!) |
| Tone Value Increase / Dot Gain | Murray_Davies_Dot_Pct - Nominal_Tint_Pct | +16.04% (+23.78% muddy midtones!) |
ISO 12647 Murray-Davies Apparent Dot Area & TVI Dot-Gain Formula
Validate Nominal_Plate_Tint in (0%, 100%), Paper-Zeroed Densities 0 <= D_t <= D_s, and Solid_Ink_Density D_s in [0.50, 3.00]!
=LET(pl_t, B2, dt_n, B3, ds_l, B4, IF(OR(pl_t <= 0, pl_t >= 100, dt_n < 0, ds_l < 0.5, ds_l > 3, dt_n > ds_l), "Invalid Densitometer Input", LET(md_a, ((1 - (10 ^ (-dt_n))) / (1 - (10 ^ (-ds_l)))) * 100, ROUND(md_a - pl_t, 2))))Excess Blanket Packing / Over-Emulsified Ink Muddy Midtone Check (Set D_t = 0.54)
Over-pack the offset blanket cylinder so 50% Tint Density B3 climbs from 0.44 to 0.54: Tint Reflectance E2 drops to 28.84%, Apparent Printed Dot Area E4 balloons to 73.78%, and Midtone Dot Gain E5 spikes to +23.78%—plugging shadow detail until CTP calibration curves are adjusted!
=IF(ISTEXT(E5), E5, ROUND(((1 - (10 ^ (-B3))) / (1 - (10 ^ (-B4)))) * 100, 2))Try the example
Use the original values or change them to test your understanding.