Maths and me @ Quality Production
What is Quality printing ?
A red Apple we look at as red because 100% of red color wavelength reflected from the fruit that received by our eye is the same. All matter around us reflects their own color, when we reproduce or print the original matter image it should also reflect the same amount of wavelength light, then we consider the print quality is good, but it will not work all the time in the printing process. All human eyes are not in standard reception power too, quality is approximate matching with originals.. it can be measured with instruments and compare with the samples.
Factors that affect our print quality are;
Quality of Image source and pre-production editing work that should match with our printing standard - gamut conversion from digital to print is a difficult process.
Quality of raw materials - Paper and Ink that we choose for reproduction
Printing process type and our machine performance on that day.
Environment and time for the product to withstand - handling.
Measurements of light:
Photometry is the science of measurement of light, in terms of its perceived brightness to the human eye. Words like Luminous, Lumen, Illuminates, Illuminance, Luminance etc.. that sounds similar and we have to understand the difference.
In Printing we use spectrodensitometer to measure the quality of printing, to ensure the correct density of reproduction. Our densitometer emits its own light like CIE D50 / D65 that we call daylight luminous, measured in specific angle and aperture settings like 2° / 10°. Luminance intensity is calculated and resulted in density D using formula D = LOG ( 1 / R % ) were R is luminance reflected light from the printed copy.
Amount of reflected wavelength (႓) received by us from the matter is different from one person to another.
When light sources differ, then there will be changes in color - intensity of lumens increase then luminance record or sense a different color.
Conversion of sRGB color space to CMYK printing color space have more losses in color actually what we visualize.
This phenomena occurs in image editing and also in printing, when light sources get changed we get different perception about the quality to match original.
Monitor setting alter image quality in editing image, and light source at printing gives deviation of quality to the printer.
Drying of ink to the substrate and environmental temperature alter the paper color and thus affects print quality.
We can add up more points to justify our reasons, but technology improves more we are setback to adapt to them.
Recently I have been going through nanography printing - digital printing with full computer control machine, covers wide gamut than any other printing process. The technology they use to spread the ink to paper is amazing to see and realize we are far away to reach or learn the technology to implement. From them I understood the importance of IFT (ink film thickness) and got an idea about the quality of printing.
What we spread on substrate is to reach with enough wavelength on seeing, at that time we say quality is excellent.
Why my Newspaper can't match original quality?
Quality of paper - we use below 50 GSM paper specially called Newsprint paper, they have more pores and mostly with combination of recycled and virgin fibres. This phenomena reduce paper brightness as well as whiteness which lead to alter in color gamut.
Translucent Ink we use mainly - cold-set dry with penetration method and pigment should fill the pores of paper and then to form thin layer practically it is difficult in case of high speed printing.
We have restrictions on the supply of ink due to show through problems of substrate property, over inking affects the picture on the other side. So reduction in supply of ink shrink our color gamut. TIC total image coverage is restricted to 220 in the newspaper industry.
For simple understanding I have images below one with newspaper and other with magazine 100% black ink spread over the substrate.
Magazine
Paper Art coated ≈ 90 GSM
Screen ruling 80 l/cm
Ink gloss dry by polymerization
SID >1.25 D
Newsprint
Paper newsprint 42 GSM
Screen ruling 40 l/cm
Ink cold-set dry by penetration
SID 0.98 D
Following are some of mathematical formulas related to quality checking;
How can I find correct SID for my profile?
Paper and ink is also criteria to select our SID for CMYK, CIELab value of each colour has to match with ISO standard. Worksheet can be used for this practice as shown here.
X -axis solid density value; Y - axis ∆E from 0 to higher If colour dots closer or equal to zero - it termed as good SID value.
All CMYK colour is matched with ISO standard CIELAB values- here from the image example CMYK SID 0.80, 0.86, 0.90, 1.06 are with minimum tolerance to consider.
Dot gain :
This formula has three data 1. Solid density, 2. Tint density, 3, Percentage of tint, rearranging the Dot gain formula we can get not only the gain % but also the above three.
Let us work some calculation for dot gain - SID 1.00 D ; tint density 0.32 D ; for 40% area -
How to calculate TVI ?
TVI = (( 1-10^- tD ) / ( 1-10^-sD ) * 100 ) ; ( Gain = TVI-Dot% )
Step 1; Numerator part (N) -> 10^-0.32 =0.4786300923 = 1-0.4786300923 = 0.5213699077
Step 2; Denominator part (D) -> 10^-1.0 = 0.10 = 1 - 0.10 = 0.9
Step 3; N / D = 0.5213699077 / 0.9 = 0.5792998974
Step 4; TVI Gain% = 0.5792998974 *100 TVI = 57.92
Step 5; Apparent Dot gain = 57.92 - 40% = 17.92 = 18
Inverse the formula work to calculation for tint density - SID 1.00 D ; Dot area 17.92 ; for 40% area -
What is Tint density?
Tint Density = - Log10 ( 1-( ( ( Gain + TV% ) * ( 1-10^-sD ) ) /100 ) )
Step 5; TVI Gain % = 17.92 + 40 = 57.92
Step 4; ( ( (57.92) * 0.9 ) / 100 ) = 0.5213699077 - [were 0.9 = 1-10^-1]
Step 3 ; then ( 1 - 0.5213699077 ) = 0.4786300923
Step 2 ; - LOG10 ( 0.4786300923) = 0.32
Step 1; Now tint density is 0.32 D
follow step by step gives result, like this we can calculate SID from the same formula. For quality control we can practice this method and if we get 0.32 on tint @ 40% then we say it is on control with 18 % gain.
What is the use of re-arranging formulas of dot area?
Simple by measuring tint density we can say the solid density in the particular area and % of gain too. Let me explain you, in this picture gray tint readings are formulas and others are data. Using any three we can find the fourth component and understanding the power of formulas we can do wonders.
Can we say solid density using grey bullet at bottom of newspaper?
Bullet at right has 33 % of black dot with gain of aprox. TVI = 48.62 - 33 %= 15.62, when density of tint measured is 0.25 D, then using formula we can find the solid density in that area as below
Formula for SID = -Log10 (1- ( ( 1-10^-tD ) *100 )/( Gain + TV% ) ).
Apply this formula = - Log10 (1-((1-10^-0.25) *100) / 48.62) = 1.000703 D = 1.0 D ,
so for 33 % >> Gain 15.62 >> tint 0.25 D - we get SID as 1.0 D
For another example 40 % + Gain 18 = 58 % - SID 1.0 D, tint 0.32 D
from above 33% and 40% we are able to calculate SID and tint density as well.
From this picture can you see CMYK dots in graph, all are density data in 40% area . Density value in y axis, now doted red line show prediction based on printed solid and solid red line is the actual readings, gray line are target readings.
What this picture says? --
Yellow and black are below density - reduce water supply to balance
Our red line square dots to move closer to gray line round dots.
This picture use above dot gain formula to give graphical representation for easy understanding.
Here are some of the example picture chart when measured with two samples different density readings, from the image chart we can say the character of 40% tint in each color. Fig. A and B are having different gain value and density too, analyzing them are simple now.
Which one is good A or B - we say B is best deviation with in tolerance - Design chart and table in sheet gives you better understanding.
Simple calculation some times give visual solution to the problem. Work sheet may be designed in this manner to identify the test element and just particular entry say SID, 40% ,70% and match with ISO standard can give the result. This may be done in faster manner as our production time is crucial, time limit is less to find problem like water balance, ink leveling, substrate show through, imaging etc.. only thing is understanding and visual clearance can solve our problems. --[ In this project after entering data SID 40 and 70 % density review table shows suggestion, and we able to identify the problem as things shown as graph. ]
TVI (tonal value increase curve) :
TVI curve is used mainly to decide on what % gain is applicable to the midtone tint 40-50% usually, for example when I use 26% gain curve @ 40% tint - 1.0 D solid gives 0.40 D, were as in case of 18% gain curve @ 40% tint - 1.0 D solid gives you 0.32 D when measuring. With difference in 0.08 D we can reduce ink consumption largely. It is clear now TVI curve decide our print quality based on substrate (paper) too..
How to plot this curve?
Using following formula we can plot TVI curve ;
=a*-4*tv/100*(tv/100-1)+l*((21*tv/100*(tv/100-1)*(tv/100-0.5)))+b*((-64*tv/100*(tv/100-1)*(tv/100-0.5)^2))
- all we have formulas in internet, we have to spend time to know more about polynomial curve setting on working with this TVI curve.
Ink trapping:
Calculating ink trap is also good practice above example for Red Apple colour depend on ink trapping, yellow overlap magenta with good trapping like this chart - reproduce good CIELAB value. We can provide reference value and check quality of ink transparency to our setup.
% Trap = ( DOP - D1 ) / D2 x 100
Where: DOP = Density of 2-color overprint, D1 = Density of 1st ink down, D2 = Density of 2nd ink down.
Trap formula uses the density values measured with the complementary filter of the second down ink, you must know the printing sequence of the inks.
Print contrast curve & Hue grayness:
Like Ink trapping we can also calculate print contrast setting reference and monitor our print contrast shown in picture, all just plot data in excel and creating a report to our custom setup.