Mixture design experiments applied for the formulation of a textile ink with reproduction of the NATO IRR green color used in military camouflage

Abstract

This paper presents the development of a mathematical model for pigment formulations used for screen printing textile inks in order to reproduce the NATO IRR green standard using four highly performant pigments: Hostaperm Yellow H4G (CI 13980), Irgazin Red A2BN (CI 65300), Heliogen Blue (CI 74160), and Lamp Black (CI 77266). In order to study the influence of each pigment on the final CIE L*a*b* parameters, a quadratic mathematical model (Scheffé type) was created and experimentally validated. The model was used and verified for generating pigment compositions for textile inks that reproduce the NATO IRR green. A total of 22 possible solutions were developed and experimentally performed. Studies regarding the reflectance in the visible-near-infrared domain were conducted, ensuring compliance with the standard. The optimal composition of the pigment mixture was 66.55% Hostaperm Yellow H4G, 7.66% Heliogen Blue, 12.01% Irgazin Red A2BN, and 13.78% Irgazin Red A2BN. The mixture was added to textile ink in the proportion of 5% and was applied via serigraphy.

Keywords

military camouflage NATO green high performance pigments design of experiments visible-near-infrared reflectance

Objects that reflect similar colors to those of the environment are considered to be camouflage. Camouflage implies deceiving or mimicking and has the role of hiding or reducing the possibility of detection. In military terminology, it represents a system that disguises both personnel and equipment against detection by the enemy. Once military forces become more advanced and sophisticated in their impact power, equipment, and weaponry, the ability to protect life and equipment through camouflage becomes increasingly important.¹

Currently, to operate against remote sensing equipment and detection systems, camouflage applies not only in the visible region, but also in a much wider area of the electromagnetic spectrum. Remote sensing is the process of obtaining information from the surrounding environment using sensors, which are not in physical contact with the studied object. Together with the detection systems, remote sensing is mainly of military use and has been widely developed, especially for the infrared (IR) domain.^2–5

The purpose of visible camouflage is to hide or distort the outline of a person or an object observed in visible light conditions. This is accomplished by reducing or eliminating the object salience against the background and by disguising its outline. The visible camouflage should correspond to the color, gloss, texture, and overall aspect of the environment. When scanning the surroundings, the human visual system seeks abnormalities in the general model, such as prey (human or animal) in the middle of the meadow vegetation or forest. To prevent detection by the enemy, adequate colors and patterns are selected in such a way that they match those present in the environment; also, the outline is distorted by using contrasting bold colors.^4,6

The first camouflage patterns were developed in 1909 by artists, using concepts such as color theory, Cubism, Impressionism, and Futurism, together with disruptive contours and abstraction to mask the subject. During the Second World War, the supplementary function of identifying friends or foes was added. Because of this, every country had to develop its own camouflage pattern.^5–8

The country-specific patterns and colors were empirically developed through extensive measurements and attempts. The national differences help distinguish between friends and foes on the battlefield. The model for temperate zone forest of the NATO military, specific for European armies, uses four colors (green, khaki, brown, and black) in a material with distorted patterns (DPM), which works best when seen on a background of bushes, swamps, or trees.^8–10

Figure 1 shows the requirements for the reflectance curves corresponding to all types of woods from the temperate zone, including the NATO-specific green.¹¹ Each of the four colors should ideally meet the specified reflectance values between 1000 and 1200 nm, as shown in Figure 1, or according to other specifications. Also, between 750 and 1200 nm, the reflectance value in IR region for the NATO green standard should be 35.5%. Moreover, the global value of the reflectance, which is integrated as a function of the imprinted area corresponding to each color, must fit in the green IRR NATO envelope, according to the following equation¹²

\begin{matrix} R_{NATOgreen} = 0.16 \times R_{black} + 0.35 \times R_{brown} \\ + 0.34 \times R_{green} + 0.15 \times R_{khaki} \end{matrix}

(1)

Figure 1.

Camouflage reflectance requirements (four color disruptive-pattern prints).

The pigments used to produce green coatings for both forest and jungle areas are selected for their capacity to mimic the reflectance properties of chlorophyll – the green pigment responsible for the characteristic color and the high IR reflectance of the vegetation.

The reflectance spectrum of chlorophyll¹¹ exhibits a maximum value near 550 nm, decreased values in the red region of the visible spectrum, and a drop in the 650–680 nm region, followed by a pronounced increase until 710 nm and steady high values over 720 nm. The camouflage coating materials used for forested areas must match this spectrum and also control the reflectance in the near-infrared (NIR) region, between 700 and 1200 nm – the most important area being 700–900 nm.¹² Here, a sharp increase up until 720 nm is required and the mean reflectance between 700 and 900 nm should exceed that in the 600–690 nm region.

To conceal the military equipment and the personnel, synthetic green pigments are incorporated in coatings. However, the conventional ones do not resemble the spectral behavior of chlorophyll in the IR region, as they absorb light rather than reflect it.

Other studies^13,14 present the use of thermochromic paints, as received or combined with inorganic substrates (graphite, kaolinite), to design different colors for the jungle vegetation model. Graphite is added to increase the thermal conductivity of the fabric, so the heat distribution and color change are faster and better in comparison with the typical thermochromic coatings. Multi-walled carbon nanotube (MWCN) particles were also added to some of the printing pastes.¹⁵ The presence of MWCNT formulations was found to cause considerable decline in the NIR reflectance, concurrently with an increase in the visible reflectance of the samples. The addition of different concentrations of TiO₂, ZnO, and Al₂O₃ nanoparticles leads to a reflectance decrease in the IR area.¹⁶ To receive an IR concealment property, the textiles can be dyed, painted, printed, coated, or treated with dyes and pigments during the melt spinning process. For radiation absorbance in the NIR spectrum, so soldiers can be hidden at night and undetectable by IR cameras, carbon black has been implemented in military uniforms for several decades.

Using an optimal content of the colored organic pigments and carbon black particles during the melt spinning operation can lead to the achievement of desirable NIR reflectance properties in poly(ethylene terephthalate) drawn filament yarns.¹⁷ Also, the existence of both black and activated carbon nanoparticles in the print paste in combination with vat or disperse dyes has a significant effect on reducing the reflection in the IR range. Also, it changes the number of color components in the printed fabrics.¹⁸

Starting from these considerations, in the present study, forest green textile inks for screen printing were formulated according to the NATO and USA standards^19–21 by the experimental mixture design, a special type of the response surface methodology (RSM). The proposed textile ink aimed at the reproduction of NATO green, which is specific to camouflage materials used for the forest vegetation of the temperate climate and implemented for both uniforms and military technique in NATO armies. By mixing, the final green textile ink was obtained using highly performant commercial pigments – yellow, blue, red, and black. Moreover, to ensure a good match with the standardized requirements, the influence of the pigment mixture over the absorbance/reflectance in the sensitive areas of the visible-near-infrared (VIS-NIR) domain was studied.

Materials and methods

All the used materials and their origin are presented in Table 1. The chemical structures of the commercial pigments used are shown in Figure 2.

Table 1.

Used materials

Material	Purpose	Commercial name	Producer
Yellow pigment (PY)	Pigment	Hostaperm Yellow H4G (CI 13980)	Clariant
Red pigment (PR)	Pigment	Irgazin Red A2BN (CI 65300)	BASF
Blue pigment (PB)	Pigment	Heliogen Blue (CI 74160)	BASF
Black pigment (PK)	Pigment	Lamp Black ((CI 77266)	Haojian
Transparent base for textile ink	Binder	Hydra Clear 77	QUAGLIA
Antifoaming agent	Additive	FoamStar SI 2210	BASF
Dispersion agent	Additive	Dispex Ultra FA 4483	BASF

The textile inks were prepared by dispersing the pigment mixture (5 g) in water (15 mL) in the presence of both dispersing (2 g) – Dispex Ultra FA4483 – and antifoaming (1 g) – FoamStar SI 2210 – agents for 60 min at 3000 rpm using the laboratory disperser Dissolver 492 L (Erichsen). Subsequently, 77 g of the transparent base (HydraClear 77) were added and the stirring was maintained for another hour. The final pigment concentration is 5%. The imprinting was done on a textile material (65% cotton, 35% polyester) using a screen printing mesh with 61–64 mesh count/cm.

The reflectance spectra were measured with an ultraviolet-visible (UV-VIS) Jasco V570 spectrometer equipped with a 60 mm integrated sphere and Spectra Manager 1 as the software. The calibration was carried out with high purity BaSO₄ (Spectralon). For measurements in standard light conditions, a portable spectrometer, Spectro-guide 45/0 (BYK) with 45/0 measurement geometry, D65 standard light system, and 10° observation angle was used.

Results and discussion

Obtaining the necessary four disruptive-type camouflage colors by mixing the already-mentioned pigments provides the advantage of a better chromatic homogeneity compared with using mono-pigmented colors. This occurs as the compatibility between absorption intensities is ensured. Using the same pigments in both military uniforms and battle technique (buildings) provides a compatibility advantage in confusing the observers. The selected pigments are characterized by very good fastness to both light and physico-chemical agents. Considering the above aspects, their use represents an advantage compared with conventional methods, where vat dyes for textiles or inorganic pigments for paints are used.

To better reproduce the standardized colors, the CIE L*a*b* trichromaticity coordinates for the samples were compared with the standards.

Color description in the CIE L*a*b* system²² is based on the following parameters: L*, which defines the lightness and varies between 0 (absolute black) and 100 (absolute white); a^∗, which measures the greenness (–a*) or the redness (+a*); b*, which measures the blueness (–b*) and the yellowness (+b*).

C_ab* (chroma, saturation) is a measure of color intensity and h_ab (hue, color angle) is the attribute of appearance by which a color is identified according to its resemblance to red, yellow, green, or blue, or a combination of two of these attributes in sequence. The cylindrical coordinates of C_ab* and h_ab are calculated from the a* and b* parameters using the following equations:

C_{ab}^{*} = (a^{* 2} + b^{* 2})^{1 / 2}

(2)

h_{ab} = tan^{- 1} (b^{*} / a^{*})

(3)

CIE parameters (L*, a*, b*) were determined using a portable spectrometer Spectro-guide 45/0 equipped with a D65 illuminant and an observer angle of 10°.

Furthermore, to ensure the requirements for the sensitive areas of VIS and NIR light, the reflectance spectra for the 400–1200 nm domain were measured. Figure 3 shows the reflectance spectra and the CIE L*a*b* coordinates values of the used pigments. The analysis of the four spectra shows that yellow pigment (PY), blue pigment (PB), and red pigment (PR) exhibit a 70% reflectance in the 800–1200 nm area, while black pigment (PK) has an extremely low reflectance on the entire spectral domain, of only 5%. The CIE L*a*b* coordinate values are in accordance with the perceived colors. Based on these considerations, it is necessary to emphasize the influence of each pigment on the final mixture. Thus, to achieve a good reproduction of the standardized color, a mathematical model that correlates the final pigment blend with the CIE parameters (L*, a*, b*) of the individual pigments was generated.

Figure 2.

Structures of the commercial pigments used in formulations.

Figure 3.

Reflectance spectra of the four used pigments.

Design of experimental model for pigment mixing

A systematic approach to apply statistical methods in experimental processes in order to improve input–output factors and process parameters is represented by the experimental design. It is commonly used as a methodology for selecting the levels of independent factors, which provides the least variation on the required quality. In statistics, RSM explores the relationship between explanatory variables and one or more response variables. A statistical model is a description of a relationship between these variables in the form of mathematical equations. RSM reduces the number of experimental trials required in multi-factor experiments. In addition, depending on the preferences of the experimenter about the increments of the input parameters, the relevant responses can be optimized by considering criteria such as most desired value (the target value), maximization or minimization. RSM is an effective method for analyzing and determining effects in multi-factor experiments.

Mixture design, a special type of RSM, is a very effective method to establish the ratio of variables (components) in a blend.²³

A q-component mixture is shown in the following equation

0 \leq x_{i} \leq 1 i = 1, 2, \dots, q \sum_{i = 1}^{q} x_{i} = 1

(4)

Simplex-lattice designs consist of all the feasible combinations of the mixing proportions wherein each proportion comprises the values (0, 1/m, 2/m,…,m/m = 1) for a given integer parameter m > 1. The response in a mixture experiment is usually described by a polynomial function, which represents how the components affect the response.

Scheffé proposed the use of {q, m} symmetric canonical polynomial models obtained by reparameterization of standard polynomials of degree m for q components by using Equation (4).²³ The quadratic Scheffé polynomials for response E(y) of the mixtures are

E (y) = \sum_{i = 1}^{q} β_{i} x_{i} + \sum_{i \neq j}^{q} β_{ij} x_{i} x_{j}

(5)

In the experimental design, the concentration of each pigment (A = %PY, B = %PB, C = %PR, D = %PK) was used within the limits: 0% (lower limit) and 100% (upper limit) with the condition: %PY + %PB + %PR + %PK = 100. The selected responses were the CIE coordinates values L*, a*, and b*. A total of 20 runs of pigment formulations, based on the simplex-lattice method, were generated and randomized by the software program (DESIGN EXPERT 11-)²⁴ – see Table 2. The quadratic polynomial equation (Scheffé-type model) was fitted to the data collected at each experimental point. The predicted equation for each parameter was obtained and contour plots were generated. The positive and negative coefficients represent a synergistic and an antagonistic effect, respectively.

Table 2.

Experimental design for CIE L*a*b* coordinates along with experimental and predicted responses for pigment compositions

Run	PY	PB	PR	PK	L*	a*	b*	L*	a*	b*
Run	%	%	%	%	(prediction)			(experimental)
1	62.50	12.50	12.50	12.50	37.12	–6.89	6.56	37.02	–5.58	6.47
2	0.00	0.00	100.00	0.00	48.30	46.25	13.61	48.10	46.44	14.97
3	12.50	62.50	12.50	12.50	34.23	–17.14	–18.74	32.91	–17.11	–19.66
4	25.00	25.00	25.00	25.00	26.88	–5.34	–7.58	25.64	–4.18	–8.46
5	0.00	0.00	50.00	50.00	27.16	1.76	1.81	28.00	0.96	2.40
6	50.00	50.00	0.00	0.00	43.17	–37.61	–11.27	44.01	–38.41	–10.67
7	100.00	0.00	0.00	0.00	63.88	–5.77	47.49	63.68	–7.59	47.35
8	0.00	100.00	0.00	0.00	44.25	–18.94	–37.62	46.19	–18.74	–36.26
9	50.00	0.00	50.00	0.00	41.24	29.21	9.32	41.50	28.81	9.63
10	0.00	100.00	0.00	0.00	44.25	–18.94	–37.62	46.19	–18.74	–36.26
11	0.00	50.00	0.00	50.00	33.89	3.74	0.10	27.08	2.97	0.68
12	12.50	12.50	62.50	12.50	33.08	15.37	–0.36	32.99	15.48	–1.34
13	0.00	50.00	50.00	0.00	33.74	–4.81	–12.00	34.58	–5.31	–16.73
14	100.00	0.00	0.00	0.00	63.88	–5.77	47.49	63.68	–7.59	47.35
15	50.00	0.00	50.00	0.00	41.24	29.21	9.32	41.50	28.81	9.63
16	0.00	0.00	0.00	100.00	23.54	0.84	2.83	25.48	–0.96	2.68
17	0.00	0.00	100.00	0.00	48.30	46.25	13.61	48.10	46.44	14.97
18	0.00	0.00	0.00	100	23.54	0.84	2.83	25.48	–0.96	2.68
19	12.50	12.50	12.50	62.50	21.19	–1.77	–3.64	19.87	–0.54	–3.66
20	50.00	0.00	0.00	50.00	18.29	–2.46	–5.14	19.13	3.84	–4.77

PY: yellow pigment; PR: red pigment; PB: blue pigment; PK: black pigment.

An analysis of variance (ANOVA) of the mixture design for CIE coordinates are presented in Tables 3–5 for L*, a*, and b*, respectively. The data show that, for the regression model, both the lack of fit and the Fisher (F) test (p < 0.05) are significant. The fineness of the model was evaluated using the determination coefficient R². In the case of L, the determination coefficient (R²= 0.9779) indicated that 2.21% of the total variation is not explained by the model. The adequate precision used to measure the signal-to-noise ratio is supposed to be greater than 4. In this case, the value of 27.01 revealed that the empirical model is of an adequate signal and can be used to navigate the design space. The adjusted and predicted coefficients of this model are 0.9618 and 0.9246, respectively.

Table 3.

Analysis of variance for the quadratic model for Response 1: L*

Source	Sum of squares	df	Mean square	F-value	p-value
Model	3078.46	8	384.81	60.78	<0.0001	Significant
Linear mixture	1902.47	3	634.16	100.17	<0.0001
%PY · %PB	108.23	1	108.23	17.09	0.0017
%PY · %PR	313.63	1	313.63	49.54	<0.0001
%PY · %PK	589.20	1	589.20	93.06	<0.0001
%PB · %PR	143.12	1	143.12	22.61	0.0006
%PR · %PK	69.97	1	69.97	11.05	0.0068
Residual	69.64	11	6.33
Lack of fit	69.64	6	11.61
Corrected total	3148.10	19

Table 4.

Analysis of variance for the reduced quadratic model for Response 2: a*

Source	Sum of squares	df	Mean square	F-value	p-value
Model	8725.42	8	1090.68	199.71	<0.0001	significant
Linear mixture	6899.10	3	2299.70	421.09	<0.0001
%PY · %PB	581.83	1	581.83	106.54	<0.0001
%PY · %PR	114.43	1	114.43	20.95	0.0008
%PB · %PR	313.22	1	313.22	57.35	<0.0001
%PB · %PK	148.58	1	148.58	27.21	0.0003
%PR · %PK	433.00	1	433.00	79.29	<0.0001
Residual	60.07	11	5.46
Lack of fit	60.07	6	10.01
Corrected total	8785.49	19

Table 5.

Analysis of variance for the reduced quadratic model for Response 3: b*

Source	Sum of squares	df	Mean square	F-value	p-value
Model	8643.96	8	1080.49	352.48	<0.0001	Significant
Linear mixture	6786.15	3	2262.05	737.93	<0.0001
%PY · %PB	239.38	1	239.38	78.09	<0.0001
%PY · %PR	640.30	1	640.30	208.88	<0.0001
%PY · %PK	843.06	1	843.06	275.02	<0.0001
%PB · %PK	278.16	1	278.16	90.74	<0.0001
%PR · %PK	37.46	1	37.46	12.22	0.0050
Residual	33.72	11	3.07
Lack of fit	33.72	6	5.62
Corrected total	8677.68	19

For a*, the determination coefficient R² is 0.9932, the adequate precision 53.49, and the adjusted and predicted coefficients of the model are 0.9882 and 0.9779, respectively. Furthermore, for b*, the determination coefficient R² is 0.9961, the adequate precision 72.46, and the adjusted and predicted coefficients of the model are 0.9933 and 0.9874, respectively.

Moreover, the experimental design obtained using the simplex-lattice method was fitted and can be explained by the subsequent first-order polynomial equations

\begin{matrix} L^{*} = 0.638807 \times % PY + 0.442454 \times % PB + 0.48301 \\ \times % PR + 0.235367 \times % PK - 0.00435782 \times % PY \\ \times % PB - 0.0059412 \times % PY \times % PR - 0.0101678 \\ \times % PY \times % PK - 0.00501135 \times % PB \times % PR \\ - 0.00350389 \times % PR \times % PK \end{matrix}

(6)

\begin{matrix} a^{*} = - 0.0576988 \times % PY - 0.18937 \times % PB + 0.462513 \\ \times % PR + 0.00842651 \times % PK - 0.0101041 \times % PY \\ \times % PB + 0.00358948 \times % PY \times % PR - 0.00738716 \\ \times % PB \times % PR + 0.00511426 \times % PB \times % PK \\ - 0.00871658 \times % PR \times % PK \end{matrix}

(7)

\begin{matrix} b^{*} = 0.474877 \times % PY - 0.376166 \times % PB + 0.136071 \\ \times % PR + 0.0282955 \times % PK - 0.00648107 \times % PY \\ \times % PB - 0.00849093 \times % PY \times % PR - 0.0121194 \\ \times % PY \times % PK + 0.00699767 \times % PB \times % PK \\ - 0.00256365 \times % PR \times % PK \end{matrix}

(8)

where %PY, %PB, %PR, and %PK are percent concentrations of pigments PY, PB, PR, and PK, respectively, in the final pigment mixture.

The model had been optimized for achieving the NATO IRR green CIE values²⁵ (L* = 36.98, a* = –2.11, b* = 8.04 – sample from the Romanian Army) with a tolerance range of ±1. Figure 4 shows the concentration influence of the four pigments on the CIE L*a*b* coordinates, which were obtained based on the regression model.

Figure 4.

Influence of the component pigments concentration over the CIE L^*a^*b^* parameters.

The analysis of the L* coordinate shows that the most significant positive influence is due to PY. To reach the high values required by the optimal case, a high concentration of PY is needed. Low concentrations of PK lead to important alterations of the L* parameter, while PB and PR finely adjust its final value. For the a* coordinate, PR has the highest influence, whereas, for the b* coordinate, PY and PB have the highest positive and negative influences, respectively.

Experimental validation of the model and generation of the NATO IRR green standard pigment formulations

The model was used and verified for generating pigment compositions for textile inks that reproduce NATO IRR green. A total of 22 possible solutions were generated and experimentally performed. The samples were analyzed spectrally with the determination of the CIE L*a*b* coordinates. The obtained data are presented in Table 6. To verify the experimental model, the total color difference (ΔE_prd*) was calculated using the following equation²⁶

Δ E_{prd}^{*} = \sqrt{(L^{*} - L_{pr}^{*})^{2} + (a^{*} - a_{pr}^{*})^{2} + (b^{*} - b_{pr}^{*})^{2}}

(9)

where L*, a*, and b* are the CIE values determined experimentally; L_pr*, a_pr*, and b_pr* are the CIE values calculated according to the mathematical model.

Table 6.

Comparison between the CIE L*a*b* model prediction and the experimental determination of given pigment compositions

Sample	PY	PB	PR	PK	Model prediction			Experimental determination			ΔE_pr	ΔE_std	ΔC_std	Δh_std
Sample	%	%	%	%	L_pr*	a_pr*	b_pr*	L*	a*	b*	ΔE_pr	ΔE_std	ΔC_std	Δh_std
GR-1	63.60	8.80	13.80	13.80	36.58	–3.28	7.81	2.87	–1.89	4.22	2.70	2.87	–1.89	4.22
GR-2	63.60	8.83	13.78	13.79	36.59	–3.32	7.80	3.36	1.33	18.06	2.12	3.36	1.33	18.06
GR-3	64.46	8.14	12.76	14.64	36.44	–3.37	8.23	3.26	–1.93	4.57	3.25	3.26	–1.93	4.57
GR-4	66.55	7.66	12.01	13.78	37.61	–3.48	9.85	0.68	–0.52	1.10	2.73	0.68	–0.52	1.10
GR-5	65.87	9.15	14.27	10.71	38.96	–3.35	9.94	35.49	–5.17	8.13	4.32	3.40	1.32	17.75
GR-6	61.48	8.54	13.32	16.67	34.49	–3.27	5.92	36.03	–4.75	7.13	2.45	2.95	0.25	19.00
GR-7	66.58	9.98	12.86	10.58	39.39	–4.93	10.19	34.66	–3.36	5.53	6.82	3.64	–1.84	16.60
GR-8	68.37	8.96	11.55	11.12	39.78	–4.94	11.46	34.58	–3.34	6.23	7.54	3.24	–1.24	13.46
GR-9	67.50	10.54	13.57	8.39	40.89	–5.04	11.25	37.08	–3.98	6.10	6.49	2.70	–1.03	18.43
GR-10	70.23	7.48	8.78	13.51	39.25	–5.39	12.38	36.97	–2.94	7.18	6.19	1.20	–0.56	7.55
GR-11	70.63	7.57	9.75	12.05	40.16	–4.93	13.07	36.47	–3.06	7.03	7.31	1.47	–0.64	8.81
GR-12	71.25	8.15	10.50	10.11	41.47	–5.03	13.95	37.12	–3.60	7.57	7.85	1.57	0.07	10.74
GR-13	69.6	9.8	15.2	5.4	43.30	–3.44	13.79	41.82	–3.98	7.54	6.45	5.21	0.21	13.11
GR-14	58.44	14.67	9.78	17.11	33.97	–9.33	2.85	33.36	–5.13	2.93	4.24	6.95	–2.40	45.56
GR-15	74.01	6.53	7.66	11.79	41.73	–5.47	15.85	30.97	–2.17	5.87	15.03	6.38	–2.05	5.58
GR-16	75.50	6.16	7.22	11.12	42.76	–5.50	17.29	35.14	–2.44	7.42	12.84	1.97	–0.51	3.47
GR-17	53.72	16.33	10.89	19.06	31.96	–9.29	–0.03	32.66	–4.71	2.00	5.06	7.87	–3.20	52.29
GR-18	76.84	5.82	6.83	10.51	43.71	–5.53	18.63	36.18	–2.60	8.98	12.58	1.33	1.04	1.45
GR-19	49	18	12	21	30.24	–9.17	–2.46	32.92	–4.34	1.05	6.54	8.39	–3.85	61.69
GR-20	45	18	15	22	29.02	–7.49	–3.79	30.00	–3.96	1.02	6.05	10.07	–4.22	60.85
GR-21	48.00	18.00	11.00	23.00	29.35	–9.28	–3.04	31.43	–4.32	1.54	7.07	8.83	–3.73	55.67
GR-22	47.47	16.16	11.11	25.25	28.24	–7.99	–3.15	29.93	–3.68	1.48	6.55	9.76	–4.35	53.39

PY: yellow pigment; PR: red pigment; PB: blue pigment; PK: black pigment.

To select the best options for generating the NATO green standard, the total color difference, ΔE_std*, as a function of the CIE L*a*b*, coordinates was calculated according to the following equation:

Δ E_{std}^{*} = \sqrt{(L^{*} - L_{st}^{*})^{2} + (a^{*} - a_{st}^{*})^{2} + (b^{*} - b_{st}^{*})^{2}}

(10)

where L*, a*, and b* are the CIE values determined experimentally; L_st* = 36.98, a_st* = –2.11, and b_st* = 8.04 are the CIE values for the standard.

To ensure the best color reproduction, a comparison against the standard was performed according to the chroma (ΔC_std) and hue (Δh_std) differences as follows

Δ C_{std} = C - C_{std}

(11)

Δ h_{std} = h - h_{std}

(12)

where C and h correspond to the sample; C_std = 8.31 and h_std = 104.7⁰ correspond to the NATO IRR green standard calculated with Equations (2) and (3).

The data analysis considering the validity of the mathematical model shows few color differences between the experimental values and the estimated ones. Regarding the correlation between the model-offered solutions and the standard, there are several variations that afford acceptable values for ΔE_std*, ΔC_std, and Δh_std. These are represented in Figure 5 as color difference coordinates.

Figure 5.

Pigment formulations suitable for reproducing the NATO IRR green standard (representation in a CIE L^*a^*b^* color difference plot).

The best results regarding the concordance with the CIE L*a*b* coordinates of the NATO green standard were for sample GR-4. Besides this, several formulations are within the tolerance (ΔE_std* < 3.5 and ΔC_std < 2), which implies color detection by a trained eye.²⁷

Spectral analysis of the obtained pigment formulations

As stated earlier, an important factor about camouflage dyes and pigments used for masking both equipment and personnel is the spectral behavior in the VIS and NIR domains. Also, a precise reproduction of the vegetation reflectance curve is required. The reflectance spectra of the samples were analyzed using a JASCO UV-VIS-NIR V570 spectrometer. Only samples satisfying the CIE L*a*b* coordinates were further analyzed, and these are presented in Figures 6 and 7.

Figure 6.

Visible-near-infrared reflectance spectra of the pigment formulations for the reproduction of the NATO green standard (samples GR-1, GR-3, GR-6, GR-9, GR-10, GR-12).

Figure 7.

Visible-near-infrared reflectance spectra of the pigment formulations for the reproduction of the NATO green standard (samples GR-4, GR-8, GR-11, GR-16, GR-18).

The targeted criterion was ensuring the reflectance enclosure in the IRR NATO envelope. Data analysis shows that all the samples are in the required reflectance limits for the 400–750 nm domain. Moreover, with a few exceptions, all the reflectance spectra show favorable values for the 800–1200 nm region. As expected, in the NIR area, the reflectance is influenced by the quantity of PB used in the pigment compositions; a high amount leads to a significant reflectance decrease, which makes the enclosure in the IRR NATO envelope difficult.

Samples GR-4 and GR-10 are the formulations that ensure an accurate color and VIS-NIR reflectance reproductions.

The developed mathematical model provides suitable formulations for the NATO green standard reproduction, while respecting the VIS-NIR reflectance criteria. Also, it can be used to reproduce the other colors required for the disruptive-type military camouflage.

Conclusion

Pigment formulations for screen printing textile inks for the reproduction of the NATO green standard used in military camouflage were developed by mixing four highly performant pigments.

A mathematical model was created to generate accurate compositions that satisfy the three CIE L*a*b* parameters of the standardized color. The model was experimentally validated, noting a good predictability of the proposed solutions.

Spectral analyses of the pigment formulations were performed, ensuring the reflectance enclosure in the IRR NATO envelope. Data analysis showed the viability of the proposed solutions in both theoretical and experimental studies. Using high-performance pigments and screen printing, a suitable dyeing considering both chromatic homogeneity and superior resistance was achieved.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Romanian Ministry of Research and Innovation, CCCDI – UEFISCDI (project number PN-III-P1_PCCDI-2017-0395/70-PCCDI- CBRN Hazard contingency and means of improving the National Security (SECURE_NET)”- component project 5 – “Multispectral camouflages consisting of chromogenic -polymer systems-MULTICAM”, within PNCDI III).

ORCID iDs

Aurelian Cristian Boscornea

Aurel Diacon

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