1 Introduction

Additive manufacturing, also known as 3D printing, is an expanding technology with diverse applications across sectors, including industry [1], medicine [2], and construction [3]. It comprises various techniques, each utilizing specific materials such as concrete or UV-curable resins, depending on the chosen technique [4, 5]. Many common 3D printing techniques are monochromatic, producing outputs of a single color.

However, certain 3D printing methods, for example Poly-Jet 3D printing, enable multi-color output. In Poly-Jet 3D printing, multi-color samples are generated through the halftoning of Cyan-Magenta-Yellow-Black (CMYK) inks onto the object surface. CMYK halftoning is employed because it allows the generation of a wide range of colors and shades using a limited set of primary inks [6]. The capability for multi-color 3D printing has led to the development of Graphical 3D printing, where the main goal is to reproduce the material appearance of a given object [7]. This has been found to have applications in several areas, such as industrial manufacturing [8], medical prosthetics [9, 10], and cultural heritage [11].

Material appearance is determined by several attributes, with color, gloss, translucency, and texture being primary [12]. In graphical 3D printing, accurate material appearance reproduction depends on object geometry, surface characteristics, and the properties of the inks used. Furthermore, interactions between appearance attributes are significant, and the alteration of one attribute can noticeably affect others [13, 14].

Color has been identified as a highly important attribute for evaluating object appearance [12, 15]. Consistent and accurate color reproduction is essential for high-quality 3D reproduction, and this can be achieved through device characterization. Device characterization provides a method for understanding the color reproduction behavior of a 3D printer. This is typically accomplished by establishing a transformation between device-dependent (e.g., printer CMYK) and device-independent (e.g., CIELAB, hereby referred to by its axes names, L*a*b*) color spaces [16]. These transformations are often defined using ICC profiles [17].Footnote 1

Device characterization in 3D printing is influenced by substrate and ink types [6], with ink properties being critical for color output. In traditional painting techniques, color manipulation has long involved layering and substrate considerations. Oil painters, for example, use underpainting, often with white or earth tones, to influence the final color, where the thickness of translucent color glazes over a white underpainting creates luminous effects, and thicker applications produce saturated colors. The opacity and translucency of oil paints, combined with layering, allow artists to control color and achieve depth [18, 19]. Similarly, acrylic paints, which also exhibit varying degrees of translucency, are often applied over a white primer like gesso to manage the substrate’s influence. In acrylic painting, as with oil, layering is crucial, and underlying colors affect subsequent layers [20, 21]. These historical techniques demonstrate that interactions between underlying materials, layering, and translucency are fundamental to color reproduction. While 3D printing employs different materials, it still employs the same layering process using white ink as a substrate, which means that these principles are still highly relevant for 3D printing applications.

Therefore, as 3D printer inks exhibit variations in optical properties, particularly translucency and scattering, the printing process should be adapted based on material characteristics. As demonstrated in [22], accurate color reproduction in 3D printing can be achieved by optimizing error diffusion halftoning to incorporate the translucency properties of the ink. Translucent inks can introduce color errors due to layer variations and printing inaccuracies, which can affect the 3D color characterization process.

One of the notable aspects that influence the final 3D-printed object’s color reproduction is its size. This relates to how Poly-Jet 3D printers operate. Unless specified otherwise by the user, they print only the outermost layer (approximately 0.5 mm from the surface) of the 3D object using colored inks. The rest of the 3D-printed object is, by default, filled with white ink. However, it can also be filled with any other ink used by the printer if specified by users. Hereby, the white ink filling is referred to as “white core” in this paper. Similar to the colored inks used in 3D printing, white ink also shows varying intrinsic characteristics, both in translucency and scattering. Consequently, white ink induces light loss, due to scattering, when light travels through it. That’s one of the reasons why the size of the white core matters in color determination because of the altering of light interactions that take place in said core. Therefore, white ink characteristics and white core size are important factors that can affect the final color of a 3D-printed object. This effect is visible when using translucent inks, as light travels through the colored ink layers to reach the white core, creating more light interactions with the ink and white core. This interaction affects the final appearance in terms of the color of the printed object.

We hypothesize that varying the white core thickness along with the translucent-colored ink layers will have an impact on the final color of the 3D-printed objects. This entails that color correction needed for the 3D objects printed with varying white core thickness and translucent ink layers will require different characterization profiles, hereby referred to as ‘color profiles’ in this paper, depending on the 3D object size and the white core thickness when printed using translucent inks.

The objectives of this work are to study the change in color as a function of varying white core thickness in the 3D-printed objects and to improve the methodology used for color characterization of 3D printers by taking into consideration the object thickness as a variable. This enhanced methodology will result in improved color output for applications utilizing color 3D printers.

First, we present the details related to the 3D printing process followed in this study, along with the color measurements and testing, in Section 2. We present the results of our color characterization and discuss its performance in Sections 3 and 4, respectively. Finally, we conclude the study with a summary of our findings presented in Section 5.

Fig. 1
figure 1

The printed output when using VeroTM family of inks: each of these printed cubes is made purely of one of the inks in the VeroTM family. The printed cubes are glossy and translucent

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2 Methodology

2.1 3D printing

To print the samples required for this study, we used a Poly-Jet Full-Color 3D printer, the Stratasys J55 [23]. The J55 has a resolution of 300 DPI (Dots-Per-Inch) in the [X, Y] axes and 1354 DPI in the Z-axis, which translates to voxels that are 0.08 × 0.08 × 0.018 mm in size. The colored inks used by the J55, and consequently in this study, are part of the VeroTM family of inks consisting of CMYKW inks, with SUP710TM as support material. The inks of this family are called: VeroPureWhiteTM, VeroBlackPlusTM, VeroCyanVTM, VeroMagentaVTM, and VeroYellowVTM. These inks, shown in Fig. 1, are characterized by a translucent and glossy appearance. The white ink, VeroPureWhiteTM, is also translucent and scattering, matching the intrinsic properties in our hypothesis. While the precise chemical composition of the inks used in our study is proprietary to Stratasys, it is important to discuss the general characteristics of inks used in PolyJet 3D printing. These inks are typically photopolymers, which are cured by UV light. They consist of a mixture of monomers, oligomers, photoinitiators, and colorants (pigments or dyes). The colorants, whether pigments or dyes, play a crucial role in determining the ink’s color, translucency, and scattering properties. Pigments are solid particles that are dispersed in the ink, while dyes are soluble colorants. The concentration, particle size, for pigments, and the refractive index of the colorants and the surrounding medium influence the ink’s translucency and scattering behavior, which interacts with the white core and affects the final color. [24]

Fig. 2
figure 2

Steps of the 3D design process of the different TCs used in the study

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Fig. 3
figure 3

Printed output: a a stack of TCs with different white core thicknesses and b color output for 2 TCs of different white core thicknesses: 1 mm (Left) and 4.69 mm(Right). The color shift is apparent in columns A,B,Q, and R

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We designed eight 3D samples with varying white core thicknesses while maintaining the default number of colored layers where all the inks are used, as opposed to the white core where only white ink is used. The colored layers are 0.5 mm in thickness, which translates to 27 layers with the J55 resolution. The X-Rite RGB 2.83 Test Chart(TC), comprising of 294 color patches, was used. This TC is 14.7 * 10.3 cm and can fit on the J55 printing tray. Dividing the TC into small parts and placing them at different locations of the rotary tray may introduce printing variations that may affect the color reproduction as shown in [25], which is why we keep its original size.

To create the 3D models with the color TC incorporated, we use Blender 3.0. In Blender, we create cuboids of the same length and width as the TC. The only variable between the cuboids is their height, which will translate, when 3D-printed, into different white core thicknesses. In total, 7 cuboids were created, with heights ranging from 1 to 4 mm with a step of 0.5 mm, plus one cuboid at a height = 4.69 mm, making 8 cuboids in total. The cuboids were then exported as *.OBJ files, with the texture being provided in a separate *.MTL file containing a *.PNG image of the TC as color input. The color input to the 3D printer is in the RGB color space.

We 3D-print each sample with two different finishes: matte and glossy. Therefore, 16 TCs were printed: 8 matte and 8 glossy. The process of preparing the TC for the study and an example of the print is illustrated in Figs. 2 and 3.

2.2 Measurements

The printed color patches on each TC were measured using two measurement devices: a hyperspectral camera, HySpex VNIR-1800, and a handheld spectrophotometer, X-Rite I1Pro, otherwise referred to as X-Rite EyeOne Pro. The HySpex VNIR-1800 hyperspectral camera has 186 bands covering the visible and VNIR spectral range (400 to 1000 nm wavelengths, with a step of approximately 3 nm). The 45:0 measurement geometry was used with the HySpex instrument. The cuboids were illuminated using two halogen lamps, as shown in Fig. 4. The X-Rite EyeOne Pro uses a D50 illuminant at 2°observer and 0:45 measuring geometry. Cuboids with a thickness of less than 2.5 mm were measured using an automation table, the X-Rite I1-IO table, to automate the measurements. The X-Rite I1-IO can measure samples with a thickness of less than 2.5 mm only, and therefore, the cuboids with higher thicknesses were measured manually using the X-Rite EyeOne Pro. Figure 5 shows the X-Rite I1-IO automation table used for the measurement of the cuboids having a thickness less than 2.5 mm. We refer to each measurement set by the name of the device used for the color measurements: the EyeOne set and the HySpex set.

Fig. 4
figure 4

HySpex camera setup: a Illustration with the different components of the setup and b TCs positioning in the laboratory setup

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Fig. 5
figure 5

X-rite EyeOne setup in the iO table

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The color of an object’s surface can be determined using the spectral reflectance from the object surface, as the latter holds information relating to the intrinsic properties of a surface. The spectral range we require to measure color is the visible spectral range between 400 and 800 nm. Spectral reflectance is the ratio of the reflected radiance to the incident radiance, giving a normalized measure of how reflective a surface is.

Both the X-Rite EyeOne Pro and the HySpex camera measure the spectral radiance as the sample surface. The output of X-Rite EyeOne Pro is spectral reflectance, which is calculated using the measured spectral radiance at the sample surface and the spectral radiance measured of a reference white surface (white calibration tile) after normalizing the measurements to a white calibration tile. HySpex Camera, however, outputs the spectral radiance measured at the sample surface. Spectral reflectance of the cuboid surface is therefore calculated using Eq. 1

$$\begin{aligned} \rho (\lambda ) = \frac{L(\lambda ) \cdot I_{Reference}(\lambda )}{L_{MeasuredWhite}(\lambda )} \end{aligned}$$
(1)

In Eq. 1, \(L(\lambda )\) is the spectral radiance measured at the cuboid surface, \(I_{Reference}(\lambda )\) is the spectral reflectance of the reference white surface used as a calibration tile, \(L_{MeasuredWhite}(\lambda )\) is the spectral radiance measured at the calibration tile surface, and \(\rho (\lambda )\) is the spectral reflectance at the cuboid surface. CIEXYZ tristimulus values are calculated using Eq. 2.

$$\begin{aligned} X= & \frac{1}{N}\sum \nolimits _{\lambda }\rho (\lambda )I(\lambda )\bar{x}(\lambda ), \hspace{4.5mm} Y = \frac{1}{N}\sum \nolimits _{\lambda }\rho (\lambda )I(\lambda )\bar{y}(\lambda ), \nonumber \\ Z= & \frac{1}{N}\sum \nolimits _{\lambda }\rho (\lambda )I(\lambda )\bar{z}(\lambda ), \hspace{4.5mm} N = \sum \nolimits _{\lambda }I(\lambda )\bar{y}(\lambda ), \end{aligned}$$
(2)

In Eq. 2, \(I(\lambda )\) is the spectral power distribution of the illuminant, \(\bar{x}, \bar{y}\), and \(\bar{z}\) are the CIE color matching functions as defined in [26]. N is a scaling factor that guarantees that the maximum value for CIEXYZ Y is 1.0 [26] and \(\rho (\lambda )\) is the spectral reflectance at the cuboid surface measured using the X-Rite EyeOne Pro and calculated using Eq. 1 using the HySpex measurements. For the Hyspex camera measurements, we take into account an averaged spectral reflectance from an area of 5*5 pixels for each color patch. L*a*b* values are then calculated using the CIEXYZ values for each color patch on the cuboid according to [26].

According to [27], measurements performed using the X-Rite EyeOne Pro can be unsuitable for color measurements for 3D objects printed using translucent and/or light-scattering ink material. With such type of ink, light transport can be unpredictable with light existing at the surface outside the measurement aperture of the X-Rite EyeOne Pro handheld spectrophotometer instrument, given the small illumination and measurement aperture. This loss of light may result in a lower value of the measured radiance, which in turn may lead to erroneous reflectance measurements. The illumination aperture of X-Rite EyeOne Pro is 8 mm, and the measurement aperture is 2 mm. To add certainty to the results and avoid the small illumination and measurement aperture size limitation from the X-Rite EyeOne Pro instrument, we measured the cuboids using the Hyspex setup. The Hyspex setup uses a hyperspectral camera that records an image of the object, which makes the acquisition process fast. On the contrary, for samples with a thickness greater than 2.5 mm, the X-Rite I1 EyeOne Pro needs to be used in manual mode, thus having to perform approximately 2350 measurements of the color patches in the TC cuboids. This becomes time-consuming and error-prone.

Fig. 6
figure 6

Mean color difference between TC pairs of consecutive thicknesses. Each point on the X-axis corresponds to a pair of TCs of neighboring thicknesses, e.g., [1:1.5] mm shows the comparison between TCs 1 and 1.5 mm

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Also, the HySpex offers a higher level of convenience when doing the measurements as it allows for the spectral data acquisition of multiple TCs wholly in one image. This, along with the possible automation of the spectral reflectance extraction, can make data analysis significantly faster. Indeed, the EyeOne requires manual measurements for thicker TCs (2.5mm onwards), meaning that every color patch of every TC must be measured individually. In the present case, this means that the measurements have to be performed on 2352 color patches manually. The task becomes even more tedious for larger TCs with more color patches, this can become absurdly time-consuming. So, the HySpex can offer a more convenient alternative for the color measurements and the subsequent data analysis.

ICC color profile [17] was generated using the obtained measurements and X-Rite Profile Maker v.5.0.5 for each TC cuboid printed at different core thicknesses. From these measurements, we generate color profiles for each TC thickness using the X-Rite ProfileMaker v.5.0.5. This results in 16 profiles for each set of measurements, making the number of generated profiles equal to 32. We also generate, for each measurement set, an ICC profile encompassing all data for all TC thicknesses for the two types of finishes, matte and glossy. These general profiles were generated by averaging the values measured over all the thicknesses for each color patch. This brings the total number of ICC profiles generated to 36: 16 generated using the measurements from the X-Rite EyeOne Pro spectrophotometer, and 16 using the measurements from the HySpex setup. Two generalized ICC profiles were generated by averaging the measurements from the X-Rite EyeOne Pro instrument (one for matte finish and one for gloss finish object), and two using the average measurements from the HySpex setup.

We evaluate these ICC profiles using the roundtrip test for transformation accuracy. In a roundtrip test, the measured L*a*b* values for each TC are converted to a device-dependent color space (sRGB in this case) by applying the B-to-A transform with a media-relative colorimetric rendering intent from the ICC color profile that was generated using the corresponding white core thickness. The obtained RGB values are transformed back into L*a*b* using the A-to-B color transform from the same ICC color profile and the same rendering intent. The final output is a set of L*a*b* values that should ideally be the same as the input L*a*b* [28]. The difference between these two sets of values, measured using CIEDE2000 [26], is an indicator of the color error induced when the B-to-A and A-to-B transforms of the corresponding ICC color profile are applied. This colorimetric error might be caused by insufficient data from the measurements or a limited measurement dataset (total number of color patches in the TC) to train the ICC color profile transformation when generating the ICC color profiles. The round-trip test helps to verify whether the number of color patches in our selected TC is sufficient enough to generate an accurate ICC color profile.

3 Results

Figures 6 and 7 illustrate the color difference (CIEDE2000) between the TCs printed with different white core thicknesses and the distribution of CIEDE2000 for all TC color patches, respectively. The color difference in Fig. 6 was calculated for the same color patch of between two TCs of consecutive thicknesses, whereas the color difference in Fig. 7 is that of the measured color values with the reference RGB values of the patches provided by the manufacturer. The color gamut is calculated in the L*a*b* color space using the obtained measurements to see the effect on color reproduction as a function of the white core thickness in the 3D-printed objects. Figure 8 shows the calculated color gamut in the L*a*b* color space of the TC cuboids printed with matte and gloss finishes and measured using both measurement setups. Figure 8 showcases the evolution of the color output seen for each measurement device and finish type. Figures 9, 10, 11, and 12 show the change in the measured L*a*b* values as the thickness increases, for the color patches laying on the edge of the measured L*a*b* values, i.e., maximum and minimum values of measured L*, a*, and b* for each TC. Figures 13 and 14 show the CIEDE2000 calculated between the measurements and the values obtained after implementing the A-to-B and B-to-A transforms in the round-trip test.

Fig. 7
figure 7

Color difference distribution for all color patches through all measurement sets. We calculated the color difference between the reference RGB values provided with the TC2.83 data and the measured RGB values using both the X-Rite EyeOne Pro and the HySpex measurement setup

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Fig. 8
figure 8

L*a*b* gamut comparison between the different measurement sets: a Matte vs. Gloss EyeOne sets, b Matte vs. Gloss HySpex sets, c Gloss EyeOne vs. HySpex sets, and d Matte EyeOne vs. HySpex sets

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Fig. 9
figure 9

Color variation at each thickness(T1 to T8) for the gamut limit points of each measurement set: a HySpex Gloss set and b HySpex Matte set

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4 Discussion

In Fig. 6, we see that the CIEDE2000 calculated between TCs of neighboring thicknesses tends to decrease when the thickness increases. This means that the color stabilizes with thickness. We can see that for the measurements carried out using the X-Rite EyeOne Pro, the color difference for thicknesses higher than 2 mm, independently of the finish type, is around \(\approx \) 1.0 CIEDE2000. A CIEDE2000 around 1.0 is perceptually not noticeable. However, the same cannot be said for the measurements obtained using the HySpex measurement setup, where, even though the same decrease of color difference is seen for both finishes, the CIEDE2000 value is around 2.0. A CIEDE2000 around 2.0 can perceptually be noticeable, and therefore, a noticeable shift in color between the different thicknesses can be visible. Interestingly, we see some spikes in color difference that go against this trend, mainly for white core thicknesses of 1 mm, 1.5 mm, and 2 mm and also for the 4 mm and 4.69 mm as well. What is peculiar is that it only occurs for the gloss finish TCs measured with both measurement setups. We suspect that these points are anomalies, but we would require more proof of outlying results to determine the correctness of our assumption.

To analyze the overall color difference, we look at Fig. 7. We can see that the color difference for the measurements obtained from the X-Rite EyeOne Pro and the HySpex measurement setup show similar distributions across the TC cuboids printed using the different white core thicknesses, albeit with different scales, depending on the finish type. Therefore, the results obtained from the two measurement setups are coherent. However, when comparing the Gloss vs. Matte for the same set, be it the HySpex setup or X-Rite EyeOne Pro setup, we see that at thicknesses 1.0 mm, 1.5 mm, and 4.69 mm, the color difference distribution is different compared to the other white core thicknesses. This difference is showcased by a different shape of the distribution and a different median and mean value of the distribution. This can be confirmed from Fig. 6, which validates that these white core thicknesses can be anomalies.

Looking at Fig. 8, we can see the change in the L*a*b* gamut between the different sets of measurements. We observe that the gloss finish, for both X-Rite EyeOne Pro and the HySpex setup, represents a wider gamut that includes darker shades and more yellowish shades as well compared to the matte finish, as it is skewed towards the positive b* values. As for the difference between the measurement setups, we see that, for the same finish type, the EyeOne presents a slightly wider gamut that is skewed towards the negative b* values, thus showing a shift towards bluish shades. It is expected to have a difference in gamut when the finish type changes, but also, we see that the difference in gamuts between the X-Rite EyeOne Pro and the HySpex setup measurement sets is noticeable.

Fig. 10
figure 10

L*a* variation at each thickness for the gamut limit points of each measurement set: a HySpex Gloss set and b HySpex Matte set

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Fig. 11
figure 11

L*b* variation at each thickness for the gamut limit points of each measurement set: a HySpex Gloss set and b HySpex Matte set

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To explain such a difference, we refer back to the literature presented in [27] and in Section 2.2, where the precision of the X-Rite EyeOne Pro spectral measurements on the translucent 3D samples was questioned. Indeed, we see in Fig. 8 that the X-Rite EyeOne Pro gives different measured values than the HySpex. We hypothesized that this is due to light loss from the translucent and scattering ink used in 3D printing when measuring with the X-Rite EyeOne Pro. This light loss is less prevalent when using the HySpex measurement setup because, considering that our measuring area is that of a single HySpex camera pixel, the difference between the illuminated and measured areas is large enough to overcome the light loss observed while using the X-Rite EyeOne Pro. However, we can presume that this wide illumination area spanning multiple color patches while using the HySpex measurement setup can lead to cross-talk between the different color patches, which can be a source of error when measuring with the HySpex measurement setup. But, for the sake of simplicity and convenience of use, we choose to rely on the measurements from the HySpex measurement setup and will henceforth present only the results from the said measurements.

To delve deeper into the effect of thickness on the color gamut, we look at Figs. 9, 10, 11, and 12, showcasing the change in L*a*b* values for each thickness at the edge of the L*a*b* gamut. From Figs. 9, 10, 11, and 12, we first see that highly saturated colors and colors with lower lightness values tend to be more influenced by variations in white core thickness. these colors exhibited L*a*b* differences when the white core thickness was changed, as can be seen from the distance of the point clusters from the initial point T1. This can be attributed to the fact that these colors, having a higher colorant concentration, still exhibit translucency, and the influence of the white core is significant. In contrast, less saturated colors are less affected. We can observe a change in the L*a*b* values when the white core thickness increases. The change in the L*a*b* values mostly follows the same direction. This sort of progression is apparent for the matte finish TCs, irrespective of the measuring device. However, for the gloss finish, for both the X-Rite EyeOne Pro and the HySpex measurement setup, there seems to be a difference in behavior, mainly for thicknesses T2 and T8 (1.5 mm and 4.69 mm, respectively). Nevertheless, by overlooking the behavior of the outlying thicknesses, we can see that the different white core thicknesses form tight clusters, indicating that there are no vast changes in color when the thickness increases, an observation we also observed in Fig. 6.

Fig. 12
figure 12

a*b* variation at each thickness for the gamut limit points of each measurement set: a HySpex Gloss set and b HySpex Matte set

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Fig. 13
figure 13

Color difference distribution after round-trip test on general profiles

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From all of the observations listed above, it would be possible to say that the TCs with a gloss finish, at thicknesses 1 mm, 1.5 mm, and 4.69 mm, are anomalies to the rest of the TCs. We reckon that the printing intent was changed when the printing process was underway, as the printing of the TCs was done in batches of 3, which means that the batch containing gloss TCs at 1.0 mm, 1.5 mm, and 4.69 mm was probably printed with a different rendering intent, hence the noticeable changes in color and measurement behavior. However, we can still look at the matte TCs of the same thicknesses for insights on color change and stability for lower thicknesses (1 mm and 1.5 mm).

With that in mind, for the non-anomalies, we can see a certain stability both from the color difference values (CIEDE2000) that are \(\approx \) 1.0 as seen in Fig. 6, and from the clustering of points in Figs. 10, 11, and 12. Therefore, we can safely assume that from 2 mm white core thickness onward, the printed colors are mostly similar and are reproduced the same way no matter the variation in the white core thickness of the printed model. Therefore, color profiles derived for any of these thicknesses can be used for all thicknesses \(\ge \) 2 mm. However, it would be difficult to conclude the same about thicknesses that are \(\le \) 2 mm for the following reasons:

  1. 1.

    As we have seen, for thicknesses \(\le \) 2 mm, the data we have for gloss TCs are anomalies and cannot be used to extract useful conclusions,

  2. 2.

    We can see from Fig. 6 that the color difference starts to stabilize from 2 mm white core thickness onward but is still decreasing for thicknesses \(\le \) 2 mm, meaning that the reproduced colors are still visually different.

Fig. 14
figure 14

Color difference distribution per thickness after round-trip test on: a HySpex Gloss set and b HySpex Matte set

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As for the round-trip test results presented in Figs. 13 and 14, we observe that:

  • The generalized ICC color profiles present a CIEDE2000 value of \(\approx \) 1 across all measurement sets and printing finishes. We can, therefore, say that the error induced to the color reproduction when using these ICC color profiles is unnoticeable,

  • For the ICC color profiles generated using individual white core thicknesses, we observe a color difference between the measurement sets but not between the finish types. The ICC color profiles generated using the HySpex measurement setup show color difference values of \(\approx \) 2.0, which shows that the round-trip test does not induce a noticeable color difference. However, the color difference shown in the round-trip test could be due to the higher color difference already seen in the HySpex measurements, as shown in Fig. 7.

Overall, we can deduce that the number of color patches used to generate the profiles is enough to generate profiles without inducing a noticeable color change. However, as we are on the limit of the noticeable color difference with a CIEDE2000 of 2.0, it would be wise to add information to the profiles by using TCs that have more color patches to decrease the color error induced by the generated ICC color profiles.

However, we acknowledge that some underlying variables can influence our findings. These variables are due to the printing process and mainly concern the structural integrity and material composition of the 3D-printed samples. As shown by Pérez-Ruiz et al. [29], respecting the structural integrity of the 3D-printed samples leads to smoother printed surfaces, which in our application concerning color, means more precise and consistent color reproduction. Therefore, we ensured that the sample faces were flat and that the thicknesses chosen did not affect the structural integrity of the samples. This was the case as the TCs did not have any signs of structural defaults. Also, from our findings in Fig. 6, we can see that the structural integrity of our TCs is unscathed thanks to the observed color consistency at higher thicknesses.

Another variable to keep in mind is the material composition and interaction between the different inks used, as it can also cause behavioral changes between the samples, as shown by Pyka et al. [30]. In our investigation, the TCs do not exhibit any of these behavioral changes because we used the same input color data and the same ink family for all our 3D-printed TCs.

Finally, we must keep in mind that, while this study is centered on the impact of white core thickness on color reproduction using Poly-Jet 3D printing, the broader scope of additive manufacturing techniques requires optimization and involves a multitude of considerations, each demanding a tailored approach. As is shown in [30] and [29], different 3D printing techniques using different materials will showcase different material properties and interactions. These properties and interactions must be taken into account when reproducing the methodology of this investigation using other 3D printing techniques.

5 Conclusion and perspectives

In this study, we investigate the effect of the white core on the color output of a 3D printer that uses translucent ink. The white core is highly scattering and alters the light trajectory going through the 3D-printed object, thus affecting its perceived color. To explore this hypothesis, we 3D-printed 16 color TCs in which we had 8 different white core thickness levels and 2 surface 3D-print finishes, matte and gloss. After printing, we measured the color patches of each TC using 2 different measurement setups and generated ICC profiles using these measurements. From the color measurements, we can see that the color reproduction is uniform, with color differences being \(\le 2\) meaning that they are not visible, for the TCs printed with a thickness of more than 2 mm. This implies that the same color transformation ICC color profile generated from a thickness of 2 mm or higher is applicable for all the objects 3D printing with a thickness of more than 2 mm. This indicates that for thicker 3D-printed objects, device characterization does not require multiple ICC color profiles for color correction. However, the same cannot be said for thinner objects from this work, where the color shift at different thicknesses was visible, with color difference values as high as six.

These findings approve our initial hypothesis that the white core thickness has a significant effect on the reproduced color when using translucent ink. Ultimately, this means that sample thickness, i.e., white core thickness, should be taken into account when optimizing the 3D printing pipeline for enhanced color reproduction.Our findings have significant implications for applications where accurate color reproduction is critical. For instance, in the production of realistic medical models for surgical planning, precise color representation of different tissues is essential for accurate diagnosis and treatment. As an example, consider 3D-printed models of organs where subtle color variations indicate pathological conditions. Our research provides valuable insights into controlling color accuracy in these models by managing the white core thickness. Another important application is in the creation of cultural heritage object extensions and replicas for exhibition purposes. Achieving accurate color matching with the original cultural heritage object is crucial for the aesthetic and psychological acceptance of the replicas. Our study contributes to this field by providing a methodology for optimizing color reproduction in 3D-printed conservation, ensuring a more natural and realistic appearance. As an example, consider a 3D-printed extension used to restore a missing piece of a historical statue where the color needs to match the statue’s appearance under different lighting conditions. This holds for other applications requiring accurate color reproduction, such as art/decor, figurine manufacturing, or medical prostheses manufacturing.

An interesting perspective for this work would be a more thorough exploration of the color stability for white core thicknesses \(\le \) 2 mm, with smaller steps than 0.5 mm between consecutive TCs. Also, corroborating the findings with scattering/translucency measurements on the TCs and linking said measurements to the observed color shift can bring more understanding to the results of this work.