A schematic diagram depicts the authenticity assessment process for artworks based on OCT technology (Figure 1). Three artworks were selected for the OCT analysis according to the time of the production, the artist's expertise, and the characteristics of the cracks. Thirty oil paintings were leased for this research. The three artworks were oil painting by Korean artists who agreed with the contents of this study. Two of the artworks were produced by Eunyeong Ko who specializes in oil painting and art restoration and the third painting was produced by Joon Ja Jun who works in oil. Natural cracks occur due to various causes such as physical and chemical reactions at the painted surface for each work, and these cracks were analyzed using OCT technology (Figure 1a). The art restoration expert, who created two of the artworks, produced forgery works for each of his two artworks and one of other artworks with the permission of the original artist. The art restoration expert could accurately understand the color combination of the original work, the thickness of the paint layer, the texture of the surface, and the painting style because these abilities are essential for restoring damaged areas in artworks. Therefore, it was difficult to differentiate between the original works and the forged works produced by professional forgery methods. Specifically, by replicating the color combination of the paints and the thickness of the paint layer, the forged artworks had similar paint techniques to the original works. In addition, forged cracks with the same directions, thickness, and positions to the natural cracks in the original works were artificially created in the forged artworks (Figure 1b).
Before analyzing the paintings with OCT technology, several cracks that represent he characteristics of the artworks were selected from among several cracks in each original work. In the counterfeit works, the artificial cracks, made in locations similar to those of the selected original work, were selected. The OCT scanning was performed by selecting a measurement area of 2 mm × 2 mm × 1.7 mm in the crack position at the artwork surface (Figure 1c and d). Next the 3D modeling data containing information on the depth, width, cross section, and shape of the cracks were obtained, and a cross-sectional image in the middle plane of the cracks was extracted as representative for the quantitative analysis of crack morphologies. In the cross-sectional image, various parameters such as width, depth, and shape were measured according to the morphological diversity and complexity of the cracks. In particular, the width and depth were subdivided into three, which was intended to analyze the crack characteristics in detail as much as possible (Figure 1e and f). Based on the data obtained in this way, the characteristics of the cracks were classified and analyzed according to the cause of the crack, and the foundation for the authenticity of the artwork was established. In addition to the studies selected, various oil paints were analyzed, and a quantitative analysis of the OCT cross-sectional images and crack parameters was conducted. These works were also original works, and focused on analyzing the characteristics of cracks that occurred in various works of art. This analysis was referred to when analyzing the cracks in this study (Figure S2-11).
3.2 Oil paintings and forged works prepared for 3D analysis of cracks based on the OCT system
To analyze the differences between the original and forged cracks on the artworks, we obtained three oil paintings created on canvas by two professional artists (Figure 2a, b and c). With the permission of the original artist, the restoration expert produced counterfeit works of the original works using the appropriate oil paint and medium after observing the style, color, and cracks of the original work through the naked eye and a magnifying lens (Figure 2d, e and f). The forged cracks on the counterfeit works were reproduced through common methods of creating fake cracks, such as knife tools. The main cracks that reveal the characteristics of the paint layer in the real work were similarly produced in counterfeits. The geometric characteristics of natural and artificial cracks were analyzed, based on the OCT image appearing in each crack.
Artwork 1: Figure 2a shows the oil painting with light brown and darker brown upper layers on top of a light green undercoat layer applied to a canvas. Cracks occur in both the light brown and darker brown upper layers, except for the under layer of paint. This also occurred because the amount of the painting medium in the upper paint layers was not adequately controlled.
Artwork 2: In Figure 2b, the artwork has multiple layers composed of a black underpainting layer and upper layers with a mixture of white, light blue, and green colors. The cracks occurred on the upper layers because the upper painted layers contained relatively little medium.
Artwork 3: We obtained an oil painting produced by Joon Ja Jun in 1964 (Figure 2c). The title of this artwork is “figure” (45 cm × 38 cm). In this work, the artist attempted to overlay the surface of the artwork with light purple paint to cover the cracks occurred naturally in the work. This work was selected for art authentication based on OCT analysis because of occurrence of various crack types in paint layers with varied thicknesses. Because the new canvas has good elasticity and does not crack easily, a canvas that was produced approximately 25 years ago was used as the substrate of the forged artwork. In addition, the thickness of the paint layer on the forged artwork was similarly drawn by observing the original product with the naked eye (Figure 2f).
3.3 The appearance and location of the cracks selected to measure OCT system in original works and forgery works painted by oil painting
Target regions for the OCT analysis were selected at three locations where cracks were generated in each work. The three selected points represented crack locations that were expected to provide particularly meaningful information for art authentication based on the OCT analysis of cracks.
Artwork 1: In Figure 3a, cracks occurred because the proportion of oil painting mediums used in the upper paint layers (light brown/dark brown) was not adequately controlled like the conditions of optimized combinations for preventing cracks in the painting. Forged cracks were produced in both the light and dark brown paint layers to match the locations at which the original cracks were generated. The cracks were produced by drawing thin lines similar to cracks using sharp knives on the paint layers with detailed control so that the color on the bottom side of the paint layer was visible (Figure 3b).
Artwork 2: In Figure 3c, the under layer of the artwork was painted black, and the colors of the upper layer were composed of a mixture of white, light blue, and light green paint. Unlike Artwork 1, cracks were generated because there was little paint medium in both the upper and under layers. Some cracks were relatively thin so that the color of the underlayer was not visible. Although the location of the cracks in the forged work was not similar to the location of the original cracks, the forged cracks were made so that it was difficult to distinguish between the cracks with the naked eye (Figure 3d). In addition, the thickness of the forged cracks was controlled to be as similar to the original as possible.
3.4 Comparison of cross-sectional images of the real cracks and the counterfeit cracks analyzed by using the OCT system
The cracks created in the original and counterfeit artworks were measured using the OCT system, and cross-sectional images of the cracks were compared to analyze the differences in the morphologies of the original and forged cracks (Figure 4). The images were extracted from the 3D images of the crack and the cross-sectional images of natural and counterfeit cracks were compared to examine the differences in the morphologies, such as the depth and shape. These images contain adequate information because they can clearly identify the 3D visual features of the crack that cannot be observed by the naked eye or by a microscope.
Artwork 1 (Figure 4a): In Figure 4, the cracks caused by the combination of media occur for each color, but the shape of the cracks for each color was not significantly different. The most prominent feature in the OCT cross-sectional image of the original cracks in Artwork 1 is a rectangular shape in which the side interface of the crack is shaped like a cliff and the bottom surface of the cracks is flat. This means that when the mediums in the upper painted layer dried, they left many gaps in the paint, resulting in a complete loss of internal adhesion. As the upper layer dried, the internal bonding decreased, which is why the side of the crack was clean. However, the surface of the forged cracks, such as surface roughness, tended to be uneven. It appeared similar on the top side, but there was a clear difference in the OCT cross-sectional images.
Artwork 2 (Figure 4b): The lower layer of paint had more medium than the upper layer, and as the medium solutions dried, small empty pores were created inside the space of the lower painted layer. As a result, the adhesion inside the lower painted layer decreased and this phenomenon seems to have affected the occurrence of cracks in the upper layer of paint. The main characteristic of the cracks is that the width of the cracks is very thin, so that the color of the lower layer is not visible, and the aspect ratio (depth/width) of the cracks was quite large. The original cracks had thin and deep rectangular shapes, but the counterfeit cracks had triangular shapes with rough surfaces. A concentrated force was applied with knives to create counterfeit cracks with the thin width similar to that of original cracks. As a result, the counterfeit cracks appeared to be relatively shallow in depth.
3.5 Quantitative analysis of an OCT cross-section image of original and forged cracks of Artworks 1 and Artwork 2
The widths (top width, center width and bottom width) and depths (left depth, center depth, and right depth) of each crack were quantified using cross-sectional image analysis. Figure 5 shows the morphology of the cracks formed in the forgery and original works of art, and the quantitatively measured values of the scale parameters of each crack were classified into various types. These representative values were selected from the largest values of the crack widths and depths and were used to compare the original artworks and counterfeit artworks (Figure 5b-d).
Artwork 1: The cracks of the original artworks have a rectangular shape, so they were measured equally for each measurement parameter of the crack width. On the other hand, the cracks in the forged artworks have inverted triangular shapes and the measured values were different for each parameter type, and the bottom parameter values were not measured. The depth of cracks in counterfeit artworks and original artworks differed by (Ⅰ) 93.9 µm, (Ⅱ) 97.9 µm, and (Ⅲ) 73.3 µm, respectively (Figure 5a). It seems that the depth of the crack increased as the force is applied to the painting layer with a knife to make the original cracks similar in width.
Artwork 2: The medium combination problem occurs in the lower paint layer. The depth value was observed to be approximately 2.5 times larger than the width of the crack (Figure 5b). In the case of thin and deep cracks, the cross-sectional shape of the crack was either a thin rectangular or an inverted triangle shape. The weakened bonding force in the lower paint layer affected the upper layer, and it was judged that the crack at the upper part occurred in a thin width.
3.6 Location and enlarged images for a comparison of original and forged cracks in Artworks 3
To analyze the original cracks created by other factors and the counterfeit cracks, we borrowed oil paintings on canvas produced by Joon Ja Jun. Five cracks were classified into five types according to the characteristics of the original artworks and the cause of cracks occurrence. The forged cracks were produced by scratching with knives and stabbing with pointed tools and broadly similar to techniques used to counterfeit artworks in the real world.
Craquelure Ⅰ: These cracked areas occurred due to aging and shrinkage of the canvas at the paint layers that are thinner than the others (Figure 6a' Ⅰ). This speculative rationale is that wrinkles appeared in the same direction on the back of the canvas as the cracks advanced on the painted surface. These cracks occurred in locations painted with various pigments, regardless of the colors of the paint layers. To imitate the visual morphology of the original crack, thin mass tools were used by finely tuned slash to create long paths of the dynamic cracks in the painting layer of the forged work (Figure 6b' Ⅰ). As a result, counterfeit cracks with thicknesses and directions similar to those of the original cracks were created.
Craquelure Ⅱ: Similar to the reason for the occurrence of Craquelure I, Craquelure Ⅱ also occurred in the aged area of the canvas (Figure 6a' Ⅱ). It is common for the cracks in the paint layers to occur in the direction of the thick wrinkles on the back of the canvas, but the difference is that the thickness of the paint layer at this location (Craquelure Ⅱ) is relatively thicker. The forged Craquelure Ⅱ was produced using the same slashing method used to create forged Craquelure I (Figure 6b' Ⅱ).
Craquelure Ⅲ: Craquelure Ⅲ may appear at painted surfaces during the drying process by chemical environmental changes in the layers of paint (Figure 6a' Ⅲ). The cracks were generated across painted layers with the mixture of three colors that were applied thicker than the surrounding layers of paint. In the middle of the paint layer, it seems that painting mediums were poorly mixed, and this led to the drying cracks occurring in large areas of the painted surface. Forged cracks were also produced in a pale-yellow color of an undercoated layer through a deliberate process in which the force was appropriately adjusted with a thin knife (Figure 6b' Ⅲ).
Craquelure Ⅳ: Craquelure Ⅳ occurred under unintentional physical impacts on completed painting by the artist and appeared to be scratched by an ambiguous tool (Figure 6a' Ⅳ). An ivory color of a lower layer of paint was visible in an exposed area. During the drying process, the width of the cracks widened with the formation of many branches in the cracks. When these cracks were forged, they were created by applying deliberate force to the painted surface using a stainless-steel tool. The width of the forged crack was suitably widened, and the lower surface layer was clearly visible, similar to the original cracks (Figure 6b' Ⅳ).
Craquelure Ⅴ: These cracks occurred in the thickest areas of the artwork (Figure 6a' Ⅴ). Cracks were observed across both the upper layer (white color) and a sublayer (blue color). To replicate the original cracks, a thicker knife was used to apply a relatively stronger force to the painted surface layer (Figure 6b' Ⅴ).
3.7 Visual comparison based on the OCT cross-sectional images of cracks selected from an original and a fake artwork.
Craquelure Ⅰ: The cross-sectional shape of the original Craquelure Ⅰ has an inverted triangular shape in the upper painted layer (Figure 7a Ⅰ). The shape is formed into a sharp point toward the undercoated layers, and the height of both side layers along the crack remains approximately constant without protruding outer layers. The upper painted layers were affected by shrinkage that occurred due to the aging of the canvas, and the cracking process may have advanced in the top layer of the paint. Thin thread-like structures are exposed in the inner side of the cracks. This may have occurred because the ratio of medium mixture to oil painting is different for each colored layer and result in uncompleted separation inside the painted layers. Likewise, the cross-sectional morphology of the forged cracks represents a similar inverted triangle, but they have a larger gap and a slightly shorter depth (Figure 7b Ⅰ). The outer surface of the forged cracks appears only on one side of the protrusion phenomenon of the painted layers because of the physical influence of drawing the crack lines.
Craquelure Ⅱ: The crack formation has an inverted triangle with a slight incline (Figure 7a Ⅱ). The width of the cracks is relatively narrower than that of the original Craquelure Ⅰ. The inner spacing of the cracks has an uneven structure without a thread-like fiber. In the cross-sectional image of the counterfeit cracks, one side of the painted layers has a slightly overhung outer painted surface (Figure 7b Ⅱ). The forged cracks have a relatively shallow depth, and the sidewalls of the cracks are neat similar to the forged Craquelure Ⅰ.
Craquelure Ⅲ: The cross-sectional shape of the crack shows an inverted triangle with a tip that has a relatively blunt shape (Figure 7a Ⅲ). The central axis of the inverted triangle is slightly inclined. The thin width of the counterfeit cracks was produced to reveal the color of the underlying paint layer, like the original cracks (Figure 7b Ⅲ). Although the widths of the two cracks appear similar to each other, the foremost difference between these two cracks can be accurately distinguished according to the depth and shape in only the OCT cross-sectional images.
Craquelure Ⅳ: Cracks with a large width are visible on the top of the outer painted layer, and a sharply thin inverted triangle shape with a sharp tip is evident in the deeper undercoated layer (Figure 7a Ⅳ). The forging process was conducted under circumstances where the coating thickness is not exactly known. These forged cracks were produced to reveal the ivory-color of the under layer similar to the original cracks, but the difference in depth and shape is evident in the OCT cross-sectional image (Figure 7b Ⅳ).
Craquelure Ⅴ: The sidewall of the cracks appears to be relatively neat, as the painted layer appears to have dried the most (Figure 7a Ⅴ). The original Craquelure Ⅴ has a wide crack width, but the color of the lower layer is not visible. Because the paint layer is thick, the crack is not deep enough to reveal the color of the lower layer. The forged Craquelure Ⅴ was extended and widened by applying more force than the process of producing other forged cracks The sidewall of the cracks appears to be relatively neat, as the painted layer appears to have dried the most (Figure 7b Ⅴ). Therefore, the upper layers were extruded from the edges of the cracks. In addition, the side of the forged crack was neatly made in a straight line, but the detailed appearance with a zigzag shape from the paint layer of the original crack could not be forged.
3.8 Quantitative analysis of OCT cross-section image of original and forged cracks of Artworks 3
Craquelure Ⅰ: The natural cracks were generated by canvas shrinkage and are 70.2 µm in width and 370.2 µm in depth (Figure 8a Ⅰ). In contrast, the dimensions of the forged cracks are approximately 95.7 µm in width and 142.5 µm in depth. This observation may indicate that forged cracks have been a wider and shallower crack spacing than the original cracks. There is a statistically significant difference of about 227.7 µm in crack depth between the original and forged cracks. Although the force was finely adjusted to create the thin width, it was almost impossible to control the depth with any precision.
Craquelure Ⅱ: Cracks in counterfeit Craquelure Ⅱ are also wider and shallower than the original cracks, as in the dimensional case of counterfeit Craquelure Ⅰ. When compared with than Craquelure Ⅰ, the crack widths are relatively thinner by a difference of 20 µm, but the depth is shallower with a difference of 134 µm (Figure 8a Ⅱ). The original Craquelure Ⅰ and Ⅱ were created by canvas aging and Craquelure II occurred in thicker paint layers than in Craquelure Ⅰ. However, it is very difficult to counterfeit cracks according to tendency of natural crack shapes, produced according to the thickness of the paint layer. As a result, the shapes and dimensions of the original Craquelure Ⅰ and Ⅱ are different, but forged Craquelure Ⅰ and Ⅱ have similar shapes, widths, and depths.
Craquelure Ⅲ: The aging conditions of the canvas directly contribute to the occurrence of Craquelure Ⅰ and Ⅱ, but Craquelure Ⅲ occurred as a direct cause of drying in the upper paint layers. The width of the crack is approximately 89.4 µm, showing a relatively wider appearance. Conversely, the depth is relatively shallow at 180.9 µm (Figure 8a Ⅲ). The Craquelure Ⅰ and Ⅱ were produced by the influence of shrinkage in the canvas below the paint layer and have a relatively thinner and deeper shape. In contrast, Craquelure Ⅲ was caused by the drying of the paint layer and is represented a reverse shape with a relatively broad width and shallow depth.
Craquelure Ⅳ: Craquelure Ⅳ was artificially created by the artist's mistake, caused by a thin sharp tool scraping the artwork’s surface. The original cracks show a larger upper width with the shape of an inverted triangle, and the counterfeit cracks show a large bottom width. The original crack was approximately 191.5 µm in depth, which is greater than the forged crack depth of 68.0 µm (Figure 8a Ⅳ). It may resemble that original cracks were initially scratched, and after considerable time, the cracks deformed in width and depth under paint conditions such as paint drying. In addition, the width/depth ratio of the original cracks and the forged cracks have similar dimensions.
Craquelure Ⅴ: The Craquelure Ⅴ are 123.4 µm in width and 219.1 µm in depth (Figure 8a Ⅴ). Compared with the Craquelure Ⅲ that occurred in the thinner paint layer, the width in Craquelure Ⅴ was wider by 34.0 µm than in Craquelure Ⅲ, and the depth in Craquelure Ⅴ was 38.2 µm deeper than that in Craquelure Ⅲ. This was observed in the opposite tendency of the original Craquelure Ⅰ and Ⅱ, which were affected by the canvas underneath the painted layers. If natural cracks are directly influenced by the condition inside the upper painted layers, the thicker painted layers generate cracks with a greater width and depth at the painted surface. On the contrary, if cracks occur because of the influence of the canvas layer, the thicker the paint layer, the thinner and shallower the crack. Forged cracks were 68.1 µm in width and 104.3 µm in depth. Various cracks with similar widths can be artificially produced, but the depth is difficult to control and not as deep as the original cracks (Figure 8b-d).