We study how accurately a naked human eye can determine the thickness of thin films from the observed color. Our approach is based on a color-matching experiment between thin-film samples and a simulated color field shown on an LCD monitor. We found that the human color observation provides an extremely accurate evaluation of the film thickness, and is comparable to sophisticated instrumental methods. The remaining color differences for the matched color pairs are close to the literature value for the smallest visually perceivable color difference.
© 2015 Optical Society of America
Thin films play a crucial role in a vast number of applications, from manufacturing of antireflective coatings to solar panels [1–4]. Characterization of the film thickness is typically conducted by nondestructive methods, such as ellipsometry or spectroscopy, or by destructive methods, such as scanning electron microscopy (SEM) [5,6]. Although the spatial resolving power of the human eye is orders of magnitude too weak to directly characterize film thicknesses, the interference colors are well known to be very sensitive to variations in the film . Such a high sensitivity is sometimes employed by skilled engineers to quickly estimate film thicknesses at accuracy from the color of the film. However, this requires that a person estimating the thickness from the color observation has strong expertise on the properties of the particular type of thin film and that the light source is fixed.
The limits of color discrimination of human eyes and its dependence on viewing conditions are among the major current trends in color science . One often estimates that the color discrimination threshold is roughly one color difference unit [9,10] or less . In principle, it is therefore a straightforward task to estimate theoretical limits for thin-film characterization by the naked eye. However, in practice this is not the case, since one has to have a reliable reference to which the color of the sample is compared. This creates a major obstacle because physical reference samples with small enough spacing in the film thickness are usually not available.
Our main purpose is to address the problem by generating the reference color with a color-characterized computer monitor, which also illuminates the physical samples to be characterized. With such an approach we ensure, first, that the lightness levels of the sample and the reference are similar, which is an essential prerequisite in color-matching experiments, and second, that the color gamut of the monitor is capable of producing the required reference. In addition to the thin-film characterization itself, our work addresses how small color differences between physical and simulated samples can be observed by humans. To study these issues, we fabricated seven titanium dioxide () film samples with thickness values between 40 and 200 nm on round fused-silica substrates with 2 in. (5.08 cm) diameter each, with the aim of producing a set of differently colored filters. A composed photo of all the samples is shown in Fig. 1. Although an even thickness of the layer was pursued, some defects can be seen at the edges of some samples. The figure also shows simulated colors after the color-matching experiments.
The experimental setup is shown in Fig. 2. The thin-film sample was in direct contact with the screen of the Eizo ColorEdge CG-246-BK LED backlight LCD monitor, and a circular adjustable color field of the same diameter was displayed next to the sample. The viewing distance was between 40 and 60 cm, ensuring that no decrease of color discrimination due to small sample size is present [12,13]. The color of the adjustable field was controlled by six keys, allowing simple and fast adjustment: number buttons “4” and “1” were used for adjusting the lightness, “5” and “2” the redness–greenness, and “6” and “3” the yellowness–blueness of the field. These three adjustable quantities are equal to the , , and coordinates of the CIECAM02 color appearance model .
Contrary to the CIE recommendations for color difference evaluation , the surroundings of the sample and adjustable color field were white. We made this choice for the following reasons: since a neutral gray background corresponds to a luminance level that is about 20% of the maximum luminance of the display, it would be much dimmer than the thin-film sample or the adjustable color field. Hence under the test conditions the color fields would become the brightest visual objects, which the dark-adapted eye tries to interpret as white light sources, especially when the color difference between the fields becomes small. Thus a neutral gray background must be surrounded by a white frame. Our preliminary tests with both gray and white backgrounds did not give a definite answer on the best choice of the background color. Hence more tests have to be carried out to evaluate the influence of background illumination on the color discrimination for dark viewing conditions. Also due to the circular shape of the sample and field, their direct contact is only possible at one point. Furthermore, we conducted the experiments in a dark room with the monitor as the sole light source. To avoid any negative influence due to the lighting conditions, all test subjects had to wait until the eyes were adapted.
We selected 26 human subjects, all with normal color vision, which we confirmed with the Farnsworth–Munsell 100 hue color vision test . The ages of the subjects ranged from 24 to 52 years (average 35.1). Before the color-matching experiment, we carefully explained the principle of the color adjustment to each subject. To get used to the color adjustment the subjects had to complete the experiment twice for the first sample, but only the results of the second try were included in the data.
We color characterized the monitor with a Konica–Minolta CS2000 spectroradiometer. To maintain high color reproduction accuracy, we repeated the characterization measurements four times during the two-week test period. Based on the spectroradiometric measurements, the remaining total color differences for the reproductions of seven thin-film colors were in the range of 0.4–0.6 CIECAM02-UCS color difference units , which describes the accuracy of the color reproduction method. For comparison, the minimum step of the standard -bit color scale corresponds to about 0.25–0.5 CIECAM02-UCS units depending on the reference color and the primary color channel that is adjusted. During the test period we set the luminance of the display to about , and the correlated color temperature was about 6560 K. We also measured the thin-film thickness with three reference methods: ellipsometer (Woollam VASE), spectrophotometer (PerkinElmer Lambda 1050), and scanning electron microscope (LEO 1550), which requires cutting of the samples and hence must be conducted after all other experiments. The spectrophotometer-based method consists of measuring the transmittance spectrum and then performing the RMS fitting of it to the theoretical thin-film formula (see below). The measured surface roughnesses of thin films were 2 nm.
Before proceeding to investigate the results, let us study the mapping between the color coordinates and the film-thickness values in detail. First, the transmittance of a homogeneous thin film of thickness is given by the well-known thin-film interference formula . Since the thickness of the substrate is much larger than the coherence length of the light, the total transmittance of our component is simply the product of the thin-film transmittance and the transmittance of the air–substrate boundary. Hence19,20], and summing the element-wise products over the entire wavelength range of the visible spectrum.
Figure 3 shows the CIECAM02 plot of all selections by the subjects. The figure also shows the results of the reference measurements by the ellipsometer and the spectrophotometer, and a theoretical curve for the chromaticities of thin films with thickness. The film thickness corresponding to each selection is obtained by finding the smallest color difference, , between the curve and the XYZ-tristimulus values of the selection. In practice, this process can be integrated in the software so that each result of the color matching directly gives the thickness value.
Note that due to the close proximity of the theoretical curve for some pairs of thickness values, the color difference was only calculated in a fixed area of around the targeted film thickness. Such a practice is justified because thicknesses with similar tristimulus values are typically rather different, and hence cannot usually be confused. Figure 4 shows thicknesses corresponding to human selections for all seven samples along with the reference measurements, and Table 1 summarizes the results and the estimated accuracy of the methods. We see at once from the figure and the table that most of the selections are within just a few nanometers of each other and from the ellipsometer result. This shows that the human color observation in general gives a very accurate estimation of the thin-film thickness, provided that a reliable reference exists. It is of interest to note that the difference between the ellipsometer- and spectrophotometer-based approaches is 2 nm. This may be partly due to the fact that the measured roughness of the samples is in the same order. The results for the SEM measurements are inconclusive as for these specific types of samples the contrast between the substrate and the film was very poor, thus preventing not just accurate, but in some cases any, results.
Let us next focus on a closer investigation and interpretation of the results. Studying Fig. 3, we first note that the human observations tend to be biased towards the white of the display (having coordinates , ). A possible explanation for this result is the effect of light backscattered from a subject and the walls, reflected again from the front surface of the thin-film sample. Since the surface of the LCD is coated with an antireflection layer, the effect of reflected light is small or at least different at the adjustable color field compared with the sample that has no antireflecting coating. However, this phenomenon has, in general, little influence on the final result of the measurement. It may affect the accuracy for film-thickness values for which the curve in Fig. 3 bends strongly, since systematic deviation of the selection from the curve may lead to a “wrong” projection.
According to  the value of the smallest observable color difference is about for achromatic dark colors and about for brilliant green and yellow to red colors. If we want to estimate the average color discrimination ability under the test conditions, we have to remove all factors leading to color differences between the thin-film sample and its reproduction. Such factors are fabrication errors, measurement errors of the spectroradiometer used for display characterization, errors of the color reproduction method, and temporal and spatial instability of the display. The effect of these factors can be removed if we make the assumption that the mean of the human estimates is the best representative for the observed color, and the color discrimination limit can be estimated by the deviations (or color differences) of selections from their mean value. The second column of Table 2 shows that the observed variation in the selections by humans varies from 0.6 to 1.6 CIECAM02-UCS color difference units (or 0.5–1.7 units when the CIELAB total color difference formula  is used). In our experiment, the color discrimination does not seem to follow the rules given in , but instead decreases when the film thickness is increased—a probable consequence of pronounced defects at the edges of the thin-film samples. However, it is important to note that here we compare physically different types of objects, and hence the setup is somewhat nonideal to study the ultimate color discrimination ability.
Another vital point is the dependence of the results on the training of the subjects. From the results gathered so far one can see that the accuracy and precision are more dependent on the specific film thickness and the sample quality than the number of tests completed. All subjects began with sample 1 and hence had more experience when measuring the last sample. Therefore, it seems unlikely that our results would be significantly improved with more experienced subjects. Furthermore there was no significant difference between subjects that had no experience in color-matching experiments and those that had participated in our earlier study .
Our results show that the color discrimination capabilities of the naked human eye are so accurate that naked-eye characterization of thin-film thickness is often possible at an accuracy of a few nanometers. Such an accuracy is better than in the color-based estimation of the depth of binary gratings . This is not a real surprise, since here we are dealing with a one-dimensional inverse problem rather than a two-dimensional one such as in . The color differences between the human selections are somewhat above the smallest observable differences discussed in the literature . This is mainly due to the fact that here we are comparing simulated colors shown on the screen to colors of light transmitted through physical components, and hence the setup does not represent a fully ideal color-matching experiment. In addition, the uncertainty of observations is undoubtedly affected by the surface roughness of the samples, which is in the order of 2 nm.
We thank all subjects for participating, Tommi Itkonen for SEM measurements, and Pertti Pääkkönen for ellipsometry measurements.
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