Principle of thickness determination using integrated optical microscopy

The developed method for thickness determination of soft matter samples, i.e., nanoporous water-filled polymer membranes, utilizes the stage position and the autofocus of the CCD camera of the tabletop µXRF instrument as illustrated schematically in Fig. 1a. Initially, a 3D-printed sample holder was designed and constructed in-house, incorporating a rigid acrylic glass plate on which the sample can be placed and an X-ray transparent foil that covers the thin water-filled porous membrane sample (see Fig. 1b and c). The function of the covering foil is to prevent the samples from drying out during the measurement process.

Fig. 1

a) Schematic illustration of thickness determination using integrated optical microscopy of µXRF instrument’s X-Y-Z stage. b) Schematic of side few of sample holder and c) picture of sample holder.

The measurement procedure is straightforward as outlined in the following: Initially, the CCD camera focuses on the upper surface of the empty sample holder, subsequently on the top of a respective sample. It is evident that the thickness of the specimen directly correlates with the stage's Z-movement to achieve optimum focus. The thickness \(_\) of the sample \(i\) at a defined sample spot can be determined by the following Eq. (1), provided that the coordinates of the stage have been saved:

where \(_\) is a position on the Z-coordinate without sample and \(_\) the height of the stage with sample \(i\).

The following three aspects were considered in regard to the feasibility, optimisation and validation of the proposed method for thickness measurement, in the following referred to as ‘integrated optical microscopy stage method’, short ‘IOM stage method’:

A.

(How) Can the focus be determined highly reproducibly at different spots and on different samples?

B.

Is the Z-movement of the built-in stage, when used with the designed sample holder, accurate and reproducible enough to measure thicknesses of a few hundred µm with an acceptable margin of error?

C.

Is the proposed method applicable to water-filled (nano)porous soft matter matrices?

Reproduceable determination of focus

The focus of the tabletop µXRF instrument used here can be set manually or automatically. Preliminary tests (with n = 10) demonstrated that manual focusing is less accurate, resulting in significantly higher combined relative standard deviation of approximately 72% compared to 12% when employing autofocus. The autofocus is achieved through the identification of the most significant contrast: Initially, a manual coarse adjustment is executed at 10 times magnification of a CCD camera, and subsequently, to achieve fine focusing the autofocus is used at 100 times magnification. Consequently, the autofocus function was utilized to initiate the focusing process, commencing from a z-position that was evidently lower than the actual sample height.

In order to further optimize the autofocusing process by identifying the highest contrast, a set of experiments was conducted. The contrast is evaluated by determining the grey value spread [47]. Namely, the greater the grey value spread, the better the image is in focus and the sharper the picture (see exemplary images in Supporting Information (SI), Figure S5). Accordingly, different LED lighting intensities (low: 11 a.u.; high: 30 a.u.) within the sample chamber of the µXRF instrument were tested in conjunction with pen markings of two distinct colors, i.e., silver and blue, on the coverage film of simulated samples of diverse colouration (white, grey and black paper). It is hypothesized that optimizing these parameters to obtain high contrast will allow for more precise autofocus, even on unicoloured samples, thereby impacting the accuracy of thickness measurements.

Both pens can be used to create shades of color, depending on how much ink is applied to the film (see Fig. 2c). The elemental composition of the inks was examined by using total reflection X-ray fluorescence spectrometry (TXRF; see SI, Table S1) to exclude any potential overlap between existing elements and future unknown analytes.

Fig. 2

Grey value spread for a) blue and b) silver marks on coverage film on white, grey and black simulated sample using high (30 a.u.) and low (11 a.u.) lighting intensity. c) Photo of blue and silver marks on exemplary simulated sample

The results presented in Fig. 2 show that both marking colors result in suitable grey value spreads for autofocusing. However, the silver markings generally exhibit higher contrasts except for the white samples. Moreover, our hypothesis that the precision of thickness determination would be better for a higher grey value spread was confirmed when we evaluated replicate autofocusing for the highest and lowest grey value spreads (see SI, Table S2). The obtained standard deviations of the Z-coordinate represent the depth of focus of the proposed method and range from ± 3 µm for a grey value spread of 94.52 ± 0.01 (n = 10; silver marking, black sample, high illumination of 30 a.u.) to ± 6 µm for a value of 2.22 ± 0.01 (n = 10; silver marking, white sample, high illumination of 30 a.u.). Considering that the specimen range in thickness from fifty to a few hundred micrometers, a variation of 3 µm or 6 µm is reasonable. In conclusion, the respective marking color can be selected methodically for analyzing real samples of various colors.

Verification of thickness determination

Calibration foils with certified thicknesses ranging from 21.9 to 1,000 µm were used to verify the thickness measurements obtained using the IOM stage method in accordance with Eq. (1). In Fig. 3 the values obtained for the determined thicknesses are plotted against the certified values. The corresponding recovery function, which includes all data points, results in a recovery rate of 101 ± 1% (n = 3; N = 91; P = 95%). Evaluation of the two individual marking colors reveals no significant difference in accuracy, but slightly lower precision when using the blue marker, namely a relative residual standard deviation of 6% compared to 5% for the silver marker.

Fig. 3

a) Recovery function obtained for thicknesses determination of calibration foils using IOM stage method and differently colored marks. Recovery function: \(}\boldsymbol=\boldsymbol\left(1.01\boldsymbol\pm \boldsymbol0.01\right)}+\boldsymbol(4.08\boldsymbol\pm \boldsymbol2.09)\). Error bars reflect combined standard deviations of replicate measurements with n = 3. b) Combined standard deviations for thickness determination at 6 different positions on the calibration foils. Number of replicate measurements at one position was n = 3

Repeated measurements taken at 6 different positions on a calibration foil produced consistent results, with an arithmetic mean of the combined standard deviations of ± 18 µm and a maximum deviation of ± 25 µm (see Fig. 3b). In conclusion, the precision achieved by Z-movement of the built-in stage in combination with our designed sample holder is sufficiently accurate for determining the thicknesses of solid, uniform samples in range from about 50 µm to 1000 µm providing an uncertainty of a few 10 µm.

The next intermediate step was to analyze self-prepared gelatine films to evaluate the IOM stage method's suitability for determining the thickness of dark matter materials. These films exhibit a combination of flexibility and rigidity, which makes them less uniform than the calibration foils with defects such as surface scratches and air inclusions. However, thickness can still be determined using a micrometer and a light microscope as reference methods. Furthermore, the gelatine pieces are smaller than the calibration foils, meaning they only sit in the middle of the sample holder rather than between the frames. The thickness of six gelatine foil samples was measured at multiple points on the films using the IOM stage method with blue and silver markings, as well as a micrometer, and at one of the edges using a light microscope. The results obtained ranged from 94 µm to 111 µm, and were except for two outliers all consistent with one another (see SI, Figure S6a). The observed outliers - i.e., slightly higher values observed by the IOM stage method - can be attributed to the challenges encountered during sample preparation, namely the inserting of the sample into the holder can be problematic, as the gelatine foil pieces tend to repel the carrier and cover foil. In order to verify accuracy of thickness determination by the IOM stage method over a greater thickness range, up to four films were arranged in a superimposed configuration and measured using a micrometer for a reference (SI, Figure S6b). To minimize repulsion, the individual layers were carefully pressed together after the samples were placed in the measurement setup. Following this optimized sample preparation, the obtained thickness values are reasonably consistent (recovery: 90 ± 4%), confirming the feasibility of using the IOM stage method for soft matter materials within the tested size range of 100 to 400 µm.

Application to water-filled nanoporous polymer membranes

Finally, the IOM stage method was applied to determine the thickness of a real sample: a nanoporous block copolymer membrane functionalised with a POM-based catalyst and a Ru-based photosensitiser. These membranes are based on polystyrene-block-poly(2-(dimethylamino)ethyl methacrylate) (PS-b-PDMAEMA), and were prepared using the doctor blade technique, followed by storage in water [32].

First, five circular pieces measuring 38.5 mm2 were punched out of the membrane sheet (Membrane A) and then measured individually several times using the IOM stage method after six markings had been applied to random positions. Evaluation of the two marking colors revealed significantly higher precision with a mean deviation of ± 13 µm when using the silver marker. The mean thicknesses obtained for the five membrane pieces range between 86 ± 17 µm and 157 ± 7 µm (all values see SI; Table S3). As it is not possible to use a micrometer or light microscope to determine the reference thickness here, the thickness determined by the IOM stage method could only be verified indirectly. To this end, the individual membrane pieces were stacked and their thickness was determined and compared to those calculated from the thicknesses of the individual membranes. Figure 4a shows the recovery function obtained for this experiment (recovery rate: 97 ± 7%; intercept: 33.4 ± 24.5 µm), confirming good agreement between the measured and calculated thicknesses of the stacked membranes, and the absence of proportional systematic error. However, it is evident that the overall precision in this recovery experiment is significantly lower than in the preceding experiments. This can be explained by the difficulties involved in the stacking of the membrane pieces in the sample holder. Attraction or repulsion may occur during stacking, given that the membranes are positively charged and the thickness of the water films between them may vary. These difficulties would not arise if there was a thicker membrane instead of a stack of thinner membranes.

Fig. 4

a) Recovery function obtained by determination of thickness of membrane stacks using IOM stage method compared to calculated thickness derived from the sum of individual thickness of membrane pieces (Membrane A). X-error bars represent uncertainty as derived from Gaussian error propagation of replicate measurements with N = 15 and P = 95%; Y-error bars represent combined standard deviation of replicate measurements with n = 9 and P = 95%. b) Thickness determined for membranes of the same composition with either higher porosity (Membrane B; half-filled diamonds) or lower porosity (Membrane C; filled diamonds). Error bars represent combined standard deviation of replicate measurements with n = 3 and P = 95%

Therefore, the next step was to investigate two membranes with identical polymeric compositions but distinct porosities, which were achieved by using different solvent ratios during the membrane formation process. Five circular pieces measuring 20 mm2 were again punched out of the respective block copolymer Membranes B and C and silver marking were applied on three random positions before measuring thickness by the IOM stage method. As would be anticipated, Membrane B, which is more porous, exhibits a greater average thickness in comparison to Membrane C, which is more dense and therefore thinner, as can be seen in Fig. 4b. In addition, both experiments reveal a certain inhomogeneity in the thickness of the membrane sheets themselves. This is why no significant statistical difference between Membranes B and C can be proven. The spread of the data points reveals differences in thickness of up to 70 µm for one sample, which are most probably caused by synthesizing and probing different positions, rather than being a result of the analysis method.

To check this hypothesis further, systematic investigations were performed comparing the measured thicknesses under the following variations: a) Same x/y-position, but with the top or bottom of the membrane facing upwards (Membrane D); b) after storing the membrane for 11 days (Membrane D); and c) at 15 different x/y-positions (Membrane B). A modified Welch's t-test for unpaired samples (see SI) revealed no significant difference in the determined membrane thickness when the top or bottom of a membrane piece faced upwards. Two measurement series, one performed on the same day and the other after 11 days of storage, also produced no significantly different results when tested using a paired Student's t-test (see SI). These results confirm on the one hand that the measurements by the IOM stage method are reproducible and on the other hand that handling and storage conditions do not affect membrane thickness. (The results for these experiments can be found in Table S4 in the SI.) Conversely, the thicknesses determined at 15 randomly selected x/y-positions on Membrane B range from 89.33 ± 7.96 µm to 160.33 ± 11.94 µm (see SI, Figure S7) confirming variation in thickness of up to 71 µm.

Laterally resolved thickness determination

As the membranes exhibit deviations in thickness greater than the measurement accuracy of the proposed method, we tested whether it was possible to achieve some form of lateral resolution in thickness determination. To this end, a checkered silver marking was applied to the cover film (see SI, Figure S8) and thickness measurements of catalyst-loaded Membrane E were taken at the nine crossing points distributed across the membrane, covering a sample area of 38.5 mm2. To obtain comparable results, an autofocus area of 1.39 mm2 was used, as in the above-described experiments. This corresponds to 80% of the CCD camera's image area at 100-fold magnification. A significantly higher resolution in thickness determination could be achieved by reducing the autofocus area to a minimum of 0.02 mm2 using this instrument. However, testing this was beyond the scope of this work. As can be seen in Fig. 5d, a thickness gradient is observed from left to right along the X-coordinate. This finding is consistent with the elemental mapping of the metals W and Co (Fig. 5a and b), assuming that the POM catalyst (here [Co4(H2O)2(PW9O34)2]10−) is loaded homogeneously onto the membrane [31]. The highest intensity was detected in position P9(3/3), while significantly lower intensities were observed in positions P1(1/1) to P3(1/3), reflecting less material. Conversely, when the same piece of membrane is placed onto a chromium-coated foil, a lower intensity of Cr Kα is observed in the thicker areas of the membrane (see Fig. 5c). For homogeneous, thin samples, it has been suggested that the attenuation of X-ray fluorescence from an underlying material can be used to evaluate thickness in accordance with Lambert–Beer's law [48,49,50]. The advantage of this approach is that this information is obtained simultaneous to the elemental distribution of the analytes, making the process less time-consuming. However, the material-dependent attenuation coefficient µ must first be shown to be constant across the probed area; in other words, the matrix must be both structurally and chemically homogeneous. Therefore, using attenuation could lead to an inaccurate interpretation of physical thickness for samples with highly heterogeneous element distribution and/or structural inhomogeneities, such as porosity or humidity. This is because, unlike the IOM stage method proposed herein, attenuation is not directly related to the physical thickness of the sample, but rather to its optical thickness.

Fig. 5

a) Element map for Co Kα (6.9 keV) and b) W Lα (8.4 keV) of POM catalyst-loaded Membrane E, and indication of selected x/y-positions used for thickness measurement. c) Element map of Cr Kα (5.4 keV) of sputtered foil beneath Membrane E and indication of selected x/y-positions used for thickness measurement. d) Determined thicknesses of Membrane E at nine selected x/y-positions. e) Correlation of thickness determined using IOM stage method with C/R ratio corrected Co Kα and W Lα intensities derived from point spectra. (dashed line Co: \(}\boldsymbol=\boldsymbol\left(0.140\boldsymbol\pm \boldsymbol0.032\right)}-\boldsymbol\left(3.653\boldsymbol\pm \boldsymbol2.973\right)\); R2 = 0.729; N = 9, P = 95%); straight line W: \(}\boldsymbol=\boldsymbol\left(0.017\boldsymbol\pm \boldsymbol0.004\right)}-\boldsymbol(0.496\boldsymbol\pm \boldsymbol0.321)\); (R2 = 0.774; N = 9; P = 95%). X-error bars reflect combined standard deviations of replicate measurements with n = 4.)

To enable a more quantitative interpretation of the obtained data, µXRF point measurements were taken at each position where the thickness was determined. Initially, we checked whether the Compton and Rayleigh scattering peaks correlated with the thicknesses of the membrane found, as the correction of elemental intensities using either the Compton scattering intensity or the ratio of Compton to Rayleigh scattering peaks has been suggested in the literature as a means of compensating for the inherent differences in the thicknesses and densities of thin soft matter materials [24, 51]. As can be seen in SI, Figure S9, the scattering intensities and their ratio do not correlate with the thickness found at positions P1 to P9. However, the Compton-to-Rayleigh scattering ratio (C/R) is not constant across the nine probing positions, which indicates that the membrane's average absorption properties vary slightly. In this context, it should be noted that the sample holder—a 3 mm-thick acrylic glass slide—contributes significantly, albeit evenly, to X-ray scattering and absorption. Therefore, the slight variations observed seem plausible, as they merely reflect differences within the membrane. Since the C/R ratio is proportional to the average atomic number of a sample [27, 52], and since the polymer membrane is highly porous with water-filled pores, variations in pore structure result in different water-to-polymer ratios. Accordingly, the Co and W intensities measured at the nine sampling points were corrected for the C/R ratio before being correlated with the measured thicknesses (see Fig. 5e). The resulting linear regressions are reasonable, with regression coefficients (R2) ≥ 0.73 and no intercept, i.e., no intensity at zero thickness, and a linear increase in W and Co with increasing sample thickness. This demonstrates the method's potential for performing thickness scans and providing more reliable quantitative information on element distributions in non-homogeneous, thin soft matter materials.