1. Introduction

In a multitude of manufacturing processes, the accurate assessment of thickness across large optically transparent layers, within the range of 0.1–1 mm, is critically important. One prominent example is the slot-die coating of optical clear resin (OCR), an adhesive increasingly used in the lamination process for curved and free-form displays in automotive displays [1,2]. During the coating process, the slot width of the coater is dynamically adjusted to match the non-rectangular shape of the display panel. This adjustment, however, can cause non-uniform coating due to pressure changes within the slot nozzle. Therefore, the need for rapid thickness measurements across the entire OCR film area has become paramount to optimize the coating process and maintain consistent quality control, which otherwise diminishes production yields. Other applications requiring thickness measurement and mapping include the manufacturing of glass substrates for liquid crystal displays (LCDs), which typically span a thickness of 0.2–0.7 mm [3]. Variations in substrate thickness can not only limit the lithography’s depth of focus but also result in non-uniform cell gaps, leading to noticeable contrast deviations in displays [4]. Similarly, maintaining uniform thickness in carrier glass wafers, usually ranging from 0.1–0.5 mm, is vital for achieving even thinning of silicon wafers in three-dimensional stacked integrated circuit (3DS-IC) applications [5].

Numerous non-contact measurement systems have been developed for gauging thicknesses between 0.1–1 mm. These systems encompass displacement sensors such as capacitive sensors [6,7], laser triangulation sensors [8], and confocal displacement sensors [9]. While these sensors are capable of measuring thickness, they are more commonly used for surface measurements. Commercial thickness measurement systems often employ these sensors in a dual sensor geometry, where two sensors face each other and measure opposite sides of a sample to determine absolute thickness [10]. This dual sensor approach, however, has two notable drawbacks. First, it typically measures a single point or a few points at a time on the specimen, making it too slow for area measurement. Second, the necessity of access to both sides of the specimen can be inconvenient or even impossible during processes such as OCR coating. Alternatively, one-sided optical thickness measurements can be achieved with high precision using (chromatic) confocal microscopy [11–15] and various interferometry approaches [16–21]. Yet, like the dual sensor approach, these methods are often too slow for area measurement as they also typically measure a single point or a few points at a time. Compared to interferometry methods, spectroscopic reflectometry (SR) [22,23] offers a simpler optical configuration and is less susceptible to environmental disturbances, making it an ideal solution for cost-effective inline measurements in industrial settings. However, SR also primarily measures a point, and line measurement needed for inline area mapping has not been well established.

In this study, we introduce line spectroscopic reflectometry (LSR), a one-dimensional (1D) extension of point SR. LSR employs line beam illumination to simultaneously measure several thousand points on a specimen and captures the spectroscopic reflectance image with an area camera. We detail the principles of our optical system and provide the optical design for thickness measurement of dielectric films or layers in the range of 0.1–1 mm. We also build a proof-of-concept testbench and use it to demonstrate thickness measurements of microscope coverslips, glass slides, and OCR films on glass substrates over a measurement line length of up to 68 mm. By 1D scanning the OCR coated substrate, we demonstrate the inline area measurement capability of LSR, with measurement rates limited only by camera readout rates.

2. System design

2.1 Concept of line spectroscopic reflectometry (LSR)

Spectroscopic reflectometry utilizes the reflectance spectrum of self-interference within the specimen to measure thickness. As illustrated in Fig. 1(a), for a double-layer structure specimen, the total reflectance (R) [24] for a point of illumination can be formulated as

 

Fig. 1. Conceptual representation of spectroscopic reflectometry for thickness measurement. (a) Reflectance from a two-layer structure. (b) Simulated spectral reflectance signals for a Gaussian-shaped spectral source with a central wavelength (λ_C) of 885 nm and a full width at half maximum (FWHM; Δλ) of 35 nm. The incidence angle (${\theta _{in}}$) is 0°; Layer 1 exhibits a refractive index (${n_1}$) of ∼1.3907 (OCR) and a thickness (${d_1}$) of 100 µm; Layer 2 exhibits a refractive index (${n_2}$) of ∼1.5156 (soda-lime) and a thickness (${d_2}$) of 500 µm. (c) Spectral reflectance signals plotted over wavenumber (1/λ). (d) FFT magnitude spectrum of R.

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Here, r_{(j)(j + 1)} denotes the Fresnel reflection coefficients at the dielectric interface between j^th and (j + 1)^th media (i.e., j = 0 in air, j = 1 in layer 1, j = 2 in layer 2, and j = 3 in air), and ${\beta _j} = 2\pi {\lambda ^{ - 1}}{n_j}{d_j}\cos {\theta _j}$ where n_j, d_j, and θ_j are the refractive index, physical thickness, and transmission angle in the j^th layer (j = 1, 2), respectively. If the sample is a single layer (no layer 2; ${r_{23}} = 0$), Eq. (1) reduces to

For a chromatic light source with a central wavelength (λ_C) and a wavelength band (Δλ), the exponential term $\textrm{exp}({ - i2\beta } )$ induces oscillation in R with wavelength, under the envelope of source strength (Fig. 1(b)). This oscillation happens with a shorter period in space for a shorter center wavelength and thicker layer(s). Notably, at zero incidence angle, R becomes independent of light polarization. In our target thickness range of 0.1–1 mm, the fast Fourier transform (FFT) method is recognized as an effective technique for thickness retrieval [25]. The numerator of Eqs. (1) and (2) can be conceptually viewed as a linear superposition of a basis function of the form of $\textrm{exp}({ - i2\beta } )$ (as the denominator is close to one). By comparing this basis function with the FFT kernel function, $\textrm{exp}({ - i\pi fo} )$, it becomes evident that the FFT operation transforms R presented in the “spectroscopic wavenumber” ($f = 1/\lambda )$ domain (Fig. 1(c)) to the signal with several peaks at ${o_i}$ (Fig. 1(d)) in the “optical coordinate” ($o = 2nd\cos \theta $). Therefore, given the values of $\theta $ and n, the thickness ($d$) can be theoretically estimated from ${o_i}$, i.e., ${d_1}$ = 280.4/2/1.3907 = ∼100.8 µm and ${d_2}$ = 1530.7/2/1.5156 = ∼505.0 µm. However, the refractive index (n) is not a constant but varies with wavenumber. Relying on a constant refractive index value at the central wavelength can thus lead to a thickness overestimation of ∼1%. Such bias errors can be minimized by employing effective refractive indices [25]. These indices, while constant, account for the dispersion property of the layer material. In our above example, using the effective refractive index values reduced the bias errors to below 0.004%.

As illustrated in Fig. 2, LSR can be implemented using a cylindrical lens to generate line illumination in the y direction on the sample. The spectral reflectance for each y position is simultaneously captured by a complementary metal oxide semiconductor (CMOS) camera. This setup enables the measurement of sample thickness along a line in the y direction. Moreover, two-dimensional (2D) area measurement can be achieved by moving either the sample or the rest of the measurement system in the x direction, a scenario that occurs in OCR coating or substrate glass production. As there are no moving parts in the optical setup, the measurement speed is solely limited by the camera frame rates.

 

Fig. 2. (a) Proposed optical layout for line spectroscopic reflectometry (LSR). L, lens; Cyl, cylindrical lens; BS, beam splitter; G, grating. (b) An alternative LSR layout employing a spectrometer slit.

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Our LSR system in Fig. 2(a) is composed of three primary sections: illumination, relay optics, and spectroscopic detection. In the illumination section, a light source from a single mode fiber (SMF) is first collimated by the L1 lens, then cylindrically focused to form a line beam right after passing a beam splitter (BS). This intermediate line beam is located at the entrance slit plane of the spectrometer, with its width and length related to the spectral resolution and the camera sensor height in spectroscopic detection, respectively. The 2f-2f relay optics, implemented by L2 and L3 lenses, telecentrically expand the line beam to achieve a longer measurement length (h) and provide a sufficient working distance between L3 and the sample. The spectroscopic detection section includes a collimator (L4 lens), a diffraction grating (G), a focusing lens (L5), and a camera, where the reflectance signals are dispersed by wavelength in the x direction. To further simplify the setup, we chose not to use an entrance slit for the spectrometer, assuming that the line beam generated from an SMF source is sufficiently narrow and does not blur significantly upon transmission through the relay optics. If necessary, an alternative configuration using a spectrometer slit and an additional lens (L6) can be considered, as illustrated in Fig. 2(b).

In addition, among possible working wavelengths from visible to infrared (IR), we opt for an NIR band because the optical design of high spectral resolution spectroscopy (for capturing rapidly oscillating R in thicker samples) is less challenging than with visible light and NIR cameras are typically an order of magnitude cheaper than IR cameras. We thus selected a fiber-coupled superluminescent diode (SLD880S-A25, Thorlabs) with a center wavelength of λ_C = ∼885 nm (spectral FWHM: ∼35 nm) and an NIR-enhanced camera (acA2040-90umNIR, Basler; 2048 × 2048 pixels; pixel pitch: 5.5 µm) with a maximum frame rate of 90 frames/s.

2.2 System design

For a proof-of-concept demonstration, we designed an LSR system that can measure sample thickness within the range of 0.1–1 mm over a measurement line length of h = ∼65 mm. As per our simulation, the estimated period of reflectance signal oscillation for 1 mm-thick soda-lime glass substrate (n = ∼1.5156) was ∼0.256 nm near the central wavelength. Thus, we aimed to design a spectrometer with a two-fold higher spectral resolution (0.128 nm), considering practical aspects such as variations of oscillation periods within the wavelength band and the aberration-induced spectral resolution degradation by commercial lenses. The spectrometer was designed following the design guide [26] that details associated design variables and governing equations. According to Ref. [26], the focal length of L5 is given by

To generate the intermediate line beam with a width close to ∼13.6 µm, we used a 75 mm focal length for L1 (AC254-075-B-ML, Thorlabs) and a 150 mm focal length for the cylindrical lens (ACY254-150-B, Thorlabs). The intensity profile along the length of the line beam was close to Gaussian with an e^-2 diameter of ∼13.5 mm, which was larger than the height of the entire camera sensor. The illumination light was coupled into the system through a beam splitter (#14-644, Edmund optics). The lateral magnification of the relay optics was set to 6 via a pair of achromatic doublet lenses (f50, AC254-50-B-ML, Thorlabs and f300, Ø3-inch, #88-597, Edmund Optics), so that a measurement length of h = ∼67.6 mm on the sample was mapped into the full 2048 pixels of the camera sensor with a sampling interval of 33 µm.

3. Experimental setup

A test bench for LSR was constructed as shown in Fig. 3. The setup is built on an aluminum bread board, allowing the entire setup to be erected for a vertical arrangement, which is ideal for applications involving large-area substrates. The camera and linear stage were electronically controlled via a computer. To examine the illumination profile of the cylindrically focused line beam, we added an optical bypass (indicated by a yellow dotted line in Fig. 3), which involved a flipping mirror placed between L4 and the grating, a lens (f = 100 mm), and a secondary camera (pixel pitch: 2.74 µm). As shown in Fig. 4, the FWHM of the experimental line beam was 9.5 µm at y = 0 mm (30% narrower than our design requirement) and gradually increased up to ∼125 µm due to the decreasing working numerical aperture (NA) in the cylindrical lens for the circular intensity profile of the incident beam.

 

Fig. 3. (a) A photograph of the LSR setup (SMF, single-mode fiber). The green line visible on the sample indicates the measurement line, which extends ∼67.6 mm in the y direction.

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Fig. 4. (a) Two-dimensional illumination profile of the line beam. (b) The FWHM of the line beam across the y coordinate.

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Given the narrowband of wavelengths (FWHM: ∼35 nm), we assumed uniform spectral transmission through the lenses and grating, and uniform quantum efficiency of the NIR camera. Spectral response calibration may not be as critical in our target thickness range, as the thickness is primarily determined by the oscillation frequencies of spectral reflectance signals, rather than their overall amplitude envelope. However, wavelength calibration is of paramount importance. For this, we connected an SMF-coupled tunable femtosecond laser (Chameleon Vision II, Coherent) to the fiber adapter of our NIR source, loaded a 4” silicon wafer as a mirror sample, and captured 20 spectroscopic images by sweeping the command wavelength of the laser from 930 nm to 835 nm (Fig. 5(a)). The horizontal (x) cross-sectional intensity profiles in each spectral image were fitted with a skewed Gaussian model to find the location of the peak wavelength with sub-pixel accuracy for each y-pixel index. These data of 20 constant wavelength lines were fitted using a 3^rd order xy polynomial function, yielding a 2D wavelength map on the camera detector as depicted in Fig. 5(b). We note that the slightly curved spectral images in Fig. 5(a) were mainly due to conical diffraction [27] from our grating, which was fully incorporated in our wavelength calibration. The calibrated spectral sampling interval was ∼0.052 nm near λ = 885 nm, closely aligning with our first-order design (∼0.0517 nm).

 

Fig. 5. Wavelength calibration of the spectrometer camera. (a) Images captured by the spectrometer camera of a calibration laser source at varying input wavelengths. The numbers indicate the actual peak wavelength of the source, as measured by a spectrometer (CCS200/M, Thorlabs). (b) A two-dimensional wavelength map over the camera pixels, generated from the image data in (a).

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For thickness measurements, we captured spectroscopic images with a typical frame exposure time of 60-80 µs and ran the camera at 90 frames/s to showcase inline measurement. While thickness analysis could be performed in real time, we conducted post image processing as a proof-of-concept demonstration in the following procedure in MATLAB. The horizontal axis of the image data was resampled in terms of wavenumber with uniform sampling intervals, using a 2D interpolation function (interp2). The resampled images, $R({1/\lambda ,y} )$ with 2048 × 2048 data points, were then 1D Fourier transformed using the fft function with 1× zero padding (4096 data points in the wavenumber dimension) to double the sampling resolution in the transformed optical coordinate (o). The FFT data were interpolated with cubic splines from the interp2 function to locate peak positions with much enhanced accuracy, from which the thickness information of the sample was extracted.

4. Measurement results

4.1 Single layer measurement

To assess the measurement performance for thickness near the lower design boundary, we evaluated a #1.5 H microscope coverslip (thickness: 170 ± 5 µm, CG15KH1, Thorlabs). The coverslip, with dimensions of 25 × 50 mm², was measured over a 50 mm length. The captured spectral reflectance image displayed high contrast fringes modulated under the light source spectrum (Fig. 6(a)). The reflectance spectrum exhibited an oscillation period of ∼1.9 mm^-1 and a fringe visibility, $({{I_{\textrm{max}}} - {I_{\textrm{min}}}} )/({{I_{\textrm{max}}} + {I_{\textrm{min}}}} )$, of 0.81 at around 1.13 µm^-1 wavenumber. The 1D FFT of this spectral image in the wavenumber direction produced a prominent peak at o = ∼522 µm (Fig. 6(b)). Figure 6(c) shows the retrieved thickness profile using the effective refractive index of the coverslip glass (D 263 M, Schott) of 1.5284 for λ = 832-941 nm (n = 1.5124 at λ = 832 nm and n = 1.5103 at λ = 941 nm). The calculated coverslip thickness averaged 170.63 µm with a total thickness variation (TTV) of ∼300 nm over the 50 mm length. The spatial fluctuation of the thickness profile in the y direction, calculated by the difference between the original thickness profile and a moving averaged thickness profile over a 1 mm span, was about 20 nm at the line center (y = 0 mm) and increased to ∼85 nm near the line edge (y = ±25 mm). This increased fluctuation could be due to the reduced fringe visibility (∼0.4) at the line edge, lowering the magnitude of the FFT peak from 8 (at y = 0 mm) to ∼2 (at y = ±25 mm). Such reduced visibility resulted mainly from a wider line beam profile (Fig. 4(b)).

 

Fig. 6. Thickness measurement of a #1.5 H microscope coverslip. (a) A spectral reflectance image in wavenumber space, with its cross-sectional profile at y = 0 mm. (b) 1D FFT magnitude of the reflectance image from (b), along with its cross-section at y = 0 mm. (c) Reconstructed thickness profile.

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Next, we assessed the measurement performance at the upper design boundary of 1 mm thickness using a standard microscope glass slide (material: soda-lime, dimensions: 76 × 26 mm²), measured along its 76 mm length direction. The procedure for data acquisition and analysis was the same as the procedure applied to the coverslip measurement. As shown in Fig. 7(a), the fringe visibility from such a thick sample was lower than that from the coverslip, measuring ∼0.18 at y = 0 mm. Nonetheless, fast-changing fringes with a period of ∼5 data points (or ∼0.33 mm^-1) were successfully captured. This fringe period corresponded to ∼0.26 nm in wavelength space, which aligned well with the 0.256 nm considered in our system design. The lower visibility resulted in a weaker magnitude of the FFT peak at o = ∼3009 µm when represented in optical coordinate (Fig. 7(b)), and the peak magnitude further reduced with increasing $|y |$ due to the decreasing visibility (as low as ∼0.05 at y = 17 mm). We retrieved thickness only when this peak magnitude exceeded 20 times the magnitude of neighborhood background noise levels, leading to the thickness profile over a 33 mm length in Fig. 7(c). We note that the 33 mm measurement length matched the 36 mm length of the line beam (Fig. 4(b)) over which the beam width stayed below 27.2 µm, a requirement for measuring a thickness of 1 mm. The glass slide was found to have an average thickness of 992.0 µm and a TTV of ∼1.6 µm across the 33 mm length, using the effective refractive index of soda-lime glass. Compared to the coverslip, the spatial fluctuations of thickness profile were larger, i.e., ∼82 nm at y = 0 mm and ∼474 nm at both ends (y = −16.2 mm or 16.8 mm), yet these were <0.05% of their own averaged thickness in both samples.

 

Fig. 7. Thickness measurement of a 1 mm-thick microscope glass slide. (a) A spectral reflectance image in wavenumber space, with its cross-sectional profile at y = 0 mm. The inset shows a zoomed view near 1.13 µm^-1. (b) 1D FFT magnitude of the reflectance image from (b), along with its cross-section at y = 0 mm. (c) Reconstructed thickness profile.

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To evaluate measurement repeatability, we conducted 1000 continuous measurements for the loaded coverslip and glass slide samples (from Figs. 6 and 7) respectively, and calculated the standard deviation of their thickness profiles as shown in Fig. 8. The standard deviation between the coverslip and the glass slide seemed roughly proportional to their thicknesses at y = 0 mm: 9.2 nm for the coverslip (170.6 µm) and 55 nm for the glass slide (992.0 µm). Due to the visibility degradation of spectral reflectance with $|y |$, the standard deviation also deteriorated accordingly. Yet, the standard deviation of the coverslip stayed below 20 nm over the entire 50 mm length of measurement, and the standard deviation of the glass slide was below 60 nm over a 22 mm length of measurement. We believe that designing a more uniform line beam width over y than in current demonstration, or using a spectrometer slit, will yield better uniformity in standard deviation across the entire measurement length.

 

Fig. 8. Standard deviations from 1000 repeated thickness measurements of (a) coverslip and (b) slide glass.

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4.2 Two-layer measurement

We also evaluated a two-layered sample, an OCR coated film on a 0.5 mm-thick soda-lime substrate (n = 1.5156 at λ = 885 nm), where OCR (XE14-D0059, Momentive Inc.; n = 1.3907 at λ = 885 nm) was slot-die coated in the y direction with a target thickness of 100 µm. As shown in Fig. 9(a), the measured reflectance image exhibited a fringe pattern containing a few harmonics, which mirrored our simulation results (Fig. 1(c)) except for a degraded visibility. This degradation could be due to the finite spectral resolution of our spectrometer, which our simulation did not account for. Using the 1D FFT analysis of the spectral reflectance image (Fig. 9(b)), the first two spectral peaks (at o = ∼293 µm and ∼1607 µm) that represent OCR and substrate thicknesses, respectively, were clearly identified. The OCR thickness profile was successfully retrieved over the full 67.6 mm line length in Fig. 9(c), providing an average thickness of 102.7 µm with a TTV of 6.0 µm. Across this measurement line, the coating uniformity (calculated as TTV over average thickness) was 5.8%, which is within the typical 10% process tolerance in OCR coating. Despite a small refractive index difference (∼0.12) between OCR and soda-lime substrate, the 0.5 mm-thick glass substrate was simultaneously measured well over a 42 mm length, which was wider than 33 mm for the 1 mm-thick glass side. The glass substrate was found to have an average thickness of 530.0 µm and a TTV of ∼0.6 µm (Fig. 9(c)).

 

Fig. 9. Thickness measurement of an OCR film on a glass substrate. (a) A spectral reflectance image in wavenumber space, with its cross-sectional profile at y = 0 mm. (b) 1D FFT magnitude of the reflectance image from (a), along with its cross-section at y = 0 mm. (c) Reconstructed thickness profiles of the OCR film and the substrate.

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4.3 Inline area measurement

To demonstrate the inline area measurement capability of LSR, we measured the thickness of the OCR sample (previously measured in Fig. 9) while scanning the sample in the x direction over a span of 100 mm at a speed of 3.0 mm/s (Fig. 10(a)). We note that although our scan direction was not parallel to the OCR coating direction (instead being orthogonal in this demonstration), this measurement is still sufficient for demonstrating inline measurements. The camera frame rate was maxed out at 90 frames/s (frame exposure time: ∼70 µs), resulting in a measurement interval in the x direction of ∼33 µm. Given the high brightness of the spectral reflectance signals (as shown in Fig. 9(a)), the inline measurement speed was limited only by the camera frame rate. We post-analyzed a series of 3030 spectral reflectance images to reconstruct the area maps of thickness for both OCR and substrate layers (Fig. 10(a)). This post-image processing task was completed in 162 s in MATLAB, achieving a rate of ∼18.7 images/s. This processing rate could be significantly improved by harnessing graphics processing unit (GPU) computing, enabling real-time implementation of such image processing. The measurement widths in the y direction for the OCR and substrate layers were maintained as demonstrated in Fig. 9(c). The substrate was measured to have an average thickness of 529.1 µm with a TTV of ∼3.0 µm over the area, while the OCR film showed an average thickness of 103.7 µm with a TTV as large as ∼9.9 µm across the measured area. Interestingly, vacuum table grid patterns with a grid interval of ∼35 mm (marked with black arrows) were visible in the OCR thickness profile, which were caused by the different intensity distribution of ultraviolet light near those vacuum grids used for OCR curing. Our method allowed to examine spatial thickness uniformity across the coating line of the slot-die coater at different coating times (Fig. 10(b)) and coating roughness of local areas (Fig. 10(c)). These results underscore the potential of our method for inline and area measurement of thickness, which could be useful for diagnosing coating processes and monitoring coating quality.

 

Fig. 10. Area measurement of thickness. (a) Schematic of an OCR film on a soda-lime glass substrate, accompanied by area maps of the reconstructed thickness profile for each layer. The sample underwent scanning in the x direction. (b) Cross-sectional thickness profiles, indicated as blue and red lines in (a). (c) Enlarged view of the white boxed region in (a) under an adjusted colormap, along with two cross-sectional thickness profiles.

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5. Conclusion and discussion

LSR represents a substantial advancement over traditional SR techniques by extending from point to line measurement, accelerating the measurement speed by a factor of over two thousand. This method, which combines line probe beam with line spectroscopy, offers a simple and cost-effective optical solution, with a measurement speed constrained only by the camera’s frame rate. Our method is fully compatible with the simultaneous thickness measurement of multi-layered transparent samples, making it an excellent choice for large-area inline measurements across a range of industrial applications, including OCR coating for free-form displays and glass substrate/wafer manufacturing for the display and semiconductor industries.

In our preliminary demonstration, we attained a line measurement span of 33–68 mm and a measurement repeatability of 9–55 nm, both primarily dictated by sample thickness. Generally, thinner samples (0.1 mm thick) produce a slowly-changing reflectance spectrum that can be captured with high visibility, leading to superior repeatability in thickness measurement. The restricted measurement length to 33 mm for the 1 mm-thick glass slide was due to the overly wide line beam width beyond this length in our implementation, a result of the cylindrical focusing of circular NIR light. We anticipate that the use of a Powell lens [28], renowned for generating a more uniform beam width and intensity profile across the line beam, could extend the measurement line length. Alternatively, a mechanical slit could be used to maintain the spectral resolution of the line spectrometer, as shown in Fig. 2(b). Considering commercially available telecentric lenses offering a maximum field of view (FOV) of ∼240 mm (designed for visible light), we believe that the measurement line could be extended to a similar level with the development of large FOV, NIR telecentric lenses. Furthermore, arranging multiple LSR heads with these large FOV telecentric lenses in parallel could enable high-throughput inline area measurement of OCR films, even for large generation displays.

We note that preliminary comparisons of the thickness profile for the 1-mm-thick slide glass, using our method and a commercial chromatic confocal sensor, have shown good agreement, though these results are not included here. Comprehensive validations with other measurement approaches across a broader range of specimens will be a crucial next step in our studies. Moreover, while a comprehensive uncertainty analysis is planned for future studies, we recognize key sources of uncertainty in our thickness measurements. The accuracy of the refractive index is critical; a typical 0.2% measurement error, which equates to Δn = ∼0.003 for glass, can lead to a 0.2% thickness discrepancy. Our analysis suggests that a deviation of 0.5 nm in wavelength calibration results in a 0.11% thickness error. The FFT peaks in the optical coordinate (o) are discerned with a resolution of ∼8 nm, translating to a 0.008% error for 100 µm-thick samples. Testing our method’s repeatability over 1000 measurements yielded a minimal error of ∼0.005% (1σ) of the sample thickness. We also posit that our method remains stable against environmental disturbances, as the reflectance spectra (R) are from the sample’s internal self-interference. Given these considerations, we believe that our method meets the accuracy needed to evaluate the 10% uniformity standard in OCR coating and other industrial applications that require discerning variations of a few percent in thickness uniformity.

While our demonstration primarily addressed up to two transparent layers, reflecting the typical configurations in the highlighted industrial applications, our system inherently has the capability to measure specimens with more layers. For successful measurements, several conditions are essential: both the total optical thickness of the specimen and the thinnest optical thickness of any layer must fall within the system’s designed measurement range; a discernible refractive index difference between adjacent layers is needed, ideally at least 0.02; each layer should have a distinct optical thickness to ensure accurate identification; and prior knowledge of the layer sequence is crucial, as our method does not automatically determine the layer order.