Interferometry of surfaces with well-defined topography in the surface force apparatus

Journal of Colloid and Interface Science 412 (2013) 82–88

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Interferometry of surfaces with well-defined topography in the surface force apparatus Rohini Gupta 1, Joëlle Fréchette ⇑ Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, United States

a r t i c l e

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Article history: Received 16 July 2013 Accepted 4 September 2013 Available online 17 September 2013 Keywords: Surface forces apparatus Topography Surface structure Multiple beam interferometry

a b s t r a c t We studied the multiple beam interferometry of surfaces with well-defined microscale features in the surface force apparatus (SFA). The structures investigated consist of hexagonal arrays of microscale cylindrical posts made out of the photoresist SU-8. The ability of the SFA to visualize the profile and topography of the interacting surfaces leads to the observation of discontinuities in primary fringes of equal chromatic order that are caused by the microscale structural features. The shift in wavelengths has been analyzed to extract the post height and compared to independent profilometry measurements. The analysis based on the shift in wavelength is shown to be viable only when the order of the fringe and the position of the discontinuity is precisely known and within the field of view. Analysis of the full profile of the interacting surface for two orthogonal 2-dimensional slices can be used to determine how the surface lattice is oriented within the point of closest approach. Finally, we discuss cases in which the structural features detrimentally affect the spatial resolution of the SFA. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The surface force apparatus (SFA) [1–5] is a technique to measure the interactions between two macroscopic surfaces. Central to the SFA is its exquisite ability to resolve absolute surface separation within 0.1–0.3 nm using multiple beam interferometry (MBI) [6,3,7]. The traditional Fabrey–Perot interference filters employed for MBI in SFA consist of a medium bound by two thin (2– 4 lm), transparent, and molecularly smooth mica pieces coated with 50 nm of silver on the back. The presence of the two semitransparent bounding (silver) films facilitates analysis of transmitted light [3]. Alternatively, reflected light can be analyzed for interferometers where one of the bounds is opaque or non-transparent [8]. Furthermore, the surfaces that can be investigated using the SFA are not limited to mica, and may not necessarily be molecularly smooth. Over the years, substrates such as mica coated with metal [9–15], inorganic [16,17], organic [18–20], and polymer [21–27] thin films, and standalone polymer [28] and inorganic [29] surfaces, have also been explored. The use of generic surfaces in the SFA has been exploited for the investigation of rough [22,23,28,30,31] or patterned [22,32,33] surfaces and has helped address scientific and technical concerns such as surface adhesion, deformation, friction, and wear that are relevant in engineering

⇑ Corresponding author. Fax: +1 (410) 516 5510. E-mail address: [email protected] (J. Fréchette). Present address: Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, United States. 1

0021-9797/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2013.09.008

applications. Most generic surfaces including metal films bear nanoscale surface roughness, and MBI can be employed not only to resolve absolute surface separation but also to estimate surface roughness (for example how the roughness varies with applied load or when in contact with another surface) [9,10]. Furthermore, non-optical capacitance-based estimation of surface separation in a modified surface force apparatus can be employed for opaque or non-transparent surfaces, further extending the capabilities of SFA (this method does not provide topographical information about the surfaces) [34–40]. Both interferometry and capacitance-based surface force apparatus offer similar resolution for surface separation [37]. Surfaces with well-defined topographical features (length scales significantly larger than surface roughness) are at the heart of the design of biomimetic adhesives, superhydrophobic surfaces, and metamaterials, where topography plays a central role in surface adhesion, friction, wetting, and optical properties. The SFA with MBI has so far been limited to the investigation of surfaces with intrinsic random nanoscale roughness or nanoscale patterns e.g., friction caused by a structured surface inspired by the gecko has been studied using SFA [41–44], but without interferometrybased surface separation estimation. It is important, to demonstrate the compatibility of structured surfaces with MBI, especially considering the advantages of measuring absolute surface separation and bearing in mind a possible loss of resolution in surface separation caused by the surface features. The ability to introduce surfaces with microscale topographical features in the SFA and resolve absolute surface separation using MBI would allow us to

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expand the range of materials and surfaces that can be investigated with this technique and help uncover how surface structures modulate surface interactions. Here, we demonstrate the design, fabrication, and use of surfaces with well-defined microscale features that are compatible with the surface force apparatus. The structured surfaces, here, consist of hexagonal arrays of SU-8 cylindrical posts prepared using standard photolithography procedure on the silver side of the mica pieces. We show how microscale structural features (with length scales significantly larger than the nanoscale roughness present on the surfaces) are mirrored as discontinuities in primary fringes and that the shift in their wavelengths is consistent with a difference in optical path. Using analysis proposed by Zeng et al. [32] for rough polymer films, we highlight how MBI can be employed to extract topographical dimensions of the structural features and discuss limitations of the method.

1.1. Background When white light is incident normally through a Fabrey–Perot interference filter, multiple beam interferometry (MBI) [6,3,7] results in transmission of discrete wavelengths that satisfy the criteria for constructive interference, upon being reflected repeatedly between the two reflective films. The resulting fringes of equal chromatic order (FECO), or an infinite series of alternating sharp bright and dark bands (see Fig. 1a as an example of FECO), are dispersed via a grating spectrograph. The positions of the known discrete spectral wavelengths of mercury are used to calibrate the spectrograph. The wavelengths of ‘‘primary’’ fringes are sensitive to the thickness and index of refraction of the components of the interference filter. The nanoscale roughness associated with generic surfaces has been shown to result in small yet discernible shift in the wavelengths of the primary fringes due to a change in the optical path [9,10]. Zeng et al. also employed arguments based on the difference in optical path to characterize the height of surface features in polymer films [32]. The use of highly reflective silver suppresses the secondary, tertiary, and gap fringes. The secondary fringes, if observed, do not undergo wavelength shift with a change in the optical path between the two reflective surface, but their shape is susceptible to the topography and deformation of the surfacemedium interface [45]. MBI, therefore, allows for accurate and independent determination of the thickness and/or refractive index and roughness of the component(s) of interference filter under investigation.

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The interference filter is mounted onto rigid and optically transparent cylindrical lenses (radius of curvature, R  1–2 cm) arranged orthogonal to each other, a configuration that is geometrically equivalent to that of a sphere interacting with a plane. In this configuration the interference filter acquires curvature, which makes the medium thickness and, consequently, wavelengths of the FECO a function of the lateral position as shown in Fig. 1b. The use of macroscopic surfaces enables the visualization of the 2-dimensional geometry of the interacting surfaces, which is reflected in the shape of the FECO. For example, the sphere-plane geometry is visible in the curved fringes observed for two crossedcylinders as shown in Fig. 1a, with the vertex of the parabola corresponding to the point of closest approach (PCA) between the two surfaces. For two crossed-cylinders in contact with each other, the FECO exhibit a flat section that corresponds to the zone of contact and reflects the elastic deformation inside and outside the interference filter. Due to the finite width of the FECO, their corresponding wavelengths are represented by the center of mass (CoM) of the transmitted light intensity measured at a given lateral pixel position, as shown in Fig. 1c for the lateral pixel position corresponding to the point of closest approach indicated by the white line in Fig. 1a. The wavelengths of primary fringes are sensitive to the thickness and index of refraction of the components of the interference filter. The FECO undergo red shift with an increase in the optical path via an increase in either the thickness or index of refraction of either of the components of the interference filter, and vice versa. The shift in the wavelengths of the FECO can, therefore, be used to resolve changes in medium thickness within 0.1– 0.3 nm and index of refraction within 0.001–0.01 [3,46]. Sharp changes in index of refraction result in discontinuities in the FECO only in even (and not odd) fringes for small medium thickness, which can be used to visualize and investigate the presence of heterogeneities in the optical path e.g., capillary condensation resulting in an annular liquid meniscus between surfaces in the presence of condensable vapors [47–51]. The final step is to convert the wavelengths of FECO to surface separation (and/or refractive index). Analytical solutions for simultaneous estimation of medium thickness (less than 200 nm) and index of refraction are available for the following interference filters: symmetric three and five layer [3], asymmetric two layer [3], general three layer [52,53], and three layer with two outer layers of the same material but different thicknesses [52]. These analytical solutions require one in-contact fringe wavelength and its fringe order; the medium thickness and index of refraction can

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Fig. 1. (a) FECO resulting from an asymmetric silver/SU-8/oil/SAM/silver interference filter, (b) wavelength versus pixel position translated to surface separation versus lateral dimension corresponding to the white box in (a), and (c) transmitted light intensity as a function of wavelength at a given lateral pixel position indicated by the white line in (a).

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then be estimated from the shift in the wavelength. The multilayer matrix method [54,55] based on the solution of Maxwell equations to calculate the intensity of each of the transmitted wavelengths has been used for more complicated multi-layer asymmetric interference filters. To facilitate the transformation or inversion of the transmitted intensity to a medium thickness and/or index of refraction using the multilayer matrix method, Heuberger devised an elegant numerical algorithm called Fast Spectral Correlation [56], which is employed here. The Fast Spectral Correlation enables fast and accurate analysis of MBI spectra (multiple fringes at once) wherein the sum of transmitted intensity is calculated for multiple fringes for a given medium thickness and/or index of refraction; the unknown parameter or combination of parameters (here oil thickness or surface separation) that maximizes the sum of transmissivities is the optimal solution.

3 min, 95 °C for 5 min and 65 °C for 3 min. Upon exposing to ultraviolet radiations at 140 mJ/cm2 followed by post-exposure bake identical to the previous baking step, spin-coated SU-8 forms a contiguous layer resulting in uniform SU-8 surfaces with nanoscale roughness. Thinner SU-8 2000.5 or 2002 of appropriate thickness is spin-coated onto the existing SU-8 contiguous layer followed by baking (same procedure as earlier). The second thinner layer is exposed to ultraviolet radiations at 100 mJ/cm2 through a chromeon-glass mask, followed by the post-exposure bake and developing for 3 min. Excess SU-8 developer is removed using isopropanol, and the sample is dried with compressed air to form structured SU-8 surfaces. The silvered mica piece with SU-8 is removed from the backing sheet and glued (Epon 1004 epoxy) mica side down onto a cylindrical lens (radius of curvature, R  2 cm), followed by hard baking at 150 °C for 30 min. The cylindrical lens is then screwed onto the fixed (immobile) top mount of the SFA.

2. Materials and methods 2.4. Surface characterization 2.1. Surface preparation

The backing sheet with silvered mica pieces were immersed in 1 mM hexadecane thiol (92%, Aldrich) solution in ethanol (200 proof) overnight to render the silver hydrophobic (water contact angle 107°). Thereafter, the backing sheet was removed and rinsed thoroughly with ethanol to remove any excess reagents. The smaller mica piece with hydrophobic silver is removed from the backing sheet and glued (Epon 1004 epoxy) mica side down onto the cylindrical lens (radius of curvature, R  2 cm). The cylindrical lens is then mounted on the cantilever connected to the microstepping motor inside the SFA.

The structured SU-8 consists of a hexagonal array of cylindrical posts as shown in Fig. 2a. The diameter of cylindrical posts d and the channel width w are dictated by the pre-designed chromeon-glass mask. The post height or channel depth D, however, is controlled via the thickness of the second SU-8 layer and is determined by stylus profilometry measurements performed on the step height in the structured SU-8 layer on top of the thicker contiguous SU-8 layer. The topographical features of the different surfaces investigated here are presented in the Table 1. The epoxybased negative photoresist SU-8 is chosen as the material for the structured surfaces because of its ease of fabrication using standard photolithography procedure and transparency. Hydrophobic silver is chosen as the second surface to reduce the number of layers in the optical filter. Both of the surfaces are submerged in silicone oil (loil = 1.4022). A schematic illustrating the topographical features of structured SU-8 investigated in this work along with a representative scanning electron micrograph and SFA configuration of structured SU-8 (Surface B) interacting with a hydrophobic silver film across viscous silicone oil are shown in Fig. 2. The mica on both top and bottom surfaces is not part of the interferometer,

2.3. Uniform or structured SU-8 (top surface)

Table 1 Structured SU-8 surfaces investigated in this work.

1 cm  1 cm muscovite mica pieces (Ruby, ASTM V-1, S&J Trading) were cleaved, cut using hot platinum wire, and placed on a larger and thicker freshly cleaved mica backing sheet in a laminar hood. Thermal evaporation (Kurt J. Lesker Nano38) was used to deposit 50 nm of silver (99.999% purity, Alfa Aesar) on the cleaved mica pieces (thickness = 2–8 lm) at a rate of 3–4 Å/s. 2.2. Hydrophobic silver (bottom surface)

The cleaved and silvered mica piece is used to support and handle both uniform and structured SU-8 (negative photoresist SU-8 2007, 2002, and 2000.5; MicroChem) surfaces. Prior to spin-coating SU-8 2007 onto the silver side at 5500 rpm for 1 min, the backing sheet with one of the silvered mica pieces is taped to a glass slide. The smaller mica piece with SU-8 is then removed and placed on a freshly cleaved mica backing sheet followed by baking at 65 °C for

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Fig. 2. (a) Schematic of the hexagonal array of cylindrical posts constituting the structured surfaces and (b) a scanning electron micrograph (tilt angle of 30°) of structured SU8 Surface B. (c) Schematic for the SFA configuration employed here showing a structured SU-8 and hydrophobic silver separated by silicone oil.

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but its silver film serves as one of the two reflective layers (the layers constituting the interferometer are shown in Fig. 2c). 2.5. Interferometry analysis Note that the structural features under consideration are micron scale and are much larger than the nanoscale roughness that is also present on all the surfaces considered here. The SU-8 and self-assembled monolayer (SAM) thicknesses are estimated using the wavelengths of the in-contact FECO at the top of a post, which may undergo a small shift (ignored in our measurements) due to nanoscale surface roughness associated with both the self-assembled monolayer and the SU-8 [9,10]. For an asymmetric silver/ SU-8/oil/SAM/silver interference filter, Fast Spectral Correlation [56] devised by Heuberger in conjunction with the multilayer matrix method [54,55] is used to estimate the unknown medium (here, oil) thickness. Out of contact, wavelengths of the FECO can be translated to surface separation or oil thickness as a function of the lateral position and used to calculate the radii of curvature of the interacting cylinders as shown in Fig. 1b. The lateral resolution needed to calculate the radii of curvature is dictated by the optical magnification e.g., the lateral resolution in our case is 2.64 lm/pixel for 7.4 lm-sized pixel, 8  8 binning, and 22.42 optical magnification. The wavelengths at the vertex of the parabolic fringes are used to estimate the surface separation at the point of closest approach for a sphere-plane configuration as shown in Fig. 1c. 3. Results and discussion The interferometry of three distinct structured surfaces with different topographical features (Table 1) was investigated using the surface force apparatus. The ability of the SFA to visualize the geometry of interaction of the two surfaces allows for the microscale structural features present on the surface to appear as discontinuities in the FECO due the difference in optical path. The FECO shown in Fig. 3a, d, and g correspond to asymmetric silver/structured_SU-8/oil/SAM/silver interference filters for Surfaces A and B and consist of hexagonal arrays of SU-8 cylindrical posts of diameter d separated by channels of width w and depth D prepared using standard photolithography (see Fig. 2a for a schematic). An increase in optical path, as in the case of light transmitted through the SU-8 posts versus the channels filled with oil results in a red shift in the wavelengths of the FECO. For an individual fringe (for example see the white box in Fig. 3a, d, and g), the wavelength corresponding to the center of mass (CoM) of the transmitted light intensity can be plotted as a function of lateral pixel position, such as shown in Fig. 3b, e, and h. As expected, the wavelengths of FECO corresponding to the channels filled with oil of a lower index of refraction vis-à-vis SU-8 are blue-shifted compared to those corresponding to the SU-8 posts. If the index of refraction of oil and SU-8 were equal, the discontinuities would disappear. The shift in the wavelength due to the difference in optical path for the post versus the channel can be used to independently determine the channel depth D using the arguments proposed by Zeng et al. using Eq. (1) [32].

D¼

nðkn;p  kn;c Þ ; 2ðln;p  ln;c Þ

ð1Þ

where kn;p and kn;c are the wavelengths corresponding to post and channel, respectively, ln;p and ln;c are the index of refraction of SU-8 and oil, respectively, and n is the fringe order as given by n ¼ kn1 =ðkn1  kn Þ. We observe excellent agreement between the channel depth independently measured using profilometry and that calculated using Eq. (1) as shown in Table 1. Care must be taken to

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insure the wavelengths for the post and channel used are of the same fringe order. As the depth of the channel increases, the same order fringe for the posts and channels will not be present at once in the field of view of the imaging spectrometer (this critical depth will be a function of the dispersion of the diffraction grating employed). This resolution limit also depends strongly on the difference in refractive index between the medium and the structured material, a larger difference in refractive indices will lead to a lower limit in the maximum depth that can be resolved (to have the same order fringe present in the field of view). In these cases, the structural features are still visible as discontinuities in the FECO but Eq. (1) cannot be employed. Alternatively a more detailed multilayer matrix solution for the differences in thickness can still be achieved or an analysis based on fringes of different order [53] could potentially also be employed. An additional constraint based on our experimental observation illustrates that this equation cannot be employed for channel depths greater than 0.8 lm, which is the depth when the channel of a certain order of fringe is observed to overlap/merge with the post of the higher order fringe as in the case of Surface C (discussed at length later in the article). To extract the surface separation or oil thickness from wavelengths of FECO, we need to determine independently the total SU-8 thickness for the two layers (contiguous thick layer and patterned thin layer, if present). To do so, we bring the two surfaces in contact and use the wavelengths of FECO corresponding to the top of a post in the zone of contact. When the two surfaces are not in contact, the vertex of the parabolic FECO with respect to the posts corresponds to the point of closest approach between the two surfaces in a sphere-plane configuration. The wavelengths of FECO corresponding to the point of closest approach are transformed to the minimum oil thickness or surface separation for the structured surfaces using Fast Spectral Correlation in conjunction with multilayer matrix method. Furthermore, the wavelengths of FECO and therefore, surface separation as a function of the lateral position can be used to calculate the radii of curvature of the interacting cylinders as shown in Fig. 3c, f, and i. Note that the surface separation or oil thickness for structured surfaces is measured from the top of a post, and therefore is not related to the channel depth. We can use interferometry to reconstruct independently the structural features of the surface under observation by combining the lateral imaging (resolution of 2.64 lm/pixel) and the shift in wavelengths caused by the difference in optical path of SU-8 posts vis-à-vis the channels filled with lower refractive index oil, as shown in Fig. 3a–c. Using this lateral mapping, we ascertain that the width of the channels are roughly a tenth of the diameter posts for Surface A, which is consistent with the size of the patterned features on the surface as determined by the design of chrome-onglass mask used. The width of the channels and posts obtained from a 2D interferometry slice is only equal to the microfabricated feature sizes if the slice is aligned with the center of the posts in the h1 0i direction, any other orientation will give different sizes for the channels and posts. Therefore, we can determine the orientation of the individual 2D slices on the structured surfaces by using the lateral imaging for two orthogonal directions (Surface B: Fig. 3d–f and g–i). For example, on Surface B we show how two orthogonal directions are aligned on the structured surface (shown by red lines in Fig. 2a, which is centered on a post). It can be a challenge, however, to determine the orientation of individual slices because the positioning has two degrees of freedom: rotation and translation with respect to a hexagonal array of cylinders. Certain combination of the dimensions of the topographical features results in more complicated (or interesting) observations. Surface C (as shown in Fig. 4a) for instance has a channel width that is comparable to the lateral resolution and the channel depth

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Fig. 3. Surface structure resulting in discontinuities in FECO for Surfaces (a) A, (d) B (0°), and (g) B (90°). Wavelength as a function of pixel position (b, e, and h) converted to surface separation as a function of lateral dimension (c, f, and i) and their corresponding radius of curvature (RoC).

is such that the channel of a certain order of fringe overlaps/merges with the post of the higher order fringe. In this special case, we cannot isolate the channels from the posts based on both lateral imaging and optical path difference arguments. Consequently, the center of mass (CoM) of the transmitted light intensity as a function of pixel position does not reflect the structure of Surface C as shown in Fig. 4b. One question that might arise when working with structured surfaces is whether the presence of discontinuities in the FECO leads to a loss in our ability to resolve accurately surface separation. Similar to smooth surfaces, sharp fringes obtained for structured Surfaces A and B can be modeled as Cauchy–Lorentz distribution of intensity of transmitted light with respect to wave-

length as shown in Fig. 5b, implying that the ability to resolve surface separation is the same as that for smooth surfaces. On the other hand, broad fringes, such as those obtained with Surface C can be modeled as a normal distribution as shown in Fig. 5d. In this scenario, the breadth of fringes in terms of distribution of intensity of transmitted light adversely affects our ability to resolve surface separation. The mean of the normal distribution of intensity of transmitted light with respect to wavelength can be used to determine the surface separation such that the standard error of the mean corresponds to the error associated with the estimation of surface separation. For Surface C, the breadth of the fringes leads to a ± 3 Å error in the estimation of wavelengths of FECO as indicated by the two vertical lines in Fig. 5d. If we assume that the

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mean of the normal distribution of transmitted intensity correspond to the posts, the wavelengths of the in-contact FECO can be used to estimate the SU-8 thickness. Furthermore, when out of contact, wavelengths of FECO at the same lateral pixel position as the in-contact FECO enables us to resolve the surface separation or oil thickness at the point of closest approach with respect to the posts within ±4 nm, which is an error much larger than what is usually attained in typical SFA experiments but still sufficiently accurate for many force measurements.

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In the SFA, well-defined microscale features present on surfaces appear as discontinuities in the FECO due to the ability to visualize the profile and topography of the interacting surfaces and are a result of the difference in optical path of the posts versus the channels. Here, the wavelengths of FECO corresponding to the channels filled with an oil of a lower index of refraction vis-à-vis SU-8 are blue-shifted compared to those corresponding to the SU-8 posts. The shift in the wavelength due to the difference in optical path for the post versus the channel can be used to determine independently the channel depth D when the fringe order and the position of discontinuity are precisely known. The comparison of 2-dimensional slices of the interacting surfaces at 0° and 90° provides valuable information regarding the orientation of the interacting surfaces with respect to the periodic array of the features present on the surface. For certain structured surfaces, broadening of fringes may result in larger error in surface separation (here up to ±4 nm), which is an error much larger than what is usually attained in typical SFA experiments.

Acknowledgments This work is supported by the Office of Naval Research – Young Investigator Award (N000141110629), the National Science Foundation under Grant No. CMMI-0709187, and partially by the Donors of the American Chemical Society Petroleum Research Fund under Grant No. 51803-ND5. We would like to acknowledge the help of Huy Vo during the use of Clark Hall Microfabrication Facility, Mark Koontz for the scanning electron micrograph, and Yumo Wang for experimental verification.

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[1] [2] [3] [4] [5]

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[6]

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[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

0.6

[18] [19]

0.4 [20] [21] [22]

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Wavelength (A) Fig. 5. (a and b) Cauchy–Lorentz distribution for sharp fringes that correspond to Surface A. (c and d) Normal distribution for broad fringes that correspond to Surface C and the associated ±3 Å error in the wavelength as shown by the vertical lines in (d).

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