Letter pubs.acs.org/ac
Distortion Correction for a Brewster Angle Microscope Using an Optical Grating Zhe Sun, Desheng Zheng, and Steven Baldelli* Department of Chemistry, University of Houston, Lamar Fleming Jr. Building, 3585 Cullen Boulevard, Room 112, Houston, Texas 77204-5003, United States S Supporting Information *
ABSTRACT: A distortion-corrected Brewster angle microscope (DC-BAM) is designed, constructed, and tested based on the combination of an optical grating and a relay lens. Avoiding the drawbacks of most conventional BAM instruments, this configuration corrects the image propagation direction and consequently provides an image in focus over the entire field of view without any beam scanning or imaging reconstruction. This new BAM can be applied to both liquid and solid subphases with good spatial resolution in static and dynamic studies.
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reconstructed with these stripes after they had been treated digitally to remove the distortion. The scan could be done by either moving the samples or the objective. This remarkable scanning method leads to good images, but the application range of chemical systems will be limited by blurring combinations of the separated images which results from the fast motion of the sample during scanning. Moreover, when aiming to quantitatively analyze a film’s properties,21−23 thickness for example, this digital correction might give artificial intensity so that the calculations and applications will be less reliable. To improve the imaging quality and avoid these drawbacks, Henon et al. constructed a BAM using a custom-made objective.17 The objective was assembled with a combination of two aplanetic lenses and two concentric spherical mirrors by which the entire plane of illuminated area was kept in focus with a resolution of 1 μm. This design acquired better BAM images without any other moving optics or image reconstruction software; however, the special objective was difficult and costly to fabricate. Also, its working distance, 3 mm, is quite small compared to modern long working distance objectives, which limits the space for experimental operation around the interface area. An alternative approach is described here using a commercial reflection grating to solve the problems of conventional BAM. The new distortion-corrected BAM (DC-BAM) minimizes the distortion at the oblique angle of incidence and is able to focus the entire field of view to match the observation plane without scanning or image reconstruction software. This inexpensive design can be applied to both solid and liquid subphases with
rewster angle microscopy (BAM) is an imaging technique based on the reflection of light at the Brewster angle. Theoretically, when an interface is illuminated by a collimated laser beam polarized in the plane of incidence at the Brewster angle of a substrate, the reflected beam will disappear.1 Generally, this angle can be calculated based on the Brewster condition: tan θB = nt/ni, where θB is the Brewster angle of a substrate, nt and ni are the refractive index of the substrate and incident medium, respectively. For an authentic interface, the reflection intensity at the Brewster angle shows a minimum but does not totally vanish due to the bulk inhomogeneity and the surface roughness.2 The presence of a thin film at the substrate surface will introduce a change of the interfacial Brewster angle, and consequently the area covered by the film will display a different reflectivity while the free area will remain at the reflectivity minimum. This reflectivity contrast reveals film properties, such as the molecular density, thickness of the film, optical anisotropy in the surface layer,3 and the interfacial morphology which are visualized through a microscope inclined at the Brewster angle. Since the first BAM was built,3,4 it has become an attractive and advantageous technique as a direct and noninvasive method to analyze the thin films on water surfaces. A wide range of BAM studies discussing morphology transformation of chemicals are reported every year, especially for amphiphilic molecules forming Langmuir and Langmuir−Blodgett films,5−8 investigation of the interfacial chemical reactions,9−12 and characterization of nanoparticles.13−15 Very few studies,2,16−19 however, focus on the improvements of the BAM instrument itself. Inherently, the limitation accompanying a conventional BAM is that the oblique angle configuration makes it difficult to magnify the entire sample onto the observation plane without spatial distortion.20 Meunier et al.3 applied a solution to these problems by confocal scanning the area of interest, retaining only a narrow stripe around the focal line each time. The final image was then © XXXX American Chemical Society
Received: November 29, 2016 Accepted: January 27, 2017
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DOI: 10.1021/acs.analchem.6b04738 Anal. Chem. XXXX, XXX, XXX−XXX
Letter
Analytical Chemistry
sample plane and the objective observation plane to be mismatched so that only a thin stripe in the field of view is in focus. Second, the shape of the captured image is severely distorted due to an uneven magnification in transverse and longitudinal direction by the so-called “keystone” effect.24 Quantitatively, this effect can be estimated by the equation: tan v = M tan θ1, where M is the transversal magnification of the objective and v is the image angle between the optical axis and the image normal. Hence, a sample will be much more distorted when an objective with higher magnification is utilized. Both effects are observed in Figure 3a, and only a
good contrast and resolution. Since it is scanning-free method, it can also be applied to the study of a dynamic interface.
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EXPERIMENTAL SECTION The DC-BAM is constructed based on a ruled optical reflection grating as shown in Figure 1. The resolution of the DC-BAM is
Figure 1. Side view of the DC-BAM setup. Figure 3. Images of an USAF 1951 optical target taken by (a) a conventional BAM and (b) the DC-BAM. Parts a and b are captured at the same position. Images taken by the DC-BAM of the (c,d) DPPC/ water interface and (e) SA/quartz interface.
tested with an USAF 1951 optical target. A Langmuir monolayer of dipalmitoylphosphatidylcholine (DPPC) on the water surface and a Langmuir−Blodgett monolayer of stearic acid (SA) on a z-cut quartz surface are tested by DC-BAM. More details of the instrument and experimental procedures are found in the Supporting Information.
narrow slice between element 3 and element 4 is in focus and the original square patterns composed of three dark stripes are magnified unevenly by “keystone” distortion to be trapezoids. The DC-BAM is designed to solve these problems concurrently by introducing a 1:1 relay lens and an optical grating. The relay lens transfers the image of a sample onto the grating surface with the image spatial ratio 1:1 so that the shape of the original object remains. The optical grating corrects the image propagating direction ensuring the entire field of view of the image stays in focus for the objective. The prerequisite of these corrections is that the three planes, objective focal plane, image plane, grating surface plane, are parallel, which determines the position of the grating and the relay lens. Since it is required that the image travels perpendicular to the objective focal plane, the grating should be carefully selected based on the grating diffraction angle and the grating efficiency. Typically, the first-order diffraction angle is considered because the diffracted beam in the first-order usually carries the highest diffraction efficiency among all orders. The grating diffraction angle is properly chosen according to the grating groove density and the incidence beam wavelength so that the image, which is carried by the diffraction beam, travels normal to the grating surface, i.e., the angle between the incident beam to the grating surface and the first-order diffraction beam equal to the Brewster angle of the substrate. This condition is achieved with certain selected grating groove density N given by the grating equation:
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RESULTS AND DISCUSSION Distortion Correction. The image distortion, which is inevitable in conventional BAM, results in two different effects: limited depth of focus and differential magnification effect. As shown in Figure 2, first, unlike the conventional optical microscope, the oblique incident angle θ1 of a BAM causes the
sin α + sin βm = Nmλ
Figure 2. Scheme of a conventional oblique viewing system. B
DOI: 10.1021/acs.analchem.6b04738 Anal. Chem. XXXX, XXX, XXX−XXX
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Analytical Chemistry Table 1. Length−Width Ratio Measurement of Group 5 Elements on USAF 1951 Optical Target in Figure 3a,ba length−width ratio measurement in transverse direction length in pixels elements
DC-BAM
BAM
1 2 3 4 5
154.67 144.33 126.00 110.33 103.67
111.33 95.00 82.67 73.00 72.00
length in pixels
width in pixels DC-BAM
ratio
BAM
DC-BAM
31.00 19.33 4.99 29.00 15.67 4.98 25.33 12.33 4.97 22.00 11.00 5.02 20.67 11.33 5.02 length−width ratio measurement in longitudinal direction width in pixels
aberration (%) BAM
DC-BAM
BAM
5.76 6.06 6.70 6.64 6.35
0.21 0.46 0.51 0.30 0.31
15.19 21.25 34.10 32.73 27.10
ratio
aberration (%)
elements
DC-BAM
BAM
DC-BAM
BAM
DC-BAM
BAM
DC-BAM
BAM
1 2 3 4 5
151.33 135.67 124.33 111.00 97.33
168.00 142.00 125.33 112.33 71.67
30.33 27.00 25.00 22.33 19.33
37.67 32.00 24.00 23.00 20.00
4.99 5.02 4.97 4.97 5.04
4.46 4.44 5.22 4.88 3.58
0.21 0.50 0.54 0.58 0.70
10.80 11.25 4.44 2.32 28.33
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For each element, the length and width of the target stripes in the transverse and longitudinal directions are measured three times at different position in the same element based on the image taken by both DC-BAM and conventional BAM. The average numbers are displayed.
where α and βm are the incident angle and diffraction angle, N is the groove density, m is the diffraction order, and λ is the incidence wavelength. The correction requires that α equals the Brewster angle of the subphase, and the first-order diffraction angle β1 equals 0° to align the image propagation direction along the surface normal. As an example, for a water substrate, considering the laser wavelength of 532 nm and the water Brewster angle of 53.06°, the calculated groove density is 1502 mm−1. The closest commercially available grating has a groove density of 1500 mm−1, which will lead to a final diffraction beam off about 0.06° compare to the ideal condition. This difference is small enough to be neglected. The maximum grating efficiency can be achieved with the grating Littrow configuration,25 at which the blaze wavelength matches the laser wavelength 532 nm. Considering all the conditions above, a comparable commercially available grating with a groove density of 1500 mm−1 and blaze wavelength of 510 nm is chosen for the DC-BAM, giving rise to a grating efficiency of 30% for p-polarized light. Figure 3a,b displays the images of an USAF 1951 target taken, respectively, by the conventional BAM and the DC-BAM at the same position. Compared to the conventional BAM, the DC-BAM keeps the whole image in focus and corrects the “keystone” distortion for the entire field of view. The correction can be quantified by the length-width ratio of each squarepattern element in group 5 as shown in Table 1. The ratios are compared in each element and both directions between the DC-BAM and the conventional BAM. As measured in the Table 1, for DC-BAM pictures, the experimental ratio of each element in both directions matches well with the designed length-width ratio of an USAF 1951 target which is equal to 5.00. The average ratios in transverse and longitudinal directions are 5.00 ± 0.02 and 5.00 ± 0.03, respectively. While for the conventional BAM, the ratios, averaging 6.30 ± 0.40 in the transverse direction and 4.52 ± 0.62 in the longitudinal direction, are distorted severely from the designed target. Approximately 26.07% and 11.43% aberrations in transverse and longitudinal directions are noticed in the conventional BAM picture, whereas the DC-BAM minimizes the aberrations to be only 0.36% and 0.51% in both directions. Table 1 provides clear evidence that the satisfied
correction achieved in both directions by the new instrument. Better images can be acquired by choosing a specifically designed grating that both groove density and blaze wavelength matching well with the ideal conditions. More images are listed here captured by the new BAM are shown in Figure 3c−e to illustrate the capability of the DCBAM in different chemical systems. In Figure 3c, the image of the DPPC/water interface displays clear DPPC domains formed during the DPPC phase transition from the liquid expanded (LE) to the liquid condensed (LC) phase. More detailed domains structures are revealed in the extended image of Figure 3d, in which each of the DPPC LC phase island has approximately a 30 μm diameter. In Figure 3e, the morphology of the stearic acid Langmuir−Blodgett monolayer deposited onto the quartz surface is also clearly monitored. The bright band-like patterns are the SA LB monolayer formed when withdrawing the quartz substrate out from a LB trough at constant speed. The darker area is the quartz free substrate although the small bright dots of quartz defects are also noticed. Resolution. The resolution of the BAM is limited by the digital camera pixel size and the optical components’ numerical apertures (N.A.). Usually, the pixel size of a digital camera depends on the imaging sensor chip. The sensor of the Nikon D5000 camera is a Nikon D2X-format complementary metal oxide semiconductor (CMOS) chip, of which each pixel has the size of 5.5 μm × 5.5 μm. Since in the DC-BAM the objective will magnify the original sample 20 times, the smallest area can be resolved by the camera is 0.55 μm × 0.55 μm, which is double the smallest sensor size on the CMOS chip for separating the adjacent pixels. Comparatively, the camera resolution is much better than the resolution given by the optical components N.A., which limits the final resolution of the entire imaging system. The resolution R of the optical microscope can be estimated by the Rayleigh criterion (see the Supporting Information). Since the smallest N.A. limits the resolution of the entire imaging system, the BAM resolution is thereby determined by the relay lens (N.A. is 0.124), yielding a final resolution of 2.6 μm. However, because of its oblique viewing configuration, the resolutions in the transverse and longitudinal directions of a sample are different. C
DOI: 10.1021/acs.analchem.6b04738 Anal. Chem. XXXX, XXX, XXX−XXX
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Analytical Chemistry The resolution of the DC-BAM is analyzed based on the BAM picture of an USAF 1951 optical target as shown in Figure 4a. Intensity analyses curves along the two directions are
Figure 5. Edge response function (a,b) and line spread function (c, d) in both transverse and longitudinal direction of the square pattern on the USAF 1951 optical target. Full width at half-maximum of LSF is given on the side.
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Figure 4. Resolution analyses curves of the (a) new BAM image of group 6 and group 7 elements on an USAF 1951 optical target. Both the longitudinal direction (b) and transverse direction (c,d) are tested.
CONCLUSION A new Brewster angle microscope is designed and constructed, which corrects the image distortion and keeps the entire field of view in focus with good spatial resolution tested by intensity analyses curves and the line spread function method. This inexpensive configuration does not require scanning nor further imaging reconstruction method and thereby widens the application range to various chemical systems. Therefore, we expect that this distortion-corrected design will become an advantageous improvement to the conventional BAM.
shown in Figure 4b−d in which the triplet dips represent the three stripes of each element. Longitudinally, the dips shown in Figure 4b characterize the stripes of elements 4, 5, and 6 in group 7, allowing for the evaluation of the line-width of the stripes on the target. Well-separated triplets are observed up to element 5 implying the longitudinal resolution limit is up to 2.46 μm. Along the transverse direction (Figure 4c,d), the width of the dip in each triplet increases from left to right with the decreasing element number. All of the triplet-dips in group 6 (Figure 4c) are well separated, whereas in group 7 (Figure 4d) well-separated triplets can only be recognized up to element 3, indicating that the line-width of element 3 in group 7, 3.10 μm, is the best transverse resolution. Another approach, line spread function (LSF) and edge response method,26,27 is also applied here to evaluate the resolution of the DC-BAM. Since all of the common edge responses have a similar shape,28 the error function is used here to express the edge response. In this way, the Gaussian function LSF is simply the derivative of the edge response. The full width at half-maximum (fwhm) of the LSFs represent the resolution of the microscope. Similar to the intensity analyses, both transverse and longitudinal directions of the square pattern on the target are tested as shown in Figure 5. Error functions of each direction are simulated as the red curves based on the edge response. The line spread function is then derived from the error function. The fwhm of each LSFs characterizes the resolution of the microscope: 3.22 μm in the transverse direction and 2.41 μm in the longitudinal direction. These resolutions match well with the resolution given by the intensity analyses curves and the theoretical estimation based on the Rayleigh criterion. Therefore, a possible way to boost the resolution, which is dominated by the optical N.A., down to 1 μm, for example, is using a relay lens with a higher N.A. of 0.325.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b04738. New Brewster angle microscope setup, Langmuir and Langmuir−Blodgett film preparation, and resolving power by Rayleigh criterion (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Steven Baldelli: 0000-0002-5747-259X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by W.M. Keck Foundation and National Science Foundation (NSF) Grant CHE-1610453. REFERENCES
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