Step beyond Kohler illumination analysis for far-field quantitative imaging : Angular ILluminationASymmetry ( ANILAS ) maps

For far-field optical imaging of three-dimensional objects and such critical applications as quantitative optical imaging, optical metrology, and optical lithography, it is necessary not only to meet the Kohler illumination condition (i.e. uniform spatial intensity) but also to minimize Angular Illumination ASymmetry (ANILAS) at the sample plane. The presence of ANILAS results in distorted optical images, and most likely in erroneous quantitative measurements. ANILAS results from optical and illumination aberrations, optical misalignment and other problems. We present a detailed procedure to measure and create maps of ANILAS across the field-of-view (FOV). ANILAS maps enable visualization of the state of illumination at the sample plane. Since the presence of ANILAS is detrimental to quantitative measurements, it is important to know the magnitude and type of ANILAS across the FOV before making any attempt to correct it. Here we intentionally create different types of illumination distortions and generate corresponding ANILAS maps, which help us evaluate the state of illumination beyond the Kohler illumination criterion. We expect that the ANILAS maps will be helpful for a wide range of far-field imaging applications. © 2016 Optical Society of America OCIS codes: (180.0180.) Microscopy; (220.4840.) Testing; (220.1140.) Alignment; (220.2945.) Illumination design. References and links 1. T. Bernas, D. Barnes, E. K. Asem, J. P. Robinson, and B. Rajwa, "Precision of light intensity measurement in biological optical microscopy," Journal of microscopy 226, 163-174 (2007). 2. J. C. Waters and T. Wittmann, "Concepts in quantitative fluorescence microscopy," Method Cell Biol 123, 1-18 (2014). 3. M. Butzlaff, A. Weigel, E. Ponimaskin, and A. Zeug, "eSIP: A Novel Solution-Based Sectioned Image Property Approach for Microscope Calibration," Plos One 10(2015). 4. P. Memmolo, L. Miccio, F. Merola, O. Gennari, M. Mugnano, P. A. Netti, and P. Ferraro, "Lab on chip optical imaging of biological sample by quantitative phase microscopy," in 2015), 933625-933625-933625. 5. Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, "Markerfree phase nanoscopy," Nat Photon 7, 113-117 (2013). 6. R. Attota and R. G. Dixson, "Resolving three-dimensional shape of sub-50 nm wide lines with nanometer-scale sensitivity using conventional optical microscopes," Appl Phys Lett 105(2014). 7. B. J. Lin, "Optical lithography present and future challenges," Cr Phys 7, 858-874 (2006). 8. R. Attota, R. M. Silver, T. A. Germer, and M. Bishop, "Application of through-focus focus-metric analysis in high resolution optical metrology," Metrology, Inspection, and Process Control for Microlithography XIX, Pts 1-3 5752, 1441-1449 (2005). 9. R. Attota, P. P. Kavuri, H. Kang, R. Kasica, and L. Chen, "Nanoparticle size determination using optical microscopes," Appl Phys Lett 105(2014). 10. H. Kang, R. Attota, V. Tondare, A. E. Vladár, and P. Kavuri, "A method to determine the number of nanoparticles in a cluster using conventional optical microscopes," Appl Phys Lett 107, 103106 (2015). 11. J. Song, W. Chu, T. V. Vorburger, R. Thompson, T. B. Renegar, A. Zheng, J. Yen, R. Silver, and M. Ols, "Development of ballistics identification-from image comparison to topography measurement in surface metrology," Measurement Science and Technology 23(2012). 12. J. Song, T. Vorburger, T. Renegar, H. Rhee, A. Zheng, L. Ma, J. Libert, S. Ballou, B. Bachrach, and K. Bogart, "Correlation of topography measurements of NIST SRM 2460 standard bullets by four techniques," Measurement Science and Technology 17, 500 (2006). Optics Express Vol. 24, Issue 20, pp. 22616-22627 (2016) https://doi.org/10.1364/OE.24.022616 13. R. M. Zucker, "Quality assessment of confocal microscopy slide-based systems: Instability," Cytom Part A 69A, 677-690 (2006). 14. R. M. Zucker and O. Price, "Evaluation of confocal microscopy system performance," Cytometry 44, 273-294 (2001). 15. K. M. Kedziora, J. H. M. Prehn, J. Dobrucki, and T. Bernas, "Method of calibration of a fluorescence microscope for quantitative studies," Journal of microscopy 244, 101-111 (2011). 16. M. Halter, E. Bier, P. C. DeRose, G. A. Cooksey, S. J. Choquette, A. L. Plant, and J. T. Elliott, "An Automated Protocol for Performance Benchmarking a Widefield Fluorescence Microscope," Cytom Part A 85a, 978-985 (2014). 17. R. Attota, R. M. Silver, M. Stocker, E. Marx, J. Jun, M. Davidson, and R. Larrabee, "A new method to enhance overlay tool performance," Metrology, Inspection, and Process Control for Microlithography Xvii, Pts 1 and 2 5038, 428-436 (2003). 18. D. J. Coleman, P. J. Larson, A. D. Lopata, W. A. Muth, and A. Starikov, "Accuracy of overlay measurements: tool and mark asymmetry effects," in 1990), 139-161. 19. R. Attota and R. Silver, "Optical microscope angular illumination analysis," Opt Express 20, 6693-6702 (2012).


Introduction
Usage of the far-field optical imaging technique for quantitative measurements has been increasing in recent years.Standardization and calibration of optical microscopy systems have become important due to the increasing role of biological imaging in high-content screening technology [1].The field of sectioning fluorescence microscopy has also rapidly advanced in recent years, allowing experimenters the opportunity to extract more and more information from a given sample by utilizing spectral analysis in multispectral systems, high temporal resolution in fast imaging systems, and high spatial resolution in systems employing molecular switches or structured illumination [2].To yield consistent quantitative information, all these systems must be calibrated [3].Quantitative imaging and threedimensional (3D) morphometric analysis of flowing and non-adherent cells are important for diagnostic purposes at Lab on a Chip scale [4,5].High quality, far-field imaging optical tools are required for semiconductor metrology and optical lithography [6][7][8].The same applies for metrology of non-semiconductor nanoscale targets such as nanoparticles [9,10].Use of optical imaging for forensic examination of bullets and cartridge cases to uniquely identify ballistic signatures also requires high-quality optical systems [11,12].
Many ideas have been proposed to improve quantitative measurements and enhance their accuracy.Several tests have been suggested to make confocal microscopy work properly, including laser power, laser stability, field illumination, colocalization, spectral registration, spectral reproducibility, lateral resolution, axial (Z) resolution, lens cleanliness, lens characteristics, and Z-drive reproducibility [13,14].A onestep absolute intensity calibration and an estimate ofprecision and sensitivity of a fluorescence microscope system were proposed for quantitative studies [15].A technique for estimation of temporal variability of signal and noise in microscopic imaging was proposed to increase precision for biological measurements using optical microscopes [1].The U.S. National Institute of Standards and Technology proposed an easy-to-use benchmarking method for the analytical performance of a microscope that would facilitate the use of fluorescence imaging as a quantitative analytical tool in research applications [16].This method would also aid the determination of instrumental method validation for commercial product development applications.'Tool induced shift', commonly known as TIS, has been used in the semiconductor industry to minimize the overlay measurement errors that resultfrom imperfections in opticalmicroscopes,including illumination imperfections, [17,18].
We describe and explain in this paper another aspect of far-field imaging that can be important to obtain quantitative values with enhanced accuracy using any optical microscope.The majority of the modern day far-field imaging optical microscopes have a Kohler illumination scheme that produces spatiallyuniform optical intensity (irradiance) at the sample plane.For qualitative optical imaging, the Kohler illumination scheme is sufficient, but while this scheme is also necessary for critical and quantitative measurements and analyses, it is not sufficient.Angular illumination uniformity across the field-of-view is also necessary for hifidelity and consistent imaging, especially for the imaging of three--dimensional objects which includes almost all the targets.For example, uniform, angular illumination produces, in principle, more accurate 3D shape reconstruction in holographic and tomographic optical imaging of 3D biological samples [4,5], even if the illumination at different angles is done separately.
Unfortunately, angular illumination may not be uniformly symmetric across the field-ofview (FOV)for optical microscopes, even when the spatial intensity is uniform.We demonstrate this in Fig. 1 using a commercially-available, research-grade optical microscope that has good Koehler illumination.Intensity profiles of an overlay target were compared by placing the same target at the five different locations shown in Fig. 1(a).A typical intensity profile is shown in Fig. 1(b).Under the conditions employed, differences in the profiles can be easily identified at the lower portions of the profiles as designated by the red box in Fig. 1(b).For this reason, only the lower portions of the profiles are magnified and shown in Figs.1(c1) to 1(c5).The outer and the inner two lines are identical and hence should produce identical profiles.However, differences in the profiles can be observed indicating imperfect illumination at the sample plane.If the illumination is symmetric, it produces a profile with equal minima as highlighted within the red box in Fig. 1(c5).Non-symmetric illumination produces unequal minima as shown within the red box in Fig. 1(c1).The imperfect illumination at the sample plane could be a result of optical and illumination aberrations, optical misalignment, or by a combination of causes.Since the measured quantitative overlay value (the distance between the centers of the outer and the inner boxes) has been shown to depend on the intensity profile [17], there is a high probability that the overlay values of the target (or any quantitative measurement) measured at five different locations will produce five different values.This is not a desirable situation.The first step to resolve thissituation is to determine if the differences in the profiles are due to Angular Illumination ASymmetry (ANILAS) present across the FOV. Figure 2 illustrates ANILAS and its effect on the image (from [19]).In a Koehler scheme, plane waves at many incident angles illuminate the target.Unequal intensities of illumination (on either side of the normal to the target) produce an asymmetric illumination condition resulting in a distorted image profile as shown in Figs.2(a) and 2(c), while symmetric intensity produces symmetric profile (Figs.2(b) and 2(d)).If ANILAS is present, the second step is to mitigate it so that variations in the profiles can be minimized.In a previous publication [19], we proposed a method to evaluate the ANILAS magnitude at a point in the FOV, including the theory.An ANILAS value is proportional to the degree of angular illumination intensity asymmetry at the sample.A zero ANILAS value implies nearly perfect illumination with no illumination intensity asymmetries.Measuring and plotting ANILAS magnitudes across the FOV produces an ANILAS map.An ANILAS map is a convenient way to visualize angular illumination conditions present at the sample plane.Different types of illumination imperfections result in different types of ANILAS maps.In the current paper, we first intentionally create known illumination imperfections and then evaluate corresponding ANILAS maps.In this way, a given ANILAS map can be correlated with a known imperfect illumination.This information acts as a database or a look-up table.Having this correlation helps us to determine the type of illumination imperfections by simply measuring and then comparing the ANILAS maps of a microscope (with an unknown type of illumination imperfections) with the known ANILAS maps.Having identified the illumination imperfections in this way, the next step is to mitigate illumination imperfections so that variations in the intensity profiles can be minimized across the FOV.In the absence of the ANILAS maps, we may not be able to realize the presence of ANILAS in microscopes.

Modeling
We present schematics of creating different types of illumination imperfections using principles of ray optics in Fig. 3, by moving aperture diaphragm (or stop, located at a conjugate back focal plane) with respect to the field diaphragm (or stop), the optical axis and FOV.For the sake of convenience lateral movement from the optical axis is assigned with (X,Y) coordinates with respect to the center of the FOV.Optical axis is assigned the Z coordinate.The coordinate of the correct aperture stop is (0,0,0).The aperture stop moved axially toward or away from the field stop is assigned a positive or negative Z value, respectively.A well designed and aligned optical microscope with the uniform illumination source and aperture stop at the correct location produces an angularly symmetric uniform illumination (Fig. 3(a)) at the sample plane.A magnified view of the illumination at the sample plane (Fig. 3(a1)) shows all locations in the FOV getting symmetric angular illumination as highlighted by the blue circles (in this case schematically shown by all the five angles of illumination).Moving the aperture stop axially toward the field stop (0,0,z) produces illumination as shown in Fig. 3(b).This type of illumination produces angularly symmetric illumination mostly at the center of the FOV (Fig. 3(b1)).Similarly, moving the aperture stop axially away from the field stop (0,0,-z) also produces angularly symmetric illumination mostly around the center of the FOV (Figs. 3(c) and 3(c1)).However, the amount of illumination received around the center of the FOV differs between these two cases.
Moving the aperture stop both axially and laterally (-x,0,z) produces illumination shown in Fig. 3(d).In this case, the location of the symmetric angular illumination moves away from the FOV center (Fig. 3(d1)).In the last case, moving the aperture stop laterally (x,0,0) at the correct axial location (Fig. 3(e)) produces uniformly asymmetric angular illumination at the sample plane (Fig. 3(e1)).In all the cases presented, we can expect the degree of asymmetry to be proportional to the amount of movement of the aperture stop from the correct location.
ANILAS magnitude will, by definition, be zero (or nearly zero) at the locations where angular illumination is symmetric [19].For this reason, we can expect a near zero ANILAS magnitude over the entire FOV for the ideal, symmetric illumination condition shown in Fig. 3(a1); only around the center of the FOV for the illumination conditions shown in Figs.3(b1) and 3(c1), and away from the FOV center for the illumination condition shown in Fig. 3(d1).For the illumination condition shown in Fig. 3(e1) we can expect a uniformly positive ANILAS magnitude over the entire FOV.In the following section, we experimentally measure ANILAS maps under these different illumination conditions and confirm if they are as expected.

Experimental Methods
We have used a commercially available, research-grade optical microscope in the reflection mode to generate the ANILAS maps.The microscope specifications are as follows: illumination source = 520 nm light emitting diode (with a band-pass filter), objective magnification = 50X, numerical aperture (NA) = 0.55, working distance = 9.1 mm, par focal length = 45 mm, Peltier-cooled monochrome digital camera native resolution = 1040x1384 pixels.For most of the measurements, we used a 400 m aperture diaphragm as an aperture stop to produce an illumination NA (INA) of 0.15.This aperture diaphragm was mounted on an X-Y-Z stage so that its position could be moved along the optical axis and laterally using micrometers.We also generated an ANILAS map using the original manufacturer supplied aperture diaphragm placed at the manufacturer-recommended location.The original aperture diaphragm was closed down to a minimum which produced an INA of 0.28.A system of trenches in SiO2, with a nominal width of 100 nm, over a Si substrate with 1000 nm pitch was used as a grating target.The focus metric (FM) [8] value, which is akin to the measure of average contrast in an image, was calculated and plotted in Fig. 4 from the acquired throughfocus [8] images using the grating target at the two INAs selected.For the method to work, it is important to obtain a valley in the FM values between any two peaks.Only a few throughfocus images on either side of the central valley (minimum) FM are needed to create the ANILAS maps.For this reason, only the through-focus images highlighted within the red boxes of Fig. 4 were acquired for the subsequent analysis.Unless otherwise noted, all the ANILAS maps presented use the 400 m aperture stop (INA = 0.15) and are the averages of five repeats.We present below a step-by-step procedure to create the ANILAS maps.
1. Select an appropriate grating target (Fig. 6(a)) such that it (i) produces a suitable image of the grating lines with sufficient contrast (gratings will not be seen if the pitch is too small), (ii) results in at least one FM valley between any two FM peaks when the FM is plotted as a function of the focus position (Fig. 4), and (iii) fills the FOV for the final magnification selected.The peaks and the valleys are generally functions of gratings pitch, line width, wavelength, INA, and CNA. 2. Select the through-focus [8] imaging range such that several images are obtained on the either side of the FM minimum.We recommend a focus step size between 100 nm to 200 nm (smaller than this is even better).3. Collect through-focus images of the selected grating in the horizontal orientation.
Make sure that the FOV (or the digital optical image) is square-shaped (or select the central square area for analysis, if the image is rectangular).4. Divide the (square) FOV into n x n equidistant locations, where preferably n is any odd number greater than 9. 5. Extract intensity profiles across the lines at each of these locations.The length of the profiles can be about one to two grating pitches.To reduce noise, several profiles can be averaged along the lines from the same location.6.Using the extracted profiles, evaluate the FM value as a function of the focus position at each of the selected n x n locations, i.e., over the entire FOV (refer to Fig. 5 for a detailed method of FM calculation [8]).Figure 5 presents a detailed procedure to calculate the FM.The FM is related to the mean of the absolute intensity gradient in the region of interest.The FM magnitude depends on several factors such as illumination intensity, digital camera exposure time, gratings image contrast, the length of the profile (Fig. 5(c)) and the amount of shift in the two profiles (Fig. 5(d)).The gratings image contrast itself depends on gratings pitch, illumination wavelength, gratings material, line width, INA, and CNA.ANILAS map creation from the horizontal and the vertical ANILAS maps is shown in Fig. 6.

Results and Discussions
Experimentally measured ANILAS maps for the intentionally created illumination imperfections are presented here.An ANILAS magnitude of zero (or nearly zero) indicates symmetric angular illumination.Figure 7(a) (Fig. 7(a1)) shows an ANILAS map with the aperture stop close to the correct location of (0,0,0) (Fig. 3(a)).As expected this condition produced very low (less than 0.1) ANILAS values over the entire FOV, indicating nearly symmetric angular illumination.A low degree of non-uniformity can be observed that results in the FOV center with even better illumination, however, the variation is small.Under this condition, we can expect a nearly consistent image no matter where the target is located in the FOV.This is the most desirable illumination condition for high precision and quantitative optical imaging.
Moving the aperture stop about 1000 m along the optical axis from the correct location towards ((0,0,1000± 5) m) as in Fig. 3(b), or away ((0,0, -1000± 5) m) as in Fig. 3(c) from the field stop produce the ANILAS maps shown in Figs.7(b), 7(b1) and in Figs.7(c), 7(c1), respectively.As predicted earlier, these conditions resulted in symmetric angular illumination only around the center of the FOV (as in Figs.3(b1) and 3(c1)).ANILAS increased toward the edges, being highest at the four corners.What this means is that a symmetric target results in a symmetric image (intensity profile) only if located near the center of the FOV for these two conditions.However, there seems to be some difference in the area coverage of the low asymmetry.Comparing the central blue areas (Figs.7(b) and 7(c)), where we can expect enhanced symmetric illumination, we can see that the aperture stop moved away from the field stop (Figs.7(c) and 6(e)) appears to have a larger blue area compared to the aperture stop moved closer towards the field stop (Fig. 7(b)).This indicates that axial motion of the aperture stop moving from the correct location away from the field stop ((0,0, -z)) gives better angular illumination symmetry than the axial motion of the stop moving toward the field stop ((0,0, z)), by the same amount, for the current microscope configuration.Figure 8 shows the effect of lateral movement of the aperture with respect to the optical axis.The lateral displacement in conjunction with the axial displacement ((20 ± 2, 0, 1000 ± 5) m) produces the ANILAS map shown in Fig. 8(a).We can clearly see that the low ANILAS region moves away from the center in the X-axis direction matching the prediction of the model shown in Fig. 3(d).As expected, the aperture stop displaced laterally in both the X and Y axes directions, in addition to the axial displacement ((20 ± 2, -20 ± 2, 1000 ± 5)m) moves the low ANILAS region away from the center of the FOV in both the X and Y axes directions as shown in Fig. 8(b).For these two conditions, the aperture stop was also displaced axially from the correct location towards the field stop.However, the lateral movement of the aperture stop near the correct axial location (Fig. 3(e), (20 ± 2, 0, 0)m) exhibits a different kind of ANILAS map as shown in Fig. 8(c).For this case the entire FOV shows uniformly large ANILAS value, indicating that no region in the FOV has symmetric illumination.This also matches the model prediction shown in Fig. 3(e1).It is important to know the correlation between ANILAS values and the consequent amounts of image distortion.We present that correlation here using measurements.We have created imperfect illumination condition by moving the aperture stop to (10 ± 2, 40 ± 2, -2000 ± 5)m, resulting in the ANILAS map shown in Fig. 9(a).Images of the same line placed vertically at the different locations in the FOV, shown in Fig. 9(a), were then acquired for comparison.For a well-aligned microscope with good illumination condition, in principle, all the profiles should be identical, irrespective of the location in the FOV.However, as the ANILAS values are varying across the FOV for the current illumination condition, substantial variations in the intensity profiles can be observed.As expected, the best and the worst symmetry in the intensity profiles can be observed at the locations where the ANILAS value is the lowest (Fig. 9(c)) and the highest (Fig. 9(f)), respectively.Asymmetries (or distortions) in the profiles are in the opposite direction for the locations on the opposite side of the lowest ANILAS point (Fig. 9(b) and Fig. 9(d)).This suggests that the distortions in the profile depend not only on the magnitude of the ANILAS value, but also on the relative directionality from the region of lowest ANILAS values.To better explain the directionality of the ANILAS magnitude, we superimposed lines representing the magnitude and the orientation of the points on the map from the location of the lowest values on the ANILAS map (Fig. 9(a)).As a point of interest in the FOV is displaced further away from the region of lowest ANILAS values, the ANILAS value associated with it increases (represented as increased length of the green lines), and the direction of the ANILAS representing line points radially with respect to the lowest ANILAS location as the center.Based on this explanation, we can expect similar ANILAS values for points located on the green circle shown in Fig. 9(a).However, the profile asymmetry also depends on the orientation of the target relative to the direction toward the minimal ANILAS region.For example, a vertical line located at point 'p' (perpendicular to the direction toward the minimal ANILAS region) shows the highest asymmetry, whereas the same line located at point 'q' (parallel to that direction) shows the lowest asymmetry for those locations.Similarly, a horizontal line located at points 'p' and 'q' shows the least and the highest asymmetries for those locations, respectively.For this reason, even though the line profile in Fig. 9(d) has a lower ANILAS value based on its closer distance to the lowest value ANILAS location, it shows a larger asymmetry compared to the line profile in Fig. 9(e) because of its orientation.A more generalized inference could be that for the intensity profiles extracted parallel or perpendicular to the ANILAS radial lines show the highest and the lowest asymmetries, respectively, for that location.It is also important to note that a line oriented parallel to the ANILAS direction should in principle produce symmetric profile no matter how far away it is located from the lowest ANILAS location.However, we can expect variations in the line profiles for lines located along any ANILAS radial line due to changing illumination conditions, even if they are symmetric.
We have also tested the original aperture stop supplied by the microscope manufacturer for its ANILAS map.Axial location of this aperture is fixed due to the manufacturer assigned slot.However, there is provision for lateral alignment for the stop.While carefully centering the aperture (both in the X and Y directions), we chose an ANILAS map that produced the lowest ANILAS region close to the center of the FOV (Fig. 7).The original aperture stop produced an ANILAS map with low values, albeit with slightly larger values compared to Fig. 7(a).Based on the observation that the coverage of the blue area is smaller similar to Fig. 7(b), we could guess that the original aperture axial location is a bit off from the correct axial

Fig. 1 .
Fig. 1.Differences in the intensity profiles depending on the location in the field-of-view.(a) A typical optical image of the selected box-in-box type of overlay target located at the top-right.A schematic of the cross-sectional profile of this overlay target is shown in the blue inset.(b) A typical optical intensity profile of the selected target.Figs. 1 (c1 to c5) The lower portion (as designated by the red box in (b)) of the intensity profiles of the same overlay target from the five locations in the field-of-view indicated by the red circles in (a).Dimensions of the line outer box are the same.Similarly, dimensions of the trench inner box are the same.Outer box center-to-center width = 18 m, illumination NA = 0.55, collection NA = 0.55,  = 520 nm.

Fig. 2 .
Fig. 2. The effect of ANILAS.Schematic representation of (a) asymmetric and (b) symmetric angular illumination intensity conditions.For the sake of simplicity, only one symmetrically opposite illumination angle is shown.In (a) the illumination intensity from the left (red arrows) is more than from the right (blue arrows).Simulated intensity profiles of an isolated line for (c) asymmetric and (d) symmetric illuminations.Line width=200 nm; Line height=200 nm; Illumination NA=0.4; collection NA=0.8, =546 nm; Si line on Si substrate.

Fig. 3 .
Fig. 3. Schematics showing angular illumination at the sample plane for different intentionally created illumination imperfections by moving an aperture stop at a (conjugate) back focal plane.The fixed size aperture stop (a) at the correct axial and lateral location (X = 0, Y = 0, Z = 0), (b) moved axially closer to the field stop (X = 0, Y = 0, Z = z), (c) moved axially away from the field stop (X = 0, Y = 0, Z = -z), (d) moved both closer to the field stop and laterally (X = x, Y = 0, Z = z), and (e) at the correct axial location but moved laterally (X = x, Y = 0, Z = 0).Figs. 3 (a1), (b1), (c1), (d1) and (e1) show the magnified view of the angular illumination at the sample plane for the illumination shown in (a), (b), (c), (d) and (e), respectively.Blue circles indicate the locations of symmetric angular illumination at the sample plane.The assigned (X,Y,Z) coordinates of the aperture stop are indicated at the top of each schematic.

Fig. 4 .
Fig. 4. Large focus range focus-metric plots obtained using (a) the 400 m custom aperture (INA = 0.15 ± 0.01), and (b) the original stop with about 700 m aperture (INA = 0.28 ± 0.01).The red boxes represent the approximate focus range needed for creating the ANILAS maps.Inset figures in (b) show optical images of the selected grating at those focus positions.

7 .
Extract the individual minimum FM values (at the valley) using the through-focus FM values.Interpolation of the FM curve followed by extraction of the minimum FM value improves the accuracy of the result.8. Plot the extracted minimum FM values at their corresponding locations in the FOV to produce a horizontal ANILAS map (Fig. 6(c)).9. Repeat this process (steps 3 to 8) using the same grating target in the vertical orientation (Fig. 6(b)) to obtain a vertical ANILAS map (Fig. 6(d)).10.Plot the mean ANILAS values calculated from the horizontal and the vertical ANILAS maps to produce the final ANILAS map as shown in Figs.6(e) and 6(f).

Fig. 5 .
Fig. 5. FM calculation procedure: From a typical optical image of (a) the grating (only a portion of the image is shown for clarity), (b) select a portion from a given location of the image.(c) Extract the intensity profile by averaging along the direction of the lines.(d) Make a copy (in red) of the original profile (shown in blue) and move it with respect to the original profile (four pixels to the right in this case).(e) Equalize the length of the profiles and take a difference in the intensity between the original and the shifted copy.(f) Square and sum the intensities to produce an FM value.

Fig. 6 .
Fig. 6.Optical images of the grating in the (a) horizontal and (b) vertical orientations (only a portion of the grating image is shown here for clarity).ANILAS maps from the grating oriented in the (c) horizontal and

Fig. 9 .
Fig. 9. Variations in the optical intensity profiles as a function of location on the ANILAS map.(a) ANILAS map for the aperture stop location at (10 ± 2, 40 ± 2, -2000 ± 5)m.ANILAS green radial lines with respect to the lowest ANILAS location are also indicated.(b), (c), (d), (e), (f), and (g) Intensity profiles of the same vertical line placed at different locations shown by the arrows.Dotted lines indicate the location of the extracted intensity profile.