Structured illumination assisted microdeflectometry with optical depth scanning capability

Abstract

Microdeflectometry is a powerful noncontact tool for measuring nanometer defects on a freeform surface. However, it requires a time-consuming process to take measurements at different depths for an extended depth of field (EDOF) and lacks surface information for integrating the measured gradient data to height. We propose an optical depth scanning technique to speed up the measurement process and introduce the structured illumination technique to efficiently determine the focused data among 3D observation and provide surface orientations for reconstructing an unknown surface shape. We demonstrated 3D measurements with an equivalent surface height sensitivity of 7.21 nm and an EDOF of at least 250 μm, which is 15 times that of the diffraction limited depth range.

Phase measuring deflectometry (PMD) has been widely implemented for testing specular freeform surfaces in past years [1–4]. A typical PMD system uses a display placed in front of the surface under test and uses a camera to observe the displacement of the displayed fringes reflected from surface. As the demanded spatial resolution goes higher, the limited working space leads to the introduction of auxiliary elements into the PMD system, such as adding a beam splitter [5] or a singlet [6] near the testing surface. In the microscopic regime, microdeflectometry modifies the typical PMD system and uses a setup similar to the reflective light microscope [7], where the illumination module shares the optical path with the camera detection through the microscope objective and projects an aerial fringe image in front of the surface. By observing the fringe displacement, microdeflectometry measures a small slope variation within a large angular range equivalent to numerical aperture (NA) with micron-level lateral resolution, which enables inspection of the nanometer defect within hundreds of microns of freeform surface height variation.

However, several disadvantages limit the use of the state-of-the-art microdeflectometry as an independent metrology tool. First, due to the limited depth of field (DOF) of a standard microscope objective, testing a sample with a large depth requires taking multiple measurements at different depths and extracting the focused data for an EDOF, which is a time-consuming process. Second, it is difficult to determine whether the surface is in focus when testing a finished optics. The focusing error in the captured data not only lowers the lateral resolution, but also leads to a reconstruction error on the surface shape. Third, for reconstructing the actual shape of an unknown surface, microdeflectometry requires a supplementary tool, such as the laser tracker [8] or stereophotogrammetry [1] used in PMD, which provides at least the absolute slope of a reference point in the integration of surface gradient data.

In this Letter, we propose a structured illumination assisted microdeflectometry technique enhanced with optical depth scanning capability. Instead of a fixed-focus microscope objective, a varifocal microscope objective is implemented to perform focus scanning at high speed without the involvement of any mechanically moving parts. The objective was carefully designed to be object-space telecentric, which maintains strict system constancy for precision measurement within an extended depth range. Consequently, the focused measurements of a thick sample can be taken from different depths and can then be combined directly for an EDOF scene without the need to be scaled or interpolated. Additionally, structured illumination microscopy (SIM) [9] was introduced to the same setup as a surface shape probe for efficiently determining the focused data in 3D and providing surface orientations for shape reconstruction. The implementation of the SIM technique does not require modifying the system configuration and only needs to displace the projected fringe pattern to the conjugate position of the camera focus. Although SIM has been implemented in metrology independently [10], it has a lower measuring sensitivity for local variation than microdeflectometry. By integrating the two techniques into the same system setup, the SIM technique, with low but adequate resolution, was utilized to ensure that the microdeflectometric data were taken within the DOF and provide global orientations with a milliradian-level resolution. Overall, the optical depth scanning capability and the natural advantage of the wide angular dynamic range in microdeflectometry provide a portable solution without the need for high-precision tilt and translation stages that are required for mechanically scanning the object. The resulting system has a great potential for in-line measurement.

Figure 1 shows the schematic of our proposed setup, where the dashed lines and solid lines indicate the illumination and detection paths, respectively. Following the illumination path, the fringe pattern emitted from a microdisplay (SVGA OLED-XL, eMagin) was coupled by a tube lens and directed by a beam splitter into a varifocal microscope objective. An aerial fringe image was then projected by the objective in front of the surface under test for microdeflectometry. Following the detection path, the light reflected from the tested surface was collected by the shared objective, refracted through the beam splitter and a tube lens, and focused on the camera sensor. To acquire optimal resolution, the camera was focused on the tested surface, which is separated from the aerial fringe image by a distance d. Since only the reflected ray within the angular range of the objective numerical aperture would be detected, the captured cone of light is centered at the surface normal and, hence, the observed fringe displacement Φ is directly proportional to the surface slope α with the relationship Φ = d × α. By calculating the fringe displacement via the phase-shifting method, the surface gradient data were quantitatively measured.

Fig. 1.

Schematic of the microdeflectometric setup with the capability of optical depth scanning. (a) Overall system setup. (b) Zoom-in view of the varifocal microscope objective.

The varifocal microscope objective is the key of the system that enables us to rapidly scan focus through a large depth range without mechanically moving parts, while maintaining the constancy of a deflectometric relationship. As shown in Fig. 1(b), it consists of an electrically tunable lens (ETL) (EL-10-30, Optotune), which varies its focal length precisely as the applied current changes, and a designed microscope objective, which releases a proper distance for the ETL placed at its rear focal plane. The aperture of the ETL serves as the stop of the objective, which forms an object-space telecentric varifocal system similar to the optical layout in [11,12]. The strict telecentricity ensures constant optical magnifications of both the fringe image and the camera detection during focus scanning. When the focal length of the ETL was changed, both the fringe image and the camera focus were shifted simultaneously. The amount of focus shift, s, is proportional to the change of optical power Δϕ_var for the ETL and is given by $s=n\times f_{\text{obj}}^2\times \mathrm{\Delta }{\varphi }_{var}$, where n is the refractive index in the object space and f_obj is the effective focal length of the objective. It can be noted that the focus shift is independent from the marginal ray focus. Thus, the distance, d, between the fringe image and the camera focus was fixed as the microdeflectometric system took measurements at different depths. In our prototype system, the varifocal microscope objective has a 10 mm pupil diameter, a 0.25 NA with 2.12 μm spatial resolution, and a 2 mm maximum field of view (FOV). Corresponding to the applied current resolution of 0.07 mA for the ETL, the minimum focus scanning resolution is 1.98 μm, which is sufficiently smaller than the diffraction limited DOF of 8 μm. The available depth scanning range can be up to 2000 μm, and the response time for refocusing to another depth could be as fast as 3 ms, which provides rapid focus scanning ability for EDOF microdeflectometric measurement.

To experimentally determine the magnification of the system, we captured the image of a bar resolution target and fit its intensity cross profile with a sinusoidal function to find the corresponding fringe period with sub-pixel accuracy. By displacing the target axially via a translation stage and finding the highest contrast image via optical depth scanning, the variation of system magnification as a function of focusing depth was measured, and it can be assumed to be a linear response with a fitted slope, as shown in Fig. 2. For instance, the amount of magnification change corresponding to a 250 μm depth range was demonstrated to be 0.05%, which is barely perceivable for the image with a dimension of 1000 pixels. Although the applicable EDOF range may vary depending on the requirement for precision measurement, we demonstrated that our system has at least a 250 μm depth range with strict system constancy, which is about 15 times the diffraction limited DOF.

Fig. 2.

Variation of system magnification with focusing depth.

Figure 3(a) describes the experimental procedure for obtaining an EDOF microdeflectometric measurement with the assistance of SIM. Two parallel experiments were performed for the SIM and microdeflectometry. To avoid collecting unnecessary defocused data, it is preferred to first perform the SIM step to obtain surface shape information which guides efficient depth sampling for microdeflectometry. Figure 3(b) illustrates the transition between the SIM and the microdeflectometric setups. To perform the SIM measurement, the projected fringe pattern was shifted to coincide with the conjugate position of the camera focus plane, while it was separated from the camera focus plane by a distance d in the microdeflectometric setup. A preliminary alignment was required for recording the SIM display position. The system was expected to achieve the highest fringe contrast when the local surface was in focus. Therefore, after taking a series of fringe images at the focusing depths though the object under test, the corresponding surface shape were recorded in 2D pixels and could simply be encoded by the applied current order. With the guidance of the sampling depths from the encoded SIM map, the microdeflectometric system is able to take measurements at different sampled depths within a determined depth range without the need for taking 3D measurements at its highest depth resolution through the depth of interest, which substantially speeds up the focus scanning process. After taking focus stack data of microdeflectometric measurements, the focused data were extracted from each sampled slice image pixel by pixel with the assistance of SIM and combined to be a raw EDOF phase image. The same experimental procedure should even be used for measuring a flat surface when the microscopic system exists with a significant amount of field curvature. The combination of the techniques automatically corrects the defocusing issue and always investigates the surface quality with optimal contrast.

Fig. 3.

(a) Flowchart of the experimental procedure for obtaining EDOF microdeflectometry with the assistance of SIM. (b) Required transition from a microdeflectometric system to SIM operation.

As the phase-shifting technique and the phase-unwrapping algorithm were used to efficiently quantify the slope variation according to the fringe displacement, the absolute slope values were missing in microdeflectometry. Although the provided slope variation data were considered to be sufficient for investigating the surface quality, the surface shape and the height of surface defect were also highly desired in many applications. The absolute slope values were then required for converting surface gradient into height via numerical integration. It is especially essential when the object under test is largely tilted; the heights of the surface defects would be scaled improperly if the surface orientations were not considered.

Besides the use of the SIM measurements to obtain EDOF microdeflectometric measurements and despite having lower measuring sensitivity compared to microdeflectometry, the SIM technique provides absolute surface height measurement, which has complementary information to the surface slopes obtained from microdeflectometry. For a non-complex object under test, such as a planar target or a rotationally symmetric surface, surface orientations could be easily acquired via a fitting, whereas for a complex object, such as a largely varied freeform surface, SIM may provide sufficient reference points for accurately reconstructing the surface shape. The targets experimentally measured in this Letter were globally flat surfaces. Therefore, we acquired the fitted trends of the surface shape obtained from the SIM measurement which were utilized to substitute the relative slope maps in microdeflectometry as the mean values. More specifically, the measured global tilt in the x-direction was added to the slope map in the x-direction that had subtracted the mean, and the same procedure was applied for the slope map in y-direction. The estimation of the absolute slope values was then obtained for reconstructing an unknown surface shape via numerical integration. As we will demonstrate by the examples, the reconstruction is validated with the interferometric result that directly measures surface heights.

By calculating the root mean square (RMS) error of the measurement for a reference flat (PF10-03, Thorlabs), we determined that the slope sensitivity of our microdeflectometric system can be as small as 3.4 milliradian, which corresponds to an equivalent surface height sensitivity of 7.21 nm, calculated by multiplying system spatial resolution. With the NA of the objective that limits signal-to-noise ratio and the low display resolution sharing with the microdeflectometric setup, our SIM system has a surface height sensitivity of 3.35 μm, which is also obtained by taking the RMS error of the flat measurement. Nevertheless, it still corresponds to a minimum global orientation resolution of 1.68 milliradian, considering the maximum field of 2 mm, which is sufficiently smaller than the local slope measuring uncertainty in the microdeflectometric setup.

Figure 4 demonstrates the measuring sensitivity of our system by picking up the tool marks on a diamond-turned microlens surface. The cross profile of the region marked by the black dashed line on the surface height map, shown as an inset at the top-right corner of the graph, is comparable with the validatory data measured by interferometry (Zygo Surface Profiler) that determined the tool marks with the magnitude within ±10 nm. The magnification of the microscopic system used in the interferometer is 2.6 times that of the microscope system in our system; thus, the interferometer resolves finer structures of surface defects, but compromises with 0.42 times FOV compared to our microscope.

Fig. 4.

Measurement of the tool marks on the surface.

Figure 5 validates the success of the surface reconstruction by the measurement of a blazed grating on a transparent plastic substrate. The SIM probe enforced the microdeflectometric system to focus on the transparent surface and ensured the surface normal of the grating substrate being parallel to the optical axis of the portable microscope. Thus, the measured microdeflectometric slope maps should have mean values equivalent to zeros, which determines the absolute slopes for reconstructing the surface height map, as shown in Fig. 5(a) via numerical integration. Figure 5(b) shows the cross profile of the measured blazed grating marked in Fig. 5(a), as well as the validatory profile of the same grating taken from interferometry, where the heights and angles of the reconstructed structure were confirmed with the direct surface height measurement. The central structures were slowly departed from the average due to the periodic errors occurring on the slope maps. Carefully calibrating the sinusoidal profile of the illuminating fringe pattern or averaging the slope maps from a set of measurements with different rotated fringe angles should effectively reduce this periodic error that resulted from the inaccurate phase shift in the phase stepping process.

Fig. 5.

(a) Surface height map for a blazed grating reconstructed from microdeflectometric data. (b) Cross profile marked in (a) compared with the interferometric measurement.

Figure 6 shows an example of obtaining the EDOF microdeflectometric measurement. Figure 6(a) shows the fitted focusing map obtained from the SIM probe that guides the sampling depths and focus extraction of the microdeflectometric measurements. Figures 6(b)–6(d) show the examples of the microdeflectometric data with the limited DOF of the objective taken at the sampled focusing depths, where the slope maps in the vertical direction were focused on the top, middle, and button regions marked by the color windows, which correspond to the blue, green, and red regions in Fig. 6(a), respectively. With the rapid optical depth scanning capability and the assistance of a SIM focusing probe, the focused data taken from different depths were efficiently extracted and combined for the EDOF image at each phase step and through a phase-shifting algorithm and phase unwrapping to form an EDOF slope map, as shown in Fig. 6(e).

Fig. 6.

Demonstration of the EDOF microdeflectometric image. The slope map in the vertical direction was focused on the top region in (a), the middle region in (b), and the button region in (c). The combined EDOF slope map is shown in (d).

Figure 7 further demonstrates the shape reconstruction from the EDOF microdeflectometric measurement with the surface orientations provided by the SIM measurements. Figure 7(a) shows the picture of the measured razor blade, which was largely tilted when under test. The measured region is indicated by the white box that includes the knife bevel (on the left) and the edge (on the right) separated by the centering grind line. The example presented in Fig. 6 shows the measuring result of a portion of the knife edge with the same setup. With the supplemental information provided from the fitted surface shape in the SIM measurement, the averaged tilts of the 0.05 rad in the x-direction and 0.2 rad in the y-direction were determined and substituted to the EDOF slope maps in the x- and y-directions as their mean values, respectively. The absolute slope maps in both directions were then obtained and numerically integrated to reconstruct the surface shape, as shown in Fig. 7(b), where the surface was plotted using a shaded lighting effect to express the surface quality. Figure 7(b) presents the consistent surface roughness through a depth range close to 250 μm, while a 0.05 rad angle between the knife bevel and edge measured by microdeflectometry was reserved after the reconstruction. Such a rough surface cannot be measured by interferometry, since the speckle noise would largely affect measuring quality. Figure 7(c) shows the cross profile of the region marked by the black dashed line in Fig. 7(b) after rotation for removing the linear trend, where the tool marks with an averaged magnitude of ±0.2 μm and an approximate period of 50 μm were exposed on the knife edge, which demonstrates the fine surface height resolution over a largely extended depth range.

Fig. 7.

Demonstration of the surface shape reconstruction from EDOF microdeflectometric measurement. (a) The tested knife. (b) The reconstructed surface of the white box in (a). (c) The cross profile along the dashed line in (b) removing linear trend.

In conclusion, we proposed a structured illumination assisted microdeflectometric system enhanced with optical depth scanning capability. By properly integrating with an ETL, the custom-designed varifocal microscope objective enables rapid optical focus scanning without any mechanically moving parts. The object-space telecentric nature of the objective maintains system constancy for precision measurement while performing focus scanning. Therefore, the data taken from different depths can be directly combined to obtain EDOF microdeflectometric measurements without the need for scaling or interpolation. Additionally, with a simple displacement of the system display, the SIM technique was also introduced to the same setup as a surface shape probe. We demonstrated the use of the SIM measurements to obtain focused microdeflectometric measurements and provide surface orientations for reconstructing an unknown shape from the microdeflectometric data. We demonstrated a surface measurement with a 7.21 nm height sensitivity and a largely extended 250 μm depth, which is 15 times that of a diffraction limited DOF. We believe the combination of the SIM and microdeflectometric techniques with the capability of optical scanning provides an efficient portable freeform measuring tool, which has the potential to be used for in-line measurement.