Application of LADAR in the Analysis of Aggregate Characteristics (2012)

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4This chapter presents the design configuration of the FTI aggregate imaging and analysis system. The FTI system is actually a noncontact 3-D surface profilometer, using a simple fiber optic coupler to form a Young’s double-pinhole interferometer. A fiber optic switch is adopted to control the input of laser signals from two sources with wavelengths of 675 nm and 805 nm, respectively. The Young’s fringes are projected onto a 45°-angled mirror for fringe projection on the aggregate surface. The image of the aggregate surface in the mirror is captured by a CCD camera and analyzed using the Fourier transform method, which uses the phases of the fringe pattern on the aggregate surface to reconstruct the surface profile. Figure 2-1 presents a picture of the FTI aggregate imaging system as built. 2.1 System Layout and Geometry Figure 2-2 shows the basic FTI system geometry. The mea- sured system geometry is summarized in Table 2-1. Figure 2-3 plots the layout of the fringe generator of the FTI system. The fringe generator consists of a pair of fiber couplers. The couplers are pigtailed to the laser source through a fiber cable, which allows the laser to be located remotely. Light from the laser source is evenly split between the two output arms of the fiber coupler. These arms are aligned close together, form- ing the pinholes in a Young’s interferometer. Fringes are pro- jected from the generator to the object and then viewed with the CCD camera. The locations of the fringes are governed by Eq. 2-1. I x y I a D kxp, cos( ) = + −   2 1 2 0 ∆φ Eq. 2-1 where I(x, y) is the projected interferogram intensity at loca- tion (x, y), I0 is the Gaussian beam spot pattern, 2a is the separation between the fibers (or pinholes), D is the distance from the pinholes to the aggregate, k = 2p/l, l is the wave- length, xp is a spatial coordinate parallel to a line joining the pinhole centers, and Df accounts for any phase difference at the end faces of the two fibers. The fringe pattern depends on the distance to the aggregate surface and is a function of the aggregate surface profile (coordinates). The pair of laser sources is coupled to optical fibers and routed through a 2 × 1 fiber optic switch. With an included USB interface, the switch allows users to easily control the laser wavelength from the main imaging computer. The out- put from the switch is routed through an optical fiber to the fringe projection source, which sits in a sealed enclosure. All optical fibers are designed for single-mode operation above 600 nm. There are three main components within the main enclo- sure: the fringe source, the CCD camera and lens system, and the adjustable-height particle tray and mirror (shown in Fig- ure 2-4). During aggregate imaging operation, an aggregate is (or several aggregates are) placed on the tray, and the enclo- sure door is closed to block all stray light from entering the system. The application of the enclosure is to improve fringe visibility by eliminating ambient light that otherwise could make the dark areas of the image slightly brighter. The CCD camera is positioned perpendicular to the adjustable-height particle tray on the optical axis. The fringes are projected at an angle b relative to the imaging axis. 2.2 Image Collection System Figure 2-5 shows the assembly of the CCD camera, bel- lows, and lens. The electrostatically cooled CCD camera is a Starlight Xpress SXVF-H9 monochrome camera with 16-bit resolution. Its own noise floor limits the actual resolution of the CCD camera. Besides the CCD camera, a macro lens is adopted to help provide the best possible horizontal resolu- tion (x-, y-axis) over the range of desired particle sizes. It is a Schneider Makro-Symmar 5.6/80 lens with a focal length of 80 mm. C h a p t e r 2 Fourier Transform Interferometry Aggregate Image System

5 The aggregate is placed on an adjustable-height tray (shown in Figure 2-6), and users can move the surface into the field of view to maximize the clarity of images. The maximum adjust- able height of the tray is 25 mm. The tray is covered with a black matte surface so that high contrast can be achieved between the particle surface and the tray background. Three images are captured to generate the 3-D coordinates for the surface of an aggregate particle (one image taken with vis- ible light and two images captured with lasers of wavelengths of 675 nm and 808 nm). 2.3 FTI Aggregate Image Analysis Program Figure 2-7 shows the graphical user interface (GUI) of the FTI software developed for the aggregate imaging system and analysis. Figure 2-8 shows the flowchart of the FTI aggregate image program. There are three main subroutines: the main program, the error correction program, and the morphologi- cal analysis program. 2.3.1 Main Program The main program was developed for surface identifica- tion and reconstruction from the images acquired by the FTI system. It calculates the unwrapped phase with the FTI algo- rithm by identifying and tracking a reference fringe on each surface (Figure 2-10); after that, each surface profile is calcu- lated by shifting the phase. After inputting the three images taken using the FTI system, the surface boundary shown in Figure 2-9 is mapped at the beginning of the program to improve efficiency by working only within boundaries in later operations. Prior to boundary mapping, a background adjustment can be made to perform top-hat filtering to achieve better contrast between the back- ground and the aggregate surfaces. Then boundary maps can be generated from the visual images, which are taken under the fluorescent light inside the system enclosure without any fringe present. With the surface boundaries identified, a reference fringe (Figure 2-10) can be entered to calculate the surface coordi- nates by tracking fringes. Before the operation of the inter- ferogram data, a pre-filtering step is implemented to improve the quality of the data prior to the FTI filtering. A band-pass digital finite impulse response (FIR) filter is applied in the horizontal direction, and a low-pass FIR filter smooth- ens the data vertically. After that, a desired reference fringe is manually chosen for each surface. The reference fringe extends to the upper and lower bounds of the particle so that the entire surface can be mapped. The FTI processing algo- rithm and subsequent fringe referencing steps are performed Figure 2-1. FTI aggregate image system. Figure 2-2. Basic FTI system geometry (Lally, 2010). Parameter Variable Measured Value Pinhole-to-Object Distance dP 264.7 mm Projection Angle β 16.39 deg. Pinhole Separation 2a 289 µm Fringe Frequency f0 1.552 mm -1 Primary Wavelength 1λ 675 nm Reference Wavelength 2λ 805 nm Table 2-1. FTI system geometry.

6Figure 2-3. Fringe source: fiber-coupled laser sources and 1  2 fiber switch. Figure 2-4. Angled mirror and adjustable-height particle tray (left), and the CCD camera, bellows, and lens system (right) (Lally, 2010). Figure 2-5. CCD camera, bellows, and lens assembly. Figure 2-6. Adjustable-height particle tray. row by row, and only rows that contain a reference point can be reconstructed. The fringe-tracking algorithm locates the exact fringe peak in each row of the surface fringe projection by starting at a reference row and then looping up through the image and analyzing each row sequentially. For each subsequent row in the loop, the rounded value of the peak from the last row is served as a new center point, fitting a quadratic func- tion that is forced to fit the fringe data around the peaks with windowed curves, as shown in Figure 2-10. Once the tracking algorithm reaches the upper extent of the bounded surface, it starts over from a new row and tracks down to the lower extent of the bounded surface. These tracking steps are performed for both laser images within the same loop. The fringe peak shift is only dependent on the projection angle, b, which is governed by Eq. 2-2. Therefore, the entire surface pattern shifts horizontally when the mean surface height changes. Two interferograms are projected at different wavelengths, and each will experience an identical shift. ∆ ∆z Mx z0( ) = − tanβ Eq. 2-2 where Dzx0(M) is the shift value for the Mth order fringe and Dz is the aggregate surface height. After the selected reference fringe is tracked, the fringe order lookup table is automatically generated to determine the unique fringe order. First, a set of roughly 12 fringes is selected based on the average x0 value, and then the specific fringe is identified by matching the measured value of peak location difference shown in the lookup table, which is rep- resented in Figure 2-11. Fringe tracking and averaging is a highly effective means of noise reduction.

7 Once the reference fringe order is determined, it must be applied to the unwrapped phase map ju(x, y), calculated only once for the entire image, regardless of surface boundary or reference fringe selection. All subsequent operations can be thought of as independent modifications of the master phase map to prepare it for surface reconstruction over different areas of the image. 2.3.2 Error Correction Program After running the main program, the procedure will continue by running an error correction module. In the error correction program, surface errors are identified by users, and a secondary reference fringe is selected to reprocess the z(x, y) matrix to modify and improve the reconstructed surface map. Since many errors can be caused by steep edges along the surface boundary, a windowing algorithm that automatically locates these erroneous data regions and removes bad data from the z(x, y) matrix was developed. By manually entering the variable height of the particle tray measured with a built-in micrometer, the surface height map can be converted to measure the particle thick- ness above its resting plane (i.e., the tray that the aggregate rests on). If row errors are present, they are clearly identifiable during visual inspection of the reconstructed surface pro- file. A secondary reference fringe is selected near the center of the bad data region. Based on the mechanism for error propagation, it can be assumed that the source of the errors is located near the interface between smooth and erroneous Figure 2-7. GUI of the FTI software.

8Startt rt Image acquisition in FTI systemI i iti i I t Input images in FTI software Map surface boundaries Choose reference fringe Track fringe Determine fringe order Pre-filter fringe images Shift phase Basic FTI algorithm Calibration matrices Calculate surface profile Surface error correctionrf rr r rr ti Narrow boundary windowingrr r i i Convert to relative heightrt t r l ti i t Output data of 3D coordinatest t t f r i t Original z(x,y) Two-dimensional Fourier Analysis Sphericity, Flatness ratio, Elongation ratio, Angularity, Texture End Choose alternative fringe Track fringe Determine fringe order Input height of particle tray z’(x,y) Better than original pahseMerge data Main Program Error Correction Program Morphology Analysis Program No Yes Lookup fringe table For surface i (i=1,2,…,n) Output Output Shift phase Lookup fringe table Final 3D aggregate coordinates z(x,y) Output Figure 2-8. Flowchart of the FTI aggregate image analysis program. Figure 2-9. Surface reconstruction from the reference fringe. data. The secondary reference is tracked and its order iden- tified using the lookup table representation shown in Fig- ure 2-11. When this occurs, the original unwrapped phase map is shifted to match the secondary reference fringe, resulting in two data sets (i.e., the data set by use of the main reference fringe and data set by use of the secondary reference fringe). To correct the errors, the method of mul- tiple references is adopted to perform automatic decision making to combine two data sets processed with different reference fringes. Figure 2-12 shows the map of surface errors used in the narrow windowing algorithm. The windowing algorithm works directly with the reconstructed surface map, identifies error areas, and constructs a narrow boundary to exclude the erroneous data. To achieve this goal, original Cartesian coor- dinates are converted to polar coordinates, and a piecewise cubic polynomial curve fitting is applied akin to inflating a balloon inside the good area of the surface data.

9 610 615 620 625 630 635 640 645 650 0 2000 4000 6000 8000 10000 12000 14000 16000 Fringe Track Fitting: Painted Glass Target @ 808nm, row 300 Fringe Data Peak Fit Figure 2-10. Narrow window curve fitting during fringe peak tracking (Lally, 2010). -12.0 -8.0 -4.0 0.0 4.0 8.0 12.0 200 400 600 800 1000 1200 Pe ak L oc at io n D iff er en ce Δ x 0 (p ixe ls) Fringe Peak Location x0(λ1) (horizontal pixel number) Low Z High Z 0 - 1 - 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20 - 21 - 22 - 23 - 24 Figure 2-11. Graphical representation of the lookup table for fringe order identification (Lally, 2010). 2.4 Accuracy and Resolution 2.4.1 Calibration To reconstruct aggregate surfaces pixel by pixel, the system must undergo a one-time calibration to generate the quadratic fit matrices, and a 2-in.-square optical flat plate painted white was adopted as the calibration plate. In the calibration process, the optical flat plate sprayed with white paint was imaged at 19 points throughout the 25-mm mapping height range that the adjustable-height particle tray could be adjusted within. The particle tray height can be adjusted using the Vernier 2.3.3 Output Data Format Figure 2-13 plots the geometry configuration of the out- put data format. The output z(x, y) matrix from the FTI software is a matrix giving surface height z for every (x, y) coordinate as a three-dimensional surface map that has been bounded, corrected, and windowed. The mapped boundary data of the imaged particle are also included in the output to give the exact dimensions of the particle in the horizontal plane. These data could be interpreted as the vertical distance between a point on the aggregate top surface and the particle tray at the bottom.

10 x y z x 1 x 2 z ( x 1 ) z ( x 2 ) S i d e V i e w 3 D M a p p e d R e g i o n M a p p e d B o u n d a r y z y x M a p p e d B o u n d a r y 3 D M a p p e d R e g i o n T o p V i e w T a l l z S h o r t z Figure 2-13. Three-dimensional output data format of z(x, y) (Lally, 2010). Figure 2-12. Surface error map used for windowing (Lally, 2010). micrometer underneath the adjustable-height particle tray to take fringe images on the calibration plate. Then the phase of each interferogram was calculated using the FTI process. After compilation of 19 phase maps at varying z-values, a pixel-by-pixel quadratic fit was performed to calculate z(x, y). The z-value was assumed to be constant in each image; the z(x, y) matrices were reconstructed based on the images. The direct measurement of z(x, y) was calculated at each pixel; the quadratic fit in the calibration process automatically accounts for misalignment and aberration errors in the system. The calibration step is time consuming, but it only needs to be performed once. Figure 2-14 plots the fringe patterns in the calibration process, and Figure 2-15 illustrates the pixel- by-pixel quadratic calibration process.

11 Figure 2-14. Quality of fringes generated with fiber coupler: calibration coefficient deviation (left); fringe pattern (right). Figure 2-15. Pixel-by-pixel quadratic fit calibration process. 2.4.2 Flat Target Accuracy and Resolution The nominal resolution of the FTI system is 35.4 µm per pixel in both x-axis and y-axis directions, and the measured z-axis resolution is 22 µm per pixel. The true horizontal reso- lution of the system is primarily limited by the FTI filtering operations. The accuracy and resolution of the FTI system are determined during calibration. It is important to note that the accuracy and resolution measurements are not simply a repetition of the calibration process. During resolution and accuracy testing, six of the calibration fringe images were recalled and processed using the full FTI algorithm with the application of the fitted calibrated data. The reconstructed surface profiles were checked for variations above the mean and deviations from the true nominal surface value to yield accuracy and resolution information. Resolution was quoted as twice the 2-D standard deviation, and accuracy was the 2-D root-mean-square (RMS) deviation from the true sur- face height. Figure 2-16 shows that the maximum single-point surface error varies from 45 µm to 75 µm with the surface height, and the resolution varies from 19 µm to 22 µm. Results in this figure show that the best resolution and accuracy are achieved when the adjustable particle tray is positioned between Z = 10 mm and Z = 15 mm. The best height is illustrated in Figure 2-17. RMS error is better than 15 µm across the entire range, with a minimum value of 10 µm in the center. Table 2-2 shows the resolution of the FTI system. 2.5 Safety Concern The major safety risk incurred by the users of the system is the risk of eye damage associated with the laser source. The risk of ocular damage can be managed by limiting the power of the HeNe laser source for the interferometer. Any collimated beam at a power level less than 1 mW is safe to work around without eye protection, although eye damage can occur if the user stares directly into the beam for several seconds. The risks associated from power levels of less than 10 mW can be safely managed by wearing a basic pair of attenuating glasses designed for the

12 HeNe laser wavelength of 633 nm. Such glasses are relatively inexpensive and widely available. The proposed CCD camera, the Starlight Xpress SXVF- H9, was originally designed for astronomical imaging, and therefore it can be operated at relatively low power levels. For this reason, the system can effectively operate at an input power level of between 1 mW and 5 mW. Due to the varied, Note: STD = standard deviation, abs = absolute value Figure 2-16. z-axis resolution and accuracy calculation (Lally, 2010). Z = 100-15 mm Vernier micrometer Figure 2-17. Illustration of best height range of the adjustable-height particle tray. Over Entire Range Over Z = 10–15mm Surface Height Resolution ±25 µm ±20 µm Surface Height Accuracy (RMS Error) ±15 µm ±10 µm Table 2-2. Resolution of the FTI system. inhomogeneous structures of the particles being imaged, any calculation of the reflected power is at best a rough estimate. For this reason, the input power level must be experimentally confirmed before a particular laser is selected. We are confi- dent that, regardless of the object under test, the proposed design will be able to operate effectively at a safe power level appropriate for a user with basic eye protection.