9 Perspective Compensation of 2D-DIC Measurements by Combination with Speckle Imaging 77 Fig. 9.3 (Left) Measured speckle size per f-number vs. defocus distance. (Right) Measured speckle size vs. defocus distance center. The resulting autocorrelation map contains a central peak whose width at half-height represents the statistical average speckle size. Figure 9.3 (Left) shows the measured speckle sizes per f-number for different defocus distances, as well as the theoretical subjective speckle diameter per f-number calculated using Equation (9.1). The speckle patterns recorded using f #11.0 and f #22.0 have values that are very close to the theoretical expectation, while the speckle size recorded at f #5.6 was higher than expected. Figure 9.3 (Right) shows a comparison between the measured speckle sizes and the theoretical objective speckle size determined from Equation (9.2) using the specific illumination and imaging parameters. At large defocus distances, the measured speckle sizes converge close to the theoretical line, independent of the aperture size. 9.6 Discussion It is possible to distinguish three different regions in the speckle size graphs. At small defocus distances (0-100 mm), perspective effects cause the observed speckle size to be inversely proportional to defocus distance. When the camera moves further away, the effective magnification reduces, causing the imaging scale to become smaller, similar to 2D-DIC. At very large defocus distances (hundreds of mm’s), on the other hand, the speckle size increases linearly with defocus distance, similar to objective speckle imaging. Between these two extremes, at moderate defocus distances (around 200-400 mm), there is a transition region where the speckle size reaches minimum values. This can be explained by noting that each point on the sensor plane of a defocused camera receives light from a finite-area blur circle whose diameter defines the effective spot diameter. Because the blur circle increases linearly with defocus distance, the effective spot size expands until the blur diameter reaches the physical spot diameter. In this regime, the ratio ΔL/dspot in Equation (9.2) remains almost constant, leading to the flat section around the minimum speckle diameter position. Because blur diameter is inversely proportional to the f-number, the effective spot diameter of f #5.6 reaches the physical spot diameter at smaller defocus distances thanf #11.0 or f #22.0, as indicated by Equation (9.4). Correspondingly, f #5.6 begins to correlate with the theoretical objective speckle diameter at smaller defocus distances than the two smaller apertures. 9.7 Conclusion The linear dependence between the speckle size and defocus at small defocus distances is valuable for perspective compensation because a reduction in speckle size can be related to an increase in object distance. In addition, this regime is the most practical range for full-field measurements, since moderate defocus maintains high spatial resolution. If the speckle
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