76 J. Heikkinen and G. S. Schajer According to Eq. (9.1), the subjective speckle size depends linearly on the lens numerical aperture. Therefore, the ratio Ssubj/f # should be a constant when L =0. Conversely, at large defocus distances, the observed speckle size should be independent of the lens aperture and scale linearly with L. Based on the geometry shown in Fig. 9.1, the blur diameter depends on both the defocus distance and the aperture diameter according to relation: dlens do = dblur L (9.3) Therefore, the minimum defocus distance required for the speckle size to obey the theoretical Equation (9.2) must be such that the blur diameter equals the illuminated spot diameter, dblur =dspot. Thus, the minimum defocus distance is Lmin, obj = do dlens dspot = dodspot f f# (9.4) 9.5 Speckle Size vs. Aperture Size vs. Defocus The speckle size dependence on aperture size and defocus distance was experimentally investigated. The object was a flat medium-density fiberboard (MDF) plate with a diffuse surface. A single-mode green laser source (JDS Uniphase, λ =532 nm) with a diverging beam illuminated the object surface at a 31◦ angle with respect to the surface normal. The illuminated spot size was controlled by placing an aperture element in front of the laser so that only the central portion of the beam(dspot =19.5 mm) with approximately uniform intensity profile passed through. The scattered interference speckle pattern was imaged using a Canon EOS 100D DSLR camera (resolution 5184x3456 pxl2, pixel diameter dpixel =4.3 μm) fitted with a Canon EFf =50mmf #1.8 lens. A 34 mm extension tube was attached between the camera body and the lens to reduce the focus distance, giving a magnification M=0.83. The interference speckle pattern was sampled at different defocus distances ranging from –20 mm (far focus, focal plane behind the object surface) to 1350 mm (near focus, focal plane in front of the object surface). For each defocus distance, the speckle pattern was imaged using three different numerical apertures, f #5.6, f #11.0, and f #22.0. The defocus distance was changed by moving the camera along an optical rail rather than changing the lens focus settings. This arrangement maintained constant magnification throughout the measurements. Figure 9.2 shows the experimental setup and an example speckle pattern. For each speckle image, the average speckle size was determined using a two-dimensional normalized autocorrelation, implemented in Matlab. The autocorrelation window consisted of a cropped 201×201pxl2 region extracted from the image Fig. 9.2 (Left) Experimental setup. (Right) Example speckle pattern captured at L=0 andf #22.0
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