9 Perspective Compensation of 2D-DIC Measurements by Combination with Speckle Imaging 75 indicated by the soft image edges. The blur occurs because a point on the sensor receives light from an extended surface area with a finite diameter dblur. Although not accurately focused on the specimen surface, a “defocused” camera is accurately focused at a focal plane in the adjacent space whose position depends on the camera focus adjustment. In the case of monochromatic laser illumination, a 3D speckle field exists in the space around the illuminated surface [4]. High speckle contrast is present at all spatial locations within that space, not just at the specimen surface. Consequently, a defocused camera accurately images a cross-section of the 3D speckle field that exists at the focal plane of the camera. In Fig. 9.1b, this corresponds to the line segment on the focal plane bounded by the red lines. If the defocus distance ΔLis so high that the blur diameter reaches the size of the illuminated laser spot, then the resulting speckle pattern is exactly the same as would be observed by a bare (without lens) camera sensor placed in that plane. A highly defocused camera thus has the characteristics of OSI [3, 5]. A defocused camera has the advantage of not requiring to be placed physically within the speckle field. Instead, it may measure the speckle field remotely and “reach into” it according to the position of its focal plane. The sampling position can be varied simply by adjusting the camera (de)focus [5]. 9.3 Research Objective While OSI is attractive for measuring rigid body motions at high sensitivity, the inherent loss of spatial resolution makes it impractical for full-field measurement applications where 2D-DIC is commonly used. Therefore, the interest in this research is to study the intermediate region between Subjective and Objective Speckle Imaging. This region mixes characteristics of both regimes and allows them to be used simultaneously. If speckle imaging is performed using moderately defocused camera, then each point on the sensor receives light from limited, small area on the object surface, and the resulting speckle patterns maintain reasonable spatial resolution. In Fig. 9.1b, the intermediate range is characterized by small defocus distances so that the extent of blur on the object is much smaller than object dimensions. However, defocused speckle imaging differs from 2D-DIC in that its sensitivity increases with defocus distance rather than decrease. Therefore, if the in-plane motions of a near-focused object are measured using both DIC and speckle imaging, the resulting sensitivity difference can be used to compensate for the effects of perspective changes. 9.4 Speckle Pattern Characterization There is a trade-off between spatial resolution and sensitivity, so for effective use, the character and extent of the intermediate region between Subjective and Objective Speckle Imaging needs to be well understood. The average speckle diameter is a statistical parameter that characterizes the speckle imaging geometry. Importantly, the subjective speckle size is governed by different geometric parameters than objective speckle size. Therefore, determining the speckle size as a function of defocus distance provides a practical way to assess the transition from subjective to objective speckles, as well as the extent of the intermediate regime of moderate defocus. The diffraction limited subjective speckle diameter can be defined as [6] Ssubj =1.22 λ (1+M) f dlens = 1.22 λ (1+M) f# (9.1) where λis the laser wavelength, f is the camera lens focal length, dlens is the lens aperture diameter, f # =f /dlens is the lens f-number, M=di/do is the camera magnification, di is the image distance, and do is the object distance. The diffraction-limited objective speckle diameter is [6] Sobj =1.22 λM L dspot (9.2) where Lis the defocus distance and dspot is the diameter of the illuminated spot. For objective speckle imaging setup, L is the object–sensor distance andM=1. If a highly defocused camera is used instead, Lis the object–focal plane distance, and Mis the camera in-focus magnification ratio.
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