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Zoom Lens Working Distance Spatial Resolution DOF 1 DOF 2
3× 285 mm 3.07µm/pixel 250 µm 350 µm
2× 285 mm 5.18µm/pixel 300 µm 400 µm
1.5× 250 mm 6.34µm/pixel 350 µm 450 µm
1.5× 285 mm 7.07µm/pixel 400 µm 500 µm
1.5× 320 mm 7.80µm/pixel 450 µm 750 µm
1.5× 350 mm 8.35µm/pixel 500 µm 800 µm
Table 5.1.: Spatial resolutions and DOFs of the optical system. DOF 1 had an aperture
of 65 mm, while DOF 2 had a 35 mm aperture.
and the image plane, and the angle at which the first minimum intensity of light
occurs [3],
sin θ ≈ 1.22 λ d , (5.10)
where λ is wavelength of the light, d is the diameter of the aperture. This approximation
is valid because the angle is in general very small. Taking a typical wavelength
for visible light as λ =550 nm for a quick estimation, θ yields 0.000 61° with
the diameter of the aperture of QM100 being 63 mm. The distance l is roughly 1 m,
so that the diameter of the Airy disc is 21 µm. Diffraction blur occurs when the diameter
of the Airy disc exceeds one pixel pitch. Apparently, bigger pixels are less
vulnerable to the diffraction blur.
In shadowgraph imaging, the diffraction pattern appears differently from the
typical Airy disk pattern. Firstly, the illumination is usually inherent, therefore
the diffraction pattern is a superposition of Airy patterns corresponding to various
wavelengths. Secondly, the object casts a shadow in the image, instead of a bright
spot. The final compound effect was that both the bright background and the dark
interior of the object was invisibly influenced, but the edges appeared blurred. The
minimum aperture was experimentally found out for each magnification, and was
avoided.
The maximum applicable DOF listed in Table 5.1 was still narrower than the half
width of the impact surface. Consequently, simultaneous focus of the drop and a
flat impact surface is impossible, because the drop impacts at the center line of
the impact surface, while the shadow in the image is casted by one edge of the
impact surface, which is outside the DOF. In order to bring both the drop and the
impact surface inside the DOF, a curvature with a radius of 5 mm was applied to
the impact surface, so that the most front outline of the impact surface was the
152 5. Experimental Setup