Test procedures Measurement methods and test procedures Numerical aperture 3.2.3 Technique 3-Scan of the spatial field pattern(see figure 3) 3.2.3.1 Fibre output end support apparatus Provide a means of supporting and aligning the specimen output end that allows stable and repeatable positioning 3.2.3.2 Far-field transformation and projection Create a spatial representation of the far field of the specimen by suitable means(for example, by usi a microscope objective or other well corrected lens to obtain the Fourier transform of the fibre output ear-field pattern Scan this pattern or its image using a pinhole aperture as to enable the far-field intensity to be recorded The size of the pinhole aperture shall be less than, or equal to one-half the diffraction limit of the system 1.22 2 f 2D the d is the diameter of the pinhole, in um M is the magnification from the back focal plane of the transforming lens to the scanning plane A is the spectral wavelength emitted from the fibre in nm f is the focal length of the transform lens, in mm D is the fibre core diameter, in um The numerical aperture of the lens, L1, should be large enough so as not to limit the numerical aperture of the fibre specimen Where the far-field pattern is represented by a lens, care should be taken that, especially with high apertures, the diameter of the relay lens, L2, is sufficiently large so as to avoid darkening the periphery: 12>2f tan c (6) D12 is the diameter of the relay lens, in mm f is the focal length of the transform lens, in mm; sin is the numerical aperture NA Far field Lens L1 Lens L2 Figure 3- Technique 3- Scan of the spatial field pattern 3.2.3.3 Scanning system Provide a method of scanning the far-field pattern with respect to the pinhole aperture and detector 3.2. 3 4 System calibration Perform a calibration to measure the conversion factor that relates the distance of movement of the canning system to the actual distance scanned in the back focal plane of the far-field transforming lens In addition, determine the factor that relates scan position in the field pattern transformation plane(the o A pattern of known dimensions, carefully placed in the back focal plane, L1, can be used for this purpos back focal plane of Li in figure 3 to emission angle, 0, with respect to the specimen output end axis is the distance from the axis to the spatial field pattern; f is the focal length of the transform lens, L1 e is the angle with respect to the optical axisTest procedures Page: 3 of 5 Subject: Originated by: Wu Jia Measurement methods and test procedures – Numerical aperture 3.2.3 Technique 3 – Scan of the spatial field pattern (see figure 3) 3.2.3.1 Fibre output end support apparatus Provide a means of supporting and aligning the specimen output end that allows stable and repeatable positioning. 3.2.3.2 Far-field transformation and projection Create a spatial representation of the far field of the specimen by suitable means (for example, by using a microscope objective or other well corrected lens to obtain the Fourier transform of the fibre output near-field pattern). Scan this pattern or its image using a pinhole aperture as to enable the far-field intensity to be recorded. The size of the pinhole aperture shall be less than, or equal to, one-half the diffraction limit of the system: where d is the diameter of the pinhole, in µm; M is the magnification from the back focal plane of the transforming lens to the scanning plane; λ is the spectral wavelength emitted from the fibre, in nm; f is the focal length of the transform lens, in mm; D is the fibre core diameter, in µm. The numerical aperture of the lens, L1, should be large enough so as not to limit the numerical aperture of the fibre specimen. Where the far-field pattern is represented by a lens, care should be taken that, especially with high apertures, the diameter of the relay lens, L2, is sufficiently large so as to avoid darkening the periphery: where D12 is the diameter of the relay lens, in mm; f is the focal length of the transform lens, in mm; sin Φ is the numerical aperture, NA. 3.2.3.3 Scanning system Provide a method of scanning the far-field pattern with respect to the pinhole aperture and detector. 3.2.3.4 System calibration Perform a calibration to measure the conversion factor that relates the distance of movement of the scanning system to the actual distance scanned in the back focal plane of the far-field transforming lens. A pattern of known dimensions, carefully placed in the back focal plane, L1, can be used for this purpose. In addition, determine the factor that relates scan position in the field pattern transformation plane (the back focal plane of L1 in figure 3) to emission angle, θ, with respect to the specimen output end axis as y = f sin θ (7) where y is the distance from the axis to the spatial field pattern; f is the focal length of the transform lens, L1; θ is the angle with respect to the optical axis