Diffraction patterns of simple apertures

Smith, Richard C.; Marsh, James S.

doi:10.1364/josa.64.000798

Cited by 49 publications

(23 citation statements)

References 3 publications

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“…They deduce the distribution of the two sincs functions for a rectangular aperture (Figure 6(h)). The next figure to analyze is a triangular aperture [9] ( Figure 6(i)). Students, by using the specific tool in the software, can determine the angles of the actual aperture.…”

Section: Resultsmentioning

confidence: 99%

Teaching Fraunhofer diffraction via experimental and simulated images in the laboratory

et al. 2012

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Diffraction is an important phenomenon introduced to Physics university students in a subject of Fundamentals of Optics. In addition, in the Physics Degree syllabus of the Universitat Autònoma de Barcelona, there is an elective subject in Applied Optics. In this subject, diverse diffraction concepts are discussed in-depth from different points of view: theory, experiments in the laboratory and computing exercises. In this work, we have focused on the process of teaching Fraunhofer diffraction through laboratory training.Our approach involves students working in small groups. They visualize and acquire some important diffraction patterns with a CCD camera, such as those produced by a slit, a circular aperture or a grating. First, each group calibrates the CCD camera, that is to say, they obtain the relation between the distances in the diffraction plane in millimeters and in the computer screen in pixels. Afterwards, they measure the significant distances in the diffraction patterns and using the appropriate diffraction formalism, they calculate the size of the analyzed apertures. Concomitantly, students grasp the convolution theorem in the Fourier domain by analyzing the diffraction of 2-D gratings of elemental apertures.Finally, the learners use a specific software to simulate diffraction patterns of different apertures. They can control several parameters: shape, size and number of apertures, 1-D or 2-D gratings, wavelength, focal lens or pixel size. Therefore, the program allows them to reproduce the images obtained experimentally, and generate others by changing certain parameters. This software has been created in our research group, and it is freely distributed to the students in order to help their learning of diffraction.We have observed that these hands on experiments help students to consolidate their theoretical knowledge of diffraction in a pedagogical and stimulating learning process.

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Section: Resultsmentioning

confidence: 99%

Teaching Fraunhofer diffraction via experimental and simulated images in the laboratory

et al. 2012

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“…However, the circular focusing spot can be obtained using the same aperture, but the energy transmission is changed for the di erent beam ellipticities. According to equations (5) and (6), the energy transmission ratio can be calculated for these two kinds of aperture. In ®gure 6, the energy transmission ratio can be calculated for these two kinds of Table 1.…”

Section: Results Of Calculation and Discussionmentioning

confidence: 99%

Direct focusing modifications of elliptical Gaussian beam by non-circular apertures

Chan¹,

Shiue²,

Lu³

1998

Journal of Modern Optics

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For focusing the elliptical Gaussian beam directly, the e ects of a non-circular aperture on the focusing properties are studied. The focusing properties for di erent shapes of apertures, which include a circle, an ellipse and a rectangle, are calculated and compared. Moreover, for di erent elliptical Gaussian beams, an empirical aperture selection rule that can be used to circularize the focusing spot is proposed. The energy transmission ratios are also considered in this paper. Gaussian beams. In practical applications, there are two methods of focusing elliptical Gaussian beams. The ®rst method, which is most often used, is to use prisms or cylindrical lenses [1] to obtain a circular beam before focusing. Because of misalignment and defects of the optical elements this approach may cause unavoidable throughput losses and increase the system cost. The other method is the so-called direct focusing method, which utilizes the aperture to truncate the incident beam to get the desired characteristics of the focusing spot. Marchant [2] studied the direct focusing properties of the elliptical Gaussian beams by using the central irradiance and the line spread function. With considerations of system cost and power increase of the laser diode, Kondo [3] has used this approach for the optical heads. However, when the elliptical beam can be focused through a circular objective lens, the focusing spot will also be non-circular, and the ellipticity of the focusing spot depends on the beam ellipticity and the apodization values [2]. Kondo [3] showed that the orientation of the major or minor axis of the elliptical Gaussian beam can a ect the signal level, the spatial frequency characteristics and the cross-talk level. In some other applications, for instance the laser printer, a non-circular focusing spot is an annoying problem.According to the di raction theory, the shape of the aperture can a ect the di raction pattern in the image plane of an optical system [4±6]. The di raction of an elliptical Gaussian beam truncated by an elliptical aperture has been calculated numerically by Kathuria [7], who found that the beam ellipticity, which is not equal to the ellipticity of the aperture, can be changed in the far ®eld. In this paper, the aperture di raction method is put forward to modify the characteristics of the elliptical focusing spot. The e ects of rectangular and elliptical apertures on the

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“…For an incident electric field with m ≠ 0, the light fans overlap at positions other than the aperture's center. Since diffraction from the edges of a finite sized aperture will also produce parallel and equally spaced satellite fans [30], superposition of the many light fans will create a triangular lattice of bright spots in the Fourier plane whenever m ≠ 0. The topological charge of the vortex beam determines the size of the triangular lattice since the charge is related to how far the light fans from each edge is shifted in reciprocal space.…”

Section: Triangular Aperture Techniquementioning

confidence: 99%

Measuring the topological charge of ultrabroadband, optical-vortex beams with a triangular aperture

et al. 2012

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A simple technique for determining the topological charge of supercontinuum optical vortices is presented. The spatial dispersion inherent to generating broadband vortices with a single forked grating is compensated with a double-pass arrangement from a single spatial light modulator. The vortex charge is determined by inspecting the diffraction pattern through a triangular aperture. It is shown that the topological charge is constant, and can be consistently measured, across a wide range of colors.

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Diffraction patterns of simple apertures

Cited by 49 publications

References 3 publications

Teaching Fraunhofer diffraction via experimental and simulated images in the laboratory

Teaching Fraunhofer diffraction via experimental and simulated images in the laboratory

Direct focusing modifications of elliptical Gaussian beam by non-circular apertures

Measuring the topological charge of ultrabroadband, optical-vortex beams with a triangular aperture

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