Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2011
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/8764
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/8764
- Palabra clave:
- Degrees of freedom (mechanics)
Diffraction
Fourier optics
Gaussian beams
Microlenses
Mines
Astigmatic Gaussian beam
Diffraction phenomenon
Dirac distribution
Fractional Fourier transforms
Fractional transforms
Fresnel microlense
Radii of curvature
Transmission function
Fourier transforms
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
Summary: | According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source. |
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