Lesson plan
Sombrero function
A sombrero function (sometimes called besinc function or jinc function ) is the 2-dimensional polar coordinate analog of the sinc function, and is so-called because it is shaped like a sombrero hat. This function is frequently used in image processing. It can be defined through the Bessel function of the first kind ( J_1 ) where . \operatorname{somb} (\rho) = \frac{2 J_1(\pi \rho)}{\pi \rho}. The normalization factor makes . Sometimes the factor is omitted, giving the following alternative definition: \operatorname{somb} (\rho) = \frac{2 J_1(\rho)}{\rho}. The factor of 2 is also often omitted, giving yet another definition and causing the function maximum to be 0.5: \operatorname{somb} (\rho) = \frac{ J_1(\rho)}{\rho}. The Fourier transform of the 2D circle function ( \operatorname{circ}(\rho) ) is a sombrero function. Thus a sombrero function also appears in the intensity profile of far-field diffraction through a circular aperture, known as an Airy disk.
Article summary
A sombrero function (sometimes called besinc function or jinc function ) is the 2-dimensional polar coordinate analog of the sinc function, and is so-called because it is shaped like a sombrero hat. This function is frequently used in image processing. It can be defined through the Bessel function of the first kind ( J_1 ) where . \operatorname{somb} (\rho) = \frac{2 J_1(\pi \rho)}{\pi \rho}. The normalization factor makes . Sometimes the factor is omitted, giving the following alternative definition: \operatorname{somb} (\rho) = \frac{2 J_1(\rho)}{\rho}. The factor of 2 is also often omitted, giving yet another definition and causing the function maximum to be 0.5: \operatorname{somb} (\rho) = \frac{ J_1(\rho)}{\rho}. The Fourier transform of the 2D circle function ( \operatorname{circ}(\rho) ) is a sombrero function. Thus a sombrero function also appears in the intensity profile of far-field diffraction through a circular aperture, known as an Airy disk.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.