Siemens star

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16-pointed Siemens star, consisting of 16 black and 16 white segments
(as SVG - vector graphics )

The Siemens star is a test sample and test procedure to check the quality of optical imaging systems . The Siemens star is a circle with alternating white and black sectors .

It was developed by Siemens & Halske AG (today Siemens AG ) in the 1930s to test the lenses of Siemens cine film cameras.

As a motif, the Siemens star contains all spatial frequencies (increasing towards the center) in all directions. Due to the limitations of the resolution of all optical imaging systems , this pattern cannot be reproduced perfectly. According to the modulation transfer function (MTF) of the system, the modulation depth decreases towards the center of the Siemens star to merge into a gray circle, the gray ring . The size of the gray ring is used to determine the resolution of an optical output device or to determine the optimal focus of an optical imaging system.

construction

A single-pointed Siemens star consists of white and black sectors radially starting from a center point , each covering an angle of . At a distance from the center on a circle of the circumference , sectors are distributed which have a lateral size of

with rectangular modulation. If this can just be resolved, then this lateral size corresponds to the resolution. This can be direction-dependent, which can be clearly seen on the Siemens star.

Modifications

Newton's rings as a test target for determining the resolution
  • The sectors can go to the edge of the test board.
  • Instead of a rectangular one, a sinusoidal brightness modulation can be used.
  • Instead of a large Siemens star, a test table can contain several small Siemens stars in order to test the resolving power at several points.
  • Siemens stars are also found on many more complex test boards as components.
  • Rings can be used instead of spokes. The readability in particular of higher spatial frequencies improves.

example

Images of an 18-rayed Siemens star by two optical instruments with different resolving power.
The gray circle in the middle is different in size.

The illustration shows images of an 18-rayed Siemens star made by two optical instruments with different resolutions.
The gray circle has a diameter of D in the left part of the picture, and D in the right part .

From this it follows for the resolving power:

 ● Left-hand picture:   
 ● Partial image on the right:

If the image is 100 mm in size, the optical instrument of the left partial image resolves 2.6 mm, that of the right 1.3 mm.

Apparent resolution scanning illustration

128-point Siemens star
Siemens star (128 spokes) & Matlab code.svg
... as SVG vector graphics: scalable
The visible artifacts are inadequacies in the SVG renderer of your web browser.
  • dark core: computation performed in a non-linear, gammva-distorted space
  • irregular structures in the core: missing aliasing filter
Siemens star, 284x284 pixels, diameter 269 pixels, 128 rays.png
... as PNG pixel graphics: not scalable
Is optimally displayed with 1: 1 display on monitors with sRGB gradation.


When imaging the Siemens star by classic analog , i. H. non-scanning imaging does not produce any artifacts. The modulation depth decreases with proximity to the center point due to the increasing spatial frequency and the amplitude of the modulation transfer function which decreases with this .

With digital , d. H. Scanning images result from violation of the scanning theorem aliasing artifacts, which are very easy to recognize on the Siemens star, an extremely critical motif for these artifacts. This creates radial patterns around the center point with "wrong" spatial frequencies. Characteristic, more complex patterns result from the mostly direction-dependent resolution of the imaging system.

Effects when viewed visually

The effective resolution of the eye is modulated depending on the direction by the microsaccades of the eye and by head movements in the range of a hundred milliseconds. The size and shape of the gray ring is therefore apparently in constant motion.

Böhlerstern

To test laser scanners , the Siemens star was transferred to the third dimension as a Böhler star .

Web links

Commons : Siemens star  - collection of images, videos and audio files

Individual evidence

  1. Alexandra Kinter, Siemens AG, Siemens archive in D-80333 Munich, Oskar-von-Miller-Ring 20
  2. https://www.researchgate.net/figure/Boehler-Star-used-to-measure-the-spatial-resolution-of-laser-scanners-Boehler-et-al_fig1_281631474