Atelier Bonryu(E)
zone plate photography
Atelier Bonryu(E)
zone plate photography
Laboratory: Zone Plate Photography
Orthogonal Linear Zone Plate
One dimensional zone plate: Though Fresnel and Gabor zone plates composed of concentric circular zones are usually called “zone plates”, a photon sieve is also a zone plate. The patterns of these zone plates are two-dimensional but a zone plate with a one-dimensional pattern shown below can be considered as a kind of zone plates. As the one-dimensional zone plate in the left is vertical-striped, it converges lights at a vertical straight line on a focal plane. On the other hand as the one-dimensional zone plate of the right figure is horizontal-striped lights converge at a horizontally straight line on the focal plane.
A vertical one-dimensional zone plate.
A horizontal one-dimensional zone plate.
Orthogonal linear zone plate: As described in the page on the double slit photography a rectangular "pinhole" is created by overlapping a vertical slit plane and a horizontal one. In the same way a rectangular zone plate is created by overlapping closely a vertical one-dimensional zone plate and a horizontal one. The lower left figure shows the zone plate pattern thus created.
Let's draw a horizontal line through the center of the pattern as x axis and a vertical line as y axis. On the corresponding y (x) axis on the focal plane the diffracted lights from transparent zones of the vertical (horizontal) zone plate intensify each other due to the interference but on lines slanted from y (x) axis the "interference condition" becomes unfulfilled. However, by changing the opaque blocks surrounded by four transparent blocks to transparent ones the lights from these transparent blocks intensify each other on the focal plane. If you do nothing other than overlapping the vertical and the horizontal one-dimensional zone plates you throw aside valuable lights which would have contributed to intensify the image at the focal plane. The pattern obtained by this modification is shown as the following right figure. As there are more transparent blocks in the right pattern than in the left pattern brighter images can be obtained by this modified pattern. Actually with increasing the zone number the pattern of the modified plate becomes similar to the pattern of the usual Fresnel zone plate with concentric circular zones. We call the zone plate with the modified pattern an orthogonal linear zone plate. This type of zone plate is employed as an optical element of the satellite-based astronomical telescope projected by L. Koechlin et al. They call the zone plate of this patten an orthogonal Fresnel array.
A zone plate created by overlapping closely a vertical and a horizontal one-dimensional zone plates.
An orthogonal linear zone plate (an orthogonal Fresnel array) created by modifying the zone plate of the left figure.
Convergence of lights by an orthogonal linear zone plate: Distribution of lights passing through the zone plate is calculated as described previously for other zone plates. The calculation was carried out for an orthogonal linear zone plate with the focal distance of 100 mm and the zone number of 19. For the sake of comparison the light distribution by a conventional Fresnel zone plate with the same focal length and the same zone number was calculated. Both the calculations were carried out for a parallel beam entering perpendicularly to the zone plates.
The left figure shows the light distribution along the optical axis. As designed the light converges the focus at z=100 mm. The light intensity at the focus (an orthogonal linear zone plate, green solid line) decreases to about a half in comparison with the case of the conventional Fresnel zone plate (red solid line). The sub-focus at z=33 mm can be barely seen but the light distribution near the sub-focus is considerably different. The right figure shows the image of a point source on the focal plane. This figure shows the light distribution along x axis on the focal plane from x=-0.1 mm to x=0.1 mm. As the pattern of the orthogonal linear zone plate is not axi-symmetric unlike the conventional Fresnel zone plate both the light distributions for the horizontal direction (green solid line) and the direction slanted by 45 degree are depicted for sake of comparison. Around the center of the image there is no difference between the two directions but in the outer region the level of light intensity is very low in the slanted direction. However, it can be concluded that the widths of the images (related to the resolution) are almost the same for both the orthogonal linear zone plate and the usual Fresnel zone plate for the same zone number.
The intensity distribution of the light on the plane including the optical axis (x=0). Green solid line denotes the case of the orthogonal linear zone plate and red solid line denotes the case of the Fresnel zone plate.
The intensity distribution of the light on the focal plane (z=100 mm). Green solid line: the orthogonal linear zone plate (horizontal direction), green dotted line: the orthogonal linear zone plate (direction slanted by 45 degree), red solid line: the Fresnel zone plate.
The distribution of lights on the focal plane are non-axi-symmetric in the case of the orthogonal linear zone plate as shown in the upper graph. This is more clearly understandable in the following two-dimensional distribution diagram of the light. The figures below show the regions of 2 mm x 2 mm on the focal planes. Moreover, to make the existence of side-lobs clearly the intensities of the lights are expressed in the logarithmic scale. Hereby the rectangular side-lobs for the orthogonal linear zone plate and the circular side lobs for the Fresnel zone plate are clearly represented. By the way in this figure the shapes of the side-lobes of the Fresnel zone plate are not circular because the precision of the calculation is not sufficiently high.
Distribution of light on the focal plane (orthogonal linear zone plate).
Distribution of light on the focal plane (Fresnel zone plate).
When we take photographs we often find concentric circular patterns and concentric rectangular patterns around a small bright image, in the case of the orthogonal linear zone plate and the Fresnel zone plate, respectively. Examples of these photographs are shown below. When small bright images are not included such patterns are not found on photographs but because of existence of background lights due to weaker light sources grid-like pattern appears in the photograph by the orthogonal linear zone plate (see Gallery).
Tin jug of beer agleam with light (Orthogonal linear zone plate).
Silver angel and silver balls agleam with light (conventional Fresnal zone plate).