Atelier Bonryu(E)
zone plate photography
Laboratory: Zone Plate Photography
Taking Zone Plate Photographs
- Macro-Photography by a Zone Plate (1)-
Macro-Photography: Usually, “macro-photography” means the photography to take a photograph with an image size on a sensor or a film larger than about a half or the same of an object size. For this purpose the lens of a camera should come close to the object and, therefore, the word “macro-photography” is often used synonymously as a word “close-up photography”. But exactly these are different and the latter includes photography with lower magnification factor. In the case of a camera with a lens by making the distance from an object to the lens (a) short the distance from the lens to the image plane (b) should be made increased. Much the same is true on the case of a zone plate (the formula of image formation, Fig.1). To take a photograph by a lens camera a macro lens is usually used for the macro-photography, as a variable range of distance within which one can focus the camera is limited for each interchangeable lens.
Figure 1
The formula of image formation
Magnification: The magnification (lateral magnification) factor of an image is expressed as m=B/A, where A and B are the sizes of the object and the image (Fig. 2). For a single thin lens (or a pinhole or a zone plate) the magnification factor m can be replaced by b/a (Fig.2). By decreasing the distance a from the object to the lens, therefore, the distance b from the lens to the image increases and the magnification factor also increases.
Figure 2
Magnification of the image
Macro-photography by a pinhole camera: When one take a photograph by using a pinhole camera a size of a projected image of a point light source becomes larger than the size of the pinhole. If one brings the camera closer to the object to attain a higher magnification factor the size of the image of the point light source becomes larger accordingly and the resolution becomes deteriorated. It may be, therefore, very difficult even if it is not impossible to take a photograph with high magnification factor by using a pinhole camera.
Figure 3
The light intensity distribution of an image of a point light source on the image sensor. The zone plate is a Gabor type with a focal length f=50 mm, the zone number N=29 for the wavelength of 550 nm. The red, green, blue, and magenta lines denote the cases of magnification factor of m=2, 1.0, 0.5, and 0.11, respectively.
Figure 4
Dependences of resolution on the magnification factor m for a zone plate (red: f=50mm, number of zones=29) and pinholes (blue: the size is same as the center circle of the above zone plate, green: the distance b to the image is kept constant). We define the resolution e as the radius of the image of the point light source.
Macro-photography by a zone plate camera: As a zone plate converges light unlike a pinhole, one can take a photograph by approaching to an object without deteriorating the resolution as long as the formula of image formation is satisfied (Fig.1). Usually a zone plate imaging is considered as a deep focus and the zone plate is used by setting the focus at infinity. But, of course, one cannot bring an object into focus if the object is at an extremely short distance from the zone plate. In such a case, however, if the distance from the zone plate to the image sensor is accurately adjusted by calculating the formula of image formation (Remark *2, Fig.1) for the focal length of it and the distance to the object, macro-photography by using a zone plate is realized. The formula of image formation is written as 
. Therefore, if the relation among a/f, b/f, and m is calculated (Table 1), the values a and b for a given magnification factor m are obtained easily by multiplying the values in Table 1 by the focal length f. Figure 3 shows the light intensity distribution of the image of a point source on the image sensor. It is seen that with increasing the magnification factor m (increasing the distance to the object) the resolution is deteriorated and the peak intensity of the light decreases. The dependences of resolution on the magnification factor are summarized for a pinhole and a zone plate in Fig.4, where the resolution of the pinhole photograph is calculated as the maximum of the geometrical 
and the diffraction-limited 
resolutions. In comparison with a zone plate the resolution of a pinhole is very poor and it is very difficult to use it for the macro-photography.
Table 1
Relations among the magnification factor (m), and the distances from a zone plate to an object (a) and the image sensor (b).
Examples of zone plate macrophotography: Following pictures are macro-photographs of wild flowers including very small ones such as a Persian speedwell (diameter: about 8 mm) and a starwort (diameter: about 5 mm), taken at close range by using a Gabor type zone plate with the focal length of 50 mm and the zone number of 29 designed for the wavelength of 550 nm. As both the distances from the zone plate to objects (a) and the image sensor (b) are 100 mm, the magnification factor is about unity. The used DSLR camera is an Olympus E-300 which is a four-thirds format camera and the sensor size is 17.3 mm x 13 mm. It should be noted that even thin streak patterns on the petals of the Persian speedwell can be seen on the photograph.
