Atelier Bonryu(E)
zone plate photography
Laboratory: Zone Plate Photography
Taking Zone Plate Photographs
- Chromatic Aberration -
Chromatic aberration (*6): In order to design a zone plate pattern, the radius of the n-th zone 
is calculated by substituting values of a focal length 
and a wavelength of the light into the equation (*1). Contrarily, for a given pattern of a zone plate (given 
) and a given focal length 
the wavelength 
of a light which can be focused at the given focal point is strictly determined. Then, is it a case that we cannot take a photograph by a light with a wavelength different from the designed value? Though we cannot take a photograph by a light with a wavelength far different from the above value 
, there is a finite range for a permissible wavelength. The phenomenon that a focal length changes with changing the wavelength is called the chromatic aberration. Speaking as a photographer the chromatic aberration should be as small as possible and in the case of a usual camera with a glass lens a taking lens is fabricated to be achromatic by using an appropriate combination of various glasses with different refraction coefficients.
In the case of a zone plate, the half width of the permissible wavelength range around the design value 
is given as 
and, therefore, the permissible wavelength range is from 
to 
. By substituting concrete values to the variables 
and 
, it is found that this condition is considerably strict. However, even when this condition is not satisfied a diffracted light from the m-th zone (
, where 
, 
; 
are integer numbers) can satisfy the synchronization condition of the phase at the focal point and one can take a photograph. This means that the light waves diffracted from inner zones are still in phase even when light waves diffracted from outer zones become out of phase. Therefore, the focusing degrades gradually with increasing difference of the wavelength from its designed value.
Sharpness of images in different color channels: An appearance of a photograph taken out of the permissible wavelength range depends strongly on a kind of a photogenic object and the various conditions to take the photograph. Sometimes we can hardly perceive the existence of the chromatic aberration in a photograph. Even in such a situation, if we decompose the photograph into channels of the RGB color space, it is easily found that only the image of the G (green) channel gives a sharp impression. Here we are talking about a photograph taken by a zone plate designed for the wavelength of 550 nm (green). As a permissible wavelength range of a zone plate does not cover the whole range of the visible lights, images of the R (red) and the B (blue) channels become blurred. However, if the shape of the image in the G channel is clearly expressed, the color of the image expressed by mixing three channels looks rather natural even when the images in the R and the B channels are blurred. Therefore, a zone plate photograph unavoidably becomes unclear when the intensity of light in the G channel is relatively weak in comparison with the other channels. Anyway a looking of a zone plate photograph depends strongly on the spectrum distribution of the light from a photogenic object.
Examples of sharpness in different color channels: Three photographs of different objects at different distances taken by zone plates with different focal lengths and their RGB decomposed images are shown in the following. (a), (b), (c) are the original zone plate photographs taken by zone plates with focal lengths of 55, 90, and 180 mm, respectively. The distances a of the photogenic objects and the setting distances a’ of the zone plates of the photographs (a), (b), and (c) are, in respective order, a=1000 mm and a’=infinity, a=3000 mm and a’=infinity, and a=1500 mm and a’=1500 mm. (a-R, b-R, c-R), (a-G, b-G, c-G), (a-B, b-B, c-B) are the RGB-decomposed images of these photographs. The G channel images of three photographs are considerably in good focus but the images of the other channels are not in focus. (a) and (b) are the photographs of objects at distances of 1 m and 3 m taken by setting distances of infinity and, therefore, both are in focus within the depth of field. However, (c) was taken by a zone plate with a longer focal length and chromatic aberration became noticeable, which makes the image of the R channel blur considerably.
(Slide show)
