Atelier Bonryu(E)
zone plate photography
Atelier Bonryu(E)
zone plate photography
Laboratory: Zone Plate Photography
Taking Zone Plate Photographs
- Remark -
Remark#6: Chromatic Aberration
Chromatic aberration: Since the diffraction and interference phenomena are utilized for image formation by a zone plate, attainment of focusing directly depends on a wavelength of a light. In other words there is strong chromatic aberration in a zone plate photography. The chromatic aberration of a glass lens is caused by a fact that the refraction factor of glass of the lens depends on a wavelength of a light and, therefore, the focal length of a lens composed of such glass is different for a different wavelength of a light. In the case of a zone plate the cause of the chromatic aberration is not a feature of a medium to a light but a feature of structure of the medium. Though a focal length depends on the wavelength of the light in both the cases, mathematical procedures to evaluate the amount of the chromatic aberrations are different.
A sinusoidal wave and a phase
Numerical simulation of chromatic aberration: By the way it seems that the above limitation is not so stringent, at least, in the practical case and a photograph with a rather natural color tone can be taken. The reason is, as described in the main text on the chromatic aberration, that even when the wavelength range is fur wider than the permissible one, the color of the object is reproduced rather satisfactory if the shape of the image of the object by the design wavelength is clearly projected. The resolving power of the image by the wave other than the wave with the design wavelength must be still bad. Consequentially, we carry out a numerical simulation to know how much the size of the image of the point source with various wavelength at infinity by using zone plates designed for the wavelength of 550 nm, where the focal lengths are 100 mm and 300 mm.
Result of simulation of chromatic aberration(1)
Intensity distribution of an image of a point source at infinity. Wavelengths (lam) of the incident lights are 520, 550, and 580 nm , and a zone plate with the design value of the wavelength of 550 nm, the focal length of 100 mm, and 17 zones is used.
Result of simulation of chromatic aberration(2)
Intensity distribution of an image of a point source at infinity. Wavelengths (lam) of the incident lights are 540, 550, and 560 nm , and a zone plate with the design value of the wavelength of 550 nm, the focal length of 300 mm, and 65 zones is used.
From the result of the simulation shown in the above figure it is concluded that zone plates with 17 zones and 65 zones can focalize a light with the wavelength between 520 and 580 nm and a light with the wavelength between 545 and 555 nm, respectively, but cannot focalize a light with the wavelength outside of these ranges. As for the theoretical estimation a light with the wavelength between 518 to 582 nm and a light with the wavelength between 542 to 558 nm are focalized by zone plates with 17 zones and 65 zones, in the respective order, which is approximately in agreement with the result of the simulation. In an actual situation since a photogenic object emits lights with a wide range of wavelength effects of chromatic aberration are observed in various manner. In our experience, for example, since the zone plate with the design value of wavelength of 550 nm, the focal length of 300 mm, and 65 zones can focalize only a green light with very narrow wavelength range, it is expected that a photograph with unnatural color tone is taken. But in an actual situation a photograph with a rather natural color tone is taken. There are various reasons for this phenomenon, i.e., the color we see is not necessarily expressed by a single wavelength light, the color of an object is decomposed to RGB channels at the sensor of a digital camera and also at the optic nerve, and so on. Anyway, the relation between the number of zones and the color is very interesting problem and we would like to research this problem in more detail.