Atelier Bonryu(E)

zone plate photography

 
 

Laboratory: Zone Plate Photography

Taking Zone Plate Photographs

- Sub-Foci -

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Though it is appropriate to compare a photograph taken by using the sub-focus (the focal length of 100 mm) of the zone plate of the focal length of 300 mm with that taken by using the main focus of the focal length of 100 mm, I used the zone plate with the focal length of 90 mm which I had at hand.  Just for reference a photograph taken by using the main focus of the same zone plate with the focal length of 300 mm.  At any hand a clearer and sharper photograph can be taken by using the main focal point.  But it may be said that the cause of the vague photograph can be attributed to the background lights because even in the photograph taken by the sub-focus clear cut outline is reproduced for the brightly shining object.  Though the background lights of these photographs have been reduced by the previously described level adjustment, for the photograph taken by using the sub-focus it is rather difficult to remove the effect of the background light sufficiently as the background light is extremely strong.  However there remains a possibility to reduce the effect of the background light by using a zone plate with longer focal length and larger zone number.

Sub-Foci(*7): One of features of the zone plate which utilizes the diffraction and interference phenomena of a light is that there are a lot of sub-foci unlike a glass lens which utilizes the refraction phenomenon.  A zone plate designed for the wavelength of light λ and the focal length f,  has infinite number of sub-foci of focal lengths(
) in addition to the main focus with the focal length (
),  where +f means a focal point located at the far side of the light source and -f means a focal point located at the near side of the light source, that is, the former corresponds a focal point of a convex lens and the latter corresponds that of a concave lens. The focal length of a sub-focus is the focal length of the main focus divided by an odd number. By the way only a Fresnel type zone plate has the sub-foci but a Gabor type zone plate does not have the sub-foci. The focal point of a parallel light is at infinity and written as the zeroth focus, i.e.,
.


     The lower left figure shows the results of calculation of the distribution of the light intensity on the optical axis when the light beam enters in parallel to the zone plate with 15 zones and the focal length of 100 mm for the light wavelength of 550 nm.  A green line shows the result for the Fresnel zone plate and a red line shows the result for the Gabor zone plate.  In all the cases the light focuses at the designed position of the focal point, i.e., 100 mm from the zone plate, and in the case of the Fresnel zone plate the light focuses at the positions of 33 mm and 20 mm, too.  These points correspond to the sub-foci, the focal lengths of which are 1/3 and 1/5 of the main focal length.  Though there are other sub-foci with the focal length of 1/7, 1/9,... of the main focal length, these points are outside of the frame of this graph and are not shown in this figure.  Naturally in the case of the Gabor zone plate the graph shows there are no sub-foci.

 

The above right figure shows the calculated light distribution on the main focal plane (solid curve) and a sub-focal plane (dashed line) by a Fresnel zone plate with the focal length of 100 mm and the zone number of 15. From this figure it seems that the width of the peak is narrower at the sub-focus than at the main focus and a photograph with higher resolution may be obtained at the sub-focus.  However, in practice, it is rather difficult to take a picture with a sub-focus.  Though it will be explained minutely in *7, briefly speaking the reason of this difficulty is that the quantity of light focused at the sub-focus is decreasing sharply and the ratio of the background light is increasing abruptly with increasing order of the sub-foci.


Photography by using a sub-focus: As describe above taking a photograph by using a sub-focus is rather difficult.  However, as described in *7, there may exists an advantage point.  Thereat, we tried to take a photograph by using a sub-focus of the lowest order, which seems to be the most easy-to-use focus.  The photograph below is a trumpet creeper (campsis grandiflora) taken by zone plates with the focal length of 300 mm, the zone number of 65 and the focal length of 90 mm, the zone number of 19 in order to investigate differences of main and sub- focal points.

Trumpet creeper (campsis grandiflora) taken by using the sub-focus (the focal length of 100 mm) of a zone plate with the main focal length of 300 mm and the zone number of 65.

Trumpet creeper taken by using the main focus of a zone plate with the focal length of 300 mm and the zone number of 65.

Trumpet creeper taken by using the main focus of a zone plate with the focal length of 90 mm and the zone number of 19.

The distribution of the light intensity on the optical axis.  The light with wavelength of 550 nm enters in parallel to the zone plate with 15 zones and the focal length of 100 mm.

The light distribution on the main focal plane (solid curve) and a sub-focal plane (dashed line) by a Fresnel zone plate with the focal length of 100 mm and the zone number of 15.

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