Atelier Bonryu(E)

zone plate photography

 
 

Laboratory: Zone Plate Photography

Theories of Zone Plate Photography

- Diffraction and Interference of Light -

Zone plate simulation: A zone plate is just an optical component which utilizes these phenomena effectually.  Radii of transparent zones are determined so that all light waves diffracted at the transparent zones arrive at a focal point on a sensor (an image screen) synchronously and the brightness is enhanced.  For the sake of explaining the principle of the zone plate we calculated the intensity of light by integrating the wave amplitude over all the transparent zones of the zone plate.  The above right figure shows a result of the calculation, i.e., a behavior of the squared amplitude of the light wave on a median plane (x-z plane) on which the optical axis lies.  In an actual situation the wavelength of a visible light (400 - 700 nm)  is extremely smaller than sizes of macroscopic objects such as the focal length or the radii of zones (the ratio of a focal length to the wavelength of a light wave is more than 100,000) , and it is rather difficult to depict an intelligible figure  explaining the effect of interference and, also, it is considerably time-consuming to simulate the behavior of the light by using these realistic values.  In this calculation, therefore, we employ a very short focal length corresponding to a very small zone plate in comparison with the wavelength, i.e., the focal length f=90.0 and the wavelength
=1.0.  The total number of zones of 5 (the number of the transparent zones is only 3) corresponding to the radius of the outermost zone of 15.8 is employed.  The zone plate is located at the left part of the frame.  Parallel light is incident on the zone plate and it is clearly seen that the light focuses within a circular region with a radius of about 2.0 on a focal plane.  The lower left figure shows the 2 dimensional intensity distribution of the light on the focal plane (at a distance of 90.0 from the zone plate).   The lower right figure shows the light intensity distribution along the x-axis on the same plane.  Though the high intensity region at the center looks rectangular it is caused by a scarcity of  mesh points for calculation and by increasing the number of meshes the shape will become circular.  In the left figure concentric peaks of the light intensity can be seen but in the right figure only the central peak is seen.   This is because that we employ a logarithmic scaling in the left figure.
 

Light waves diffract and interfere: We briefly explain the principle why an image of a photogenic object is formed on an image plane by a zone plate.  As described above the zone plate imaging is not a consequence of refraction or reflection phenomena.  For the zone plate imaging we make use of diffraction and interference phenomena arising due to the fact that a light is a wave.  The lower left animation shows that a water wave which comes from the left downside propagates circularly after passing through a thin slit on a yellow shielding wall.  The phenomenon observed in this animation where a wave propagates even behind a shielding wall is called diffraction.  As a light is also a wave, we can see the similar diffraction phenomenon in the case of a light.  However, there is a condition whether the diffraction phenomenon can be clearly observed or not.  When the wavelength is far smaller than the size of a slit a quantity of the diffracted wave is small, which means that majority of the light propagates in the forward direction.  The lower right animation shows the motion of a water wave where the width of a slit is larger than the wavelength.  In the case of a light wave passing through a pinhole or a zone plate the wavelength is by far smaller and almost all lights go straight in the forward direction and only a small quantity of the light is diffracted.  A zone plate utilizes this small quantity of the diffracted light.

Diffraction of a water wave (a narrow slit case)

   A water wave passing through  a slit small in comparison with the wavelength expands as a circular wave.

Diffraction of a water wave (a wide slit case)

   A water wave passing through a slit large enough in comparison with the wavelength propagates in the forward direction (slit not shown).

Making use of diffraction and interference phenomena: If the diffraction phenomenon is utilized properly the diffracted light wave as well as the rectilinearly propagating light wave form a bright image cooperatively on the image screen and a bright lensless optical system is realized.   However, if one is to use lights diffracted at holes or slits on a light-shielding wall disorderly, an image of the object cannot be formed on the image screen.  It is because the light  observed at a certain point on the image screen consists of various diffracted lights due to different original lights coming from various directions.   Consequently in order to build up an image we should intensify lights at the necessary points and reduce unnecessary ones by making use of the interference phenomenon of light waves.  As a matter of fact, for the explanation of the diffraction phenomenon itself the concept of interference is already included but for simplicity we consider the diffraction and the interference phenomena separately.  Because a light is a wave it takes positive values and negative values with passing time.  When at a certain point one observes lights coming from two directions, i.e., one of which has a positive value and the other has negative value, these light waves compensate each other and the overall wave amplitude becomes small.  If both the waves have positive values or negative values at the same time these waves build up each other and the overall amplitude becomes large.  This phenomenon is the interference of waves.  The upper right animation shows that the water wave running through a single wide slit (not shown) propagates in the forward direction with a small divergence due to the interference phenomenon.  On the other hand in the lower left animation the interference phenomenon is more clearly observed for water waves passing through two slits.

Interference phenomenon of a water wave (two slits)

   Circularly propagating water waves passing through two slits interfere each other.

Focusing of a light wave by a zone plate

   Amplitude of a light wave coming from beneath becomes large near the focal point by a zone plate.

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By the way, how large is the realistic optical system which corresponds to the above calculated system with a wavelength of 1.0, the number of zones of 5 and a focal length of 90.0?  As the realistic zone plate is usually designed for a visible light with a wavelength of 550 nm (=0.00055 mm), the focal length of 50.0 employed for the above calculation corresponds to 50.0 (0.00055/1) mm = 0.0275 mm, and the radius of the zone plate (the outer radius of the outermost transparent zone) is 0.01738 mm, by which a light is focused within a small circular region with a radius of about 0.001 mm.  This system is extremely small but it is considered that if one can construct such a small system one will see similar results as the above calculation.

Two dimensional distribution of light intensity on the focal plane

   The light converges at the focal point and concentric intensity distribution around the focus is seen.

Intensity distribution along x-axis on the focal plane

   This figure shows the one dimensional intensity distribution along the x-axis of the left figure.

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 The following e-books (Amazon Kindle Book) have been published.

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ピンホール写真(Pinhole Photography: Japanese Edition)
ゾーンプレート写真(Zoneplate Photography: Japanese Edition)

Soft Light and Shadow (English Edition)
--Zone Plate Photo Album (1) --http://www.amazon.co.jp/dp/B00IWJIZIUhttp://www.amazon.co.jp/dp/B00M1AWVC2http://www.amazon.co.jp/gp/product/B00WKWZDP8?*Version*=1&*entries*=0http://www.amazon.co.jp/gp/product/B00WKWZDP8?*Version*=1&*entries*=0http://apple.excite.co.jp/shapeimage_4_link_0shapeimage_4_link_1shapeimage_4_link_2shapeimage_4_link_3

(English Edition)

Soft Light and Shadow

<=======(Japanese Edition)=======>

Lensless Photography

by Rings of Light

(Volume of Stones)

Lensless Photography

by Rings of Light

(Volume of Birds)

Lensless Photography

by Rings of Light

(Volume of Flowers)

Complete Guide to

ZonePlate Photography