An extension to pinhole photography, a zone plate—or a Fresnel zone plate—is used to take pictures with a camera without the use of a lens. It looks like the above picture. Think of a Fresnel zone plate as a pinhole surrounded by another pinhole which, too, is surrounded by yet another pinhole, and so on.
While it may not be obvious from the picture, each of the white rings in a zone plate covers an area of the exact same size as the pinhole in the middle of the zone plate. Thus, if there are four such zones (one pinhole and three rings) on a zone plate, it lets through four times as much light as the pinhole alone, allowing you to take a picture twice as fast. Twice, not four times, because the photograph is two-dimensional, so we divide the time by the square root of four, which is two. If we used sixteen such zones, we could take the picture four times faster, and so on.
This extra light does come at a price. The more zones you use, the smaller your f-stop is. The smaller the f-stop, the less depth of focus. Thus, when designing a zone plate, you need to consider the tradeoff of speed vs. sharpness and decide how many clear zones to choose.
The second consideration is the size of the pinhole. Since the pinhole is in the shape of a circle, its size depends on its diameter. Once we have determined the diameter of the pinhole, we can calculate the diameters of all the rings (both clear and dark) mathematically from the diameter of the pinhole.
You need to consider two factors when deciding the diameter of the pinhole: focal length and wavelength.
The focal length (or focal distance) is essentially the distance of the pinhole from the plane of the film. If you are designing a zone plate for an existing camera, just measure the distance of the film plane from the plane where you will mount your zone plate. Do your measurements in millimeters. If you think in inches, just multiply the length in inches by 25.4 to convert it to millimeters.
If you are building your own camera, or are using a view camera, you can decide what focal length to use based on the size of the film. For each film format there is a “normal” focal length, though not everyone necessarily agrees what it is. Generally, people will say that the normal focal length to use with 35 mm film is about 50mm, while with a 4x5 inch film 150-180mm.I used the word essentially in my first definition of the focal length. In true pinhole photography, we could skip that word entirely. In true pinhole photography the entire image is equally sharp—or blurred—reducing the distance of the film plane from the pinhole to the only factor. The Fresnel zone plate, however, functions as a lens. We need to consider both the distance of the film plane from the pinhole (or, actually, from the zone plate) and the distance of the object we are photographing from the pinhole (the zone plate). The farther away the object is, the less it affects the focal length. And if it is infinitely far, it has no influence on the focal length. Now, in photography infinity is often not too far. Surely, if you are taking a picture of a mountain from a fairly nice distance, you can treat it as if it were in infinity. But if you are taking a portrait, you cannot treat your subject as being at infinity.
The actual focal length can be calculated by multiplying the distance of the object from the zone plate by the distance of the film plane from the zone plate and then dividing the result by the sum of the two distances. So, if you are taking a portrait of a person standing 2 meters in front of your zone plate, and your film is 150 mm away from the zone plate, assuming you are using a 4x5 view camera, the most likely candidate for experimenting with zone plates, first you need to convert the distance from meters to millimeters. Two meters is 2000 mm. Now, the correct focal length is 2000 * 150 / (2000 + 150) = 140 mm. That is quite a difference from the 150 mm which you would get if you only considered the distance of the film plane from the zone plate.
By the way, this works in the opposite direction as well. If you have a zone plate with a 150 mm focus length and your subject is two meters in front of your zone plate, just change the plus sign in the above calculation to a minus sign to determine how far the film plane should be from your zone plate. That is, to focus at the object, you would adjust the film to zone plate distance to 2000 * 150 / (2000 - 150) = 162 mm.
The wavelength is the length of the light wave. It varies across the visible light spectrum, ranging from 400 nm at the violet end to 700 nm at the red end. Those wavelengths are very short: one nanometer is one millionth of a millimeter.
Because the wavelengths vary across the spectrum, you need to design a different zone plate for different colors. An ocean scene or a snow scene will probably be mostly blue or even violet (since there may be much ultraviolet light in the scene), so you might use a zone plate designed for 400-450nm. A sunrise or a sunset scene may be filled with red or orange light rays, so you would go for the high end, perhaps 650 nm. For a “general” photography situation you may go for the middle of the range, which is 560 nm. This is not because that is the right wavelength for most colors, but because it will be equally wrong throughout the picture. Your best zone plate pictures will acount for this chromatic dependence of the Fresnel zone plate: they will have one dominant color and the zone plate will be optimized for that color.Once you have decided on the focal length and the wavelength, determining the diameter of the pinhole is easy. Multiply the focal length (in millimeters) by the wavelength (in nanometers). The square root of the result is the radius of the pinhole in micrometers. Just double it, and you have the diameter. So, for example, if you want to shoot sunrise at 35 mm film using a “normal” focal length, you will multiply 50 (the focal length) by 650 (the wavelength) and get 32500. Its square root is 180.28 which gives the radius of 180 micrometers (0.18 mm), or a diameter of 360 micrometers (0.36 mm).
From the diameter of the pinhole you can determine the diameters of all the rings (both black and clear). The outside diameter of the first ring (black) is the diameter of the pinhole multiplied by the square root of 2. The outside diameter of the second ring (clear) is the diameter of the pinhole multiplied by the square root of 3. The next one, pinhole diameter times square root of 4. Then square root of 5. And so on, and so on.
We live in the computer age, so these calculations are very simple. But the task of creating a zone plate dealing with micrometers seems overwhelming at first. That is why many people just cough up the cash and willingly pay $20-$30 per zone plate from an “official” zone plate source.
There are some compelling reasons to make your own zone plates, however. For one, you can do it for a lot less money. Even if money is no objection, you need to fine tune your zone plate to whatever photographic situation you want to use it for. While the “official” zone plate suppliers may offer a zone plate for specific focal lengths, you may want to use a focal length that is not exactly what they are offering. And, of course, you may want zone plates with a different number of zones (rings) depending on the intensity of available light and sharpness/softness considerations which differ from picture to picture. Last but not least, you need to consider the wavelength. Chances are your “official” zone plate uses the wavelength of 550 or 560 nm which is right in the middle but is hardly suitable for all situations. Actually, it is only suitable for photographing green objects.
That means that if you are serious about zone plate photography, you need a whole slew of different zone plates (and if you are not serious, why not just use a standard camera with a lens). Outsourcing them all might end up costing you more than a set of high quality lenses!
Last but not least, most people who like to use zone plates also like to tinker with their equipment, building it all from scratch. Zone plate photography is an extension of pinhole photography, so you can use a metal can or an empty cereal box as your camera. If you build everything else, you certainly can build your own zone plates! It is much easier than at first it may seem.
The traditional way of making a zone plate is to create a large drawing of the exact image of the zone plate, then photographing it on a high contrast black and white film, thus reducing the image to the correct size. If the film used is a standard negative film, the original drawing must be color reversed. That is, the pinhole must be drawn in black, the black rings in white (or just not drawn since you would use white paper) and the clear rings in black. If, on the other hand, you use a black and white slide film, the original must simply be an enlarged drawing of the zone plate.
People have been using this method since long before the computer age. But modern computers make the creation of a zone plate this way a snap. Not only can computers calculate the diameter of the pinhole and the rings, they can produce the exact drawing of the zone plate. All you need is a high resolution bitmap of the correct zone plate, print it out on a white sheet of paper, and take the picture on high contrast black and white film. If you shoot on 35 mm film, you can produce some 36 zone plates with one roll of film for the fraction of the cost of even one “official” zone plate.
It is a matter of simple geometry to convert the large drawing into a small photoimage of the correct size. With a handheld calculator, simply divide any dimension of the drawing by the corresponding dimension on the film image. Multiply the distance of the film plane in your camera by the result of that calculation to figure out how far in front of your camera you need to place the drawing. Position your drawing (attach to a wall, perhaps), place your camera the calculated distance in front of the drawing (a tripod is a good idea here, or a copystand, if you have one), centering the bull’s eye in your viewfinder or focusing screen, and take the picture.
Play with it! Photography is an art form. Make slight variations in the size of the pinhole, automatically scaling all rings, by moving the camera closer to or farther from the drawing. Take test pictures using the different zone plates. Decide visually which one works best for whatever photographic message you want to send instead of just relying on some theory.
As an example of the calculation, suppose you have a drawing on which the rings are surrounded with a 5 inch frame. You know that reducing the frame to 1/4 inch will reduce the pinhole and the rings to the correct size. Dividing 5 by 1/4 yields 20. Now you know you need to reduce all dimensions 20 times. If you are using a 35 mm camera with a standard 50 mm lens, the lens is 50 mm in front of the film plane. Multiply 50 by 20 and you get 1000. Place the drawing 1000 mm (one meter) in front of the camera. We used inches in one calculation, millimeters in the other. As long as we have divided inches by inches and multiplied millimeters to get millimeters, we did not mix our metaphors.
What if your drawing does not have a frame that can be conveniently reduced to 1/4 inch? Then measure the diameter of the largest ring on the drawing and divide it by the diameter it needs to have in the final zone plate. You will probably know the final diameter in millimeters, so measure the drawing in millimeters as well. Suppose you have a large poster (like this one). You measure its outer diameter at 22 inches, while you have calculated (using the form below) that for your target focal length and wavelength you need to reduce it to 2.1 mm (yes, zone plates are very small). First convert the 22 inches into millimeters multiplying by 25.4, which will give you 558.8—the diameter in mm. Divide that by the desired diameter of 2.1 mm. That gives you 266.1. So to reduce all dimensions of the poster 266.1 times, place it 266.1 mm * 50 = 13,305 mm in front of your 35 mm camera. Of course, you can convert the 13,305 mm into more convenient units—13.3 meters or 43.6 feet.
Naturally, once you have a computer bitmap, you may use a more high tech way of creating the zone plate, though this would require you to have access to the proper equipment. For one, if you have a high resolution laser printer, just create the bitmap at the same resolution, then print it on a transparency sheet (of course, you can print a whole number of different—or identical—bitmaps on the same sheet, producing several zone plates on just one sheet). And if you happen to have access to a digital film recorder (they are getting much more common than they used to be, so even if you do not have one, you may know someone who does, just ask around), you could output the bitmap directly on a high resolution black and white film at exactly the same resolution as the bitmap, thus creating a perfect zone plate.
If you like to experiment and find new ways of working with photography, you may want to try things other than a standard zone plate. Some of the best pictures were taken with a multipinhole camera, that is, with a camera that has more than one pinhole. But you can even go beyond that: How about playing with a large number of pinholes spread out along the Fresnel zones? Because the zones get thinner and thinner as they are rippling away from the center pinhole, these holes have to get smaller and smaller. There also has to be a large number of them. For the lack of a better name, I have called it a megapinhole (though I was tempted to call it either a “starfish zone plate” or a “UFO zone plate”). It would be very hard to drill or pierce the holes of a megapinhole, but we can use the same technique as with the zone plate: Create a drawing and photograph it.
I have played around with a system of designing megapinholes mathematically. Just as with zone plates, I create them based on their focal length, wavelength, and the number of zones. But I added a new factor: density. This decides how densely packed each zone is with holes. Reasonable density values are between 5 and 41. The above picture has a density of 11.
When creating your own zone plate or megapinhole by photographing a drawing, make sure the drawing has at least one of the three dimensions you can see in this picture. As long as you can measure (or figure out) one of them and either know or can calculate what its corresponding dimension should be on the final zone plate or megapinhole, you can easily calculate how far your camera needs to be from the drawing to produce the correct zone plate megapinhole (as explained in the Reducing the Zone Plate section).
The three easily measurable dimensions are:
The frame. If you can produce an image with a discernable frame and know what its reduced size should be, use it. That is the easiest approach because all you need to measure is a side of a box. In the above image, it is the border of the black square.
The pinhole. If you do not have a frame, measure the diameter of the pinhole. You can calculate what its size should be in the actual zone plate or megapixel by the method explained in the section titled Diameter. Because in our image, it equals to the size of any of the sides of the yellow square, I will refer to it throughout these pages as “the yellow dimension”.
The outside ring. Finally, if you have no frame and are designing a Slovak style zone plate or megapixel (described at the bottom of this page) which does not have a center pinhole, measure the diameter of the outside ring. You can calculate its destination diameter by counting up which zone it is. You need to count both the white and the black zones (including the inner zone, the one where the center pinhole would be if you used it). The first one (the center) is zone 1, the next one zone 2, etc. Multiply the calculated diameter of the center zone by the square root of the zone number, and you know the correct diameter of the outside zone. In our image, it is zone 7—the spaces between the “bubbles” are thin but they are actual Fresnel zones.
This is quite easy with standard zone plates but is a bit trickier with the megapinholes. Although the megapinhole contains a number of pinholes that are spread over the outer zone, their edge is not necessarily at the theoretical edge you would get with the above calculation (see the green box in the image). So, unless you know the exact diameter of the outside ring, you are better off using either of the other two dimensions listed. But if you do not have those dimensions available (no frame, no center pinhole) and do not know the correct diameter of the outside zone, use the calculation for a standard zone plate, then take several photographs: One from the calculated diameter, one (or more) a bit closer, one (or more) a bit further. Then take pictures using the plates you have made, and decide visually which one works best for you. Again, photography is an art. Science is here to help us, not to limit us.
On the rest of these pages I will refer to this value as “the green dimension.”
All that remains is getting the bitmap. Nothing could be simpler! Just fill out the form below. This was a very simple form originally, but I kept adding more options. If this is your first time here, all you really need to specify is your focal length and click “Design the plate.” The rest is up to you. And don’t forget to let your friends know how much you enjoy zone plates. The easiest way of doing that is by wearing a zone plate T-shirt.