Binary zone plate: The areas of each ring, both light and dark, are equal.

Sinusoidal zone plate: This type has a single focal point.

A zone plate is a device used to focus light or other things exhibiting wave character.^[1] Unlike lenses or curved mirrors however, zone plates use diffraction instead of refraction or reflection. Based on analysis by Augustin-Jean Fresnel, they are sometimes called Fresnel zone plates in his honor. The zone plate's focusing ability is an extension of the Arago spot phenomenon caused by diffraction from an opaque disc.

A zone plate consists of a set of radially symmetric rings, known as Fresnel zones, which alternate between opaque and transparent. Light hitting the zone plate will diffract around the opaque zones. The zones can be spaced so that the diffracted light constructively interferes at the desired focus, creating an image there.

Design and manufacture[link]

To get constructive interference at the focus, the zones should switch from opaque to transparent at radii where

Failed to parse (Missing texvc executable; please see math/README to configure.): r_n = \sqrt{n \lambda f + \frac{n^2\lambda^2}{4}}

where n is an integer, λ is the wavelength of the light the zone plate is meant to focus and f is the distance from the center of the zone plate to the focus. When the zone plate is small compared to the focal length, this can be approximated as

Failed to parse (Missing texvc executable; please see math/README to configure.): r_{n} \simeq \sqrt{n f \lambda}

.

For plates with many zones, you can calculate the distance to the focus if you only know the radius of the outermost zone, r _N, and its width, Δ r_N:

Failed to parse (Missing texvc executable; please see math/README to configure.): f = \frac{2 r_{N} \Delta r_{N}}{\lambda}

In the long focal length limit, the area of each zone is equal, because the width of the zones must decrease farther from the center. The maximum possible resolution of a zone plate depends on the smallest zone width,

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\Delta l}{\Delta r_{N}} = 1.22

Because of this, the smallest size object you can image, Δl, is limited by how small you can reliably make your zones.

Zone plates are frequently manufactured using lithography. As lithography technology improves and the size of features that can be manufactured decreases, the possible resolution of zone plates manufactured with this technique can improve.

Unlike a standard lens, a binary zone plate produces subsidiary intensity maxima along the axis of the plate at odd fractions (f/3, f/5, f/7, etc.), though these are less intense than the principal focus.

However, if the zone plate is constructed so that the opacity varies in a gradual, sinusoidal manner, the resulting diffraction causes only a single focal point to be formed. This type of zone plate pattern is the equivalent of a transmission hologram of a converging lens.

For a smooth zone plate, the opacity (or transparency) at a point can be given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac {1 \pm \cos(kr^2)}{2}\,

Binary zone plates use almost the same formula, however they depend only on the sign:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1 \pm \sgn(\cos(kr^2))}{2}\,

where r is the distance from the plate center and k determines the plate's scale.^[2]

Free parameter[link]

It does not matter to the constructive interference what the absolute phase is, but only that it is the same from each ring. So an arbitrary length can be added to all the paths

Failed to parse (Missing texvc executable; please see math/README to configure.): r_n = \sqrt{(n+\alpha) \lambda f + \frac{(n+\alpha)^2\lambda^2}{4}}

This reference phase can be chosen to optimize secondary properties such as side lobes. ^[1]

Relation to a Fresnel lens[link]

Wave propagation can be calculated by summing over all possible ray paths. For short wave lengths, it is usually only where many paths sum coherently, meaning that they have close to the same phase (are on the same half of the complex plane), that propagation is significant, because contributions with different phases cancel each other. (For electromagnetic radiation, for example, opposite fields cancel.)

A zone plate works by blocking the paths with contributions of the opposite phase. If a phase shifter such as a refractive material is available, one can increase the collected light (or other wave) by replacing the absorbing rings with half wave length phase delays.^[1] Side lobes can be reduced by sloping these dielectric rings thicker on the inner side than on the outer. With optimal slope of the dielectric or other phase shifter, (in the thin lens approximation) the contributions from all parts of the lens can be the same, making it an ideal lens for one wave length. The jump between zones can be any integer number of wave lengths. If there is a range in wave lengths (the source is not monochromatic), then the zones are not coherent with each other, but still coherent within each zone. The diffraction limit of the resolution is then determined by the width of each zone, and the zones add incoherently (with random phase). This is called a Fresnel lens. If there is only one such zone, it is a conventional lens.

Applications[link]

Physics[link]

There are many wavelengths of light outside of the visible area of the electromagnetic spectrum where traditional lens materials like glass are not transparent, and so lenses are more difficult to manufacture. Likewise, there are many wavelengths for which there are no materials with a refractive index significantly larger than one. X-rays, for example, are only weakly refracted by glass or other materials, and so require a different technique for focusing. Zone plates eliminate the need for finding transparent, refractive, easy-to-manufacture materials for every region of the spectrum. The same zone plate will focus light of many wavelengths to different foci, which means they can also be used to filter out unwanted wavelengths while focusing the light of interest.

Other waves such as sound waves and, due to quantum mechanics, matter waves can be focused in the same way. Wave plates have been used to focus beams of neutrons and helium atoms. ^[1]

Photography[link]

Zone plates are also used in photography in place of a lens or pinhole for a glowing, soft-focus image. One advantage over pinholes (aside from the unique, fuzzy look achieved with zone plates) is that the transparent area is larger than that of a comparable pinhole. The result is that the effective f-number of a zone plate is lower than for the corresponding pinhole and the exposure time can be decreased. Common f-numbers for a pinhole camera range from f/150 to f/200 or higher, whereas zone plates are frequently f/40 and lower. This makes hand held shots feasible at the higher ISO settings available with newer DSLR cameras.

Gunsights[link]

Zone plates have been proposed as a cheap alternative to more expensive optical sights or targeting lasers ^[3].

Lenses[link]

Zone plates may be used as imaging lenses with a single focus as long as the type of grating used is sinusoidal in nature.

See also[link]

• Arago spot
• Fresnel lens
• Fresnel imager
• Diffraction grating
• Photon sieve

References[link]

1. ^ ^{a b c d} G. W. Webb, I. V. Minin and O. V. Minin, “Variable Reference Phase in Diffractive Antennas”, IEEE Antennas and Propagation Magazine, vol. 53, no. 2, April. 2011, pp. 77-94.
2. ^ Joseph W. Goodman (2005). Introduction to Fourier Optics (3rd ed.). pp. 125. ISBN 0-9747077-2-4. 
3. ^ New INL gunsight technology should improve accuracy for target shooters, hunters, soldiers, Mike Wall, Idaho National Laboratory, 5 May 2010.

External links[link]

• Magnetic Soft X-ray microscopy
• Making a photographic zone plate
• Examples of zone plate photographs
• "Telescope could focus light without a mirror or lens". New Scientist. 1 May 2008. http://space.newscientist.com/article/dn13820-telescope-could-focus-light-without-a-mirror-or-lens.html. 

Bill Freeman (born October 21, 1938) is a Canadian author who has written historical fiction for young adults, film scripts, documentaries, theatrical plays, educational videos and non-fiction books. He specializes in writing about Canada and the Canadian experience.^[1]

Biography[link]

After high school Freeman worked in Western Canada for a year and then traveled extensively in Europe. He returned to Canada to attend Acadia University in Nova Scotia. After graduating he worked as a Probation Officer and then did graduate work in sociology at McMaster University in Hamilton, Ontario.

It was while living in Hamilton that Freeman began to write the Bains Series of books for young adults. There are now nine books in the Bains Series. Each focuses on a different industrial setting in Canada in the 1870s. The first book in the series, Shantymen of Cache Lake, received the Canada Council Children’s Literature Prize for 1975 and several of the other books have received awards.

Freeman’s books for adults follow political and social themes. Local 1005 is a political study of a Steelworkers’ local in Hamilton. Their Town, co-authored with Marsha Hewitt, is an analysis of Hamilton city politics and Hamilton: a People’s History, traces the development of the political and social life of the city. Freeman also authored a social and pictorial history of Toronto Island, where he now lives, called A Magical Place and another pictorial history, Casa Loma, Toronto’s Fairy-Tale Castle and its Owner, Sir Henry Pellatt.

While working in the film industry Freeman co-authored Far From Home, Canadians in the First World War, with Richard Nielsen. This book emerged from an extensive three hour documentary film project of the same name, produced by Nielsen. That experience led to other film projects. Freeman was the researcher and writer of an extensive series of science educational videos for the high school market called the Elements of Biology, Physics, Chemistry and Earth Sciences.

Freeman’s partner on these educational videos was the well known Canadian children’s film producer Wendy Loten. The two went on to work together on Loten’s Mighty Machines 2 and 3. These films have been broadcast on TVO and Tree House Television.

Freeman also wrote two plays. Ghosts of the Madawaska is a children’s play commissioned and performed by the Great Canadian Theatre Company in Ottawa, and Glory Days, a play about the 1946 Stelco strike in Hamilton, has been performed by Theatre Aquarius.

Awards and Prizes[link]

A Magical Place: Toronto Island and Its People, Certificate of Commendation, Heritage Toronto, October 2000

Casa Loma: Toronto’s Fairy-tale Castle and its Owner, Sir Henry Pellatt, Award of Merit, Heritage Toronto, October, 1999

Prairie Fire selected for the Canadian Children’s Book Centre “Our Choice” list and nominated for the^[2] for Historical Fiction for Young People, 1998

Several books in the Bains Series were selected for “Our Choice” list.^[3] for Children’s Literature, 1984 (for a body of work, Bains Series)

Canada Council Award for Juvenile Literature, 1976 (This award is now called the Governor General’s award for Juvenile Literature)

Adult Non-fiction[link]

Glory Days, Playwrights Canada Press, 2007^[4]

Hamilton: A People’s History, James Lorimer and Co., Publishers, 2001^[5]

Far From Home: Canadians in the First World War, with Richard Nielsen, McGraw-Hill Ryerson, 1999

A Magical Place: Toronto Island and its People, James Lorimer & Company Ltd., Publishers, 1999

Casa Loma: Toronto’s Fairy-tale Castle and its Owner, Sir Henry Pellatt, James Lorimer & Company Ltd., Publishers, 1998^[6]

1005 Political Life of a Union Local, James Lorimer & Company Ltd. Publishers, 1982

Their Town: The Mafia, The Media and the Party Machine, (with Marsha Hewitt); James Lorimer & Company Ltd. Publishers, 1979

The Bains Series of Young Adult Fiction[link]

Ambush in the Foothills, James Lorimer & Company Ltd. Publishers, 2000

Sioux Winter, James Lorimer & Company Ltd. Publishers, 1999

Prairie Fire! James Lorimer & Company Ltd. Publishers, 1998

Danger on the Tracks, James Lorimer & Company Ltd. Publishers, 1987

Harbour Thieves, James Lorimer & Company Ltd. Publishers, 1984

Trouble at Lachine Mill, James Lorimer & Company Ltd. Publishers, 1983^[7]

The Last Voyage of the Scotian, James Lorimer & Company Ltd. Publishers, 1976

First Spring on the Grand Banks, James Lorimer & Company Ltd. Publishers, 1978

Shantymen of Cache Lake, James Lorimer & Company Ltd. Publishers, 1975

Young Adult Books[link]

Cedric and the North End Kids, James Lorimer & Company Ltd. Publishers, 1978

Theatrical Play produced by Theatre Aquarius:

“Glory Days,” a play with music, produced by Theatre Aquarius, Hamilton 1989

“Glory Days,” re-mounted by Theatre Aquarius in September/October Hamilton 2006

Play for Young Adults:

“Ghosts of the Madawaska,” Great Canadian Theatre Company, Ottawa, 1985

Children’s Television Series:

Script Writer, “Mighty Machines 2,” a fourteen part half hour programs for pre school children produced for TVO, TFO and Treehouse by Loten Media.

Script Writer, “Mighty Machines 3,” a fourteen part half hour programs for pre school children produced for TVO, TFO and Treehouse by Loten Media.

Educational and Documentary Videos:

Script Writer, “Canada for Children,” A three part series of videos for elementary school children. Producer: Redcanoe Productions.

Script Writer/Educational Consultant: “Elements of Earth Sciences,” six educational videos for high school students. Producer: Algonquin Educational Productions.

Script Writer/Educational Consultant: “Elements of Chemistry,” six educational videos for high school students. Producer: Algonquin Educational Productions.

Script Writer/Educational Consultant: “Elements of Physics,” six educational videos for high school students. Producer: Algonquin Educational Productions.

Script Writer/Educational Consultant and Narrator: “Elements of Biology” A series of six educational films for the high school students. Producer: Loten Media.

Historical consultant/Scriptwriter “Hamilton: Where the Rubber Meets the Road,” Producer: Red Canoe Productions

Script Writer/Narrator, “Kiev Pecherska Lavra,” Producer, 3rd Street Videos, 1995

Narrator/Researcher “Remembering Toronto,” Producer: PBS Buffalo

Works in Progress[link]

“The End of War?” a four part documentary film series and 22 part educational series on war produced by Norflicks Production for Vision TV. Bill Freeman will be the script writer and on air host.

The End of War, a book project under development

Foreplay, a theatrical play about relationships

Winner of the Governor General's Award for Juvenile Fiction[link]

In 1975 Freeman won the Governor General's Award^[8] for his book Shantymen of Cache Lake.

References[link]

External links[link]

Website[link]

• www.billfreeman.ca

Ioánnis Fokás (Greek: Ιωάννης Φωκάς), better known by the Spanish transcription of his name, Juan de Fuca (born 1536 on the Ionian island of Cefalonia; died there 1602^[1][2]), was a Greek-born maritime pilot in the service of the king of Spain, Philip II. He is best known for his claim to have explored the Strait of Anián, now known as the Strait of Juan de Fuca, between Vancouver Island, now part of British Columbia, Canada, and northwestern Washington State, United States.

Family and early life[link]

Fokás's grandfather, Emmanouíl Fokás (Gk: Εμμανουήλ Φωκάς), fled Constantinople at its fall in 1453, accompanied by his brother Andrónikos (Gk: Ανδρόνικος). The two settled first in the Peloponnese, where Andrónikos remained, but in 1470 Emmanouíl moved to the island of Cefalonia. Iákovos (Gk: Ιάκωβος), Ioánnis's father established himself in the village of Valerianos (Gk: Βαλεριάνος) on the island and came to be known as "the Valeriáno Fokás" (Gk: ο Φωκάς ο Βαλεριάνος) to distinguish him from his brothers.^[2]

It was in this village of Valeriáno that Fokás was born in 1536. Little to nothing is known about his life before he entered the service of Spain, some time around 1555.^[3]

Name[link]

The name of the man known to history as Juan de Fuca is the source of some confusion. While Juan de Fuca is clearly a Spanish rendering of Ioánnis Fokás (Gk: Ιωάννης Φωκάς), some sources cite Apóstolos Valeriános (Gk: Απόστολος Βαλεριάνος) as his "real" name. It is possible that Fokás was baptized Apóstolos and later adopted the name Ioánnis/Juan (i.e., John) because Apóstol is not much used as a name in Spanish. Given that Fokás/Fuca was the family name borne by the seafarer's father and grandfather, Valeriános is likely to be a nickname used on the island which would have been quite meaningless in the Spanish Empire.

Early career[link]

Fuca's early voyages were to the Far East, and he claimed to have arrived in New Spain in 1587 when, off Cabo San Lucas in Baja California, the English privateer Thomas Cavendish seized his galleon Santa Ana and deposited him ashore. He was a well-traveled seaman, perfecting his skill as a pilot in the Spanish fleet. The king of Spain, he also claimed, recognized him for his excellence and made him pilot of the Spanish navy in the West Indies (a title he held for forty years), but there is no record in Spanish Archives of his name or position or of his visit to the royal court.^[4] Before he made his famous trip up the northwest coast of the North American continent, he sailed to China, the Philippines and Mexico. The Strait of Juan de Fuca between the United States of America and Canada was named for him by British Captain Charles Barkley because it was at the same latitude that Juan de Fuca described as the location of the Strait of Anian.^[5]

Voyages to the north[link]

Fuca Pillar at Cape Flattery, Washington beside the Strait of Juan de Fuca.

According to Fuca's account, he undertook two voyages of exploration on the orders of the Viceroy of New Spain, Luis de Velasco, marqués de Salinas, both intended to find the fabled Strait of Anián, believed to be a Northwest Passage, a sea route linking the Atlantic and Pacific Oceans. The first voyage saw 200 soldiers and three small ships under the overall command of a Spanish captain (with Fuca as pilot and master) assigned the task of finding the Strait of Anián and fortifying it against the English. This expedition failed when, allegedly due to the captain's malfeasance, the soldiers mutinied and returned home to California.^[2] (Note that in this period, Spanish doctrine divided control of ships and fleets between the military commander, who was an army officer, and the sailing and navigation commander, who was a mariner.)

In 1592, on his second voyage, Fuca enjoyed success. Having sailed north with a caravel and a pinnace and a few armed marines, he returned to Acapulco and claimed to have found the strait, with a large island at its mouth, at around 47° north latitude. The Strait of Juan de Fuca is in fact at around 48° N, although Fuca's account of sailing into it departs from reality, describing a region far different from what actually existed there.^[6] The Strait follows directly into Puget Sound, Washington, beginning at around 47° 59' N and continuing as far south as 47° 01' N at Tumwater, Washington. During the voyage, Fuca also noted a "high pinnacle or spired rock", which may have been Fuca Pillar, a tall, almost rectangular, rock on the western shore of Cape Flattery on the northwestern tip of Washington beside the Strait of Juan de Fuca - although Fuca noted it being on the other side of the strait.^[6]

Despite Velasco's repeated promises, however, Fuca never received the great rewards he claimed as his due. After two years, and on the viceroy's urging, Fuca travelled to Spain to make his case to the court in person. Disappointed again and disgusted with the Spanish, the aging Greek determined to retire to his home in Kefallonia but was in 1596 convinced by an Englishman, Michael Lok (also spelled as Locke in English and French documents from the period), to offer his services to Spain's archenemy, Queen Elizabeth. Nothing came of Lok and Fokás' proposals, but it is through Lok's account that the story of Juan de Fuca entered English letters.^[2]

Controversy[link]

Because the only written evidence for Fokás's voyages lay in Lok's account — researchers being unable to find records of the expedition in Spanish colonial archives — there was long much controversy over his discovery and, indeed, whether he had ever even existed as a real person; several scholars have dismissed Juan de Fuca as entirely fictitious, and the 18th-century British explorer Captain Cook strongly doubted that the strait Fokás claimed to have discovered even existed^[7] (although Cook actually sailed past the Strait of Juan de Fuca without entering it and did stop at Nootka Sound on the west coast of Vancouver Island). With later English exploration and settlement of the area, however, Fokás's claims seemed much more credible.

Finally, in 1859, an American researcher, with the help of the U.S. Consul in the Ionian Islands, was able to demonstrate not only that Fokás had lived but also that his family and history were well known on the islands.^[2] While we may never know the exact truths that lay behind the account published by Lok, it must be considered unlikely that the man himself was a fiction.

Legacy[link]

When the English captain Charles William Barkley, sailing the Imperial Eagle in 1787, (re)discovered the strait Fokás had described, he renamed it the Strait of Juan de Fuca.

The Juan de Fuca Plate, a tectonic plate underlying much of the coastline he explored, is also named for Fokás.

Notes[link]

Further reading[link]

• British Columbia: From the Earliest Times to the Present, Chapter II, The Apocryphal Voyages, pp. 19-31, Ethelbert Olaf Stuart Scholefield, publ. S.J. Clarke, Vancouver, 1914

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