The field of view of a telescope or a photo camera, for example, is usually understood as the range of angular directions in which objects can be observed for a fixed orientation of the instrument. (One may of course observe a wider range by combining images from different instrument orientations.) It can be quantified in different ways:

The German government etched symbols onto the prisms of their Fresnel Lenses. This is the story of those symbols. The German government marked most of their lenses with a government certification symbol. Before 1933 and the Nazi Reich, the symbols used were the German Imperial Eagle and a symbol that looked like a castle, which represented the German Seamarks Service. These marks were etched onto the lens glass to certify that the lens met the requirements for government usage.

Some years ago Chad Kaiser of the US Lighthouse Society ran across a photograph of what was supposed to be the most powerful lighthouse in the world at 1 billion candlepower.  Yes, that is billion not million.  I became intrigued and started researching this light and its history.  This story will describe this very unusual lighthouse in France and how it came to be.  It is actually not a true lighthouse at all.  Instead it is an example of one of the earliest and most powerful Airway Beacons ever built.  But, first we need to understand a little more about air

For small angles, the full-angle field of view in radians is approximately the sensor diameter divided by the focal length; for obtaining a value in degrees, one has to multiply that with <$180\textdegree / \pi$>. For wide angle cameras, one has to use a more accurate formula:

The field of view gets particularly small when using a tele-objective, while wide field objectives are by definition made for a large field of view. Extreme versions are called fish-eye objectives; they produce substantial image distortions, which are hardly avoidable in that regime.

Field of viewhuman eye

Telescopes provide some magnification for viewing distant objects. The higher the magnification, the smaller is typically the field of view. However, there are optical designs which provide a larger field of view for given magnification. For example, a simple Keplerian telescope has a small field of view, which can be expanded by inserting an additional field lens.

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As mentioned above, the field of view of an instrument is often intentionally limited. This is often not motivated by its application, but rather because the image quality would be too much degraded by optical aberrations when permitting a larger field of view. Advanced optical designs, e.g. based on aspheric lenses or more refined combinations of lenses, can offer a wider field of view with good image quality. However, they are not always employed, e.g. for reasons of higher cost, size or weight of the instruments.

The field of view of the eye may be restricted by various kinds of devices, for example by correction glasses of small size or by magnifying glasses. In some cases, the peripheral view is completely blocked, e.g. with some laser safety glasses; that can introduce additional hazards, e.g. of bumping into items which could not be seen.

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Standard photographic objectives are made such that their field of view is similar to that of the human eye – with a full horizontal angle around 50°, when considering the range with reasonable sharp imaging.

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Most lighthouse enthusiasts think that the Fresnel lens was the first lens used in lighthouses.  However, that assumption is incorrect in that a number of lenses were proposed and put into use in the years before Augustin Fresnel designed his famous lens.  This story will give you information about these early attempts to use lenses to augment the power of lighthouse optics.

The English and Scottish lighthouse authorities wanted to produce all Fresnel lenses and other lighthouse equipment in their own country and persuaded the Cookson Glass Company to begin production of Fresnel lenses in 1834. Cookson brought in Leonor Fresnel, Augustin’s brother, as a consultant and produced Fresnel lenses from individual pieces and prisms as done by the French lens companies.  The first of these better designed Fresnel lenses, built by the Cookson Co., was installed in Scotland in 1835, in the Inchkeith lighthouse.

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Fresnel lenses represent a unique aspect of U.S. Coast Guard history.  These artifacts are highly sought by a wide variety of museums and associations.  Due to their historic significance, fragility, high value and the U.S. Coast Guard’s policy to protect and preserve these artifacts, an additional set of conditions is placed upon prospective borrowing organizations.  Requirements for the care, security and display of Fresnel lenses are as follows:

Field of view

The field of view of an optical imaging instrument is often limited by an intentionally created field stop. This is an optical aperture, e.g. in the form of a diaphragm, which is placed in an image plane or close to such a plane, such that the edges of the field of view are sharply defined. However, in some cases one obtains vignetting effects, i.e., a gradual decrease of image brightness towards the edges of the field of view. This happens when the field of view is limited by an aperture which is not in an image plane. An example for that situation can be found in the article on field lenses, where we vignetting in an optical telescope is explained. In cases with vignetting, one may define different values for the field of view – for example, the field without any vignetting, the field up to the point of half-vignetting or (is the very maximum) up to the point where the intensity vanishes.

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Many companies were involved in the development and refinement of the Fresnel lens.  Some supplied only the glass for the lenses, either in rough form, or both cast and polished.  Other companies assembled the glass elements and performed finish work on the lens elements.  Still other companies produced both the glass and the finished lenses.  This story will be divided into several parts, each discussing one or more of these companies and their contribution to the development of the Fresnel lens.

Below is a listing of the major changes in the Fresnel lens through time and in most cases who the creator of each change was.

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The French Commission for Lighthouses was established on April 29, 1811.  In 1819, Arago who had become a member of the French Commission for Lighthouses in 1813, offered to make a systematic review of possible improvements in lighthouse illumination.  He requested that Claude Mathieu and Augustin Fresnel be assigned as his coworkers on the project.  His request was granted on June 21, 1819, and Augustin agreed to serve on the committee.

The first National Lighthouse Lens Survey was released in 2001 at the Sixth Maritime Heritage Conference in Wilmington, N.C. It listed more than 400 classical Fresnel lighthouse lenses in the United States, and two pre-Fresnel, Winslow Lewis lenses. The inventory was a compilation of databases researched by Mike Vogel of the Buffalo Lighthouse Association and the American Lighthouse Coordinating Committee, and by Al and Helen Gademsky of Ohio.

In some cases, the term angle of acceptance is used instead of field of view – particularly for non-imaging optical instruments.

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A large field of view is particularly relevant, for example, for astronomical telescopes which are used in stellar surveys.

The field of view of the human eye is also not precisely defined. Maximum image resolution is only achieved in the central area, and the peripheral regions exhibit a substantially lower image quality. This is largely compensated by rapid eye movements for covering a wider angular range and accurately viewing objects of particular interest.

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The term field of view is not only used for that field itself, but also for its magnitude. In some cases, for example for telecentric lenses, it is used for the viewed area on the object plane.

The field of view of a photo camera depends on both the used photographic objective and the size of the photographic film or the image sensor. This is explained in Figure 1, which shows the optical configuration is a greatly simplified way: the objective is represented by a single lens, although it is usually a system containing multiple lenses. One can simply consider rays coming from object points and going through the center of the lens, where no ray deflection occurs.

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