The Fresnel Lens: A 19th Century Innovation with 21st Century Uses
Bill Schweber | August 09, 2016Lighthouses may seem like quaint artifacts now mostly used as tourist attractions. But as marine-based commerce expanded in the 18th and 19th centuries, they were indispensible for ship navigation and guidance.
As a result, there was a need for ever-more powerful lighthouses that could cast their light beams for tens of miles. That need drove development of increasingly powerful light sources and their "projectors."
In earlier seafaring eras, towers were built at key locations and used coal- and oil-fired lamps for bright and consistent illumination. Improvements added reflectors positioned behind the light and, eventually, a lens in front to direct and focus the beam. A mechanism was added to rotate the reflector and lens at a known rate, giving each lighthouse a "signature" enabling sailors to determine which lighthouse they were seeing.
A team of Sandia National Laboratories and Areva engineers examine the focal point of sunlight. Image source: Sandia National Laboratories/Randy Montoya But at least one problem persisted: the optical efficiency of the standard light and its focusing lens was low, so the resultant brightness and useable range were low. The problem was not a matter of height versus the curvature of the Earth, it was a matter of intensity versus distance. To reach farther, brighter lamps were needed along with larger, more efficient lens assemblies to capture the light and direct it. The largest lenses in were about 2 meters in diameter, about a meter thick at the center, weighed about 1000 kg and were approaching the limits of fabrication technology.
Seeing the Problem
New ideas were needed, and the French government in the early 1800s established a commission to investigate the lighthouse issue. It devised a contest with substantial rewards for tangible improvements.
Augustin-Jean Fresnel (1788-1827) was a French physicist, mathematician and bridge builder. Image source: Britannica Encyclopedia French engineer, physicist, and mathematician Augustin-Jean Fresnel ultimately solved the problem in the 1820s with a compact lens. His lens used a series of concentric sub-lenses with "stepped" radii. His innovation resulted in a lens that was thinner and lighter, but almost as efficient as a standard lens. Within a few years, his design was the standard lens in use.
Despite the demise of lighthouses as critical maritime infrastructure, the Fresnel lens has found other applications. Because they are relatively flat, lightweight and low cost, they are used as concentrators for solar energy impinging on photovoltaic arrays. They can be molded easily and relatively cheaply in plastic, in sizes up to several feet across and a fraction of an inch thick.
For example, in 2014 Sandia National Laboratory and Areva Solar designed the 100-foot-tall A-frame structure and compact linear Fresnel reflectors, which are mirrors arranged in rows at ground level. The goal was to test collecting and storing heat generated by the reflectors in molten salt.
"Flat" molded plastic Fresnel lenses are available for low-range magnifications (2× to 3×) with effective resolution of several hundred lines/inch, which is adequate for some bar-code scanners. And where efficient light collection or distribution is the objective rather than image quality, a Fresnel lens is often a viable option with many advantages.
Bonfires for Navigation
But such applications could not even be imagined in the early days of seafaring navigation where open bonfires were used for navigation markers. Fires were eventually enhanced with simple flat mirrors as reflectors, then spherical bowl mirrors, and finally, parabolic reflectors. Since it was not possible to make large parabolic reflectors, many installations used a stack of smaller ones. Even these enhancements offered minor benefits. After all, it was hard to align the stacked reflectors, and the light source had to be precisely placed at each focal point for it to work well. The reflectivity was moderate as well, with about 50% of the light lost at the mirror.
Fresnel realized that the bulk of a standard lens was unneeded and only the surface profile was critical. Image source: http://hyperphysics.phy-astr.gsu.edu. A lens would be better than a reflector as it loses roughly 5-10% of the light in transmission. But the lens must be close to the source to actually capture the rays, and have a short focal length and large refraction angle to yield a parallel beam. A sharply curved lens could be placed farther away, but would need to be large and thick.
Fresnel realized that he could create a large lens, but without all the bulk, by constructing it as a series of stepped lenses. The plan was to use multiple concentric sections (rings), consisting of carefully shaped prisms. Each ring would bend the light it captured; working together, they would create the large parallel beam. Because the ring idea was not possible in practice, Fresnel decided to use small polygon prisms. The prisms were a plano-convex design, flat on one side, curved on the other.
Production Challenges
First-order lighthouse Fresnel lens is similar to an early, large assembly which Fresnel demonstrated. Image source: Wikipedia Fresnel’s solution met several production challenges, however. Glass-making, casting and polishing in the early 1800s was a relatively crude process, and material purity and consistency posed issues. Flint glass was the first choice due to its high index of refraction and optical clarity. But it was much heavier than other types of glass and was difficult to lift into place in a lighthouse tower. As a result, Fresnel and the factories he worked with used crown glass, which could be molded more easily than flint glass. However, due to its lower refractive index, it had to be thicker to achieve the same effect.
The lens was only part of the solution, since the optics need a near-ideal "point source" for efficiency. Fresnel conducted tests which showed that multiple small lamp wicks produced more light than a single large one for the same amount of fuel. But this multi-wick source proved to be too large to work as a point-like source. He then worked with other engineers to develop an innovative circular multi-wick design. This was smaller yet brighter than a single large wick or a conventional multi-wick assembly.
Fresnel’s first test model consisted of a single square panel 60cm on edge that was made of 97 pieces of glass laced into a bulls-eye configuration. It offered a fairly short focal length of about 70cm (by contrast, a telescope of the period had a focal length of several meters).
In Fresnel's improved design, prisms around the edges of the lens use the principle of full internal reflection. Image source: The Free EncyclopediaHis next step was a lens assembly of multiple panels arranged in circle-like pattern. The first public tests were in February 1821, and his lens was estimated by judges to be 20 times brighter than a mirror-backed unit of the same size.
But there were more design challenges. Because of light escaping through top and bottom of the assembly, a lens only captured about half the source's emissions. Some designs added prisms above and below to capture and re-direct the light, but these could not capture light at more than 45⁰ off axis. Other developers experimented with mirrors to try to capture and direct the light to the main lens, but much of the light was still wasted. Fresnel decided to use another optical technique which he knew from his studies of light: total internal reflection. He sized and arranged prisms oriented for internal reflection around the top and bottom assembly, and was able to capture and redirect light to the lens with almost no loss.
Despite the delays in producing the first lenses, the advantages of Fresnel's approach were so dramatic and obvious that it quickly became the standard. Within a decade of the first demonstration, all new lighthouses in France and much of Europe used his lens, and many existing lighthouses were retrofitted.
There were other outcomes as well. The need for such high volume of his lenses drove advances in glassmaking materials, technology, casting and assembly. It also drove a "standards" program, as Fresnel developed a formal four-grade classification system for lenses and sizes, so each group could use common set of drawings, tooling and techniques.
Fresnel's Legacy
If all Fresnel did was develop a special lens for lighthouses, and enhance glass-making technology, he would be a historical note but perhaps not much else. However, his equations on waves and reflectivity are used in rendering computer-graphics images where there are complex reflective surfaces (water, for example). His diffraction analysis is relevant to our understanding of limits on optical microscopy, IC lithography, and even some RF imaging (radar, MRI).
And although lighthouses have been largely made irrelevant for navigation by modern electronic systems, the Fresnel lens is used as light concentration for solar panels, image magnification in optical systems, and more. Fresnel’s 19th century innovation lives on in multiple 21st century applications.
References:
2. https://insights.globalspec.com/article/156/without-relativity-gps-would-be-lost
3. "A Short Bright Flash: Augustin Fresnel and the Birth of the Modern Lighthouse," Theresa Levitt, W.W. Norton & Co., 2013
4. "Fundamentals of Physics," Halliday and Resnick, John Wiley & Sons, Inc.
