[Physics] a 3rd-order Fresnel lens

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The NPR News article and podcast Job Opening: Seeking Historian With Tolerance For Harsh Weather, The Occasional Bear talks about the Split Rock Lighthouse. That Wikipedia article links to the image title 3rd-order_Fresnel lens at Split Rock which in turn cites the Flickr image Split Rock Lighthouse; 3rd-order, Fresnel lens at Split Rock Lighthouse.

As I understand them the prism surfaces of Fresnel lenses have either flat-cut faces, curved faces that each match a best-form lens' profile at that radius.

Question: What is a 3rd-order Fresnel lens? What aspect of the lens is considered to be third order?

LakeSuperior.com's Lighthouses of Western Lake Superior seems to address "third order" somewhat, but I don't understand the limited explanation except that first order is better than seventh order, which seems counterintuitive.

When the U.S. Coast Guard deeded Split Rock Lighthouse to the state of Minnesota and the Minnesota Historical Society in 1971, it did something unusual … it left the classic Fresnel lens in place.

Amazing in design and beauty, Fresnel lenses, introduced by French physicist Augustin Jean Fresnel in 1822, were a technological leap for lighthouse beacons, significantly multiplying the lights’ range. Measured in seven orders from the most powerful First Order to the weakest Sixth Order (there is a Three-and-a-half Order), nothing larger than a Second Order was used on Lake Superior.

The Split Rock lens is a Third Order Fresnel, comprised of 252 cut-glass prisms. It measures 7 feet across, 5 feet high and weighs 2-1/2 tons. The prisms are mounted in a brass framework and the clamshell-shaped lens revolves around a central light source, floating on about 250 pounds of mercury. This revolution, driven by the original, hand-cranked clockwork mechanism, causes it to “flash” to passing ships once every 10 seconds when in use.

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Best Answer

The "order" doesn't seem to be a physical term: it's just a word used in a classification of lighthouse lenses by size. See in Wikipedia's article Fresnel lens; Lighthouse lens sizes:

Fresnel produced six sizes of lighthouse lenses, divided into four orders based on their size and focal length. In modern use, these are classified as first through sixth order. An intermediate size between third and fourth order was added later, as well as sizes above first order and below sixth.

A first-order lens has a focal length of 920 mm (36 in) and a maximum diameter 2590 mm (8.5 ft) high. The complete assembly is about 3.7 m (12 ft) tall and 1.8 m (6 ft) wide. The smallest (sixth-order) has a focal length of 150 mm (5.9 in) and an optical diameter 433 mm (17 in) high.

There's also a table of sizes in the article linked above, shown partially below:

Order     Focal Length(mm)   Height(meters)
------    ----------------   --------------
Sixth           150             0.433    
Fifth           182.5           0.541    
Fourth          250             0.722    
3 1/2           375        
Third           500             1.576    
Second          750             2.069    
First           920             2.59    
Mesoradial     1125        
Hyperradial    1330
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